Senior Phase - Department of Basic Education
Transcript of Senior Phase - Department of Basic Education
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MATHEMATIC
S
Curriculum and Assessment Policy Statement
Senior PhaseGrades 7-9
National Curriculum Statement (NCS)
MATHEMATICS GRADES 7-9
CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
disClaimer
In view of the stringent time requirements encountered by the Department of Basic Education to effect the necessary editorial changes and layout to the Curriculum and Assessment Policy Statements and the supplementary policy documents, possible errors may occur in the said documents placed on the official departmental websites.
There may also be vernacular inconsistencies in the language documents at Home-, First and Second Additional Language levels which have been translated in the various African Languages. Please note that the content of the documents translated and versioned in the African Languages are correct as they are based on the English generic language documents at all three language levels to be implemented in all four school phases.
If any editorial, layout or vernacular inconsistencies are detected, the user is kindly requested to bring this to the attention of the Department of Basic Education.
E-mail: [email protected] or fax (012) 328 9828
department of Basic education
222 Struben StreetPrivate Bag X895Pretoria 0001South AfricaTel: +27 12 357 3000Fax: +27 12 323 0601
120 Plein Street Private Bag X9023Cape Town 8000South Africa Tel: +27 21 465 1701Fax: +27 21 461 8110Website: http://www.education.gov.za
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MATHEMATICS GRADES 7-9
CAPS
FOREWORD By THE mINISTER
Our national curriculum is the culmination of our efforts over a period of seventeen years to transform the curriculum bequeathed to us by apartheid. From the start of democracy we have built our curriculum on the values that inspired our Constitution (Act 108 of 1996). The Preamble to the Constitution states that the aims of the Constitution are to:
• heal the divisions of the past and establish a society based on democratic values, social justice and fundamental human rights;
• improve the quality of life of all citizens and free the potential of each person;
• lay the foundations for a democratic and open society in which government is based on the will of the people and every citizen is equally protected by law; and
• build a united and democratic South Africa able to take its rightful place as a sovereign state in the family of nations.
Education and the curriculum have an important role to play in realising these aims.
In 1997 we introduced outcomes-based education to overcome the curricular divisions of the past, but the experience of implementation prompted a review in 2000. This led to the first curriculum revision: the Revised National Curriculum Statement Grades R-9 and the National Curriculum Statement Grades 10-12 (2002).
Ongoing implementation challenges resulted in another review in 2009 and we revised the Revised National Curriculum Statement (2002) and the National Curriculum Statement Grades 10-12 to produce this document.
From 2012 the two National Curriculum Statements, for Grades R-9 and Grades 10-12 respectively, are combined in a single document and will simply be known as the National Curriculum Statement Grades R-12. The National Curriculum Statement for Grades R-12 builds on the previous curriculum but also updates it and aims to provide clearer specification of what is to be taught and learnt on a term-by-term basis.
The National Curriculum Statement Grades R-12 represents a policy statement for learning and teaching in South African schools and comprises of the following:
(a) Curriculum and Assessment Policy Statements (CAPS) for all approved subjects listed in this document;
(b) National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and
(c) National Protocol for Assessment Grades R-12.
mrs anGie motsHeKGa, mP minister oF BasiC eduCation
MATHEMATICS GRADES 7-9
1CAPS
TABLE OF CONTENTS
seCtion 1: introduCtion and BaCKround ............................................................................... 3
1.1 Background ....................................................................................................................................................3
1.2 overview .....................................................................................................................................................3
1.3 General aims of the south african curriculum ............................................................................................4
1.4 time allocations .............................................................................................................................................6
1.4.1 Foundation Phase ..................................................................................................................................6
1.4.2 Intermediate Phase ................................................................................................................................6
1.4.3 Senior Phase..........................................................................................................................................7
1.4.4 Grades 10-12 .........................................................................................................................................7
seCtion 2: deFinition, aims, sKills and Content .................................................................... 8
2.1 introduction ....................................................................................................................................................8
2.2 What is mathematics?....................................................................................................................................8
2.3 Specificaims ..................................................................................................................................................8
2.4 Specificskills..................................................................................................................................................8
2.5 Focus of content areas ..................................................................................................................................9
mathematics content knowledge ....................................................................................................................10
2.6 Weighting of content areas .........................................................................................................................11
2.7 Specificationofcontent ..............................................................................................................................11
• Numbers, Operations and Relationships ..................................................................................................12
• Patterns, Functions and Algebra ...............................................................................................................21
• Space and Shape (Geometry) ..................................................................................................................27
• measurement ............................................................................................................................................31
• Data Handling ...........................................................................................................................................33
seCtion 3: ClariFiCation oF Content ....................................................................................... 37
3.1 introduction ..................................................................................................................................................37
3.2 allocation of teaching time .........................................................................................................................37
MATHEMATICS GRADES 7-9
2 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
3.3 Clarificationnoteswithteachingguidelines .............................................................................................38
3.3.1 Clarification of content for Grade 7 ......................................................................................................39
• Grade 7 term 1 ................................................................................................................................39
• Grade 7 term 2 ................................................................................................................................49
• Grade 7 term 3 ................................................................................................................................58
• Grade 7 term 4 ................................................................................................................................67
3.3.2 Clarification of content for Grade 8 ......................................................................................................75
• Grade 8 term 1 ................................................................................................................................75
• Grade 8 term 2 ................................................................................................................................92
• Grade 8 term 3 ..............................................................................................................................100
• Grade 8 term 4 ..............................................................................................................................113
3.3.3 Clarification of content for Grade 9...............................................................................................................119
• Grade 9 term 1 ..............................................................................................................................119
• Grade 9 term 2 ..............................................................................................................................134
• Grade 9 term 3 ..............................................................................................................................141
• Grade 9 term 4 ..............................................................................................................................147
seCtion 4: assessment ................................................................................................................ 154 4.1 introduction ...............................................................................................................................................154
4.2 types of assessment .................................................................................................................................154
4.3 informal or daily assessment ....................................................................................................................155
4.4 Formal assessment ....................................................................................................................................155
4.5 recording and reporting ...........................................................................................................................157
4.6 moderation of assessment ........................................................................................................................158
4.7 General .................................................................................................................................................158
MATHEMATICS GRADES 7-9
3CAPS
SECTION 1: INTRODUCTION AND BACKGROUND
1.1 BaCKGround
The National Curriculum Statement Grades R-12 (NCS) stipulates policy on curriculum and assessment in the schooling sector.
To improve implementation, the National Curriculum Statement was amended, with the amendments coming into effect in January 2012. A single comprehensive Curriculum and Assessment Policy document was developed for each subject to replace Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelines in Grades R-12.
1.2 overvieW
(a) The National Curriculum Statement Grades R-12 (January 2012) represents a policy statement for learning and teaching in South African schools and comprises the following:
(i) Curriculum and Assessment Policy Statements for each approved school subject;
(ii) The policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and
(iii) The policy document, National Protocol for Assessment Grades R-12 (January 2012).
(b) The National Curriculum Statement Grades R-12 (January 2012) replaces the two current national curricula statements, namely the
(i) Revised National Curriculum Statement Grades R-9, Government Gazette No. 23406 of 31 May 2002, and
(ii) National Curriculum Statement Grades 10-12 Government Gazettes, No. 25545 of 6 October 2003 and No. 27594 of 17 May 2005.
(c) The national curriculum statements contemplated in subparagraphs b(i) and (ii) comprise the following policy documents which will be incrementally repealed by the National Curriculum Statement Grades R-12 (January 2012) during the period 2012-2014:
(i) The Learning Area/Subject Statements, Learning Programme Guidelines and Subject Assessment Guidelines for Grades R-9 and Grades 10-12;
(ii) The policy document, National Policy on assessment and qualifications for schools in the GeneralEducation and Training Band, promulgated in Government Notice No. 124 in Government Gazette No. 29626 of 12 February 2007;
(iii) The policy document, the National Senior Certificate: A qualification at Level 4 on the NationalQualificationsFramework(NQF),promulgatedinGovernmentGazetteNo.27819of20July2005;
MATHEMATICS GRADES 7-9
4 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
(iv) The policy document, An addendum to the policy document, the National Senior Certificate: AqualificationatLevel4ontheNationalQualificationsFramework(NQF),regardinglearnerswithspecialneeds, published in Government Gazette, No.29466 of 11 December 2006, is incorporated in the policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and
(v) The policy document, An addendum to the policy document, the National Senior Certificate: AqualificationatLevel4ontheNationalQualificationsFramework(NQF),regardingtheNationalProtocolfor Assessment (Grades R-12), promulgated in Government Notice No.1267 in Government Gazette No. 29467 of 11 December 2006.
(d) The policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12, and the sections on the Curriculum and Assessment Policy as contemplated in Chapters 2, 3 and 4 of this document constitute the norms and standards of the National Curriculum Statement Grades R-12. It will therefore, in terms of section 6A of the South African Schools Act, 1996(ActNo.84of1996,) form the basis for the minister of Basic Education to determine minimum outcomes and standards, as well as the processes and procedures for the assessment of learner achievement to be applicable to public and independent schools.
1.3 General aims oF tHe soutH aFriCan CurriCulum
(a) The National Curriculum Statement Grades R-12 gives expression to the knowledge, skills and values worth learning in South African schools. This curriculum aims to ensure that children acquire and apply knowledge and skills in ways that are meaningful to their own lives. In this regard, the curriculum promotes knowledge in local contexts, while being sensitive to global imperatives.
(b) The National Curriculum Statement Grades R-12 serves the purposes of:
• equipping learners, irrespective of their socio-economic background, race, gender, physical ability or intellectual ability, with the knowledge, skills and values necessary for self-fulfilment, and meaningful participation in society as citizens of a free country;
• providing access to higher education;
• facilitating the transition of learners from education institutions to the workplace; and
• providing employers with a sufficient profile of a learner’s competences.
(c) The National Curriculum Statement Grades R-12 is based on the following principles:
• Social transformation: ensuring that the educational imbalances of the past are redressed, and that equal educational opportunities are provided for all sections of the population;
• Active and critical learning: encouraging an active and critical approach to learning, rather than rote and uncritical learning of given truths;
• High knowledge and high skills: the minimum standards of knowledge and skills to be achieved at each grade are specified and set high, achievable standards in all subjects;
• Progression: content and context of each grade shows progression from simple to complex;
MATHEMATICS GRADES 7-9
5CAPS
• Human rights, inclusivity, environmental and social justice: infusing the principles and practices of social and environmental justice and human rights as defined in the Constitution of the Republic of South Africa. The National Curriculum Statement Grades R-12 is sensitive to issues of diversity such as poverty, inequality, race, gender, language, age, disability and other factors;
• Valuing indigenous knowledge systems: acknowledging the rich history and heritage of this country as important contributors to nurturing the values contained in the Constitution; and
• Credibility, quality and efficiency: providing an education that is comparable in quality, breadth and depth to those of other countries.
(d) The National Curriculum Statement Grades R-12 aims to produce learners that are able to:
• identify and solve problems and make decisions using critical and creative thinking;
• work effectively as individuals and with others as members of a team;
• organise and manage themselves and their activities responsibly and effectively;
• collect, analyse, organise and critically evaluate information;
• communicate effectively using visual, symbolic and/or language skills in various modes;
• use science and technology effectively and critically showing responsibility towards the environment and the health of others; and
• demonstrate an understanding of the world as a set of related systems by recognising that problem solving contexts do not exist in isolation.
(e) Inclusivity should become a central part of the organisation, planning and teaching at each school. This can only happen if all teachers have a sound understanding of how to recognise and address barriers to learning, and how to plan for diversity.
The key to managing inclusivity is ensuring that barriers are identified and addressed by all the relevant support structures within the school community, including teachers, District-Based Support Teams, Institutional-Level Support Teams, parents and Special Schools as Resource Centres. To address barriers in the classroom, teachers should use various curriculum differentiation strategies such as those included in the Department of Basic Education’s Guidelines for Inclusive Teaching and Learning (2010).
MATHEMATICS GRADES 7-9
6 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
1.4 time alloCation
1.4.1 Foundation Phase
(a) The instructional time in the Foundation Phase is as follows:
suBJeCtGrade r (Hours)
Grades 1-2 (Hours)
Grade 3 (Hours)
Home Language 10 8/7 8/7
First Additional Language 2/3 3/4
mathematics 7 7 7
Life Skills
• Beginning Knowledge
• Creative Arts
• Physical Education
• Personal and Social Well-being
6
(1)
(2)
(2)
(1)
6
(1)
(2)
(2)
(1)
7
(2)
(2)
(2)
(1)
total 23 23 25
(b) Instructional time for Grades R, 1 and 2 is 23 hours and for Grade 3 is 25 hours.
(c) Ten hours are allocated for languages in Grades R-2 and 11 hours in Grade 3. A maximum of 8 hours and a minimum of 7 hours are allocated for Home Language and a minimum of 2 hours and a maximum of 3 hours for Additional Language in Grades 1-2. In Grade 3 a maximum of 8 hours and a minimum of 7 hours are allocated for Home Language and a minimum of 3 hours and a maximum of 4 hours for First Additional Language.
(d) In Life Skills Beginning Knowledge is allocated 1 hour in Grades R – 2 and 2 hours as indicated by the hours in brackets for Grade 3.
1.4.2 intermediate Phase
(a) The instructional time in the Intermediate Phase is as follows:
suBJeCt Hours
Home Language 6
First Additional Language 5
mathematics 6
Natural Sciences and Technology 3,5
Social Sciences 3
Life Skills
• Creative Arts
• Physical Education
• Personal and Social Well-being
4
(1,5)
(1)
(1,5)
total 27,5
MATHEMATICS GRADES 7-9
7CAPS
1.4.3 senior Phase
(a) The instructional time in the Senior Phase is as follows:
suBJeCt Hours
Home Language 5
First Additional Language 4
mathematics 4,5
Natural Sciences 3
Social Sciences 3
Technology 2
Economic management Sciences 2
Life Orientation 2
Creative Arts 2
total 27,5
1.4.4 Grades 10-12
(a) The instructional time in Grades 10-12 is as follows:
suBJeCt time alloCation Per WeeK (Hours)
Home Language 4.5
First Additional Language 4.5
mathematics 4.5
Life Orientation 2
A minimum of any three subjects selected from Group B Annexure B, Tables B1-B8 of the policy document, National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12, subject to the provisos stipulated in paragraph 28 of the said policy document.
12 (3x4h)
total 27,5
The allocated time per week may be utilised only for the minimum required NCS subjects as specified above, and may not be used for any additional subjects added to the list of minimum subjects. Should a learner wish to offer additional subjects, additional time must be allocated for the offering of these subjects.
MATHEMATICS GRADES 7-9
8 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
SECTION 2: DEFINITION, AIMS, SKILLS AND CONTENT
2.1 introduCtion
In Section 2, the Senior Phase Mathematics Curriculum and Assessment Policy Statement (CAPS) provides teachers with a definition of mathematics, specific aims, specific skills, focus of content areas, weighting of content areas and content specification.
2.2 WHat is matHematiCs?
mathematics is a language that makes use of symbols and notations to describe numerical, geometric and graphical relationships. It is a human activity that involves observing, representing and investigating patterns and quantitative relationships in physical and social phenomena and between mathematical objects themselves. It helps to develop mental processes that enhance logical and critical thinking, accuracy and problem-solving that will contribute in decision-making.
2.3 sPeCiFiC aims
The teaching and learning of mathematics aims to develop
• a critical awareness of how mathematical relationships are used in social, environmental, cultural and economic relations
• confidence and competence to deal with any mathematical situation without being hindered by a fear of mathematics
• an appreciation for the beauty and elegance of mathematics
• a spirit of curiosity and a love for mathematics
• recognition that mathematics is a creative part of human activity
• deep conceptual understandings in order to make sense of mathematics
• acquisition of specific knowledge and skills necessary for:
- the application of mathematics to physical, social and mathematical problems
- the study of related subject matter (e.g. other subjects)
- further study in Mathematics.
2.4 sPeCiFiC sKills
To develop essential mathematical skills the learner should
• develop the correct use of the language of mathematics
• develop number vocabulary, number concept and calculation and application skills
MATHEMATICS GRADES 7-9
9CAPS
• learn to listen, communicate, think, reason logically and apply the mathematical knowledge gained
• learn to investigate, analyse, represent and interpret information
• learn to pose and solve problems
• build an awareness of the important role that mathematics plays in real life situations including the personal development of the learner.
2.5 FoCus oF Content areas
Mathematics in the Senior Phase covers five main Content Areas.
• Numbers, Operations and Relationships;
• Patterns, Functions and Algebra;
• Space and Shape (Geometry);
• measurement; and
• Data Handling.
Each content area contributes towards the acquisition of specific skills. The table below shows the general focus of the content areas as well as the specific focus of the content areas for the Senior Phase.
MATHEMATICS GRADES 7-9
10 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
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ques
fo
r mak
ing
info
rmed
pre
dict
ions
, and
des
crib
ing
rand
omne
ss a
nd u
ncer
tain
ty.
• P
osin
g of
que
stio
ns fo
r inv
estig
atio
n•
Col
lect
ing,
sum
mar
izin
g, re
pres
entin
g an
d cr
itica
lly a
naly
sing
dat
a in
ord
er
to in
terp
ret,
repo
rt an
d m
ake
pred
ictio
ns a
bout
situ
atio
ns•
Pro
babi
lity
of o
utco
mes
incl
ude
both
sin
gle
and
com
poun
d ev
ents
and
thei
r re
lativ
e fre
quen
cy in
sim
ple
expe
rimen
ts
MATHEMATICS GRADES 7-9
11CAPS
2.6 WeiGHtinG oF Content areas
The weighting of mathematics content areas serves two primary purposes:
• guidance on the time needed to adequately address the content within each content area
• guidance on the spread of content in the examination (especially end-of-year summative assessment).
WeiGHtinG oF Content areas
Content Area Grade 7 Grade 8 Grade 9
Number, Operations and Relations 30% 25% 15%
Patterns, Functions and Algebra 25% 30% 35%
Space and Shape (Geometry) 25% 25% 30%
measurement 10% 10% 10%
Data Handling 10% 10% 10%
100% 100% 100%
2.7 sPeCiFiCation oF Content
The Specification of Content in Section 2 shows progression in terms of concepts and skills from Grades 7 - 9 for each Content Area. However, in certain topics the concepts and skills are similar in two or three successive grades. The Clarification of Content in Section 3 provides guidelines on how progression should be addressed in these cases. The Specification of Content in Section 2 should therefore be read in conjunction with the Clarification of Content in Section 3.
MATHEMATICS GRADES 7-9
12 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
sPeC
iFiC
atio
n o
F C
on
ten
t (P
Ha
se o
ver
vieW
)
nu
mB
ers,
oPe
rat
ion
s a
nd
rel
atio
nsH
iPs
• P
rogr
essi
on in
Num
bers
, Ope
ratio
ns a
nd R
elat
ions
hips
in th
e S
enio
r Pha
se is
ach
ieve
d pr
imar
ily b
y:
-de
velo
pmen
t of c
alcu
latio
ns u
sing
who
le n
umbe
rs to
cal
cula
tions
usi
ng ra
tiona
l num
bers
, int
eger
s an
d nu
mbe
rs in
exp
onen
tial f
orm
-de
velo
pmen
t of u
nder
stan
ding
of d
iffer
ent n
umbe
r sys
tem
s fro
m n
atur
al a
nd w
hole
num
bers
to in
tege
rs a
nd ra
tiona
l num
bers
, as
wel
l as
the
reco
gniti
on o
f irr
atio
nal n
umbe
rs
-in
crea
sing
use
of p
rope
rties
of n
umbe
rs to
per
form
cal
cula
tions
-in
crea
sing
com
plex
ity o
f con
text
s fo
r sol
ving
pro
blem
s
• N
umbe
rs, O
pera
tions
and
Rel
atio
nshi
ps in
the
Sen
ior P
hase
con
solid
ates
wor
k do
ne in
the
Inte
rmed
iate
Pha
se a
nd is
gea
red
tow
ards
mak
ing
lear
ners
com
pete
nt a
nd e
ffici
ent i
n pe
rform
ing
calc
ulat
ions
par
ticul
arly
with
inte
gers
and
ratio
nal n
umbe
rs.
• R
ecog
nisi
ng a
nd u
sing
the
prop
ertie
s of
ope
ratio
ns fo
r diff
eren
t num
bers
pro
vide
s a
criti
cal f
ound
atio
n fo
r wor
k in
alg
ebra
whe
n le
arne
rs w
ork
with
var
iabl
es in
pla
ce o
f num
bers
and
m
anip
ulat
e al
gebr
aic
expr
essi
ons
and
solv
e al
gebr
aic
equa
tions
.
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
1.1
Who
le n
umbe
rsm
enta
l cal
cula
tions
Rev
ise
the
follo
win
g do
ne in
Gra
de 6
:
• M
ultip
licat
ion
of w
hole
num
bers
to a
t lea
st 1
2 x
12
• m
ultip
licat
ion
fact
s fo
r:
-un
its a
nd te
ns b
y m
ultip
les
of te
n
-un
its a
nd te
ns b
y m
ultip
les
of 1
00
-un
its a
nd te
ns b
y m
ultip
les
of 1
000
-un
its a
nd te
ns b
y m
ultip
les
of 1
0 00
0
• In
vers
e op
erat
ion
betw
een
mul
tiplic
atio
n an
d di
visi
on
ord
erin
g an
d co
mpa
ring
who
le n
umbe
rs
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-or
der,
com
pare
and
repr
esen
t num
bers
to a
t le
ast 9
-dig
it nu
mbe
rs
-re
cogn
ize
and
repr
esen
t prim
e nu
mbe
rs to
at
leas
t 100
-ro
und
off n
umbe
rs to
the
near
est 5
, 10,
100
or
1 00
0
men
tal c
alcu
latio
ns
• R
evis
e m
ultip
licat
ion
of w
hole
num
bers
to a
t lea
st
12 x
12
ord
erin
g an
d co
mpa
ring
who
le n
umbe
rs
• R
evis
e pr
ime
num
bers
to a
t lea
st 1
00
MATHEMATICS GRADES 7-9
13CAPS
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
1.1
Who
le n
umbe
rsPr
oper
ties
of w
hole
num
bers
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-re
cogn
ize
and
use
the
com
mut
ativ
e;
asso
ciat
ive;
dis
tribu
tive
prop
ertie
s of
who
le
num
bers
-re
cogn
ize
and
use
0 in
term
s of
its
addi
tive
prop
erty
(ide
ntity
ele
men
t for
add
ition
)
-re
cogn
ize
and
use
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty (i
dent
ity e
lem
ent f
or m
ultip
licat
ion)
Cal
cula
tions
usi
ng w
hole
num
bers
• R
evis
e th
e fo
llow
ing
done
in G
rade
6, w
ithou
t use
of
cal
cula
tors
:
-A
dditi
on a
nd s
ubtra
ctio
n of
who
le n
umbe
rs to
at
leas
t 6-d
igit
num
bers
-M
ultip
licat
ion
of a
t lea
st w
hole
4-d
igit
by 2
-dig
it nu
mbe
rs
-D
ivis
ion
of a
t lea
st w
hole
4-d
igit
by 2
-dig
it nu
mbe
rs
-P
erfo
rm c
alcu
latio
ns u
sing
all
four
ope
ratio
ns
on w
hole
num
bers
, est
imat
ing
and
usin
g ca
lcul
ator
s w
here
app
ropr
iate
Cal
cula
tion
tech
niqu
es
• U
se a
rang
e of
stra
tegi
es to
per
form
and
che
ck
writ
ten
and
men
tal c
alcu
latio
ns o
f who
le n
umbe
rs
incl
udin
g:
-lo
ng d
ivis
ion
-ad
ding
, sub
tract
ing
and
mul
tiply
ing
in c
olum
ns
-es
timat
ion
-ro
undi
ng o
ff an
d co
mpe
nsat
ing
-us
ing
a ca
lcul
ator
Prop
ertie
s of
who
le n
umbe
rs
• R
evis
e:
-Th
e co
mm
utat
ive;
ass
ocia
tive;
dis
tribu
tive
prop
ertie
s of
who
le n
umbe
rs
-0
in te
rms
of it
s ad
ditiv
e pr
oper
ty (i
dent
ity
elem
ent f
or a
dditi
on)
-1
in te
rms
of it
s m
ultip
licat
ive
prop
erty
(ide
ntity
el
emen
t for
mul
tiplic
atio
n)
• R
ecog
nize
the
divi
sion
pro
perty
of 0
, whe
reby
any
nu
mbe
r div
ided
by
0 is
und
efine
d
Cal
cula
tions
usi
ng w
hole
num
bers
• R
evis
e ca
lcul
atio
ns u
sing
all
four
ope
ratio
ns o
n w
hole
num
bers
, est
imat
ing
and
usin
g ca
lcul
ator
s w
here
app
ropr
iate
Cal
cula
tion
tech
niqu
es
• U
se a
rang
e of
tech
niqu
es to
per
form
and
che
ck
writ
ten
and
men
tal c
alcu
latio
ns o
f who
le n
umbe
rs
incl
udin
g:
-lo
ng d
ivis
ion
-ad
ding
, sub
tract
ing
and
mul
tiply
ing
in c
olum
ns
-es
timat
ion
-ro
undi
ng o
ff an
d co
mpe
nsat
ing
-us
ing
a ca
lcul
ator
Prop
ertie
s of
num
bers
• D
escr
ibe
the
real
num
ber s
yste
m b
y re
cogn
isin
g,
defin
ing
and
dist
ingu
ishi
ng p
rope
rties
of:
-na
tura
l num
bers
-w
hole
num
bers
-in
tege
rs
-ra
tiona
l num
bers
-irr
atio
nal n
umbe
rs
Cal
cula
tions
usi
ng w
hole
num
bers
• R
evis
e ca
lcul
atio
ns u
sing
all
four
ope
ratio
ns o
n w
hole
num
bers
, est
imat
ing
and
usin
g ca
lcul
ator
s w
here
app
ropr
iate
Cal
cula
tion
tech
niqu
es
• U
se a
rang
e of
tech
niqu
es to
per
form
and
che
ck
writ
ten
and
men
tal c
alcu
latio
ns o
f who
le n
umbe
rs
incl
udin
g:
-lo
ng d
ivis
ion
-ad
ding
, sub
tract
ing
and
mul
tiply
ing
in c
olum
ns
-es
timat
ion
-ro
undi
ng o
ff an
d co
mpe
nsat
ing
-us
ing
a ca
lcul
ator
MATHEMATICS GRADES 7-9
14 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
1.1
Who
le n
umbe
rsm
ultip
les
and
fact
ors
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-m
ultip
les
of 2
-dig
it an
d 3-
digi
t who
le n
umbe
rs
-fa
ctor
s of
2-d
igit
and
3-di
git w
hole
num
bers
-pr
ime
fact
ors
of n
umbe
rs to
at l
east
100
• Li
st p
rime
fact
ors
of n
umbe
rs to
at l
east
3-d
igit
who
le n
umbe
rs
• Fi
nd th
e LC
m a
nd H
CF
of n
umbe
rs to
at
leas
t 3-d
igit
who
le n
umbe
rs, b
y in
spec
tion
or
fact
oris
atio
n
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
volv
ing
who
le n
umbe
rs,
incl
udin
g
-co
mpa
ring
two
or m
ore
quan
titie
s of
the
sam
e ki
nd (r
atio
)
-co
mpa
ring
two
quan
titie
s of
diff
eren
t kin
ds (r
ate)
-sh
arin
g in
a g
iven
ratio
whe
re th
e w
hole
is g
iven
• S
olve
pro
blem
s th
at in
volv
e w
hole
num
bers
, pe
rcen
tage
s an
d de
cim
al fr
actio
ns in
fina
ncia
l co
ntex
ts s
uch
as:
-pr
ofit,
loss
and
dis
coun
t
-bu
dget
s
-ac
coun
ts
-lo
ans
-si
mpl
e in
tere
st
mul
tiple
s an
d fa
ctor
s
• R
evis
e:
-P
rime
fact
ors
of n
umbe
rs t
o at
lea
st 3
-dig
it w
hole
num
bers
-LC
M a
nd H
CF
of n
umbe
rs t
o at
lea
st 3
-dig
it w
hole
num
bers
, by
insp
ectio
n or
fact
oris
atio
n
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
volv
ing
who
le n
umbe
rs,
incl
udin
g
-co
mpa
ring
two
or m
ore
quan
titie
s of
the
sam
e ki
nd (r
atio
)
-co
mpa
ring
two
quan
titie
s of
diff
eren
t kin
ds (r
ate)
-sh
arin
g in
a g
iven
ratio
whe
re th
e w
hole
is g
iven
-in
crea
sing
or d
ecre
asin
g of
a n
umbe
r in
a gi
ven
ratio
• S
olve
pro
blem
s th
at in
volv
e w
hole
num
bers
, pe
rcen
tage
s an
d de
cim
al fr
actio
ns in
fina
ncia
l co
ntex
ts s
uch
as:
-pr
ofit,
loss
, dis
coun
t and
VAT
-bu
dget
s
-ac
coun
ts
-lo
ans
-si
mpl
e in
tere
st
-hi
re p
urch
ase
-ex
chan
ge ra
tes
mul
tiple
s an
d fa
ctor
s
• U
se p
rime
fact
oris
atio
n of
num
bers
to fi
nd L
CM
an
d H
CF
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
-ra
tio a
nd ra
te
-di
rect
and
indi
rect
pro
porti
on
• S
olve
pro
blem
s th
at in
volv
e w
hole
num
bers
, pe
rcen
tage
s an
d de
cim
al fr
actio
ns in
fina
ncia
l co
ntex
ts s
uch
as:
-pr
ofit,
loss
, dis
coun
t and
VAT
-bu
dget
s
-ac
coun
ts
-lo
ans
-S
impl
e in
tere
st
-hi
re p
urch
ase
-ex
chan
ge ra
tes
-co
mm
issi
on
-re
ntal
s
-co
mpo
und
inte
rest
MATHEMATICS GRADES 7-9
15CAPS
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
1.2
expo
nent
sm
enta
l cal
cula
tions
• D
eter
min
e sq
uare
s to
at l
east
122 a
nd th
eir
squa
re ro
ots
• D
eter
min
e cu
bes
to a
t lea
st 6
3 and
cub
e ro
ots
Com
parin
g an
d re
pres
entin
g nu
mbe
rs in
ex
pone
ntia
l for
m
• C
ompa
re a
nd re
pres
ent w
hole
num
bers
in
expo
nent
ial f
orm
: ab =
a x
a x
a x
... fo
r b n
umbe
r of f
acto
rs
Cal
cula
tions
usi
ng n
umbe
rs in
exp
onen
tial f
orm
• R
ecog
nize
and
use
the
appr
opria
te la
ws
of
oper
atio
ns w
ith n
umbe
rs in
volv
ing
expo
nent
s an
d sq
uare
and
cub
e ro
ots
• P
erfo
rm c
alcu
latio
ns in
volv
ing
all f
our o
pera
tions
us
ing
num
bers
in e
xpon
entia
l for
m, l
imite
d to
ex
pone
nts
up to
5, a
nd s
quar
e an
d cu
be ro
ots
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
num
bers
in
expo
nent
ial f
orm
.
men
tal c
alcu
latio
ns
• R
evis
e:
-S
quar
es to
at l
east
122 a
nd th
eir s
quar
e ro
ots
-C
ubes
to a
t lea
st 6
3 and
thei
r cub
e ro
ots
Com
parin
g an
d re
pres
entin
g nu
mbe
rs in
ex
pone
ntia
l for
m
• R
evis
e co
mpa
re a
nd re
pres
ent w
hole
num
bers
in
expo
nent
ial f
orm
• C
ompa
re a
nd re
pres
ent i
nteg
ers
in e
xpon
entia
l fo
rm
• C
ompa
re a
nd re
pres
ent n
umbe
rs in
sci
entifi
c no
tatio
n, li
mite
d to
pos
itive
exp
onen
ts
Cal
cula
tions
usi
ng n
umbe
rs in
exp
onen
tial f
orm
• E
stab
lish
gene
ral l
aws
of e
xpon
ents
, lim
ited
to:
-na
tura
l num
ber e
xpon
ents
-am
x a
n = a
m +
n
-am
÷ a
n = a
m –
n, i
f m>n
-(a
m)n =
am
x n
-(a
x t)
n = a
n x
tn
-a0 =
1
• R
ecog
nize
and
use
the
appr
opria
te la
ws
of
oper
atio
ns u
sing
num
bers
invo
lvin
g ex
pone
nts
and
squa
re a
nd c
ube
root
s
• P
erfo
rm c
alcu
latio
ns in
volv
ing
all f
our o
pera
tions
w
ith n
umbe
rs th
at in
volv
e th
e sq
uare
s, c
ubes
, sq
uare
root
s an
d cu
be ro
ots
of in
tege
rs
• C
alcu
late
the
squa
res,
cub
es, s
quar
e ro
ots
and
cube
root
s of
ratio
nal n
umbe
rs
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
num
bers
in
expo
nent
ial f
orm
Com
parin
g an
d re
pres
entin
g nu
mbe
rs in
ex
pone
ntia
l for
m
• R
evis
e co
mpa
re a
nd re
pres
ent i
nteg
ers
in
expo
nent
ial f
orm
-co
mpa
re a
nd r
epre
sent
num
bers
in
scie
ntifi
c no
tatio
n
• E
xten
d sc
ient
ific
nota
tion
to in
clud
e ne
gativ
e ex
pone
nts
Cal
cula
tions
usi
ng n
umbe
rs in
exp
onen
tial f
orm
• R
evis
e th
e fo
llow
ing
gene
ral l
aws
of e
xpon
ents
:
-am
x a
n = a
m +
n
-am
÷ a
n = a
m –
n, i
f m>n
-(a
m)n =
am
x n
-(a
x t)
n = a
n x
tn
-a0 =
1
• E
xten
d th
e ge
nera
l law
s of
exp
onen
ts to
incl
ude:
-in
tege
r exp
onen
ts
-a–m
= 1
am
• P
erfo
rm c
alcu
latio
ns in
volv
ing
all f
our o
pera
tions
us
ing
num
bers
in e
xpon
entia
l for
m, u
sing
the
law
s of
exp
onen
ts
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
num
bers
in
expo
nent
ial f
orm
, inc
ludi
ng s
cien
tific
nota
tion
MATHEMATICS GRADES 7-9
16 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
1.3
inte
gers
Cou
ntin
g, o
rder
ing
and
com
parin
g in
tege
rs
• C
ount
forw
ards
and
bac
kwar
ds in
inte
gers
for a
ny
inte
rval
• R
ecog
nize
, ord
er a
nd c
ompa
re in
tege
rs
Cal
cula
tions
with
inte
gers
• A
dd a
nd s
ubtra
ct w
ith in
tege
rs
Prop
ertie
s of
inte
gers
• R
ecog
nise
and
use
com
mut
ativ
e an
d as
soci
ativ
e pr
oper
ties
of a
dditi
on a
nd m
ultip
licat
ion
for
inte
gers
solv
ing
prob
lem
s
Sol
ve p
robl
ems
in c
onte
xts
invo
lvin
g ad
ditio
n an
d su
btra
ctio
n w
ith in
tege
rs
Cou
ntin
g, o
rder
ing
and
com
parin
g in
tege
rs
• R
evis
e:
-co
untin
g fo
rwar
ds a
nd b
ackw
ards
in in
tege
rs
for a
ny in
terv
al
-re
cogn
izin
g, o
rder
ing
and
com
parin
g in
tege
rs
Cal
cula
tions
with
inte
gers
• R
evis
e ad
ditio
n an
d su
btra
ctio
n w
ith in
tege
rs
• m
ultip
ly a
nd d
ivid
e w
ith in
tege
rs
• P
erfo
rm c
alcu
latio
ns in
volv
ing
all f
our o
pera
tions
w
ith in
tege
rs
• P
erfo
rm c
alcu
latio
ns in
volv
ing
all f
our o
pera
tions
w
ith n
umbe
rs th
at in
volv
e th
e sq
uare
s, c
ubes
, sq
uare
root
s an
d cu
be ro
ots
of in
tege
rs
Prop
ertie
s of
inte
gers
• R
ecog
nise
and
use
com
mut
ativ
e, a
ssoc
iativ
e an
d di
strib
utiv
e pr
oper
ties
of a
dditi
on a
nd
mul
tiplic
atio
n fo
r int
eger
s
• R
ecog
nize
and
use
add
itive
and
mul
tiplic
ativ
e in
vers
es fo
r int
eger
s
solv
ing
prob
lem
s
Sol
ve p
robl
ems
in c
onte
xts
invo
lvin
g m
ultip
le
oper
atio
ns w
ith in
tege
rs
Cal
cula
tions
with
inte
gers
• R
evis
e:
-pe
rform
cal
cula
tions
invo
lvin
g al
l fou
r op
erat
ions
with
inte
gers
-pe
rform
cal
cula
tions
invo
lvin
g al
l fou
r op
erat
ions
with
num
bers
that
invo
lve
the
squa
res,
cub
es, s
quar
e ro
ots
and
cube
root
s of
in
tege
rs
Prop
ertie
s of
inte
gers
• R
evis
e:
-C
omm
utat
ive,
ass
ocia
tive
and
dist
ribut
ive
prop
ertie
s of
add
ition
and
mul
tiplic
atio
n fo
r in
tege
rs
-ad
ditiv
e an
d m
ultip
licat
ive
inve
rses
for i
nteg
ers
solv
ing
prob
lem
s
Sol
ve p
robl
ems
in c
onte
xts
invo
lvin
g m
ultip
le
oper
atio
ns w
ith in
tege
rs
MATHEMATICS GRADES 7-9
17CAPS
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
1.4
Com
mon
fr
actio
ns
ord
erin
g, c
ompa
ring
and
sim
plify
ing
frac
tions
• R
evis
e th
e fo
llow
ing
done
in G
rade
6
-co
mpa
re a
nd o
rder
com
mon
frac
tions
, inc
ludi
ng
spec
ifica
lly te
nths
and
hun
dred
ths
• E
xten
d to
thou
sand
ths
Cal
cula
tions
with
frac
tions
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-ad
ditio
n an
d su
btra
ctio
n of
com
mon
frac
tions
, in
clud
ing
mix
ed n
umbe
rs, l
imite
d to
frac
tions
w
ith th
e sa
me
deno
min
ator
or w
here
one
de
nom
inat
or is
a m
ultip
le o
f ano
ther
-fin
ding
frac
tions
of w
hole
num
bers
• E
xten
d ad
ditio
n an
d su
btra
ctio
n to
frac
tions
w
here
one
den
omin
ator
is n
ot a
mul
tiple
of t
he
othe
r
• m
ultip
licat
ion
of c
omm
on fr
actio
ns, i
nclu
ding
m
ixed
num
bers
, not
lim
ited
to fr
actio
ns w
here
one
de
nom
inat
or is
a m
ultip
le o
f ano
ther
Cal
cula
tion
tech
niqu
es
• C
onve
rt m
ixed
num
bers
to c
omm
on fr
actio
ns in
or
der t
o pe
rform
cal
cula
tions
with
them
• U
se k
now
ledg
e of
mul
tiple
s an
d fa
ctor
s to
writ
e fra
ctio
ns in
the
sim
ples
t for
m b
efor
e or
afte
r ca
lcul
atio
ns
• U
se k
now
ledg
e of
equ
ival
ent f
ract
ions
to a
dd a
nd
subt
ract
com
mon
frac
tions
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
com
mon
fra
ctio
ns a
nd m
ixed
num
bers
, inc
ludi
ng g
roup
ing,
sh
arin
g an
d fin
ding
frac
tions
of w
hole
num
bers
Cal
cula
tions
with
frac
tions
• R
evis
e:
-ad
ditio
n an
d su
btra
ctio
n of
com
mon
frac
tions
, in
clud
ing
mix
ed n
umbe
rs
-fin
ding
frac
tions
of w
hole
num
bers
-m
ultip
licat
ion
of c
omm
on fr
actio
ns, i
nclu
ding
m
ixed
num
bers
• D
ivid
e w
hole
num
bers
and
com
mon
frac
tions
by
com
mon
frac
tions
• C
alcu
late
the
squa
res,
cub
es, s
quar
e ro
ots
and
cube
root
s of
com
mon
frac
tions
Cal
cula
tion
tech
niqu
es
• R
evis
e:
-co
nver
t mix
ed n
umbe
rs to
com
mon
frac
tions
in
orde
r to
perfo
rm c
alcu
latio
ns w
ith th
em
-us
e kn
owle
dge
of m
ultip
les
and
fact
ors
to w
rite
fract
ions
in th
e si
mpl
est f
orm
bef
ore
or a
fter
calc
ulat
ions
-us
e kn
owle
dge
of e
quiv
alen
t fra
ctio
ns to
add
an
d su
btra
ct c
omm
on fr
actio
ns
• U
se k
now
ledg
e of
reci
proc
al re
latio
nshi
ps to
di
vide
com
mon
frac
tions
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
com
mon
fra
ctio
ns a
nd m
ixed
num
bers
, inc
ludi
ng g
roup
ing,
sh
arin
g an
d fin
ding
frac
tions
of w
hole
num
bers
Cal
cula
tions
with
frac
tions
• A
ll fo
ur o
pera
tions
with
com
mon
frac
tions
and
m
ixed
num
bers
• A
ll fo
ur o
pera
tions
, with
num
bers
that
invo
lve
the
squa
res,
cub
es, s
quar
e ro
ots
and
cube
root
s of
co
mm
on fr
actio
ns
Cal
cula
tion
tech
niqu
es
• R
evis
e:
-co
nver
t mix
ed n
umbe
rs to
com
mon
frac
tions
in
orde
r to
perfo
rm c
alcu
latio
ns w
ith th
em
-us
e kn
owle
dge
of m
ultip
les
and
fact
ors
to w
rite
fract
ions
in th
e si
mpl
est f
orm
bef
ore
or a
fter
calc
ulat
ions
-us
e kn
owle
dge
of e
quiv
alen
t fra
ctio
ns to
add
an
d su
btra
ct c
omm
on fr
actio
ns
-us
e kn
owle
dge
of re
cipr
ocal
rela
tions
hips
to
divi
de c
omm
on fr
actio
ns
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
com
mon
fra
ctio
ns, m
ixed
num
bers
and
per
cent
ages
MATHEMATICS GRADES 7-9
18 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
1.4
Com
mon
Fr
actio
ns
Perc
enta
ges
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-Fi
ndin
g pe
rcen
tage
s of
who
le n
umbe
rs
• C
alcu
late
the
perc
enta
ge o
f par
t of a
who
le
• C
alcu
late
per
cent
age
incr
ease
or d
ecre
ase
of
who
le n
umbe
rs
• S
olve
pro
blem
s in
con
text
s in
volv
ing
perc
enta
ges
equi
vale
nt fo
rms
Rev
ise
the
follo
win
g do
ne in
Gra
de 6
:
• re
cogn
ize
and
use
equi
vale
nt fo
rms
of c
omm
on
fract
ions
with
1-d
igit
or 2
-dig
it de
nom
inat
ors
(frac
tions
whe
re o
ne d
enom
inat
or is
a m
ultip
le o
f th
e ot
her)
• re
cogn
ize
equi
vale
nce
betw
een
com
mon
frac
tion
and
deci
mal
frac
tion
form
s of
the
sam
e nu
mbe
r
• re
cogn
ize
equi
vale
nce
betw
een
com
mon
frac
tion,
de
cim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r
Perc
enta
ges
• R
evis
e:
-fin
ding
per
cent
ages
of w
hole
num
bers
-ca
lcul
atin
g th
e pe
rcen
tage
of p
art o
f a w
hole
-ca
lcul
atin
g pe
rcen
tage
incr
ease
or d
ecre
ase
• C
alcu
late
am
ount
s if
give
n pe
rcen
tage
incr
ease
or
dec
reas
e
• S
olve
pro
blem
s in
con
text
s in
volv
ing
perc
enta
ges
equi
vale
nt fo
rms
• R
evis
e eq
uiva
lent
form
s be
twee
n:
-co
mm
on fr
actio
ns (f
ract
ions
whe
re o
ne
deno
min
ator
is a
mul
tiple
of t
he o
ther
)
-co
mm
on fr
actio
n an
d de
cim
al fr
actio
n fo
rms
of
the
sam
e nu
mbe
r
-co
mm
on fr
actio
n, d
ecim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r
equi
vale
nt fo
rms
• R
evis
e eq
uiva
lent
form
s be
twee
n:
-co
mm
on fr
actio
ns w
here
one
den
omin
ator
is a
m
ultip
le o
f ano
ther
-co
mm
on fr
actio
n an
d de
cim
al fr
actio
n fo
rms
of
the
sam
e nu
mbe
r
-co
mm
on fr
actio
n, d
ecim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r
MATHEMATICS GRADES 7-9
19CAPS
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
1.5
dec
imal
fr
actio
ns
ord
erin
g an
d co
mpa
ring
deci
mal
frac
tions
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-co
unt f
orw
ards
and
bac
kwar
ds in
dec
imal
fra
ctio
ns to
at l
east
two
deci
mal
pla
ces
-co
mpa
re a
nd o
rder
dec
imal
frac
tions
to a
t lea
st
two
deci
mal
pla
ces
-pl
ace
valu
e of
dig
its to
at l
east
two
deci
mal
pl
aces
-ro
undi
ng o
ff de
cim
al fr
actio
ns to
at l
east
1
deci
mal
pla
ce
• E
xten
d al
l of t
he a
bove
to d
ecim
al fr
actio
ns to
at
leas
t thr
ee d
ecim
al p
lace
s an
d ro
undi
ng o
ff to
at
leas
t 2 d
ecim
al p
lace
s
Cal
cula
tions
with
dec
imal
frac
tions
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-ad
ditio
n an
d su
btra
ctio
n of
dec
imal
frac
tions
of
at le
ast t
wo
deci
mal
pla
ces
-m
ultip
licat
ion
of d
ecim
al fr
actio
ns b
y 10
and
10
0
• E
xten
d ad
ditio
n an
d su
btra
ctio
n to
dec
imal
fra
ctio
ns o
f at l
east
thre
e de
cim
al p
lace
s
• m
ultip
ly d
ecim
al fr
actio
ns to
incl
ude:
-de
cim
al fr
actio
ns to
at l
east
3 d
ecim
al p
lace
s by
who
le n
umbe
rs
-de
cim
al fr
actio
ns to
at l
east
2 d
ecim
al p
lace
s by
dec
imal
frac
tions
to a
t lea
st 1
dec
imal
pla
ce
• D
ivid
e de
cim
al fr
actio
ns to
incl
ude
deci
mal
fra
ctio
ns to
at l
east
3 d
ecim
al p
lace
s by
who
le
num
bers
Cal
cula
tion
tech
niqu
es
• U
se k
now
ledg
e of
pla
ce v
alue
to e
stim
ate
the
num
ber o
f dec
imal
pla
ces
in th
e re
sult
befo
re
perfo
rmin
g ca
lcul
atio
ns
• U
se ro
undi
ng o
ff an
d a
calc
ulat
or to
che
ck re
sults
w
here
app
ropr
iate
ord
erin
g an
d co
mpa
ring
deci
mal
frac
tions
• R
evis
e:
-or
derin
g, c
ompa
ring
and
plac
e va
lue
of d
ecim
al
fract
ions
to a
t lea
st 3
dec
imal
pla
ces
-ro
undi
ng o
ff de
cim
al fr
actio
ns to
at l
east
2
deci
mal
pla
ce
Cal
cula
tions
with
dec
imal
frac
tions
• R
evis
e:
-ad
ditio
n, s
ubtra
ctio
n, m
ultip
licat
ion
and
of
deci
mal
frac
tions
to a
t lea
st 3
dec
imal
pla
ces
-di
visi
on o
f dec
imal
frac
tions
by
who
le n
umbe
rs
• E
xten
d m
ultip
licat
ion
to 'm
ultip
licat
ion
by d
ecim
al
fract
ions
' not
lim
ited
to o
ne d
ecim
al p
lace
• E
xten
d di
visi
on to
'div
isio
n of
dec
imal
frac
tions
by
deci
mal
frac
tions
'
• C
alcu
late
the
squa
res,
cub
es, s
quar
e ro
ots
and
cube
root
s of
dec
imal
frac
tions
Cal
cula
tion
tech
niqu
es
• U
se k
now
ledg
e of
pla
ce v
alue
to e
stim
ate
the
num
ber o
f dec
imal
pla
ces
in th
e re
sult
befo
re
perfo
rmin
g ca
lcul
atio
ns
• U
se ro
undi
ng o
ff an
d a
calc
ulat
or to
che
ck re
sults
w
here
app
ropr
iate
Cal
cula
tions
with
dec
imal
frac
tions
• m
ultip
le o
pera
tions
with
dec
imal
frac
tions
, usi
ng a
ca
lcul
ator
whe
re a
ppro
pria
te
• m
ultip
le o
pera
tions
with
or w
ithou
t bra
cket
s, w
ith
num
bers
that
invo
lve
the
squa
res,
cub
es, s
quar
e ro
ots
and
cube
root
s of
dec
imal
frac
tions
Cal
cula
tion
tech
niqu
es
• U
se k
now
ledg
e of
pla
ce v
alue
to e
stim
ate
the
num
ber o
f dec
imal
pla
ces
in th
e re
sult
befo
re
perfo
rmin
g ca
lcul
atio
ns
• U
se ro
undi
ng o
ff an
d a
calc
ulat
or to
che
ck re
sults
w
here
app
ropr
iate
MATHEMATICS GRADES 7-9
20 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
1.5
dec
imal
fr
actio
ns
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
invo
lvin
g de
cim
al
fract
ions
equi
vale
nt fo
rms
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-re
cogn
ize
equi
vale
nce
betw
een
com
mon
fra
ctio
n an
d de
cim
al fr
actio
n fo
rms
of th
e sa
me
num
ber
-re
cogn
ize
equi
vale
nce
betw
een
com
mon
fra
ctio
n, d
ecim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
invo
lvin
g de
cim
al
fract
ions
equi
vale
nt fo
rms
• R
evis
e eq
uiva
lent
form
s be
twee
n:
-co
mm
on fr
actio
n an
d de
cim
al fr
actio
n fo
rms
of
the
sam
e nu
mbe
r
-co
mm
on fr
actio
n, d
ecim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
invo
lvin
g de
cim
al
fract
ions
equi
vale
nt fo
rms
Rev
ise
equi
vale
nt fo
rms
betw
een:
-co
mm
on fr
actio
n an
d de
cim
al fr
actio
n fo
rms
of
the
sam
e nu
mbe
r
-co
mm
on fr
actio
n, d
ecim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r
MATHEMATICS GRADES 7-9
21CAPS
sPeC
iFiC
atio
n o
F C
on
ten
t (P
Ha
se o
ver
vieW
)
Patt
ern
s, F
un
Cti
on
s a
nd
alG
eBr
a
• P
rogr
essi
on in
Pat
tern
s, F
unct
ions
and
Alg
ebra
is a
chie
ved
prim
arily
by
-in
crea
sing
the
rang
e an
d co
mpl
exity
of:
♦re
latio
nshi
ps b
etw
een
num
bers
in g
iven
pat
tern
s
♦ru
les,
form
ulae
and
equ
atio
ns fo
r whi
ch in
put a
nd o
utpu
t val
ues
can
be fo
und
♦eq
uatio
ns th
at c
an b
e so
lved
-de
velo
ping
mor
e so
phis
ticat
ed s
kills
and
tech
niqu
es fo
r:
♦so
lvin
g eq
uatio
ns
♦ex
pand
ing
and
sim
plify
ing
alge
brai
c ex
pres
sion
s
♦dr
awin
g an
d in
terp
retin
g gr
aphs
-de
velo
ping
the
use
of a
lgeb
raic
lang
uage
and
con
vent
ions
.
• In
Pat
tern
s, F
unct
ions
and
Alg
ebra
, lea
rner
s’ c
once
ptua
l dev
elop
men
t pro
gres
ses
from
:
-an
und
erst
andi
ng o
f num
ber t
o an
und
erst
andi
ng o
f var
iabl
es, w
here
the
varia
bles
are
num
bers
of a
giv
en ty
pe (e
.g. n
atur
al n
umbe
rs, i
nteg
ers,
ratio
nal n
umbe
rs) i
n ge
nera
lized
form
-th
e re
cogn
ition
of p
atte
rns
and
rela
tions
hips
to th
e re
cogn
ition
of f
unct
ions
, whe
re fu
nctio
ns h
ave
uniq
ue o
utpu
ts v
alue
s fo
r spe
cifie
d in
put v
alue
s
-a
view
of M
athe
mat
ics
as m
emor
ized
fact
s an
d se
para
te to
pics
to s
eein
g M
athe
mat
ics
as in
terr
elat
ed c
once
pts
and
idea
s re
pres
ente
d in
a v
arie
ty o
f equ
ival
ent f
orm
s (e
.g. a
num
ber
patte
rn, a
n eq
uatio
n an
d a
grap
h re
pres
entin
g th
e sa
me
rela
tions
hip)
• W
hile
tech
niqu
es fo
r sol
ving
equ
atio
ns a
re d
evel
oped
in P
atte
rns,
Fun
ctio
ns a
nd A
lgeb
ra, l
earn
ers
also
pra
ctis
e so
lvin
g eq
uatio
ns in
mea
sure
men
t and
Spa
ce a
nd S
hape
, whe
n th
ey
appl
y kn
own
form
ulae
to s
olve
pro
blem
s.
toPi
Cs
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
2.1
num
eric
and
ge
omet
ric
patte
rns
inve
stig
ate
and
exte
nd p
atte
rns
• In
vest
igat
e an
d ex
tend
num
eric
and
geo
met
ric
patte
rns
look
ing
for r
elat
ions
hips
bet
wee
n nu
mbe
rs, i
nclu
ding
pat
tern
s:
-re
pres
ente
d in
phy
sica
l or d
iagr
am fo
rm
-no
t lim
ited
to s
eque
nces
invo
lvin
g a
cons
tant
di
ffere
nce
or ra
tio
-of
lear
ner’s
ow
n cr
eatio
n
-re
pres
ente
d in
tabl
es
• D
escr
ibe
and
just
ify th
e ge
nera
l rul
es fo
r ob
serv
ed re
latio
nshi
ps b
etw
een
num
bers
in o
wn
wor
ds
inve
stig
ate
and
exte
nd p
atte
rns
• In
vest
igat
e an
d ex
tend
num
eric
and
geo
met
ric
patte
rns
look
ing
for r
elat
ions
hips
bet
wee
n nu
mbe
rs, i
nclu
ding
pat
tern
s:
-re
pres
ente
d in
phy
sica
l or d
iagr
am fo
rm
-no
t lim
ited
to s
eque
nces
invo
lvin
g a
cons
tant
di
ffere
nce
or ra
tio
-of
lear
ner’s
ow
n cr
eatio
n
-re
pres
ente
d in
tabl
es
-re
pres
ente
d al
gebr
aica
lly
• D
escr
ibe
and
just
ify th
e ge
nera
l rul
es fo
r ob
serv
ed re
latio
nshi
ps b
etw
een
num
bers
in o
wn
wor
ds o
r in
alge
brai
c la
ngua
ge
inve
stig
ate
and
exte
nd p
atte
rns
• In
vest
igat
e an
d ex
tend
num
eric
and
geo
met
ric
patte
rns
look
ing
for r
elat
ions
hips
bet
wee
n nu
mbe
rs, i
nclu
ding
pat
tern
s:
-re
pres
ente
d in
phy
sica
l or d
iagr
am fo
rm
-no
t lim
ited
to s
eque
nces
invo
lvin
g a
cons
tant
di
ffere
nce
or ra
tio
-of
lear
ner’s
ow
n cr
eatio
n
-re
pres
ente
d in
tabl
es
-re
pres
ente
d al
gebr
aica
lly
• D
escr
ibe
and
just
ify th
e ge
nera
l rul
es fo
r ob
serv
ed re
latio
nshi
ps b
etw
een
num
bers
in o
wn
wor
ds o
r in
alge
brai
c la
ngua
ge
MATHEMATICS GRADES 7-9
22 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
toPi
Cs
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
2.2
Func
tions
and
re
latio
nshi
ps
inpu
t and
out
put v
alue
s
• D
eter
min
e in
put v
alue
s, o
utpu
t val
ues
or ru
les
for
patte
rns
and
rela
tions
hips
usi
ng:
-flo
w d
iagr
ams
-ta
bles
-fo
rmul
ae
equi
vale
nt fo
rms
• D
eter
min
e, in
terp
ret a
nd ju
stify
equ
ival
ence
of
diffe
rent
des
crip
tions
of t
he s
ame
rela
tions
hip
or
rule
pre
sent
ed:
-ve
rbal
ly
-in
flow
dia
gram
s
-in
tabl
es
-by
form
ulae
-by
num
ber s
ente
nces
inpu
t and
out
put v
alue
s
• D
eter
min
e in
put v
alue
s, o
utpu
t val
ues
or ru
les
for
patte
rns
and
rela
tions
hips
usi
ng:
-flo
w d
iagr
ams
-ta
bles
-fo
rmul
ae
-eq
uatio
ns
equi
vale
nt fo
rms
• D
eter
min
e, in
terp
ret a
nd ju
stify
equ
ival
ence
of
diffe
rent
des
crip
tions
of t
he s
ame
rela
tions
hip
or
rule
pre
sent
ed:
-ve
rbal
ly
-in
flow
dia
gram
s
-in
tabl
es
-by
form
ulae
-by
equ
atio
ns
inpu
t and
out
put v
alue
s
• D
eter
min
e in
put v
alue
s, o
utpu
t val
ues
or ru
les
for
patte
rns
and
rela
tions
hips
usi
ng:
-flo
w d
iagr
ams
-ta
bles
-fo
rmul
ae
-eq
uatio
ns
equi
vale
nt fo
rms
• D
eter
min
e, in
terp
ret a
nd ju
stify
equ
ival
ence
of
diffe
rent
des
crip
tions
of t
he s
ame
rela
tions
hip
or
rule
pre
sent
ed:
-ve
rbal
ly
-in
flow
dia
gram
s
-in
tabl
es
-by
form
ulae
-by
equ
atio
ns
-by
gra
phs
on a
Car
tesi
an p
lane
MATHEMATICS GRADES 7-9
23CAPS
toPi
Cs
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
2.3
alg
ebra
ic
expr
essi
ons
alg
ebra
ic la
ngua
ge
• R
ecog
nize
and
inte
rpre
t rul
es o
r rel
atio
nshi
ps
repr
esen
ted
in s
ymbo
lic fo
rm
• Id
entif
y va
riabl
es a
nd c
onst
ants
in g
iven
form
ulae
an
d/or
equ
atio
ns
alg
ebra
ic la
ngua
ge
• R
evis
e th
e fo
llow
ing
done
in G
rade
7:
-re
cogn
ize
and
inte
rpre
t rul
es o
r rel
atio
nshi
ps
repr
esen
ted
in s
ymbo
lic fo
rm
-id
entif
y va
riabl
es a
nd c
onst
ants
in g
iven
fo
rmul
ae a
nd/o
r equ
atio
ns
• R
ecog
nize
and
iden
tify
conv
entio
ns fo
r writ
ing
alge
brai
c ex
pres
sion
s
• Id
entif
y an
d cl
assi
fy li
ke a
nd u
nlik
e te
rms
in
alge
brai
c ex
pres
sion
s
• R
ecog
nize
and
iden
tify
coef
ficie
nts
and
expo
nent
s in
alg
ebra
ic e
xpre
ssio
ns
expa
nd a
nd s
impl
ify a
lgeb
raic
exp
ress
ions
Use
com
mut
ativ
e, a
ssoc
iativ
e an
d di
strib
utiv
e la
ws
for r
atio
nal n
umbe
rs a
nd la
ws
of e
xpon
ents
to:
• ad
d an
d su
btra
ct li
ke te
rms
in a
lgeb
raic
ex
pres
sion
s
• m
ultip
ly in
tege
rs a
nd m
onom
ials
by:
-m
onom
ials
-bi
nom
ials
-tri
nom
ials
• di
vide
the
follo
win
g by
inte
gers
or m
onom
ials
:
-m
onom
ials
-B
inom
ials
-tri
nom
ials
• si
mpl
ify a
lgeb
raic
exp
ress
ions
invo
lvin
g th
e ab
ove
oper
atio
ns
alg
ebra
ic la
ngua
ge
• R
evis
e th
e fo
llow
ing
done
in G
rade
8:
-re
cogn
ize
and
iden
tify
conv
entio
ns fo
r writ
ing
alge
brai
c ex
pres
sion
s
-id
entif
y an
d cl
assi
fy li
ke a
nd u
nlik
e te
rms
in
alge
brai
c ex
pres
sion
s
-re
cogn
ize
and
iden
tify
coef
ficie
nts
and
expo
nent
s in
alg
ebra
ic e
xpre
ssio
ns
• R
ecog
nize
and
diff
eren
tiate
bet
wee
n m
onom
ials
, bi
nom
ials
and
trin
omia
ls
expa
nd a
nd s
impl
ify a
lgeb
raic
exp
ress
ions
• R
evis
e th
e fo
llow
ing
done
in G
rade
8, u
sing
the
com
mut
ativ
e, a
ssoc
iativ
e an
d di
strib
utiv
e la
ws
for
ratio
nal n
umbe
rs a
nd la
ws
of e
xpon
ents
to:
-ad
d an
d su
btra
ct li
ke te
rms
in a
lgeb
raic
ex
pres
sion
s
-m
ultip
ly in
tege
rs a
nd m
onom
ials
by:
♦m
onom
ials
♦bi
nom
ials
♦tri
nom
ials
-di
vide
the
follo
win
g by
inte
gers
or m
onom
ials
:
♦m
onom
ials
♦bi
nom
ials
♦tri
nom
ials
-si
mpl
ify a
lgeb
raic
exp
ress
ions
invo
lvin
g th
e ab
ove
oper
atio
ns
MATHEMATICS GRADES 7-9
24 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
toPi
Cs
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
2.3
alg
ebra
ic
expr
essi
ons
• D
eter
min
e th
e sq
uare
s, c
ubes
, squ
are
root
s an
d cu
be ro
ots
of s
ingl
e al
gebr
aic
term
s or
like
al
gebr
aic
term
s
• D
eter
min
e th
e nu
mer
ical
val
ue o
f alg
ebra
ic
expr
essi
ons
by s
ubst
itutio
n
-D
eter
min
e th
e sq
uare
s, c
ubes
, squ
are
root
s an
d cu
be ro
ots
of s
ingl
e al
gebr
aic
term
s or
like
al
gebr
aic
term
s
-D
eter
min
e th
e nu
mer
ical
val
ue o
f alg
ebra
ic
expr
essi
ons
by s
ubst
itutio
n
• E
xten
d th
e ab
ove
alge
brai
c m
anip
ulat
ions
to
incl
ude:
-m
ultip
ly in
tege
rs a
nd m
onom
ials
by
poly
nom
ials
-D
ivid
e po
lyno
mia
ls b
y in
tege
rs o
r mon
omia
ls
-Th
e pr
oduc
t of t
wo
bino
mia
ls
-Th
e sq
uare
of a
bin
omia
l
Fact
oriz
e al
gebr
aic
expr
essi
ons
• Fa
ctor
ize
alge
brai
c ex
pres
sion
s th
at in
volv
e:
-co
mm
on fa
ctor
s
-di
ffere
nce
of tw
o sq
uare
s
-tri
nom
ials
of t
he fo
rm:
♦x2 +
bx
+ c
♦ax
2 + b
x +
c, w
here
a is
a c
omm
on fa
ctor
.
• S
impl
ify a
lgeb
raic
exp
ress
ions
that
invo
lve
the
abov
e fa
ctor
isat
ion
proc
esse
s.
• S
impl
ify a
lgeb
raic
frac
tions
usi
ng fa
ctor
isat
ion.
MATHEMATICS GRADES 7-9
25CAPS
toPi
Cs
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
2.4
alg
ebra
ic
equa
tions
num
ber s
ente
nces
• W
rite
num
ber s
ente
nces
to d
escr
ibe
prob
lem
si
tuat
ions
• A
naly
se a
nd in
terp
ret n
umbe
r sen
tenc
es th
at
desc
ribe
a gi
ven
situ
atio
n
• S
olve
and
com
plet
e nu
mbe
r sen
tenc
es b
y:
-in
spec
tion
-tri
al a
nd im
prov
emen
t
• D
eter
min
e th
e nu
mer
ical
val
ue o
f an
expr
essi
on
by s
ubst
itutio
n.
• Id
entif
y va
riabl
es a
nd c
onst
ants
in g
iven
form
ulae
or
equ
atio
ns
equa
tions
• R
evis
e th
e fo
llow
ing
done
in G
rade
7:
-se
t up
equa
tions
to d
escr
ibe
prob
lem
situ
atio
ns
-an
alys
e an
d in
terp
ret e
quat
ions
that
des
crib
e a
give
n si
tuat
ion
-so
lve
equa
tions
by
insp
ectio
n
-de
term
ine
the
num
eric
al v
alue
of a
n ex
pres
sion
by
sub
stitu
tion.
-id
entif
y va
riabl
es a
nd c
onst
ants
in g
iven
fo
rmul
ae o
r equ
atio
ns
• U
se s
ubst
itutio
n in
equ
atio
ns to
gen
erat
e ta
bles
of
ord
ered
pai
rs
• E
xten
d so
lvin
g eq
uatio
ns to
incl
ude:
-us
ing
addi
tive
and
mul
tiplic
ativ
e in
vers
es
-us
ing
law
s of
exp
onen
ts
equa
tions
• R
evis
e th
e fo
llow
ing
done
in G
rade
8:
-se
t up
equa
tions
to d
escr
ibe
prob
lem
situ
atio
ns
-an
alys
e an
d in
terp
ret e
quat
ions
that
des
crib
e a
give
n si
tuat
ion
-so
lve
equa
tions
by
insp
ectio
n
-us
ing
addi
tive
and
mul
tiplic
ativ
e in
vers
es
-us
ing
law
s of
exp
onen
ts
-de
term
ine
the
num
eric
al v
alue
of a
n ex
pres
sion
by
sub
stitu
tion.
-us
e su
bstit
utio
n in
equ
atio
ns to
gen
erat
e ta
bles
of
ord
ered
pai
rs
• E
xten
d so
lvin
g eq
uatio
ns to
incl
ude:
-us
ing
fact
oris
atio
n
-eq
uatio
ns o
f the
form
: a p
rodu
ct o
f fac
tors
= 0
MATHEMATICS GRADES 7-9
26 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
toPi
Cs
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
2.5
Gra
phs
inte
rpre
ting
grap
hs
• A
naly
se a
nd in
terp
ret g
loba
l gra
phs
of p
robl
em
situ
atio
ns, w
ith s
peci
al fo
cus
on th
e fo
llow
ing
trend
s an
d fe
atur
es:
-lin
ear o
r non
-line
ar
-co
nsta
nt, i
ncre
asin
g or
dec
reas
ing
dra
win
g gr
aphs
• D
raw
glo
bal g
raph
s fro
m g
iven
des
crip
tions
of
a pr
oble
m s
ituat
ion,
iden
tifyi
ng fe
atur
es li
sted
ab
ove
inte
rpre
ting
grap
hs
• R
evis
e th
e fo
llow
ing
done
in G
rade
7:
-an
alys
e an
d in
terp
ret g
loba
l gra
phs
of p
robl
em
situ
atio
ns, w
ith a
spe
cial
focu
s on
the
follo
win
g tre
nds
and
feat
ures
:
♦lin
ear o
r non
-line
ar
♦co
nsta
nt, i
ncre
asin
g or
dec
reas
ing
• E
xten
d th
e fo
cus
on fe
atur
es o
f gra
phs
to in
clud
e:
-m
axim
um o
r min
imum
-di
scre
te o
r con
tinuo
us
dra
win
g gr
aphs
• D
raw
glo
bal g
raph
s fro
m g
iven
des
crip
tions
of
a pr
oble
m s
ituat
ion,
iden
tifyi
ng fe
atur
es li
sted
ab
ove
• U
se ta
bles
or o
rder
ed p
airs
to p
lot p
oint
s an
d dr
aw g
raph
s on
the
Car
tesi
an p
lane
inte
rpre
ting
grap
hs
• R
evis
e th
e fo
llow
ing
done
in G
rade
8:
-an
alys
e an
d in
terp
ret g
loba
l gra
phs
of p
robl
em
situ
atio
ns, w
ith a
spe
cial
focu
s on
the
follo
win
g tre
nds
and
feat
ures
:
♦lin
ear o
r non
-line
ar
♦co
nsta
nt, i
ncre
asin
g or
dec
reas
ing
♦m
axim
um o
r min
imum
♦di
scre
te o
r con
tinuo
us
• E
xten
d th
e ab
ove
with
spe
cial
focu
s on
the
follo
win
g fe
atur
es o
f lin
ear g
raph
s:
-x-
inte
rcep
t and
y-in
terc
ept
-gr
adie
nt
dra
win
g gr
aphs
• R
evis
e th
e fo
llow
ing
done
in G
rade
8:
-dr
aw g
loba
l gr
aphs
fro
m g
iven
des
crip
tions
of
a pr
oble
m s
ituat
ion,
ide
ntify
ing
feat
ures
lis
ted
abov
e.
-us
e ta
bles
of
orde
red
pairs
to
plot
poi
nts
and
draw
gra
phs
on th
e C
arte
sian
pla
ne
• E
xten
d th
e ab
ove
with
spe
cial
focu
s on
:
-dr
awin
g lin
ear g
raph
s fro
m g
iven
equ
atio
ns
-de
term
inin
g eq
uatio
ns fr
om g
iven
line
ar g
raph
s
MATHEMATICS GRADES 7-9
27CAPS
sPeC
iFiC
atio
n o
F C
on
ten
t (P
Ha
se o
ver
vieW
)sP
aC
e a
nd
sH
aPe
(Geo
met
ry)
• P
rogr
essi
on in
geo
met
ry in
the
Sen
ior P
hase
is a
chie
ved
prim
arily
by:
-in
vest
igat
ing
new
pro
perti
es o
f sha
pes
and
obje
cts
-de
velo
ping
from
info
rmal
des
crip
tions
of g
eom
etric
figu
res
to m
ore
form
al d
efini
tions
and
cla
ssifi
catio
n of
sha
pes
and
obje
cts
-so
lvin
g m
ore
com
plex
geo
met
ric p
robl
ems
usin
g kn
own
prop
ertie
s of
geo
met
ric fi
gure
s
-de
velo
ping
from
indu
ctiv
e re
ason
ing
to d
educ
tive
reas
onin
g.
• Th
e ge
omet
ry to
pics
are
muc
h m
ore
inte
r-re
late
d th
an in
the
Inte
rmed
iate
Pha
se, e
spec
ially
thos
e re
latin
g to
con
stru
ctio
ns a
nd g
eom
etry
of 2
D s
hape
s an
d st
raig
ht li
nes,
hen
ce c
are
has
to b
e ta
ken
rega
rdin
g se
quen
cing
of t
opic
s th
roug
h th
e te
rms.
• In
the
Sen
ior P
hase
, tra
nsfo
rmat
ion
geom
etry
dev
elop
s fro
m g
ener
al d
escr
iptio
ns o
f mov
emen
t in
spac
e to
mor
e sp
ecifi
c de
scrip
tions
of m
ovem
ent i
n co
-ord
inat
e pl
anes
. Thi
s la
ys
the
foun
datio
n fo
r ana
lytic
geo
met
ry in
the
FET
phas
e.
• S
olvi
ng p
robl
ems
in g
eom
etry
to fi
nd u
nkno
wn
angl
es o
r len
gths
pro
vide
s a
usef
ul c
onte
xt to
pra
ctis
e so
lvin
g eq
uatio
ns.
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
3.1
Geo
met
ry o
f 2d
sh
apes
Cla
ssify
ing
2d s
hape
s
• D
escr
ibe,
sor
t, na
me
and
com
pare
tria
ngle
s ac
cord
ing
to th
eir s
ides
and
ang
les,
focu
sing
on:
-eq
uila
tera
l tria
ngle
s
-is
osce
les
trian
gles
-rig
ht-a
ngle
d tri
angl
es
• D
escr
ibe,
sor
t, na
me
and
com
pare
qua
drila
tera
ls
in te
rms
of:
-le
ngth
of s
ides
-pa
ralle
l and
per
pend
icul
ar s
ides
-si
ze o
f ang
les
(rig
ht-a
ngle
s or
not
)
• D
escr
ibe
and
nam
e pa
rts o
f a c
ircle
Cla
ssify
ing
2d s
hape
s
• Id
entif
y an
d w
rite
clea
r defi
nitio
ns o
f tria
ngle
s in
te
rms
of th
eir s
ides
and
ang
les,
dis
tingu
ishi
ng
betw
een:
-eq
uila
tera
l tria
ngle
s
-is
osce
les
trian
gles
-rig
ht-a
ngle
d tri
angl
es
• Id
entif
y an
d w
rite
clea
r defi
nitio
ns o
f qua
drila
tera
ls
in te
rms
of th
eir s
ides
and
ang
les,
dis
tingu
ishi
ng
betw
een:
-pa
ralle
logr
am
-re
ctan
gle
-sq
uare
-rh
ombu
s
-tra
pezi
um
-ki
te
Cla
ssify
ing
2d s
hape
s
• R
evis
e pr
oper
ties
and
defin
ition
s of
tria
ngle
s in
te
rms
of th
eir s
ides
and
ang
les,
dis
tingu
ishi
ng
betw
een:
-eq
uila
tera
l tria
ngle
s
-is
osce
les
trian
gles
-rig
ht-a
ngle
d tri
angl
es
• R
evis
e an
d w
rite
clea
r defi
nitio
ns o
f qua
drila
tera
ls
in te
rms
of th
eir s
ides
, ang
les
and
diag
onal
s,
dist
ingu
ishi
ng b
etw
een:
-pa
ralle
logr
am
-re
ctan
gle
-sq
uare
-rh
ombu
s
-tra
pezi
um
-ki
te
MATHEMATICS GRADES 7-9
28 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
3.1
Geo
met
ry o
f 2d
sh
apes
sim
ilar a
nd c
ongr
uent
2d
sha
pes
• R
ecog
nize
and
des
crib
e si
mila
r and
con
grue
nt
figur
es b
y co
mpa
ring:
-sh
ape
-si
ze
solv
ing
prob
lem
s
• S
olve
sim
ple
geom
etric
pro
blem
s in
volv
ing
unkn
own
side
s an
d an
gles
in tr
iang
les
and
quad
rilat
eral
s, u
sing
kno
wn
prop
ertie
s.
sim
ilar a
nd c
ongr
uent
2d
sha
pes
• Id
entif
y an
d de
scrib
e th
e pr
oper
ties
of c
ongr
uent
sh
apes
• Id
entif
y an
d de
scrib
e th
e pr
oper
ties
of s
imila
r sh
apes
solv
ing
prob
lem
s
• S
olve
geo
met
ric p
robl
ems
invo
lvin
g un
know
n si
des
and
angl
es in
tria
ngle
s an
d qu
adril
ater
als,
us
ing
know
n pr
oper
ties
and
defin
ition
s.
sim
ilar a
nd c
ongr
uent
tria
ngle
s
• Th
roug
h in
vest
igat
ion,
est
ablis
h th
e m
inim
um
cond
ition
s fo
r con
grue
nt tr
iang
les
• Th
roug
h in
vest
igat
ion,
est
ablis
h th
e m
inim
um
cond
ition
s fo
r sim
ilar t
riang
les
solv
ing
prob
lem
s
• S
olve
geo
met
ric p
robl
ems
invo
lvin
g un
know
n si
des
and
angl
es in
tria
ngle
s an
d qu
adril
ater
als,
us
ing
know
n pr
oper
ties
of tr
iang
les
and
quad
rilat
eral
s, a
s w
ell a
s pr
oper
ties
of c
ongr
uent
an
d si
mila
r tria
ngle
s.
3.2
Geo
met
ry o
f 3d
ob
ject
s
Cla
ssify
ing
3d o
bjec
ts
• D
escr
ibe,
sor
t and
com
pare
pol
yhed
ra in
term
s of
: -sh
ape
and
num
ber o
f fac
es
-nu
mbe
r of v
ertic
es
-nu
mbe
r of e
dges
Bui
ldin
g 3d
mod
els
• R
evis
e us
ing
nets
to c
reat
e m
odel
s of
geo
met
ric
solid
s, in
clud
ing:
-cu
bes
-pr
ism
s
Cla
ssify
ing
3d o
bjec
ts
• D
escr
ibe,
nam
e an
d co
mpa
re th
e 5
Pla
toni
c so
lids
in te
rms
of th
e sh
ape
and
num
ber o
f fac
es,
the
num
ber o
f ver
tices
and
the
num
ber o
f edg
es
Bui
ldin
g 3d
mod
els
• R
evis
e us
ing
nets
to c
reat
e m
odel
s of
geo
met
ric
solid
s, in
clud
ing:
-cu
bes
-pr
ism
s
-py
ram
ids
Cla
ssify
ing
3d o
bjec
ts
• R
evis
e pr
oper
ties
and
defin
ition
s of
the
5 P
lato
nic
solid
s in
term
s of
the
shap
e an
d nu
mbe
r of f
aces
, th
e nu
mbe
r of v
ertic
es a
nd th
e nu
mbe
r of e
dges
• R
ecog
nize
and
des
crib
e th
e pr
oper
ties
of:
-sp
here
s
-cy
linde
rs
Bui
ldin
g 3d
mod
els
• U
se n
ets
to c
reat
e m
odel
s of
geo
met
ric s
olid
s,
incl
udin
g:
-cu
bes
-pr
ism
s
-py
ram
ids
-cy
linde
rs
3.3
Geo
met
ry o
f st
raig
ht li
nes
Define:
• Li
ne s
egm
ent
• R
ay
• S
traig
ht li
ne
• P
aral
lel l
ines
• P
erpe
ndic
ular
line
s
ang
le re
latio
nshi
ps
• R
ecog
nize
and
des
crib
e pa
irs o
f ang
les
form
ed
by:
-pe
rpen
dicu
lar l
ines
-in
ters
ectin
g lin
es
-pa
ralle
l lin
es c
ut b
y a
trans
vers
al
solv
ing
prob
lem
s
• S
olve
geo
met
ric p
robl
ems
usin
g th
e re
latio
nshi
ps
betw
een
pairs
of a
ngle
s de
scrib
ed a
bove
ang
le re
latio
nshi
ps
• R
evis
e an
d w
rite
clea
r des
crip
tions
of t
he
rela
tions
hip
betw
een
angl
es fo
rmed
by:
-pe
rpen
dicu
lar l
ines
-in
ters
ectin
g lin
es
-pa
ralle
l lin
es c
ut b
y a
trans
vers
al
solv
ing
prob
lem
s
• S
olve
geo
met
ric p
robl
ems
usin
g th
e re
latio
nshi
ps
betw
een
pairs
of a
ngle
s de
scrib
ed a
bove
MATHEMATICS GRADES 7-9
29CAPS
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
3.4
tran
sfor
mat
ion
Geo
met
ry
tran
sfor
mat
ions
• R
ecog
nize
, des
crib
e an
d pe
rform
tran
slat
ions
, re
flect
ions
and
rota
tions
with
geo
met
ric fi
gure
s an
d sh
apes
on
squa
red
pape
r
• Id
entif
y an
d dr
aw li
nes
of s
ymm
etry
in g
eom
etric
fig
ures
enla
rgem
ents
and
redu
ctio
ns
• D
raw
enl
arge
men
ts a
nd re
duct
ions
of g
eom
etric
fig
ures
on
squa
red
pape
r and
com
pare
them
in
term
s of
sha
pe a
nd s
ize
tran
sfor
mat
ions
• R
ecog
nize
, des
crib
e an
d pe
rform
tran
sfor
mat
ions
w
ith p
oint
s on
a c
o-or
dina
te p
lane
, foc
usin
g on
:
-re
flect
ing
a po
int i
n th
e X
-axi
s or
Y-a
xis
-tra
nsla
ting
a po
int w
ithin
and
acr
oss
quad
rant
s
• R
ecog
nize
, des
crib
e an
d pe
rform
tran
sfor
mat
ions
w
ith tr
iang
les
on a
co-
ordi
nate
pla
ne, f
ocus
ing
on
the
co-o
rdin
ates
of t
he v
ertic
es w
hen:
-re
flect
ing
a tri
angl
e in
the
X-a
xis
or Y
-axi
s
-tra
nsla
ting
a tri
angl
e w
ithin
and
acr
oss
quad
rant
s
-ro
tatin
g a
trian
gle
arou
nd th
e or
igin
enla
rgem
ents
and
redu
ctio
ns
• U
se p
ropo
rtion
to d
escr
ibe
the
effe
ct o
f en
larg
emen
t or r
educ
tion
on a
rea
and
perim
eter
of
geo
met
ric fi
gure
s
tran
sfor
mat
ions
• R
ecog
nize
, des
crib
e an
d pe
rform
tran
sfor
mat
ions
w
ith p
oint
s, li
ne s
egm
ents
and
sim
ple
geom
etric
fig
ures
on
a co
-ord
inat
e pl
ane,
focu
sing
on:
-re
flect
ion
in th
e X
-axi
s or
Y-a
xis
-tra
nsla
tion
with
in a
nd a
cros
s qu
adra
nts
-re
flect
ion
in th
e lin
e y
= x
• Id
entif
y w
hat t
he tr
ansf
orm
atio
n of
a p
oint
is, i
f gi
ven
the
co-o
rdin
ates
of i
ts im
age
enla
rgem
ents
and
redu
ctio
ns
• U
se p
ropo
rtion
to d
escr
ibe
the
effe
ct o
f en
larg
emen
t or r
educ
tion
on a
rea
and
perim
eter
of
geo
met
ric fi
gure
s
• In
vest
igat
e th
e co
-ord
inat
es o
f the
ver
tices
of
figur
es th
at h
ave
been
enl
arge
d or
redu
ced
by a
gi
ven
scal
e fa
ctor
MATHEMATICS GRADES 7-9
30 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
3.5
Con
stru
ctio
n of
geo
met
ric
figures
mea
surin
g an
gles
• A
ccur
atel
y us
e a
prot
ract
or to
mea
sure
and
cl
assi
fy a
ngle
s:
-<
90o (
acut
e an
gles
)
-R
ight
-ang
les
->
90o (
obtu
se a
ngle
s)
-S
traig
ht a
ngle
s
->
180o (
refle
x an
gles
)
Con
stru
ctio
ns
• A
ccur
atel
y co
nstru
ct g
eom
etric
figu
res
appr
opria
tely
usi
ng a
com
pass
, rul
er a
nd
prot
ract
or, i
nclu
ding
:
-an
gles
, to
one
degr
ee o
f acc
urac
y
-ci
rcle
s
-pa
ralle
l lin
es
-pe
rpen
dicu
lar l
ines
Con
stru
ctio
ns
• A
ccur
atel
y co
nstru
ct g
eom
etric
figu
res
appr
opria
tely
usi
ng a
com
pass
, rul
er a
nd
prot
ract
or, i
nclu
ding
:
-bi
sect
ing
lines
and
ang
les
-pe
rpen
dicu
lar l
ines
at a
giv
en p
oint
or f
rom
a
give
n po
int
-tri
angl
es
-qu
adril
ater
als
• C
onst
ruct
ang
les
of 3
0°, 4
5°, 6
0° a
nd th
eir
mul
tiple
s w
ithou
t usi
ng a
pro
tract
or
Investigatingprop
ertiesofgeometric
figu
res
• B
y co
nstru
ctio
n, in
vest
igat
e th
e an
gles
in a
tri
angl
e, fo
cusi
ng o
n:
-th
e su
m o
f the
inte
rior a
ngle
s of
tria
ngle
s
-th
e si
ze o
f ang
les
in a
n eq
uila
tera
l tria
ngle
-th
e si
des
and
base
ang
les
of a
n is
osce
les
trian
gle
• B
y co
nstru
ctio
n, in
vest
igat
e si
des
and
angl
es in
qu
adril
ater
als,
focu
sing
on:
-th
e su
m o
f the
inte
rior a
ngle
s of
qua
drila
tera
ls
-th
e si
des
and
oppo
site
ang
les
of p
aral
lelo
gram
s
Con
stru
ctio
ns
• A
ccur
atel
y co
nstru
ct g
eom
etric
figu
res
appr
opria
tely
usi
ng a
com
pass
, rul
er a
nd
prot
ract
or, i
nclu
ding
bis
ectin
g an
gles
of a
tria
ngle
• C
onst
ruct
ang
les
of 3
0°, 4
5°, 6
0° a
nd th
eir
mul
tiple
s w
ithou
t usi
ng a
pro
tract
or
Investigatingprop
ertiesofgeometric
figu
res
• B
y co
nstru
ctio
n, in
vest
igat
e th
e an
gles
in a
tri
angl
e, fo
cusi
ng o
n th
e re
latio
nshi
p be
twee
n th
e ex
terio
r ang
le o
f a tr
iang
le a
nd it
s in
terio
r ang
les
• B
y co
nstru
ctio
n, in
vest
igat
e si
des,
ang
les
and
diag
onal
s in
qua
drila
tera
ls, f
ocus
ing
on:
-th
e di
agon
als
of re
ctan
gles
, squ
ares
, pa
ralle
logr
ams,
rhom
bi a
nd k
ites
-ex
plor
ing
the
sum
of t
he in
terio
r ang
les
of
poly
gons
• B
y co
nstru
ctio
n, e
xplo
re th
e m
inim
um c
ondi
tions
fo
r tw
o tri
angl
es to
be
cong
ruen
t
MATHEMATICS GRADES 7-9
31CAPS
sPeC
iFiC
atio
n o
F C
on
ten
t (P
Ha
se o
ver
vieW
)
mea
sur
emen
t
• P
rogr
essi
on in
Mea
sure
men
t is
achi
eved
by
the
sele
ctio
n of
sha
pes
and
obje
cts
in e
ach
grad
e fo
r whi
ch th
e fo
rmul
ae fo
r find
ing
area
, per
imet
er, s
urfa
ce a
rea
and
volu
me
beco
me
mor
e co
mpl
ex.
• Th
e us
e of
form
ulae
in th
is p
hase
pro
vide
s a
usef
ul c
onte
xt to
pra
ctis
e so
lvin
g eq
uatio
ns.
• Th
e in
trodu
ctio
n of
the
Theo
rem
of P
ytha
gora
s is
a w
ay o
f int
rodu
cing
a fo
rmul
a to
cal
cula
te th
e le
ngth
s of
sid
es in
righ
t-ang
led
trian
gles
. Hen
ce, t
he T
heor
em o
f Pyt
hago
ras
beco
mes
a u
sefu
l too
l whe
n le
arne
rs s
olve
geo
met
ric p
robl
ems
invo
lvin
g rig
ht-a
ngle
d tri
angl
es.
• M
easu
rem
ent d
isap
pear
s as
a s
epar
ate
topi
c in
the
FET
phas
e, a
nd b
ecom
es p
art o
f the
stu
dy o
f Geo
met
ry a
nd T
rigon
omet
ry.
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
4.1
are
a an
d pe
rimet
er o
f 2d
sh
apes
are
a an
d pe
rimet
er
• C
alcu
late
the
perim
eter
of r
egul
ar a
nd ir
regu
lar
poly
gons
• U
se a
ppro
pria
te fo
rmul
ae to
cal
cula
te p
erim
eter
an
d ar
ea o
f:
-sq
uare
s
-re
ctan
gles
-tri
angl
es
Cal
cula
tions
and
sol
ving
pro
blem
s
• S
olve
pro
blem
s in
volv
ing
perim
eter
and
are
a of
po
lygo
ns
• C
alcu
late
to a
t lea
st 1
dec
imal
pla
ce
• U
se a
nd c
onve
rt be
twee
n ap
prop
riate
SI u
nits
, in
clud
ing:
-m
m2
↔ cm
2
-cm
2 ↔
m2
are
a an
d pe
rimet
er
• U
se a
ppro
pria
te fo
rmul
ae to
cal
cula
te p
erim
eter
an
d ar
ea o
f:
-sq
uare
s
-re
ctan
gles
-tri
angl
es
-ci
rcle
s
• C
alcu
late
the
area
s of
pol
ygon
s, to
at l
east
2
deci
mal
pla
ces,
by
deco
mpo
sing
them
into
re
ctan
gles
and
/or t
riang
les
• U
se a
nd d
escr
ibe
the
rela
tions
hip
betw
een
the
radi
us, d
iam
eter
and
circ
umfe
renc
e of
a c
ircle
in
calc
ulat
ions
• U
se a
nd d
escr
ibe
the
rela
tions
hip
betw
een
the
radi
us a
nd a
rea
of a
circ
le in
cal
cula
tions
Cal
cula
tions
and
sol
ving
pro
blem
s
• S
olve
pro
blem
s, w
ith o
r with
out a
cal
cula
tor,
invo
lvin
g pe
rimet
er a
nd a
rea
of p
olyg
ons
and
circ
les
• C
alcu
late
to a
t lea
st 2
dec
imal
pla
ces
• U
se a
nd d
escr
ibe
the
mea
ning
of t
he ir
ratio
nal
num
ber P
i (π)
in c
alcu
latio
ns in
volv
ing
circ
les
• U
se a
nd c
onve
rt be
twee
n ap
prop
riate
SI u
nits
, in
clud
ing:
mm
2 ↔
cm2
↔ m
2 ↔
km2
are
a an
d pe
rimet
er
• U
se a
ppro
pria
te fo
rmul
ae a
nd c
onve
rsio
ns
betw
een
SI u
nits
, to
solv
e pr
oble
ms
and
calc
ulat
e pe
rimet
er a
nd a
rea
of:
-po
lygo
ns
-ci
rcle
s
• In
vest
igat
e ho
w d
oubl
ing
any
or a
ll of
the
dim
ensi
ons
of a
2D
figu
re a
ffect
s its
per
imet
er
and
its a
rea
MATHEMATICS GRADES 7-9
32 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
4.2
surf
ace
area
and
vo
lum
e of
3d
ob
ject
s
surf
ace
area
and
vol
ume
• U
se a
ppro
pria
te fo
rmul
ae to
cal
cula
te th
e su
rface
ar
ea, v
olum
e an
d ca
paci
ty o
f:
-cu
bes
-re
ctan
gula
r pris
ms
• D
escr
ibe
the
inte
rrel
atio
nshi
p be
twee
n su
rface
ar
ea a
nd v
olum
e of
the
obje
cts
men
tione
d ab
ove
Cal
cula
tions
and
sol
ving
pro
blem
s
• S
olve
pro
blem
s in
volv
ing
surfa
ce a
rea,
vol
ume
and
capa
city
• U
se a
nd c
onve
rt be
twee
n ap
prop
riate
SI u
nits
, in
clud
ing:
-m
m2
↔ cm
2
-cm
2 ↔
m2
-m
m3
↔ cm
3
-cm
3 ↔
m3
• U
se e
quiv
alen
ce b
etw
een
units
whe
n so
lvin
g pr
oble
ms:
-1
cm3
↔ 1
ml
-1
m3
↔ 1
kl
surf
ace
area
and
vol
ume
• U
se a
ppro
pria
te fo
rmul
ae to
cal
cula
te th
e su
rface
ar
ea, v
olum
e an
d ca
paci
ty o
f:
-cu
bes
-re
ctan
gula
r pris
ms
-tri
angu
lar p
rism
s
• D
escr
ibe
the
inte
rrel
atio
nshi
p be
twee
n su
rface
ar
ea a
nd v
olum
e of
the
obje
cts
men
tione
d ab
ove
Cal
cula
tions
and
sol
ving
pro
blem
s
• S
olve
pro
blem
s, w
ith o
r with
out a
cal
cula
tor,
invo
lvin
g su
rface
are
a, v
olum
e an
d ca
paci
ty
• U
se a
nd c
onve
rt be
twee
n ap
prop
riate
SI u
nits
, in
clud
ing:
-m
m2
↔ cm
2 ↔
m2
↔ km
2
-m
m3
↔ cm
3 ↔
m3
-m
l (cm
3 ) ↔ l ↔
kl
surf
ace
area
and
vol
ume
• U
se a
ppro
pria
te fo
rmul
ae a
nd c
onve
rsio
ns
betw
een
SI u
nits
to s
olve
pro
blem
s an
d ca
lcul
ate
the
surfa
ce a
rea,
vol
ume
and
capa
city
of:
-cu
bes
-re
ctan
gula
r pris
ms
-tri
angu
lar p
rism
s
-cy
linde
rs
• In
vest
igat
e ho
w d
oubl
ing
any
or a
ll th
e di
men
sion
s of
righ
t pris
ms
and
cylin
ders
affe
cts
thei
r vol
ume
4.3
the
theo
rem
of
Pyth
agor
as
dev
elop
and
use
the
theo
rem
of P
ytha
gora
s
• In
vest
igat
e th
e re
latio
nshi
p be
twee
n th
e le
ngth
s of
the
side
s of
a ri
ght-a
ngle
d tri
angl
e to
dev
elop
th
e Th
eore
m o
f Pyt
hago
ras
• D
eter
min
e w
heth
er a
tria
ngle
is a
righ
t-ang
led
trian
gle
or n
ot if
the
leng
th o
f the
thre
e si
des
of
the
trian
gle
are
know
n
• U
se th
e Th
eore
m o
f Pyt
hago
ras
to c
alcu
late
a
mis
sing
leng
th in
a ri
ght-a
ngle
d tri
angl
e, le
avin
g irr
atio
nal a
nsw
ers
in s
urd
form
solv
e pr
oble
ms
usin
g th
e th
eore
m o
f Py
thag
oras
• U
se th
e Th
eore
m o
f Pyt
hago
ras
to s
olve
pr
oble
ms
invo
lvin
g un
know
n le
ngth
s in
geo
met
ric
figur
es th
at c
onta
in ri
ght-a
ngle
d tri
angl
es
MATHEMATICS GRADES 7-9
33CAPS
sPeC
iFiC
atio
n o
F C
on
ten
t (P
Ha
se o
ver
vieW
)
dat
a H
an
dli
nG
• P
rogr
essi
on in
Dat
a H
andl
ing
is a
chie
ved
prim
arily
by:
-in
crea
sing
com
plex
ity o
f dat
a se
ts a
nd c
onte
xts
-re
adin
g, in
terp
retin
g an
d dr
awin
g ne
w ty
pes
of d
ata
grap
hs
-be
com
ing
mor
e ef
ficie
nt a
t org
aniz
ing
and
sum
mar
izin
g da
ta
-be
com
ing
mor
e cr
itica
l and
aw
are
of b
ias
and
man
ipul
atio
n in
repr
esen
ting,
ana
lysi
ng a
nd re
porti
ng d
ata
• Le
arne
rs s
houl
d w
ork
thro
ugh
at le
ast 1
dat
a cy
cle
for t
he y
ear –
this
invo
lves
col
lect
ing
and
orga
nizi
ng, r
epre
sent
ing,
ana
lysi
ng, s
umm
ariz
ing,
inte
rpre
ting
and
repo
rting
dat
a. T
he
data
cyc
le p
rovi
des
the
oppo
rtuni
ty fo
r doi
ng p
roje
cts.
• A
ll of
the
abov
e as
pect
s of
dat
a ha
ndlin
g sh
ould
als
o be
dea
lt w
ith a
s di
scre
te a
ctiv
ities
in o
rder
to c
onso
lidat
e co
ncep
ts a
nd p
ract
ise
skill
s. F
or e
xam
ple,
lear
ners
nee
d to
pra
ctis
e su
mm
ariz
ing
data
pre
sent
ed in
diff
eren
t for
ms,
and
sum
mar
ies
shou
ld b
e us
ed w
hen
repo
rting
dat
a.
• D
ata
hand
ling
cont
exts
sho
uld
be s
elec
ted
to b
uild
aw
aren
ess
of s
ocia
l, ec
onom
ic a
nd e
nviro
nmen
tal i
ssue
s.
• Le
arne
rs s
houl
d be
com
e se
nsiti
zed
to b
ias
in th
e co
llect
ion
of d
ata,
as
wel
l as
mis
repr
esen
tatio
n of
dat
a th
roug
h th
e us
e of
diff
eren
t sca
les
and
diffe
rent
mea
sure
s of
cen
tral
tend
ency
.
• Th
e fo
llow
ing
reso
urce
s pr
ovid
e in
tere
stin
g co
ntex
ts fo
r dat
a co
mpa
rison
and
ana
lysi
s th
at c
an b
e us
ed in
this
pha
se:
-C
ensu
s at
Sch
ool –
for s
choo
l bas
ed s
urve
ys
-na
tiona
l sur
veys
from
Sta
tistic
s S
outh
Afri
ca (S
tats
SA
) – fo
r hou
seho
ld a
nd p
opul
atio
n su
rvey
s.
-in
tern
atio
nal s
urve
ys fr
om U
nite
d N
atio
ns (U
N D
ata)
– fo
r int
erna
tiona
l soc
ial,
dem
ogra
phic
and
env
ironm
enta
l sur
veys
. Man
y ot
her w
ebsi
tes
may
be
cons
ulte
d, e
spec
ially
for h
ealth
an
d en
viro
nmen
tal d
ata.
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
5.1
Col
lect
, org
aniz
e an
d su
mm
ariz
e da
ta
Col
lect
dat
a
• P
ose
ques
tions
rela
ting
to s
ocia
l, ec
onom
ic, a
nd
envi
ronm
enta
l iss
ues
in o
wn
envi
ronm
ent
• S
elec
t app
ropr
iate
sou
rces
for t
he c
olle
ctio
n of
da
ta (i
nclu
ding
pee
rs, f
amily
, new
spap
ers,
boo
ks,
mag
azin
es)
• D
istin
guis
h be
twee
n sa
mpl
es a
nd p
opul
atio
ns
and
sugg
est a
ppro
pria
te s
ampl
es fo
r inv
estig
atio
n
• D
esig
n an
d us
e si
mpl
e qu
estio
nnai
res
to a
nsw
er
ques
tions
:
-w
ith y
es/n
o ty
pe re
spon
ses
-w
ith m
ultip
le c
hoic
e re
spon
ses
Col
lect
dat
a
• P
ose
ques
tions
rela
ting
to s
ocia
l, ec
onom
ic, a
nd
envi
ronm
enta
l iss
ues
• S
elec
t app
ropr
iate
sou
rces
for t
he c
olle
ctio
n of
da
ta (i
nclu
ding
pee
rs, f
amily
, new
spap
ers,
boo
ks,
mag
azin
es)
• D
istin
guis
h be
twee
n sa
mpl
es a
nd p
opul
atio
ns,
and
sugg
est a
ppro
pria
te s
ampl
es fo
r inv
estig
atio
n
• D
esig
n an
d us
e si
mpl
e qu
estio
nnai
res
to a
nsw
er
ques
tions
with
mul
tiple
cho
ice
resp
onse
s
Col
lect
dat
a
• P
ose
ques
tions
rela
ting
to s
ocia
l, ec
onom
ic, a
nd
envi
ronm
enta
l iss
ues
• S
elec
t and
just
ify a
ppro
pria
te s
ourc
es fo
r the
co
llect
ion
of d
ata
• D
istin
guis
h be
twee
n sa
mpl
es a
nd p
opul
atio
ns,
and
sugg
est a
ppro
pria
te s
ampl
es fo
r inv
estig
atio
n
• S
elec
t and
just
ify a
ppro
pria
te m
etho
ds fo
r co
llect
ing
data
MATHEMATICS GRADES 7-9
34 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
5.1
Col
lect
, org
aniz
e an
d su
mm
ariz
e da
ta
org
aniz
e an
d su
mm
ariz
e da
ta
• O
rgan
ize
(incl
udin
g gr
oupi
ng w
here
app
ropr
iate
) an
d re
cord
dat
a us
ing
-ta
lly m
arks
-ta
bles
-st
em-a
nd-le
af d
ispl
ays
• G
roup
dat
a in
to in
terv
als
• S
umm
ariz
e an
d di
stin
guis
hing
bet
wee
n un
grou
ped
num
eric
al d
ata
by d
eter
min
ing:
-m
ean
-m
edia
n
-m
ode
• Id
entif
y th
e la
rges
t and
sm
alle
st s
core
s in
a d
ata
set a
nd d
eter
min
e th
e di
ffere
nce
betw
een
them
in
orde
r to
dete
rmin
e th
e sp
read
of t
he d
ata
(ran
ge)
org
aniz
e an
d su
mm
ariz
e da
ta
• O
rgan
ize
(incl
udin
g gr
oupi
ng w
here
app
ropr
iate
) an
d re
cord
dat
a us
ing
-ta
lly m
arks
-ta
bles
-st
em-a
nd-le
af d
ispl
ays
• G
roup
dat
a in
to in
terv
als
• S
umm
ariz
e da
ta u
sing
mea
sure
s of
cen
tral
tend
ency
, inc
ludi
ng:
-m
ean
-m
edia
n
-m
ode
• S
umm
ariz
e da
ta u
sing
mea
sure
s of
dis
pers
ion,
in
clud
ing:
-ra
nge
-ex
trem
es
org
aniz
e an
d su
mm
ariz
e da
ta
• O
rgan
ize
num
eric
al d
ata
in d
iffer
ent w
ays
in o
rder
to
sum
mar
ize
by d
eter
min
ing:
-m
easu
res
of c
entra
l ten
denc
y
-m
easu
res
of d
ispe
rsio
n, in
clud
ing
extre
mes
and
ou
tlier
s
• O
rgan
ize
data
acc
ordi
ng to
mor
e th
an o
ne c
riter
ia
5.2
rep
rese
nt d
ata
rep
rese
nt d
ata
• D
raw
a v
arie
ty o
f gra
phs
by h
and/
tech
nolo
gy
to d
ispl
ay a
nd in
terp
ret d
ata
(gro
uped
and
un
grou
ped)
incl
udin
g:
-ba
r gra
phs
and
doub
le b
ar g
raph
s
-hi
stog
ram
s w
ith g
iven
inte
rval
s
-pi
e ch
arts
rep
rese
nt d
ata
• D
raw
a v
arie
ty o
f gra
phs
by h
and/
tech
nolo
gy to
di
spla
y an
d in
terp
ret d
ata
incl
udin
g:
-ba
r gra
phs
and
doub
le b
ar g
raph
s
-hi
stog
ram
s w
ith g
iven
and
ow
n in
terv
als
-pi
e ch
arts
-br
oken
-line
gra
phs
rep
rese
nt d
ata
• D
raw
a v
arie
ty o
f gra
phs
by h
and/
tech
nolo
gy to
di
spla
y an
d in
terp
ret d
ata
incl
udin
g:
-ba
r gra
phs
and
doub
le b
ar g
raph
s
-hi
stog
ram
s w
ith g
iven
and
ow
n in
terv
als
-pi
e ch
arts
-br
oken
-line
gra
phs
-sc
atte
r plo
ts
MATHEMATICS GRADES 7-9
35CAPS
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
5.3
inte
rpre
t, an
alys
e, a
nd
repo
rt d
ata
inte
rpre
t dat
a
• C
ritic
ally
read
and
inte
rpre
t dat
a re
pres
ente
d in
:
-w
ords
-ba
r gra
phs
-do
uble
bar
gra
phs
-pi
e ch
arts
-hi
stog
ram
s
ana
lyse
dat
a
• C
ritic
ally
ana
lyse
dat
a by
ans
wer
ing
ques
tions
re
late
d to
:
-da
ta c
ateg
orie
s, in
clud
ing
data
inte
rval
s
-da
ta s
ourc
es a
nd c
onte
xts
-ce
ntra
l ten
denc
ies
(mea
n, m
ode,
med
ian)
-sc
ales
use
d on
gra
phs
rep
ort d
ata
• S
umm
ariz
e da
ta in
sho
rt pa
ragr
aphs
that
incl
ude
-dr
awin
g co
nclu
sion
s ab
out t
he d
ata
-m
akin
g pr
edic
tions
bas
ed o
n th
e da
ta
-id
entif
ying
sou
rces
of e
rror
and
bia
s in
the
data
-ch
oosi
ng a
ppro
pria
te s
umm
ary
stat
istic
s fo
r the
da
ta (m
ean,
med
ian,
mod
e)
inte
rpre
t dat
a
• C
ritic
ally
read
and
inte
rpre
t dat
a re
pres
ente
d in
:
-w
ords
-ba
r gra
phs
-do
uble
bar
gra
phs
-pi
e ch
arts
-hi
stog
ram
s
-br
oken
-line
gra
phs
ana
lyse
dat
a
• C
ritic
ally
ana
lyse
dat
a by
ans
wer
ing
ques
tions
re
late
d to
:
-da
ta c
ateg
orie
s, in
clud
ing
data
inte
rval
s
-da
ta s
ourc
es a
nd c
onte
xts
-ce
ntra
l ten
denc
ies
(mea
n, m
ode,
med
ian)
-sc
ales
use
d on
gra
phs
-sa
mpl
es a
nd p
opul
atio
ns
-di
sper
sion
of d
ata
-er
ror a
nd b
ias
in th
e da
ta
rep
ort d
ata
• S
umm
ariz
e da
ta in
sho
rt pa
ragr
aphs
that
incl
ude
-dr
awin
g co
nclu
sion
s ab
out t
he d
ata
-m
akin
g pr
edic
tions
bas
ed o
n th
e da
ta
-id
entif
ying
sou
rces
of e
rror
and
bia
s in
the
data
-ch
oosi
ng a
ppro
pria
te s
umm
ary
stat
istic
s fo
r the
da
ta (m
ean,
med
ian,
mod
e, ra
nge)
-th
e ro
le o
f ext
rem
es in
the
data
inte
rpre
t dat
a
• C
ritic
ally
read
and
inte
rpre
t dat
a re
pres
ente
d in
a
varie
ty o
f way
s
• C
ritic
ally
com
pare
two
sets
of d
ata
rela
ted
to th
e sa
me
issu
e
ana
lyse
dat
a
• C
ritic
ally
ana
lyse
dat
a by
ans
wer
ing
ques
tions
re
late
d to
:
-da
ta c
olle
ctio
n m
etho
ds
-su
mm
ary
of d
ata
-so
urce
s of
err
or a
nd b
ias
in th
e da
ta
rep
ort d
ata
• S
umm
ariz
e da
ta in
sho
rt pa
ragr
aphs
that
incl
ude
-dr
awin
g co
nclu
sion
s ab
out t
he d
ata
-m
akin
g pr
edic
tions
bas
ed o
n th
e da
ta
-m
akin
g co
mpa
rison
s be
twee
n tw
o se
ts o
f dat
a
-id
entif
ying
sou
rces
of e
rror
and
bia
s in
the
data
-ch
oosi
ng a
ppro
pria
te s
umm
ary
stat
istic
s fo
r the
da
ta (m
ean,
med
ian,
mod
e, ra
nge)
-th
e ro
le o
f ext
rem
es a
nd o
utlie
rs in
the
data
MATHEMATICS GRADES 7-9
36 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
Gr
ad
e 7
Gr
ad
e 8
Gr
ad
e 9
5.4
Prob
abili
tyPr
obab
ility
• P
erfo
rm s
impl
e ex
perim
ents
whe
re th
e po
ssib
le
outc
omes
are
equ
ally
like
ly a
nd:
-lis
t the
pos
sibl
e ou
tcom
es b
ased
on
the
cond
ition
s of
the
activ
ity
-de
term
ine
the
prob
abili
ty o
f eac
h po
ssib
le
outc
ome
usin
g th
e de
finito
n of
pro
babi
lity
Prob
abili
ty
• C
onsi
der a
sim
ple
situ
atio
n (w
ith e
qual
ly li
kely
ou
tcom
es) t
hat c
an b
e de
scrib
ed u
sing
pro
babi
lity
and:
-lis
t all
the
poss
ible
out
com
es
-de
term
ine
the
prob
abili
ty o
f eac
h po
ssib
le
outc
ome
usin
g th
e de
finiti
on o
f pro
babi
lity
-pr
edic
t with
reas
ons
the
rela
tive
frequ
ency
of
the
poss
ible
out
com
es fo
r a s
erie
s of
tria
ls
base
d on
pro
babi
lity
-co
mpa
re re
lativ
e fre
quen
cy w
ith p
roba
bilit
y an
d ex
plai
ns p
ossi
ble
diffe
renc
es
Prob
abili
ty
• C
onsi
der s
ituat
ions
with
equ
ally
pro
babl
e ou
tcom
es, a
nd:
-de
term
ine
prob
abili
ties
for c
ompo
und
even
ts
usin
g tw
o-w
ay ta
bles
and
tree
dia
gram
s
-de
term
ine
the
prob
abili
ties
for o
utco
mes
of
even
ts a
nd p
redi
ct th
eir r
elat
ive
frequ
ency
in
sim
ple
expe
rimen
ts
-co
mpa
re re
lativ
e fre
quen
cy w
ith p
roba
bilit
y an
d ex
plai
ns p
ossi
ble
diffe
renc
es
MATHEMATICS GRADES 7-9
37CAPS
SECTION 3: CONTENT CLARIFICATION
3.1 introduCtion
• In this chapter, content clarification includes:
- teaching guidelines
- suggested sequencing of topics per term
- suggested pacing of topics over the year.
• Each Content Area has been broken down into topics. The sequencing of topics within terms gives an idea of how content areas can be spread and re-visited throughout the year.
• Teachers may choose to sequence and pace the contents differently from the recommendations in this section. However, cognisance should be taken of the relative weighting and notional hours of the Content Areas for this phase.
3.2 alloCation oF teaCHinG time
Time has been allocated in the following way:
• 10 weeks per term, with 4,5 hours for Mathematics per week (10 x 4 x 4,5 hours = 180 hours per year)
• Between 6 and 12 hours have been allocated for revision and assessment per term
• Therefore, 150 hours of teaching have been distributed across the Content Areas
• The distribution of time per topic, has taken account of the weighting for the Content Area as specified for the Senior Phase in Section 2.
• The weighting of Content Areas represents notional hours; therefore, the recommended distribution of hours may vary slightly across grades.
MATHEMATICS GRADES 7-9
38 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
3.3 ClariFiCation notes WitH teaCHinG Guidelines
The tables below provide the teacher with:
• content areas and topics per grade per term;
• concepts and skills per term;
• clarification notes with teaching guidelines; and
• the duration of time allocated per topic in hours.
time alloCation Per toPiC: Grade 7
term 1 term 2 term 3 term 4
topic time topic time topic time topic time
Whole numbers 9 hours Common fractions 9
hoursNumeric and geometric patterns
6 hours Integers 9
hours
Exponents 9 hours Decimal fractions 9
hoursFunctions and relationships
3 hours
Numeric and geometric patterns
3 hours
Construction of Geometric figures
10 hours
Functions and relationships
3 hours
Algebraic expressions
3 hours
Functions and relationships
3 hours
Geometry of 2D shapes
10 hours
Area and perimeter of 2D shapes
7 hours
Algebraic equations
3 hours
Algebraic expressions
3 hours
Geometry of straight lines
2 hours
Surface area and Volume of 3D objects
8 hours Graphs 6
hoursAlgebraic equations
4 hours
Transformation geometry 9
hoursCollect, organize and summarize data
4 hours
Geometry of 3D objects
9 hours Represent data 3
hours
Interpret, analyse and report data
3,5 hours
Probability 4,5 hours
revision/assessment
5 hours
revision/assessment
9 hours
revision/assessment
6 hours
revision/assessment 8hours
total: 45 hours total: 45 hours total: 45 hours total: 45 hours
MATHEMATICS GRADES 7-9
39CAPS
3.3.1Clarifi
catio
nofcon
tentfo
rGrade7
ter
m 1
– G
ra
de
7
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.1
Who
le
num
bers
men
tal c
alcu
latio
ns
Rev
ise
the
follo
win
g do
ne in
Gra
de 6
:
• m
ultip
licat
ion
of w
hole
num
bers
to a
t le
ast 1
2 x
12
• m
ultip
licat
ion
fact
s fo
r:
-U
nits
and
tens
by
mul
tiple
s of
ten
-U
nits
and
tens
by
mul
tiple
s of
100
-U
nits
and
tens
by
mul
tiple
s of
1 0
00
-U
nits
an
d te
ns
by
mul
tiple
s of
10
000
• In
vers
e op
erat
ion
betw
een
mul
tiplic
atio
n an
d di
visi
on
Wha
t is
diffe
rent
to G
rade
6?
• P
rime
fact
ors
of 3
-dig
it nu
mbe
rs
• LC
m a
nd H
CF
• M
ore
com
plex
fina
ncia
l con
text
s fo
r sol
ving
pro
blem
s
In G
rade
7 le
arne
rs c
onso
lidat
e nu
mbe
r kno
wle
dge
and
calc
ulat
ion
tech
niqu
es fo
r w
hole
num
bers
, dev
elop
ed in
the
Inte
rmed
iate
Pha
se.
men
tal c
alcu
latio
ns
men
tal c
alcu
latio
ns s
houl
d be
use
d to
pra
ctic
e co
ncep
ts a
nd s
kills
dev
elop
ed
thro
ugh
the
mai
n le
sson
, som
etim
es w
ith s
mal
ler n
umbe
r ran
ges.
Lea
rner
s sh
ould
no
t be
aske
d to
do
rand
om c
alcu
latio
ns e
ach
day.
Rat
her,
men
tal c
alcu
latio
ns
shou
ld b
e us
ed a
s an
opp
ortu
nity
to c
onso
lidat
e fo
ur a
spec
ts o
f lea
rner
s’ n
umbe
r kn
owle
dge:
• nu
mbe
r fac
ts (n
umbe
r bon
ds a
nd ti
mes
tabl
es)
• ca
lcul
atio
n te
chni
ques
( do
ublin
g an
d ha
lvin
g, u
sing
mul
tiplic
atio
n to
do
divi
sion
, m
ultip
lyin
g an
d di
vidi
ng b
y 10
, 100
, 1 0
00
• m
ultip
lyin
g by
mul
tiple
s of
10,
100
, 1 0
00,
• bu
ildin
g up
and
bre
akin
g do
wn
num
bers
, rou
ndin
g of
f and
com
pens
atin
g et
c)
• nu
mbe
r con
cept
(cou
ntin
g, o
rder
ing
and
com
parin
g, p
lace
val
ue, o
dd a
nd e
ven
num
bers
, mul
tiple
s an
d fa
ctor
s)
• pr
oper
ties
of n
umbe
rs (i
dent
ity e
lem
ents
for a
dditi
on a
nd m
ultip
licat
ion;
• co
mm
utat
ive
and
asso
ciat
ive
prop
erty
for a
dditi
on a
nd m
ultip
licat
ion;
• in
vers
e op
erat
ion
for m
ultip
licat
ion
and
divi
sion
; inv
erse
ope
ratio
n fo
r add
ition
an
d su
btra
ctio
n)
9 ho
urs
MATHEMATICS GRADES 7-9
40 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.1
Who
le
num
bers
ord
erin
g an
d co
mpa
ring
who
le
num
bers
Rev
ise
the
follo
win
g do
ne in
Gra
de 6
:
• O
rder
, com
pare
and
repr
esen
t nu
mbe
rs to
at l
east
9-d
igit
num
bers
• R
ecog
nise
and
repr
esen
t prim
e nu
mbe
rs to
at l
east
100
• R
ound
ing
off n
umbe
rs to
the
near
est
5, 1
0, 1
00 o
r 1 0
00
Prop
ertie
s of
who
le n
umbe
rs
Rev
ise
the
follo
win
g do
ne in
Gra
de 6
:
• R
ecog
nise
and
use
the
com
mut
ativ
e;
asso
ciat
ive;
dis
tribu
tive
prop
ertie
s w
ith w
hole
num
bers
• R
ecog
nise
and
use
0 in
term
s of
its
addi
tive
prop
erty
(ide
ntity
ele
men
t for
ad
ditio
n)
• R
ecog
nise
and
use
1 in
term
s of
its
mul
tiplic
ativ
e pr
oper
ty (i
dent
ity
elem
ent f
or m
ultip
licat
ion)
ord
erin
g an
d co
mpa
ring
num
bers
Lear
ners
sho
uld
be g
iven
a ra
nge
of e
xerc
ises
suc
h as
:
• A
rran
ge g
iven
num
bers
from
the
smal
lest
to th
e bi
gges
t: or
big
gest
to s
mal
lest
• Fi
ll in
mis
sing
num
bers
in
-a
sequ
ence
-on
a n
umbe
r grid
-on
a n
umbe
r lin
e e.
g. w
hich
who
le n
umbe
r is
hal
fway
bet
wee
n 47
1 34
0 an
d 47
1 35
0.
• Fi
ll in
<, =
or >
exam
ples
:
a)
247
889
*
247
898
b)
784
109
*
785
190
Prop
ertie
s of
who
le n
umbe
rs
• R
evis
ing
the
prop
ertie
s of
who
le n
umbe
rs s
houl
d be
the
star
ting
poin
t for
wor
k w
ith w
hole
num
bers
. The
pro
perti
es o
f num
bers
sho
uld
prov
ide
the
mot
ivat
ion
for w
hy a
nd h
ow o
pera
tions
with
num
bers
wor
k.
• W
hen
lear
ners
are
intro
duce
d to
new
num
bers
, suc
h as
inte
gers
for e
xam
ple,
th
ey c
an a
gain
exp
lore
how
the
prop
ertie
s of
num
bers
wor
k fo
r the
new
set
of
num
bers
.
• Le
arne
rs a
lso
have
to a
pply
the
prop
ertie
s of
num
bers
in a
lgeb
ra, w
hen
they
w
ork
with
var
iabl
es in
pla
ce o
f num
bers
.
• Le
arne
rs s
houl
d kn
ow a
nd b
e ab
le to
use
the
follo
win
g pr
oper
ties:
-Th
e co
mm
utat
ive
prop
erty
of a
dditi
on a
nd m
ultip
licat
ion:
♦a
+ b
= b
+ a
♦a
x b
= b
x a
-Th
e as
soci
ativ
e (g
roup
ing)
pro
perty
of a
dditi
on a
nd m
ultip
licat
ion:
♦(a
+ b
) + c
= a
+ (b
+ a
)
♦(a
x b
) x c
= a
x (b
x c
)
-Th
e di
strib
utiv
e pr
oper
ty o
f mul
tiplic
atio
n ov
er a
dditi
on a
nd s
ubtra
ctio
n:
♦a(
b +
c) =
(a x
b) +
(a x
c)
♦a(
b –
c) =
(a x
b) –
(a x
c)
MATHEMATICS GRADES 7-9
41CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.1
Who
le
num
bers
Cal
cula
tions
with
who
le n
umbe
rs
• R
evis
e th
e fo
llow
ing
done
in G
rade
6,
with
out u
se o
f cal
cula
tors
:
-A
dditi
on a
nd s
ubtra
ctio
n of
who
le
num
bers
to a
t lea
st 6
–di
git n
umbe
rs
-m
ultip
licat
ion
of a
t lea
st w
hole
4-
digi
t by
2-di
git n
umbe
rs
-D
ivis
ion
of a
t lea
st w
hole
4-d
igit
by
2-di
git n
umbe
rs
• P
erfo
rm c
alcu
latio
ns u
sing
all
four
op
erat
ions
on
who
le n
umbe
rs,
estim
atin
g an
d us
ing
calc
ulat
ors
whe
re a
ppro
pria
te
Cal
cula
tion
tech
niqu
es
• U
se a
rang
e of
tech
niqu
es to
per
form
an
d ch
eck
writ
ten
and
men
tal
calc
ulat
ions
of w
hole
num
bers
in
clud
ing:
-es
timat
ion
-ad
ding
, su
btra
ctin
g an
d m
ultip
lyin
g in
col
umns
-A
dditi
on a
nd s
ubtra
ctio
n as
inve
rse
oper
atio
ns
-m
ultip
licat
ion
and
divi
sion
as
inve
rse
oper
atio
ns
-0
is th
e id
entit
y el
emen
t for
add
ition
: t +
0 =
t
-1
is th
e id
entit
y el
emen
t for
mul
tiplic
atio
n: t
x 1
= t
illus
trat
ing
the
prop
ertie
s w
ith w
hole
num
bers
a)
33 +
99
= 99
+ 3
3 =
132
b)
51 +
(19
+ 46
) = (5
1 +
19) +
46
= 11
6
c)
4(12
+ 9
) = (4
x 1
2) +
(4 x
9) =
48
+ 36
= 8
4
d)
(9 x
64)
+ (9
x 3
6) =
9 x
(64
+ 36
) = 9
x 1
00 =
900
e)
If 33
+ 9
9 =
132,
then
132
– 9
9 =
33 a
nd 1
32 –
33
= 99
f) If
20 x
5 =
110
, the
n 11
0 ÷
20 =
5 a
nd 1
10 ÷
5 =
20
Cal
cula
tions
with
who
le n
umbe
rs
• Le
arne
rs s
houl
d do
con
text
free
cal
cula
tions
and
sol
ve p
robl
ems
in c
onte
xts
• Le
arne
rs s
houl
d be
com
e m
ore
confi
dent
in a
nd m
ore
inde
pend
ent a
t m
athe
mat
ics,
if th
ey h
ave
tech
niqu
es
-to
che
ck th
eir s
olut
ions
them
selv
es, e
.g. u
sing
inve
rse
oper
atio
ns; u
sing
ca
lcul
ator
s
-to
judg
e th
e re
ason
able
ness
of t
heir
solu
tions
e.g
. est
imat
e by
roun
ding
off;
es
timat
e by
dou
blin
g or
hal
ving
;
• A
ddin
g, s
ubtra
ctin
g an
d m
ultip
lyin
g in
col
umns
, and
long
div
isio
n, s
houl
d on
ly b
e us
ed to
pra
ctic
e nu
mbe
r fac
ts a
nd c
alcu
latio
n te
chni
ques
, and
hen
ce
shou
ld b
e do
ne w
ith fa
mili
ar a
nd s
mal
ler n
umbe
r ran
ges.
For
big
and
unw
ield
y ca
lcul
atio
ns, l
earn
ers
shou
ld b
e en
cour
aged
to u
se a
cal
cula
tor.
mul
tiple
s an
d fa
ctor
s
• P
ract
ice
with
find
ing
mul
tiple
s an
d fa
ctor
s of
who
le n
umbe
rs a
re e
spec
ially
im
porta
nt w
hen
lear
ners
do
calc
ulat
ions
with
frac
tions
. The
y us
e th
is k
now
ledg
e to
find
the
LCM
whe
n on
e de
nom
inat
or is
a m
ultip
le o
f ano
ther
, and
als
o w
hen
they
sim
plify
frac
tions
or h
ave
to fi
nd e
quiv
alen
t fra
ctio
ns.
• Fa
ctor
isin
g w
hole
num
bers
lays
the
foun
datio
n fo
r fac
toris
atio
n of
alg
ebra
ic
expr
essi
ons.
• U
sing
the
defin
ition
of p
rime
num
bers
, em
phas
ise
that
1 is
not
cla
ssifi
ed a
s a
prim
e nu
mbe
r
MATHEMATICS GRADES 7-9
42 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.1
Who
le
num
bers
-lo
ng d
ivis
ion
-ro
undi
ng o
ff an
d co
mpe
nsat
ing
-us
ing
a ca
lcul
ator
mul
tiple
s an
d fa
ctor
s
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-M
ultip
les
of 2
-dig
it an
d 3-
digi
t w
hole
num
bers
-Fa
ctor
s of
2-d
igit
and
3-di
git w
hole
nu
mbe
rs
-P
rime
fact
ors
of n
umbe
rs to
at
leas
t 100
• Li
st p
rime
fact
ors
of n
umbe
rs to
at
leas
t 3-d
igit
who
le n
umbe
rs
• Fi
nd th
e LC
m a
nd H
CF
of n
umbe
rs
to a
t lea
st 3
-dig
it w
hole
num
bers
, by
insp
ectio
n or
fact
oris
atio
n
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
volv
ing
who
le
num
bers
, inc
ludi
ng:
-C
ompa
ring
two
or m
ore
quan
titie
s of
the
sam
e ki
nd (r
atio
)
-C
ompa
ring
two
quan
titie
s of
di
ffere
nt k
inds
(rat
e)
-S
harin
g in
a g
iven
ratio
whe
re th
e w
hole
is g
iven
• S
olve
pro
blem
s th
at in
volv
e w
hole
nu
mbe
rs, p
erce
ntag
es a
nd d
ecim
al
fract
ions
in fi
nanc
ial c
onte
xts
such
as
:
-P
rofit
, los
s an
d di
scou
nt
-B
udge
ts
-A
ccou
nts
-Lo
ans
-S
impl
e in
tere
st
exam
ples
a)
The
mul
tiple
s of
6 a
re 6
, 12,
18,
24,
... o
r M6 =
{6; 1
2; 1
8; 2
4;...
}
b)
LCM
of 6
and
18
is 1
8
LCM
of 6
and
7 is
42
c)
The
fact
ors
of 2
4 ar
e 1,
2, 3
, 4, 6
, 12
and
24 b
y in
spec
tion
and,
the
prim
e fa
ctor
s of
24
are
2 an
d 3
d)
The
fact
ors
of 1
40 a
re 1
, 2, 5
, 7, 1
0, 1
4, 2
8, 3
5, 7
0 an
d 14
0
e)
Det
erm
ine
the
HC
F of
120
; 300
and
900
Lear
ners
do
this
by
findi
ng th
e pr
ime
fact
ors
of th
e nu
mbe
rs fi
rst.
120
= 5
x 3
x 23 .
Initi
ally
lear
ners
may
writ
e th
is a
s: 5
x 3
x 2
x 2
x 2
300
= 52 x
3 x
22
900
= 52 x
32 x
23
HC
F =
5 x
3 x
22 = 6
0 (M
ultip
ly th
e co
mm
on p
rime
fact
ors
of th
e th
ree
num
bers
)
solv
ing
prob
lem
s
• S
olvi
ng p
robl
ems
in c
onte
xts
shou
ld ta
ke a
ccou
nt o
f the
num
ber r
ange
s le
arne
rs
are
fam
iliar
with
.
• C
onte
xts
invo
lvin
g ra
tio a
nd ra
te, s
houl
d in
clud
e sp
eed,
dis
tanc
e an
d tim
e pr
oble
ms.
• In
fina
ncia
l con
text
s, le
arne
rs a
re n
ot e
xpec
ted
to u
se fo
rmul
ae fo
r cal
cula
ting
sim
ple
inte
rest
.
MATHEMATICS GRADES 7-9
43CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.2
expo
nent
sm
enta
l cal
cula
tions
• D
eter
min
e sq
uare
s to
at l
east
122
and
thei
r squ
are
root
s
• D
eter
min
e cu
bes
to a
t lea
st 6
3 and
th
eir c
ube
root
s
Com
parin
g an
d re
pres
entin
g nu
mbe
rs in
exp
onen
tial f
orm
• C
ompa
re a
nd re
pres
ent w
hole
nu
mbe
rs in
exp
onen
tial f
orm
: ab
= a
x a
x a
x...
for b
num
ber o
f fa
ctor
s
Wha
t is
diffe
rent
to G
rade
6?
• A
lthou
gh le
arne
rs m
ay h
ave
enco
unte
red
squa
re n
umbe
rs in
Gra
de 6
, the
y w
ere
not e
xpec
ted
to w
rite
thes
e nu
mbe
rs in
exp
onen
tial f
orm
.
Com
parin
g an
d re
pres
entin
g nu
mbe
rs in
exp
onen
tial f
orm
• Le
arne
rs n
eed
to u
nder
stan
d th
at in
the
expo
nent
ial f
orm
ab ,
the
num
ber i
s re
ad
as ‘a
to th
e po
wer
b’,
whe
re a
is c
alle
d th
e ba
se a
nd b
is c
alle
d th
e ex
pone
nt o
r in
dex.
indi
cate
s th
e nu
mbe
r of f
acto
rs th
at a
re m
ultip
lied.
exam
ple:
a)
a3 =
a x
a x
a;
b)
a5 =
a x
a x
a x
a x
a
• Le
arne
rs c
an re
pres
ent a
ny n
umbe
r in
expo
nent
ial f
orm
, with
out n
eedi
ng to
co
mpu
te th
e va
lue.
exam
ple:
50 x
50
x 50
x 5
0 x
50 x
50
x 50
= 5
07
• m
ake
sure
lear
ners
und
erst
and
that
squ
are
root
s an
d cu
be ro
ots
are
the
inve
rse
oper
atio
ns o
f squ
arin
g an
d cu
bing
num
bers
.
exam
ples
:32 =
9 th
eref
ore
9√
= 3
• M
ake
sure
lear
ners
und
erst
and
that
any
num
ber r
aise
d to
the
pow
er 1
is e
qual
to
the
num
ber.
Exa
mpl
e m
1 = m
• A
t thi
s po
int,
lear
ners
do
not n
eed
to k
now
the
rule
for r
aisi
ng a
num
ber t
o th
e po
wer
0. T
his
will
onl
y be
intro
duce
d in
Gra
de 8
whe
n th
ey u
se o
ther
law
s of
ex
pone
nts
in c
alcu
latio
ns.
• To
avo
id c
omm
on m
isco
ncep
tions
, em
phas
ize
the
follo
win
g w
ith e
xam
ples
:
-12
2 = 1
2 x
12 a
nd n
ot 1
2 x
2
-13 m
eans
1 x
1 x
1 a
nd n
ot 1
x 3
-10
01 = 1
00
-81
√ =
9 b
ecau
se 9
2 = 8
1
-3
27√
= 3
beca
use
33 = 2
7
-Th
e sq
uare
of 9
= 8
1, w
here
as th
e sq
uare
root
of 9
= 3
• Le
arne
rs s
houl
d us
e th
eir k
now
ledg
e of
repr
esen
ting
num
bers
in e
xpon
entia
l fo
rm w
hen
sim
plify
ing
and
expa
ndin
g al
gebr
aic
expr
essi
ons
and
solv
ing
alge
brai
c eq
uatio
ns.
9 ho
urs
MATHEMATICS GRADES 7-9
44 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.2
expo
nent
sC
alcu
latio
ns u
sing
num
bers
in
expo
nent
ial f
orm
• R
ecog
nize
and
use
the
appr
opria
te
law
s of
ope
ratio
ns w
ith n
umbe
rs
invo
lvin
g ex
pone
nts
and
squa
re a
nd
cube
root
s
• P
erfo
rm c
alcu
latio
ns in
volv
ing
all
four
ope
ratio
ns u
sing
num
bers
in
exp
onen
tial f
orm
, lim
ited
to
expo
nent
s up
to 5
, and
squ
are
and
cube
root
s
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
num
bers
in e
xpon
entia
l for
m
Cal
cula
tions
usi
ng n
umbe
rs in
exp
onen
tial f
orm
• K
now
ing
the
rule
s of
ope
ratio
ns fo
r cal
cula
tions
invo
lvin
g ex
pone
nts,
is
impo
rtant
.
exam
ple:
a)
(7 –
4)3 =
33 a
nd
no
t 73 –
43
b)
16 +
9
√ =
25
√, a
nd
no
t 16
√ +
9
√
MATHEMATICS GRADES 7-9
45CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
shap
e an
d sp
ace
(Geo
met
ry)
3.5
Con
stru
ctio
n of
geo
met
ric
figures
mea
surin
g an
gles
• A
ccur
atel
y us
e a
prot
ract
or to
m
easu
re a
nd c
lass
ify a
ngle
s:
-<
90o (
acut
e an
gles
)
-R
ight
-ang
les
->
90o (
obtu
se a
ngle
s)
-S
traig
ht a
ngle
s
->
180o (
refle
x an
gles
)
Con
stru
ctio
ns
• A
ccur
atel
y co
nstru
ct g
eom
etric
fig
ures
app
ropr
iate
ly u
sing
com
pass
, ru
ler a
nd p
rotra
ctor
, inc
ludi
ng:
-an
gles
, to
one
degr
ee o
f acc
urac
y
-ci
rcle
s
-pa
ralle
l lin
es
-pe
rpen
dicu
lar l
ines
Wha
t is
diffe
rent
to G
rade
6?
• m
easu
re a
ngle
s w
ith a
pro
tract
or
• G
eom
etric
con
stru
ctio
ns u
sing
a c
ompa
ss, r
uler
and
pro
tract
or
mea
surin
g an
gles
• Le
arne
rs h
ave
to b
e sh
own
how
to p
lace
the
prot
ract
or o
n th
e ar
m o
f the
ang
le
to b
e m
easu
red.
• Le
arne
rs a
lso
have
to le
arn
how
to re
ad th
e si
ze o
f ang
les
on a
pro
tract
or.
Con
stru
ctio
ns
• C
onst
ruct
ions
pro
vide
a u
sefu
l con
text
to e
xplo
re o
r con
solid
ate
know
ledg
e of
an
gles
and
sha
pes.
• Le
arne
rs h
ave
to b
e sh
own
how
to u
se a
com
pass
to d
raw
circ
les,
alth
ough
they
m
ight
hav
e do
ne th
is in
Gra
de 6
.
• Le
arne
rs s
houl
d be
aw
are
that
the
cent
re o
f the
circ
le is
at t
he fi
xed
poin
t of t
he
com
pass
and
the
radi
us o
f the
circ
le is
dep
ende
nt o
n ho
w w
ide
the
com
pass
is
open
ed u
p.
• m
ake
sure
lear
ners
und
erst
and
that
arc
s ar
e pa
rts o
f the
circ
les
of a
par
ticul
ar
radi
us.
• In
itial
ly, le
arne
rs h
ave
to b
e gi
ven
care
ful i
nstru
ctio
ns a
bout
how
to d
o th
e co
nstru
ctio
ns o
f the
var
ious
sha
pes
• O
nce
they
are
com
forta
ble
with
the
appa
ratu
s an
d ca
n do
the
cons
truct
ions
, th
ey c
an p
ract
ise
by d
raw
ing
patte
rns,
for e
xam
ple
of c
ircle
s or
par
alle
l lin
es.
10 h
ours
MATHEMATICS GRADES 7-9
46 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
shap
e an
d sp
ace
(Geo
met
ry)
3.1
Geo
met
ry o
f 2d
sha
pes
Cla
ssify
ing
2d s
hape
s
• D
escr
ibe,
sor
t, na
me
and
com
pare
tri
angl
es a
ccor
ding
to th
eir s
ides
and
an
gles
, foc
usin
g on
:
-eq
uila
tera
l tria
ngle
s
-is
osce
les
trian
gles
-rig
ht-a
ngle
d tri
angl
es
• D
escr
ibe,
sor
t, na
me
and
com
pare
qu
adril
ater
als
in te
rms
of:
-le
ngth
of s
ides
-pa
ralle
l and
per
pend
icul
ar s
ides
-si
ze o
f ang
les
(rig
ht-a
ngle
s or
not
)
• D
escr
ibe
and
nam
e pa
rts o
f a c
ircle
Wha
t is
diffe
rent
to G
rade
6?
• D
istin
guis
hing
and
nam
ing
trian
gles
in te
rms
of th
eir s
ides
and
ang
les
• D
istin
guis
hing
qua
drila
tera
ls in
term
s of
par
alle
l and
per
pend
icul
ar s
ides
• D
istin
guis
hing
sim
ilar a
nd c
ongr
uent
figu
res
• U
sing
kno
wn
prop
ertie
s of
sha
pes
to s
olve
geo
met
ric p
robl
ems
tria
ngle
s
• Le
arne
rs s
houl
d be
abl
e to
dis
tingu
ish
betw
een
an e
quila
tera
l tria
ngle
(all
the
side
s ar
e eq
ual),
an
isos
cele
s tri
angl
e (a
t lea
st tw
o eq
ual s
ides
) and
a ri
ght-
angl
ed tr
iang
le (o
ne ri
ght-a
ngle
).
Qua
drila
tera
ls
• Le
arne
rs s
houl
d be
abl
e to
sor
t and
gro
up q
uadr
ilate
rals
in th
e fo
llow
ing
way
s:
-al
l sid
es e
qual
(squ
are
and
rhom
bus)
-op
posi
te s
ides
equ
al (r
ecta
ngle
, par
alle
logr
am, s
quar
e, rh
ombu
s)
-at
leas
t one
pai
r of a
djac
ent s
ides
equ
al (s
quar
e, rh
ombu
s, k
ite)
-al
l fou
r ang
les
right
ang
les
(squ
are,
rect
angl
e)
-pe
rpen
dicu
lar s
ides
(squ
are,
rect
angl
e)
-tw
o pa
irs o
f opp
osite
sid
es p
aral
lel (
rect
angl
e, s
quar
e, p
aral
lelo
gram
)
-on
ly o
ne p
air o
f opp
osite
sid
es p
aral
lel (
trape
zium
)
Circ
les
• P
arts
of a
circ
le le
arne
rs s
houl
d kn
ow:
-ra
dius
-ci
rcum
fere
nce
-di
amet
er
-ch
ord
-se
gmen
ts
-se
ctor
s
10 h
ours
MATHEMATICS GRADES 7-9
47CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
shap
e an
d sp
ace
(Geo
met
ry)
3.1
Geo
met
ry o
f 2d
sha
pes
sim
ilar a
nd c
ongr
uent
2d
sha
pes
• R
ecog
nize
and
des
crib
e si
mila
r and
co
ngru
ent fi
gure
s by
com
parin
g:
-sh
ape
-si
ze
solv
ing
prob
lem
s•
Sol
ve s
impl
e ge
omet
ric p
robl
ems
invo
lvin
g un
know
n si
des
and
angl
es
in tr
iang
les
and
quad
rilat
eral
s, u
sing
kn
own
prop
ertie
s.
sim
ilarit
y an
d co
ngru
ency
• S
imila
rity
and
cong
ruen
cy c
an b
e ex
plor
ed w
ith a
ny 2
D fi
gure
s.
• Le
arne
rs s
houl
d re
cogn
ize
that
two
or m
ore
figur
es a
re c
ongr
uent
if th
ey a
re
equa
l in
all r
espe
cts
i.e. a
ngle
s an
d si
des
are
equa
l.
• Le
arne
rs s
houl
d re
cogn
ize
that
two
or m
ore
figur
es a
re s
imila
r if t
hey
have
th
e sa
me
shap
e, b
ut d
iffer
in s
ize
i.e. a
ngle
s ar
e th
e sa
me,
but
sid
es a
re
prop
ortio
nally
long
er o
r sho
rter.
Sim
ilar fi
gure
s ar
e fu
rther
exp
lore
d w
hen
doin
g en
larg
emen
ts a
nd re
duct
ions
. Ref
er to
“Cla
rifica
tion
Not
es” u
nder
3.4
Tr
ansf
orm
atio
n G
eom
etry
.
solv
ing
prob
lem
s•
At t
his
stag
e le
arne
rs c
an s
olve
sim
ple
geom
etric
pro
blem
s to
find
unk
now
n si
des
in e
quila
tera
l and
isos
cele
s tri
angl
es, a
nd u
nkno
wn
side
s an
d an
gles
in
quad
rilat
eral
s.
• Le
arne
rs s
houl
d gi
ve re
ason
s fo
r the
ir so
lutio
ns.
exam
ples
a)
If ∆A
BC
is a
n eq
uila
tera
l tria
ngle
, and
sid
e A
B is
3 c
m, w
hat i
s th
e le
ngth
of
BC
? H
ere
lear
ners
sho
uld
answ
er: B
C =
3 c
m, b
ecau
se th
e si
des
of a
n eq
uila
tera
l tria
ngle
are
equ
al.
b)
If A
BC
D is
a k
ite, a
nd A
B =
2,5
cm
and
BC
= 4
,5 c
m, w
hat i
s th
e le
ngth
of
AD
and
DC
? Le
arne
rs s
houl
d us
e th
e pr
oper
ty fo
r kite
s, th
at a
djac
ent p
airs
of
sid
es a
re e
qual
, to
find
the
unkn
own
side
s.
3.3
Geo
met
ry o
f st
raig
ht li
nes
Define:
• Li
ne s
egm
ent
• R
ay
• S
traig
ht li
ne
• P
aral
lel l
ines
• P
erpe
ndic
ular
line
s
• Li
ne s
egm
ent i
s a
set o
f poi
nts
with
a d
efini
te s
tarti
ng-p
oint
and
an
end-
poin
t.
• R
ay is
a s
et o
f poi
nts
with
a d
efini
te s
tarti
ng-p
oint
and
no
defin
ite e
nd-p
oint
.
• Li
ne is
a s
et o
f poi
nts
with
no
defin
ite s
tarti
ng-p
oint
and
end
-poi
nt.
• If
two
lines
on
the
sam
e pl
ane
are
a co
nsta
nt d
ista
nce
apar
t, th
en th
e lin
es a
re
para
llel.
exam
ple:
>E
F
>G
H
Th
is is
writ
ten
as E
F║G
H
• If
verti
cal l
ine
AO
mee
ts o
r int
erse
cts
with
hor
izon
tal l
ine
BC
at r
ight
ang
le, t
hen
AO
is p
erpe
ndic
ular
to B
C.
exam
ple: A O
CB
This
is w
ritte
n as
AO
┴B
C
2 ho
urs
MATHEMATICS GRADES 7-9
48 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
rev
isio
n/a
sses
smen
t:A
t thi
s st
age
lear
ners
sho
uld
have
bee
n as
sess
ed o
n:
• ca
lcul
atin
g an
d so
lvin
g pr
oble
ms
usin
g w
hole
num
bers
• w
orki
ng w
ith n
umbe
rs in
exp
onen
tial f
orm
• co
nstru
ctin
g ge
omet
ric o
bjec
ts
• ge
omet
ry o
f 2D
sha
pes
5 ho
urs
MATHEMATICS GRADES 7-9
49CAPS
Gr
ad
e 7
– te
rm
2
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.4
Com
mon
fr
actio
ns
ord
erin
g, c
ompa
ring
and
sim
plify
ing
frac
tions
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-C
ompa
re a
nd o
rder
com
mon
fra
ctio
ns, i
nclu
ding
spe
cific
ally
te
nths
and
hun
dred
ths
• E
xten
d to
thou
sand
ths
Cal
cula
tions
usi
ng fr
actio
ns
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-ad
ditio
n an
d su
btra
ctio
n of
co
mm
on fr
actio
ns, i
nclu
ding
mix
ed
num
bers
, lim
ited
to fr
actio
ns w
ith
the
sam
e de
nom
inat
or o
r whe
re
one
deno
min
ator
is a
mul
tiple
of
anot
her
-fin
ding
frac
tions
of w
hole
num
bers
• E
xten
d ad
ditio
n an
d su
btra
ctio
n to
fra
ctio
ns w
here
one
den
omin
ator
is
not a
mul
tiple
of t
he o
ther
• m
ultip
licat
ion
of c
omm
on fr
actio
ns,
incl
udin
g m
ixed
num
bers
, not
lim
ited
to fr
actio
ns w
here
one
den
omin
ator
is
a m
ultip
le o
f ano
ther
Cal
cula
tion
tech
niqu
es
• C
onve
rt m
ixed
num
bers
to c
omm
on
fract
ions
in o
rder
to p
erfo
rm
calc
ulat
ions
with
them
• U
se k
now
ledg
e of
mul
tiple
s an
d fa
ctor
s to
writ
e fra
ctio
ns in
the
sim
ples
t for
m b
efor
e or
afte
r ca
lcul
atio
ns
• U
se k
now
ledg
e of
equ
ival
ent
fract
ions
to a
dd a
nd s
ubtra
ct c
omm
on
fract
ions
Wha
t is
diffe
rent
to G
rade
6?
• C
ompa
re a
nd o
rder
thou
sand
ths
• m
ultip
licat
ion
of c
omm
on fr
actio
ns
• P
erce
ntag
e of
par
t of a
who
le
• P
erce
ntag
e in
crea
se o
r dec
reas
e
In G
rade
7 le
arne
rs a
lso
cons
olid
ate
num
ber k
now
ledg
e an
d ca
lcul
atio
n te
ch-
niqu
es fo
r com
mon
frac
tions
, dev
elop
ed in
the
Inte
rmed
iate
Pha
se.
Cal
cula
tions
with
frac
tions
• Le
arne
rs s
houl
d do
con
text
free
cal
cula
tions
and
sol
ve p
robl
ems
in c
onte
xts.
• It
is n
ot e
xpec
ted
that
lear
ners
kno
w ru
les
for s
impl
ifyin
g fra
ctio
ns o
r for
co
nver
ting
betw
een
mix
ed n
umbe
rs a
nd fr
actio
n fo
rms.
Lea
rner
s sh
ould
kno
w
from
wor
king
with
equ
ival
ence
, whe
n a
fract
ion
is e
qual
to o
r gre
ater
than
1.
• LC
ms
have
to b
e fo
und
whe
n ad
ding
and
sub
tract
ing
fract
ions
of d
iffer
ent
deno
min
ator
s. H
ere
lear
ners
use
kno
wle
dge
of c
omm
on m
ultip
les
to fi
nd th
e LC
M i.
e. w
hat n
umbe
r can
bot
h de
nom
inat
ors
be d
ivid
ed in
to.
• To
sim
plify
frac
tions
, lea
rner
s us
e kn
owle
dge
of c
omm
on fa
ctor
s i.e
. wha
t can
di
vide
equ
ally
into
the
num
erat
or a
nd d
enom
inat
or o
f a fr
actio
n. E
mph
asiz
e th
at
whe
n si
mpl
ifyin
g, th
e fra
ctio
ns m
ust r
emai
n eq
uiva
lent
.
exam
ple
3 4 x 2 5 =
4 20 =
3 10
or 3 4 x 2 5 =
3 10
• Le
arne
rs s
houl
d re
cogn
ize
that
find
ing
a ‘fr
actio
n of
a w
hole
num
ber’
or ‘fi
ndin
g a
fract
ion
of a
frac
tion’
mea
ns m
ultip
lyin
g th
e fra
ctio
n an
d th
e w
hole
num
ber o
r th
e fra
ctio
n w
ith th
e fra
ctio
n.
• W
hen
lear
ners
find
frac
tions
of w
hole
num
bers
, the
exa
mpl
es c
an b
e ch
osen
to
resu
lt ei
ther
in w
hole
num
bers
or f
ract
ions
or b
oth.
• Le
arne
rs s
houl
d al
so u
se th
e co
nven
tion
of w
ritin
g th
e w
hole
num
ber a
s a
fract
ion
over
whe
n m
ultip
lyin
g.
9 ho
urs
MATHEMATICS GRADES 7-9
50 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.4
Com
mon
fr
actio
ns
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
com
mon
frac
tions
and
mix
ed
num
bers
, inc
ludi
ng g
roup
ing,
sha
ring
and
findi
ng fr
actio
ns o
f who
le
num
bers
Perc
enta
ges
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-pe
rcen
tage
s of
who
le n
umbe
rs
• C
alcu
late
the
perc
enta
ge o
f par
t of a
w
hole
• C
alcu
late
per
cent
age
incr
ease
or
decr
ease
of w
hole
num
bers
• S
olve
pro
blem
s in
con
text
s in
volv
ing
perc
enta
ges
equi
vale
nt fo
rms
Rev
ise
the
follo
win
g do
ne in
Gra
de 6
:
• R
ecog
nize
and
use
equ
ival
ent f
orm
s of
com
mon
frac
tions
with
1-d
igit
or
2-di
git d
enom
inat
ors
(frac
tions
whe
re
one
deno
min
ator
is a
mul
tiple
of t
he
othe
r)
• R
ecog
nize
equ
ival
ence
bet
wee
n co
mm
on fr
actio
n an
d de
cim
al fr
actio
n fo
rms
of th
e sa
me
num
ber
• R
ecog
nize
equ
ival
ence
bet
wee
n co
mm
on fr
actio
n, d
ecim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r
exam
ples
a) C
alcu
late
4 5 of 2
0A
nsw
er:
4 5 of 2
0 =
4 5 x 20 1
= 4 1 x
4 1 = 1
6 o
r
4 5 of 2
0 =
4 5 x 20 1
= 80 5
= 1
6b)
Cal
cula
te
2 3 of 5 6
Ans
wer
2 3 of 5 6 =
2 3 x 5 6 =
1 3 x 5 3 =
5 9 o
r
2 3 of 5 6 =
2 3 x 5 6 =
1 3 x 10 18
= 5 9
Cal
cula
tion
usin
g pe
rcen
tage
s
• Le
arne
rs s
houl
d do
con
text
free
cal
cula
tions
and
sol
ve p
robl
ems
in c
onte
xts.
• W
hen
doin
g ca
lcul
atio
ns u
sing
per
cent
ages
, lea
rner
s ha
ve to
use
the
equi
vale
nt
com
mon
frac
tion
form
, whi
ch is
a fr
actio
n w
ith d
enom
inat
or 1
00.
Lear
ners
sho
uld
beco
me
fam
iliar
with
the
equi
vale
nt fr
actio
n an
d de
cim
al fo
rms
of c
omm
on p
erce
ntag
es li
ke
a)
25%
or 1 4 o
r 0,2
5;
b)
50%
or 1 2 o
r 0,5
;
c)
60%
or 3 5 o
r 0,6
.
• To
cal
cula
te p
erce
ntag
e of
par
t of a
who
le, o
r per
cent
age
incr
ease
or d
ecre
ase,
le
arne
rs h
ave
to le
arn
the
stra
tegy
of m
ultip
lyin
g by
100 1. I
t is
usef
ul fo
r lea
rner
s to
lear
n to
use
cal
cula
tors
for s
ome
of th
ese
calc
ulat
ions
whe
re th
e fra
ctio
ns a
re
not e
asily
sim
plifi
ed.
• W
hen
usin
g ca
lcul
ator
s, le
arne
rs c
an a
lso
use
the
equi
vale
nt d
ecim
al fr
actio
n fo
rm fo
r per
cent
ages
to d
o th
e ca
lcul
atio
ns.
exam
ples
:
a)
Cal
cula
te 6
0% o
f R10
5
Am
ount
= 3 5 X
R10
5 =
R63
b)
Wha
t per
cent
age
is 4
0c o
f R3,
20?
Per
cent
age
= 40
32
0 x 10
0 1 =
100 8 =
12,
5%
9 ho
urs
MATHEMATICS GRADES 7-9
51CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
c)
Cal
cula
te th
e pe
rcen
tage
incr
ease
if th
e pr
ice
of a
bus
tick
et o
f R60
is
incr
ease
d to
R84
.
Am
ount
incr
ease
d =
R24
.
Ther
efor
e pe
rcen
tage
incr
ease
= 24
60
x 10
0 1 =
40%
d)
Cal
cula
te th
e pe
rcen
tage
dec
reas
e if
the
pric
e of
pet
rol g
oes
dow
n fro
m 2
0 ce
nts
a lit
re to
18
cent
s a
litre
.
Am
ount
dec
reas
ed =
2 c
ents
. The
refo
re p
erce
ntag
e de
crea
se
= 2 20
x 10
0 1 =
10%
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.5
dec
imal
fr
actio
ns
ord
erin
g an
d co
mpa
ring
deci
mal
fr
actio
ns
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-co
unt f
orw
ards
and
bac
kwar
ds in
de
cim
al fr
actio
ns to
at l
east
two
deci
mal
pla
ces
-co
mpa
re a
nd o
rder
dec
imal
fra
ctio
ns to
at l
east
two
deci
mal
pl
aces
-pl
ace
valu
e of
dig
its to
at l
east
two
deci
mal
pla
ces
-ro
undi
ng o
ff de
cim
al fr
actio
ns to
at
leas
t 1 d
ecim
al p
lace
• E
xten
d al
l of t
he a
bove
to d
ecim
al
fract
ions
of a
t lea
st th
ree
deci
mal
pl
aces
and
roun
ding
off
to a
t lea
st 2
de
cim
al p
lace
s
Wha
t is
diffe
rent
to G
rade
6?
• D
ecim
al fr
actio
ns to
at l
east
dec
imal
pla
ces
• R
ound
ing
off t
o at
leas
t dec
imal
pla
ces
• m
ultip
ly a
nd d
ivid
e de
cim
al fr
actio
ns b
y w
hole
num
bers
• m
ultip
ly d
ecim
al fr
actio
ns b
y de
cim
al fr
actio
ns
In G
rade
7 le
arne
rs c
onso
lidat
e nu
mbe
r kno
wle
dge
and
calc
ulat
ion
tech
niqu
es fo
r de
cim
al fr
actio
ns, d
evel
oped
in th
e In
term
edia
te P
hase
.
ord
erin
g, c
ount
ing
and
com
parin
g de
cim
al fr
actio
ns
• C
ount
ing
shou
ld n
ot o
nly
be th
ough
t of a
s ve
rbal
cou
ntin
g. L
earn
ers
can
coun
t in
dec
imal
inte
rval
s us
ing:
-st
ruct
ured
, sem
i-stru
ctur
ed o
r em
pty
num
ber l
ines
-ch
ain
diag
ram
s fo
r cou
ntin
g
• Le
arne
rs s
houl
d be
giv
en a
rang
e of
exe
rcis
es s
uch
as:
-ar
rang
e gi
ven
num
bers
from
the
smal
lest
to th
e bi
gges
t: or
big
gest
to s
mal
lest
-fil
l in
mis
sing
num
bers
in
♦a
sequ
ence
♦on
a n
umbe
r grid
♦on
a n
umbe
r lin
e
♦fil
l in
<, =
or >
exa
mpl
e: 0
,4 *
0.0
4
• C
ount
ing
exer
cise
s in
cha
in d
iagr
ams
can
be c
heck
ed u
sing
cal
cula
tors
and
le
arne
rs c
an e
xpla
in a
ny d
iffer
ence
s be
twee
n th
eir a
nsw
ers
and
thos
e sh
own
by
the
calc
ulat
or.
9 ho
urs
MATHEMATICS GRADES 7-9
52 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.5
dec
imal
fr
actio
ns
Cal
cula
tions
usi
ng d
ecim
al fr
actio
ns
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-ad
ditio
n an
d su
btra
ctio
n of
dec
imal
fra
ctio
ns o
f at l
east
two
deci
mal
pl
aces
-m
ultip
licat
ion
of d
ecim
al fr
actio
ns
by 1
0 an
d 10
0
• E
xten
d ad
ditio
n an
d su
btra
ctio
n to
de
cim
al fr
actio
ns o
f at l
east
thre
e de
cim
al p
lace
s
• m
ultip
ly d
ecim
al fr
actio
ns to
incl
ude:
-de
cim
al fr
actio
ns to
at l
east
3
deci
mal
pla
ces
by w
hole
num
bers
-de
cim
al fr
actio
ns to
at l
east
2
deci
mal
pla
ces
by d
ecim
al fr
actio
ns
to a
t lea
st 1
dec
imal
pla
ce
• D
ivid
e de
cim
al fr
actio
ns to
incl
ude
deci
mal
frac
tions
to a
t lea
st 3
dec
imal
pl
aces
by
who
le n
umbe
rs
Cal
cula
tion
tech
niqu
es
• U
se k
now
ledg
e of
pla
ce v
alue
to
estim
ate
the
num
ber o
f dec
imal
pl
aces
in th
e re
sult
befo
re p
erfo
rmin
g ca
lcul
atio
ns
• U
se ro
undi
ng o
ff an
d a
calc
ulat
or to
ch
eck
resu
lts w
here
app
ropr
iate
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
invo
lvin
g de
cim
al fr
actio
ns
Cal
cula
ting
with
dec
imal
frac
tions
• Le
arne
rs s
houl
d do
con
text
free
cal
cula
tions
and
sol
ve p
robl
ems
in c
onte
xts.
• Le
arne
rs s
houl
d es
timat
e th
eir a
nsw
ers
befo
re c
alcu
latin
g, e
spec
ially
w
ith m
ultip
licat
ion
by d
ecim
al fr
actio
ns. T
hey
shou
ld b
e ab
le to
judg
e th
e re
ason
able
ness
of a
nsw
ers
rela
ting
to h
ow m
any
deci
mal
pla
ces
and
also
che
ck
thei
r ow
n an
swer
s.
• m
ultip
licat
ion
by d
ecim
al fr
actio
ns s
houl
d st
art w
ith fa
mili
ar n
umbe
rs th
at
lear
ners
can
cal
cula
te b
y in
spec
tion,
so
that
lear
ners
get
a s
ense
of h
ow
deci
mal
pla
ces
are
affe
cted
by
mul
tiplic
atio
n.
exam
ples
:
a)
3 x
2 =
6
0,3
x 2
= 0,
6
0,3
x 0,
2 =
0,06
0,3
x 0,
02 =
0,0
06
0,03
x 0
,002
= 0
,000
6 et
c
b)
15 x
3 =
45
1,5
x 3
= 4,
5
0,15
x 3
= 0
,45
0,15
x 0
,3 =
0,0
45
0,01
5 x
0,3
= 0,
0045
etc
equi
vale
nce
betw
een
com
mon
frac
tions
and
dec
imal
frac
tions
• Le
arne
rs a
re n
ot e
xpec
ted
to b
e ab
le to
con
vert
any
com
mon
frac
tion
into
its
deci
mal
form
, mer
ely
to s
ee th
e re
latio
nshi
p be
twee
n te
nths
, hun
dred
ths
and
thou
sand
ths
in th
eir d
ecim
al fo
rms.
• Le
arne
rs s
houl
d st
art b
y re
writ
ing
and
conv
ertin
g te
nths
, hun
dred
ths
and
thou
sand
ths
in c
omm
on fr
actio
n fo
rm to
dec
imal
frac
tions
. Whe
re d
enom
inat
ors
of o
ther
frac
tions
are
fact
ors
of 1
0 e.
g. 2
,5 o
r fac
tors
of 1
00 e
.g 2
, 4, 2
0,
25 le
arne
rs c
an c
onve
rt th
ese
to h
undr
edth
s us
ing
wha
t the
y kn
ow a
bout
eq
uiva
lenc
e.
• It
is u
sefu
l to
use
calc
ulat
ors
to h
elp
lear
ners
con
vert
betw
een
com
mon
fra
ctio
ns a
nd d
ecim
al fr
actio
ns (h
ere
lear
ners
will
use
wha
t the
y kn
ow a
bout
the
rela
tions
hip
betw
een
fract
ions
and
div
isio
n).
MATHEMATICS GRADES 7-9
53CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.5
dec
imal
fr
actio
ns
equi
vale
nt fo
rms
• R
evis
e th
e fo
llow
ing
done
in G
rade
6:
-re
cogn
ize
equi
vale
nce
betw
een
com
mon
frac
tion
and
deci
mal
fra
ctio
n fo
rms
of th
e sa
me
num
ber
-R
ecog
nize
equ
ival
ence
bet
wee
n co
mm
on fr
actio
n, d
ecim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r
-D
ivid
ing
who
le n
umbe
rs b
y 10
, 100
, 1 0
00, e
tc. c
an h
elp
to b
uild
lear
ners
’ un
ders
tand
ing
of p
lace
val
ue w
ith d
ecim
als.
Thi
s is
als
o us
eful
to d
o on
the
calc
ulat
or –
lear
ners
can
dis
cuss
the
patte
rns
they
see
whe
n di
vidi
ng.
-S
imila
rly c
alcu
lato
rs c
an b
e us
eful
tool
s fo
r lea
rner
s to
lear
n ab
out p
atte
rns
whe
n m
ultip
lyin
g de
cim
als
by 1
0, 1
00 o
r,1 0
00 e
tc.
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.2
Func
tions
an
d re
latio
nshi
ps
inpu
t and
out
put v
alue
s
• D
eter
min
e in
put v
alue
s, o
utpu
t va
lues
or r
ules
for p
atte
rns
and
rela
tions
hips
usi
ng:
-flo
w d
iagr
ams
-ta
bles
-fo
rmul
ae
equi
vale
nt fo
rms
• D
eter
min
e, in
terp
ret a
nd ju
stify
eq
uiva
lenc
e of
diff
eren
t des
crip
tions
of
the
sam
e re
latio
nshi
p or
rule
pr
esen
ted:
-ve
rbal
ly
-in
flow
dia
gram
s
-in
tabl
es
-by
form
ulae
-by
num
ber s
ente
nces
Wha
t is
diffe
rent
to th
e in
term
edia
te P
hase
?
• Fi
ndin
g in
put o
r out
put v
alue
s us
ing
give
n fo
rmul
ae
• Th
e ru
les
and
num
ber p
atte
rns
for w
hich
lear
ners
hav
e to
find
inpu
t or o
utpu
t va
lues
are
ext
ende
d to
incl
ude
patte
rns
with
inte
gers
, squ
are
num
bers
and
cu
bic
num
bers
Find
ing
inpu
t and
out
put v
alue
s in
flow
dia
gram
s, ta
bles
and
form
ulae
sho
uld
be
done
mor
e th
an ju
st o
nce
a ye
ar. I
t can
be
done
afte
r num
ber w
ork,
to p
ract
ise
prop
ertie
s an
d op
erat
ions
with
num
bers
and
afte
r mea
sure
men
t or g
eom
etry
to
prac
tise
solv
ing
prob
lem
s us
ing
form
ulae
.
in t
erm
2 th
e fo
cus
of F
unct
ions
and
rel
atio
nshi
ps is
on
prac
tisin
g op
erat
ions
with
who
le n
umbe
rs a
s w
ell a
s co
mm
on fr
actio
ns o
r dec
imal
fr
actio
ns a
s in
put v
alue
s, o
r inc
ludi
ng c
omm
on fr
actio
ns a
nd d
ecim
al
fractio
nsinth
erulesforfi
ndingou
tputvalues.InTerm3th
efocusof
Func
tions
and
rel
atio
nshi
ps is
on
usin
g fo
rmul
ae a
nd in
ter
m 4
, the
focu
s is
on
pra
ctis
ing
addi
tion
and
subt
ract
ion
of in
tege
rs.
• In
this
pha
se, i
t is
usef
ul to
beg
in to
spe
cify
whe
ther
the
inpu
t val
ues
are
natu
ral
num
bers
, or i
nteg
ers
or ra
tiona
l num
bers
. Hen
ce, t
o fin
d ou
tput
val
ues,
lear
ners
sh
ould
be
give
n th
e ru
le/fo
rmul
a as
wel
l as
the
inpu
t val
ues.
Flow
dia
gram
s ar
e re
pres
enta
tions
of f
unct
iona
l rel
atio
nshi
ps. H
ence
, whe
n us
ing
flow
dia
gram
s, th
e co
rres
pond
ence
bet
wee
n in
put a
nd o
utpu
t val
ues
shou
ld b
e cl
ear i
n its
repr
esen
tatio
nal f
orm
i.e.
the
first
inpu
t pro
duce
s th
e fir
st o
utpu
t, th
e se
cond
inpu
t pro
duce
s th
e se
cond
out
put,
etc.
3 ho
urs
MATHEMATICS GRADES 7-9
54 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.2
Func
tions
an
dre
latio
nshi
ps
exam
ples
a)
Use
the
give
n ru
le to
cal
cula
te th
e va
lues
of t
for e
ach
valu
e of
p, w
here
p is
a
natu
ral n
umbe
r.
t = p
x 3
+ 1
In th
is k
ind
of fl
ow d
iagr
am, l
earn
ers
can
also
be
aske
d to
find
the
valu
e of
p
for a
giv
en v
alue
t.
b)
Find
the
rule
for c
alcu
latin
g th
e ou
tput
val
ue fo
r eve
ry g
iven
inpu
t val
ue in
the
flow
dia
gram
bel
ow.
8 24 40 56 72
1
In fl
ow d
iagr
ams
such
as
thes
e, m
ore
than
one
rule
mig
ht b
e po
ssib
le to
de
scrib
e th
e re
latio
nshi
p be
twee
n in
put a
nd o
utpu
t val
ues.
The
rule
s ar
e ac
cept
able
if th
ey m
atch
the
give
n in
put v
alue
s to
the
corr
espo
ndin
g ou
tput
va
lues
.
c)
If th
e ru
le fo
r find
ing
y in
the
tabl
e be
low
is: y
= 3
x –
1, fi
nd y
for t
he g
iven
x
valu
es:
x0
12
510
5010
0
y
MATHEMATICS GRADES 7-9
55CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.2
Func
tions
an
dre
latio
nshi
ps
d)
Des
crib
e th
e re
latio
nshi
p be
twee
n th
e nu
mbe
rs in
the
top
row
and
bot
tom
row
in
the
tabl
e. T
hen
writ
e do
wn
the
valu
e of
m a
nd n
.
x1
23
412
n
y5
67
8m
34
In ta
bles
suc
h as
thes
e, m
ore
than
one
rule
mig
ht b
e po
ssib
le to
des
crib
e th
e re
latio
nshi
p be
twee
n x
and
y va
lues
. The
rule
s ar
e ac
cept
able
if th
ey m
atch
the
give
n in
put v
alue
s to
the
corr
espo
ndin
g ou
tput
val
ues.
For
exa
mpl
e, th
e ru
le
y =
x +
4 de
scrib
es th
e re
latio
nshi
p be
twee
n th
e gi
ven
x an
d y
valu
es in
the
tabl
e. T
o fin
d m
and
n, y
ou h
ave
to s
ubst
itute
the
corr
espo
ndin
g va
lues
for x
or
y in
to th
is ru
le a
nd s
olve
the
equa
tion
by in
spec
tion.
mea
sure
men
t4.
1
are
a an
d pe
rimet
er o
f 2d
sha
pes
are
a an
d pe
rimet
er
• C
alcu
late
the
perim
eter
of r
egul
ar
and
irreg
ular
pol
ygon
s
• U
se a
ppro
pria
te fo
rmul
ae to
cal
cula
te
perim
eter
and
are
a of
:
-sq
uare
s
-re
ctan
gles
-tri
angl
es
Cal
cula
tions
and
sol
ving
pro
blem
s
• S
olve
pro
blem
s in
volv
ing
perim
eter
an
d ar
ea o
f pol
ygon
s
• C
alcu
late
to a
t lea
st 1
dec
imal
pla
ce
• U
se a
nd c
onve
rt be
twee
n ap
prop
riate
S
I uni
ts, i
nclu
ding
:
-m
m2 ↔
cm
2
-cm
2 ↔ m
2
Wha
t is
diffe
rent
to G
rade
6?
• In
Gra
de 6
lear
ners
did
not
hav
e to
use
form
ulae
to c
alcu
late
are
a an
d pe
rimet
er.
•Fo
rmul
ae le
arne
rs s
houl
d kn
ow a
nd u
se a
re:
-pe
rimet
er o
f a s
quar
e =
4s
-pe
rimet
er o
f a re
ctan
gle
= 2(
l + b
) or 2
l + 2
b
-ar
ea o
f a s
quar
e =
l2
-ar
ea o
f a re
ctan
gle
= l x
b
-ar
ea o
f a tr
iang
le =
1 2 (b
x h
)
solv
ing
equa
tions
usi
ng fo
rmul
ae
• Th
e us
e of
form
ulae
pro
vide
s a
cont
ext t
o pr
actis
e so
lvin
g eq
uatio
ns b
y in
spec
tion.
exam
ple
1.
If th
e pe
rimet
er o
f a s
quar
e is
32
cm w
hat i
s th
e le
ngth
of e
ach
side
? Le
arne
rs s
houl
d w
rite
this
as:
4s =
32
and
solv
e by
insp
ectio
n by
ask
ing:
4 ti
mes
wha
t will
be
32?
2.
If th
e ar
ea o
f a re
ctan
gle
is 2
00 c
m2 ,
and
its le
ngth
is 5
0 cm
wha
t is
its w
idth
? Le
arne
rs s
houl
d w
rite
this
as:
50
x b
= 20
and
sol
ve b
y in
spec
tion
by a
skin
g:
50 ti
mes
wha
t will
be
200?
7 ho
urs
MATHEMATICS GRADES 7-9
56 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
mea
sure
men
t4.
1 a
rea
and
perim
eter
of
2d s
hape
s
exam
ples
of c
alcu
latio
ns fo
r are
a an
d pe
rimet
erC
alcu
late
:a)
P
erim
eter
of a
rect
angl
e w
hich
is 2
4 cm
long
and
18
cm w
ide.
b)
Per
imet
er o
f a re
gula
r oct
agon
if th
e le
ngth
of e
ach
side
is 1
7 cm
.
c)
Are
a of
∆A
BC
if B
C =
12
cm a
nd it
s he
ight
AT
= 9
cm
d)
Per
imet
er o
f a s
quar
e if
its a
rea
is 2
25 c
m2
For a
reas
of t
riang
les:
• m
ake
sure
lear
ners
kno
w th
at th
e he
ight
of a
tria
ngle
is a
line
seg
men
t dra
wn
from
any
ver
tex
perp
endi
cula
r to
the
oppo
site
sid
e.ex
ampl
e: A
D is
the
heig
ht o
nto
base
BC
of ∆
AB
C.
A D
B C
A D B
C
• P
oint
out
that
eve
ry tr
iang
le h
as 3
bas
es, e
ach
with
a re
late
d he
ight
or a
ltitu
de.
•Fo
r con
vers
ions
, not
e: -
if 1
cm =
10
mm
then
1 c
m2 =
100
mm
2
-if
1 m
= 1
00 c
m th
en 1
m2 =
10
000
cm2
exam
ples
of s
olvi
ng p
robl
ems
invo
lvin
g pe
rimet
er a
nd a
rea.
a)
C
alcu
late
the
area
of t
he s
hade
d pa
rt in
the
diag
ram
if A
BC
D is
a re
ctan
gle,
AB
= 1
8,6
cm, D
C =
2TC
and
BC
= 8
cm
b)
The
area
of t
he fl
oor o
f the
din
ing
room
is 1
8,4
cm2 .
How
man
y sq
uare
tile
s w
ith s
ides
of 2
0 cm
are
nee
ded
to ti
le th
e flo
or?
c)
The
leng
th o
f the
sid
e of
a s
quar
e is
dou
bled
. Will
the
area
of t
he e
nlar
ged
squa
re b
e do
uble
or f
our t
imes
that
of t
he o
rigin
al s
quar
e?
MATHEMATICS GRADES 7-9
57CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
mea
sure
men
t4.
1 a
rea
and
perim
eter
of
2d s
hape
s
exam
ples
of c
alcu
latio
ns fo
r are
a an
d pe
rimet
erC
alcu
late
:a)
P
erim
eter
of a
rect
angl
e w
hich
is 2
4 cm
long
and
18
cm w
ide.
b)
Per
imet
er o
f a re
gula
r oct
agon
if th
e le
ngth
of e
ach
side
is 1
7 cm
.
c)
Are
a of
∆A
BC
if B
C =
12
cm a
nd it
s he
ight
AT
= 9
cm
d)
Per
imet
er o
f a s
quar
e if
its a
rea
is 2
25 c
m2
For a
reas
of t
riang
les:
• m
ake
sure
lear
ners
kno
w th
at th
e he
ight
of a
tria
ngle
is a
line
seg
men
t dra
wn
from
any
ver
tex
perp
endi
cula
r to
the
oppo
site
sid
e.ex
ampl
e: A
D is
the
heig
ht o
nto
base
BC
of ∆
AB
C.
A D
B C
A D B
C
• P
oint
out
that
eve
ry tr
iang
le h
as 3
bas
es, e
ach
with
a re
late
d he
ight
or a
ltitu
de.
•Fo
r con
vers
ions
, not
e: -
if 1
cm =
10
mm
then
1 c
m2 =
100
mm
2
-if
1 m
= 1
00 c
m th
en 1
m2 =
10
000
cm2
exam
ples
of s
olvi
ng p
robl
ems
invo
lvin
g pe
rimet
er a
nd a
rea.
a)
C
alcu
late
the
area
of t
he s
hade
d pa
rt in
the
diag
ram
if A
BC
D is
a re
ctan
gle,
AB
= 1
8,6
cm, D
C =
2TC
and
BC
= 8
cm
b)
The
area
of t
he fl
oor o
f the
din
ing
room
is 1
8,4
cm2 .
How
man
y sq
uare
tile
s w
ith s
ides
of 2
0 cm
are
nee
ded
to ti
le th
e flo
or?
c)
The
leng
th o
f the
sid
e of
a s
quar
e is
dou
bled
. Will
the
area
of t
he e
nlar
ged
squa
re b
e do
uble
or f
our t
imes
that
of t
he o
rigin
al s
quar
e?
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
mea
sure
men
t4.
2
surf
ace
area
an
d vo
lum
e of
3d
obj
ects
surf
ace
area
and
vol
ume
• U
se a
ppro
pria
te fo
rmul
ae to
cal
cula
te
the
surfa
ce a
rea,
vol
ume
and
capa
city
of:
-cu
bes
-re
ctan
gula
r pris
ms
• D
escr
ibe
the
inte
rrel
atio
nshi
p be
twee
n su
rface
are
a an
d vo
lum
e of
th
e ob
ject
s m
entio
ned
abov
e
Cal
cula
tions
and
sol
ving
pro
blem
s
• S
olve
pro
blem
s in
volv
ing
surfa
ce
area
, vol
ume
and
capa
city
• U
se a
nd c
onve
rt be
twee
n ap
prop
riate
S
I uni
ts, i
nclu
ding
:
-m
m2 ↔
cm
2
-cm
2 ↔ m
2
-m
m3 ↔
cm
3
-cm
3 ↔ m
3
• U
se e
quiv
alen
ce b
etw
een
units
whe
n so
lvin
g pr
oble
ms:
-1c
m3 ↔
1 m
l
-1
m3 ↔
1 k
l
Wha
t is
diffe
rent
to G
rade
6?
• In
Gra
de 6
lear
ners
did
not
hav
e to
use
form
ulae
to c
alcu
late
sur
face
are
a an
d vo
lum
e.
•Fo
rmul
ae le
arne
rs s
houl
d kn
ow a
nd u
se:
-th
e vo
lum
e of
a p
rism
= th
e ar
ea o
f the
bas
e x
the
heig
ht
-th
e su
rface
are
a of
a p
rism
= th
e su
m o
f the
are
a of
all
its fa
ces
-th
e vo
lum
e of
a c
ube
= l3
-th
e vo
lum
e of
a re
ctan
gula
r pris
m =
l x
b x
h
•Fo
r con
vers
ions
, not
e:
-if
1 cm
= 1
0 cm
then
1 c
m3 =
1 0
00 m
m3 a
nd
-if
1 m
= 1
0 cm
then
1 m
3 = 1
000
000
mm
3 or
1 0
00 0
00 o
r 106
cm3 .
-an
obj
ect w
ith a
vol
ume
of 1
cm
3 w
ill d
ispl
ace
exac
tly 1
ml o
f wat
er; a
nd
-an
obj
ect w
ith a
vol
ume
of 1
m3
will
dis
plac
e ex
actly
1 k
l of w
ater
.
• E
mph
asiz
e th
at th
e am
ount
of s
pace
insi
de a
pris
m is
cal
led
its c
apac
ity; a
nd
the
amou
nt o
f spa
ce o
ccup
ied
by a
pris
m is
cal
led
its v
olum
e.
• In
vest
igat
e th
e ne
ts o
f cub
es a
nd re
ctan
gula
r pris
ms
in o
rder
to d
educ
e fo
rmul
ae fo
r cal
cula
ting
thei
r sur
face
are
as.
8 ho
urs
rev
isio
n/a
sses
smen
t:A
t thi
s st
age
lear
ners
sho
uld
be a
sses
sed
on:
• ca
lcul
atin
g an
d so
lvin
g pr
oble
ms
with
com
mon
frac
tions
and
dec
imal
frac
tions
• us
ing
form
ulae
to fi
nd a
rea
and
perim
eter
of 2
D s
hape
s
• us
ing
form
ulae
to fi
nd v
olum
e an
d su
rface
are
a of
3D
obj
ects
9 ho
urs
MATHEMATICS GRADES 7-9
58 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 7
– te
rm
3
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.1
n
umer
ic a
nd
geom
etric
pa
ttern
s
inve
stig
ate
and
exte
nd p
atte
rns
• In
vest
igat
e an
d ex
tend
num
eric
an
d ge
omet
ric p
atte
rns
look
ing
for
rela
tions
hips
bet
wee
n nu
mbe
rs,
incl
udin
g pa
ttern
s:
-re
pres
ente
d in
phy
sica
l or
diag
ram
fo
rm
-no
t lim
ited
to s
eque
nces
invo
lvin
g a
cons
tant
diff
eren
ce o
r rat
io
-of
lear
ner’s
ow
n cr
eatio
n
-re
pres
ente
d in
tabl
es
• D
escr
ibe
and
just
ify th
e ge
nera
l rul
es
for o
bser
ved
rela
tions
hips
bet
wee
n nu
mbe
rs in
ow
n w
ords
Wha
t is
diffe
rent
to th
e in
term
edia
te P
hase
?
• In
the
Sen
ior P
hase
the
emph
asis
is le
ss o
n m
erel
y ex
tend
ing
a pa
ttern
, and
m
ore
on d
escr
ibin
g a
gene
ral r
ule
for t
he p
atte
rn o
r seq
uenc
e an
d be
ing
able
to
pred
ict u
nkno
wn
term
s in
a s
eque
nce
usin
g a
gene
ral r
ule.
• In
vest
igat
ing
num
ber p
atte
rns
is a
n op
portu
nity
to g
ener
aliz
e –
to g
ive
gene
ral
alge
brai
c de
scrip
tions
of t
he re
latio
nshi
p be
twee
n te
rms
and
its p
ositi
on in
a
sequ
ence
and
to ju
stify
sol
utio
ns.
• Th
e ra
nge
of n
umbe
r pat
tern
s ar
e ex
tend
ed to
incl
ude
patte
rns
inte
gers
, squ
are
num
bers
and
cub
ic n
umbe
rs
• A
s le
arne
rs b
ecom
e us
ed to
des
crib
ing
patte
rns
in th
eir o
wn
wor
ds, t
heir
desc
riptio
ns s
houl
d be
com
e m
ore
prec
ise
and
effic
ient
with
the
use
of a
lgeb
raic
la
ngua
ge to
des
crib
e ge
nera
l rul
es o
f pat
tern
s.
• It
is u
sefu
l als
o to
intro
duce
the
lang
uage
of ‘
term
in a
seq
uenc
e’ in
ord
er to
di
stin
guis
h th
e te
rm fr
om th
e po
sitio
n of
a te
rm in
a s
eque
nce
num
eric
and
geo
met
ric p
atte
rns
are
done
aga
in in
ter
m 4
, whe
re p
atte
rns
can
incl
ude
inte
gers
. in
this
term
pat
tern
s sh
ould
be
rest
ricte
d to
usi
ng
who
le n
umbe
rs, n
umbe
rs in
exp
onen
tial f
orm
, com
mon
frac
tions
and
de
cim
al fr
actio
ns.
Kin
ds o
f num
eric
pat
tern
s
• P
rovi
de a
seq
uenc
e of
num
bers
, lea
rner
s ha
ve to
iden
tify
a pa
ttern
or
rela
tions
hip
betw
een
cons
ecut
ive
term
s in
ord
er to
ext
end
the
patte
rn.
exam
ples
Giv
e a
rule
to d
escr
ibe
the
rela
tions
hip
betw
een
the
num
bers
in th
e se
quen
ces
belo
w. U
se th
is ru
le to
giv
e th
e ne
xt th
ree
num
bers
in th
e se
quen
ce:
a)
3; 7
; 11;
15;
... ..
.
b)
120;
115
; 110
; 105
;... .
..
Her
e le
arne
rs c
ould
iden
tify
the
cons
tant
diff
eren
ce b
etw
een
cons
ecut
ive
term
s in
ord
er to
ext
end
the
patte
rn. T
hese
pat
tern
s ca
n be
des
crib
ed in
lear
ners
’ ow
n w
ords
as
(a) ‘
addi
ng 4
’ or ‘
coun
ting
in 4
s’ o
r ‘ad
d 4s
to th
e pr
evio
us
num
ber i
n th
e pa
ttern
’ (b)
‘sub
tract
ing
5’ o
r ‘co
untin
g do
wn
in 5
s’, o
r ‘su
btra
ct 5
fro
m th
e pr
evio
us n
umbe
r in
the
patte
rn’.
c)
2; 4
; 8; 1
6;...
...
Her
e le
arne
rs c
ould
iden
tify
the
cons
tant
ratio
bet
wee
n co
nsec
utiv
e te
rms.
Th
is p
atte
rn c
an b
e de
scrib
ed in
lear
ners
’ ow
n w
ords
as
‘mul
tiply
the
prev
ious
nu
mbe
r by
2’.
6 ho
urs
MATHEMATICS GRADES 7-9
59CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.1
n
umer
ic a
nd
geom
etric
pa
ttern
s
d)
1; 2
; 4; 7
; 11;
16;
... ..
.
This
pat
tern
has
nei
ther
a c
onst
ant d
iffer
ence
nor
con
stan
t rat
io. T
his
patte
rn
can
be d
escr
ibed
in le
arne
rs’ o
wn
wor
ds a
s ‘in
crea
se th
e di
ffere
nce
betw
een
cons
ecut
ive
term
s by
1 e
ach
time’
or ‘
add
1 m
ore
than
was
add
ed to
get
the
prev
ious
term
’. U
sing
this
rule
, the
nex
t 3 te
rms
will
be
22, 2
9, 3
7.
• P
rovi
de a
seq
uenc
e of
num
bers
, lea
rner
s ha
ve to
iden
tify
a pa
ttern
or
rela
tions
hip
betw
een
the
term
and
its
posi
tion
in th
e se
quen
ce. T
his
enab
les
lear
ners
to p
redi
ct a
term
in a
seq
uenc
e ba
sed
on th
e po
sitio
n of
that
te
rm in
the
sequ
ence
. It i
s us
eful
for l
earn
ers
to re
pres
ent t
hese
seq
uenc
es in
ta
bles
so
that
they
can
con
side
r the
pos
ition
of t
he te
rm.
exam
ples
:
a)
Pro
vide
a ru
le to
des
crib
e th
e re
latio
nshi
p be
twee
n th
e nu
mbe
rs in
this
se
quen
ce:1
; 4; 9
; 16;
... ..
. Use
the
rule
to fi
nd th
e 10
th te
rm in
this
seq
uenc
e.
Firs
tly, l
earn
ers
have
to u
nder
stan
d th
at th
e ‘1
0th
term
’ ref
ers
to p
ositi
on 1
0 in
th
e nu
mbe
r se
quen
ce. T
hey
have
to fi
nd a
rul
e in
ord
er to
det
erm
ine
the
10th
te
rm, r
athe
r tha
n co
ntin
uing
the
sequ
ence
to th
e te
nth
term
.
This
seq
uenc
e ca
n be
repr
esen
ted
in th
e fo
llow
ing
tabl
e:
Pos
ition
in s
eque
nce
12
34
10
Term
14
916
?
Lear
ners
sho
uld
reco
gniz
e th
at e
ach
term
in th
e bo
ttom
row
is o
btai
ned
by
squa
ring
the
posi
tion
num
ber i
n th
e to
p ro
w. T
hus
the
10th
term
will
be
'10
squa
red'
or 1
02 , w
hich
is 1
00. U
sing
the
sam
e ru
le, l
earn
ers
can
also
be
aske
d w
hat t
erm
num
ber o
r pos
ition
will
625
be?
If th
e te
rm is
obt
aine
d by
squ
arin
g th
e po
sitio
n nu
mbe
r of t
he te
rm, t
hen
the
posi
tion
num
ber c
an b
e ob
tain
ed
by fi
ndin
g th
e sq
uare
root
of t
he te
rm. H
ence
, 625
will
be
the
25th
term
in th
e se
quen
ce s
ince
62
5 √
= 2
5
MATHEMATICS GRADES 7-9
60 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
b)
Pro
vide
a ru
le to
des
crib
e th
e re
latio
nshi
p be
twee
n th
e nu
mbe
rs in
this
se
quen
ce: 4
; 7; 1
0; 1
3; …
... U
se th
e ru
le to
find
the
20th
term
in th
e se
quen
ce.
If le
arne
rs c
onsi
der o
nly
the
rela
tions
hip
betw
een
cons
ecut
ive
term
s, th
en th
ey
can
cont
inue
the
patte
rn (‘
add
3 to
pre
viou
s nu
mbe
r’) to
the
20th
term
to fi
nd
the
answ
er. H
owev
er, i
f the
y lo
ok fo
r a re
latio
nshi
p or
rule
bet
wee
n th
e te
rm
and
the
posi
tion
of th
e te
rm, t
hey
can
pred
ict t
he a
nsw
er w
ithou
t con
tinui
ng th
e pa
ttern
. Usi
ng n
umbe
r sen
tenc
es c
an b
e us
eful
to fi
nd th
e ru
le:
1st t
erm
: 4 =
3 (1
) + 1
2nd
term
: 7 =
3 (2
) + 1
3rd
term
: 10
= 3
(3) +
1
4th
term
: 13
= 3
(4) +
1
The
num
ber i
n th
e br
acke
ts c
orre
spon
ds to
the
posi
tion
of th
e te
rm. H
ence
, the
20
th te
rm w
ill b
e: 3
(20)
+ 1
= 6
1Th
e ru
le in
lear
ners
’ ow
n w
ords
can
be
writ
ten
as ‘3
x th
e po
sitio
n of
the
te
rm +
1
• Th
ese
type
s of
num
eric
pat
tern
s de
velo
p an
und
erst
andi
ng o
f fun
ctio
nal
rela
tions
hips
, in
whi
ch y
ou h
ave
a de
pend
ent v
aria
ble
(pos
ition
of t
he te
rm) a
nd
inde
pend
ent v
aria
ble
(the
term
itse
lf), a
nd w
here
you
hav
e a
uniq
ue o
utpu
t for
an
y gi
ven
inpu
t val
ue.
Kin
ds o
f geo
met
ric p
atte
rns
• G
eom
etric
pat
tern
s ar
e nu
mbe
r pat
tern
s re
pres
ente
d di
agra
mm
atic
ally.
The
di
agra
mm
atic
repr
esen
tatio
n re
veal
s th
e st
ruct
ure
of th
e nu
mbe
r pat
tern
.•
Hen
ce, r
epre
sent
ing
the
num
ber p
atte
rns
in ta
bles
, mak
es it
eas
ier f
or le
arne
rs
to d
escr
ibe
the
gene
ral r
ule
for t
he p
atte
rn.
exam
ple
Con
side
r thi
s pa
ttern
for b
uild
ing
hexa
gons
with
mat
chst
icks
. How
man
y m
atch
stic
ks w
ill b
e us
ed to
bui
ld th
e 10
th h
exag
on?
The
rule
for t
he p
atte
rn is
con
tain
ed in
the
stru
ctur
e (c
onst
ruct
ion)
of t
he
succ
essi
ve h
exag
onal
sha
pes:
(1)
add
1 on
mat
chst
ick
per s
ide
(2)
ther
e ar
e 6
side
s, s
o (3
) ad
d on
6 m
atch
stic
ks p
er h
exag
on a
s yo
u pr
ocee
d fro
m a
giv
en h
exag
on to
th
e ne
xt o
ne.
MATHEMATICS GRADES 7-9
61CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.1
n
umer
ic a
nd
geom
etric
pa
ttern
s
For t
he 2
nd h
exag
on, y
ou h
ave
2 x
6 m
atch
es; f
or th
e 3r
d he
xago
n yo
u ha
ve 3
x 6
m
atch
es; U
sing
this
pat
tern
for b
uild
ing
hexa
gons
, the
10t
h he
xago
n w
ill h
ave
10
x 6
mat
ches
.
Lear
ners
can
als
o us
e a
tabl
e to
reco
rd th
e nu
mbe
r of m
atch
es u
sed
for e
ach
hexa
gon.
Thi
s w
ay th
ey c
an lo
ok a
t the
num
ber p
atte
rn re
late
d to
the
num
ber o
f m
atch
es u
sed
for e
ach
new
hex
agon
.
Posi
tion
of h
exag
on in
pat
tern
12
34
56
10
num
ber o
f mat
ches
612
18
des
crib
ing
patte
rns
• It
does
not
mat
ter i
f lea
rner
s ar
e al
read
y fa
mili
ar w
ith a
par
ticul
ar p
atte
rn. T
heir
desc
riptio
ns o
f the
sam
e pa
ttern
can
be
diffe
rent
whe
n th
ey e
ncou
nter
it a
t di
ffere
nt s
tage
s of
thei
r mat
hem
atic
al d
evel
opm
ent.
exam
ple
The
rule
for t
he s
eque
nce:
4; 7
; 10;
13
can
be d
escr
ibed
in th
e fo
llow
ing
way
s:
a)
add
thre
e to
the
prev
ious
term
b)
3 tim
es th
e po
sitio
n of
the
term
+ 1
or 3
x th
e po
sitio
n of
the
term
+ 1
c)
3(n)
+ 1
, whe
re n
is th
e po
sitio
n of
the
term
d)
3(n)
+ 1
, whe
re n
is a
Nat
ural
num
ber.
MATHEMATICS GRADES 7-9
62 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.2
Func
tions
an
d re
latio
nshi
ps
inpu
t and
out
put v
alue
s
• D
eter
min
e in
put v
alue
s, o
utpu
t va
lues
or r
ules
for p
atte
rns
and
rela
tions
hips
usi
ng:
-flo
w d
iagr
ams
-ta
bles
-fo
rmul
ae
equi
vale
nt fo
rms
• D
eter
min
e, in
terp
ret a
nd ju
stify
eq
uiva
lenc
e of
diff
eren
t des
crip
tions
of
the
sam
e re
latio
nshi
p or
rule
pr
esen
ted:
-ve
rbal
ly
-in
flow
dia
gram
s
-in
tabl
es
-by
form
ulae
-by
num
ber s
ente
nces
Func
tions
and
rela
tions
hips
wer
e al
so d
one
in t
erm
2, a
nd w
ill b
e do
ne a
gain
inTerm4,focusingon
integers.Inthisterm,thefocusis
onfin
ding
outpu
tva
lues
for g
iven
form
ulae
and
inpu
t val
ues.
see
addi
tiona
l not
es a
nd e
xam
ples
in t
erm
2.
Not
e, w
hen
lear
ners
find
inpu
t or o
utpu
t val
ues
for g
iven
rule
s or
form
ulae
, the
y ar
e ac
tual
ly fi
ndin
g th
e nu
mer
ical
val
ue o
f alg
ebra
ic e
xpre
ssio
ns u
sing
sub
stitu
-tio
n.
exam
ples
Use
the
form
ula
for t
he a
rea
of a
rect
angl
e: A
= l
x b
to c
alcu
late
the
follo
win
g:
a)
The
area
, if t
he le
ngth
is 4
cm
and
the
wid
th is
2 c
m
b)
The
leng
th, i
f the
are
a is
20
cm2 a
nd th
e w
idth
is 4
cm
c)
The
wid
th, i
f the
are
a is
24
cm2 a
nd th
e le
ngth
is 8
cm
Lear
ners
can
writ
e th
ese
as n
umbe
r sen
tenc
es, a
nd s
olve
by
insp
ectio
n.
3 ho
urs
MATHEMATICS GRADES 7-9
63CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.3
alg
ebra
ic
expr
essi
ons
alg
ebra
ic la
ngua
ge
• R
ecog
nize
and
inte
rpre
t rul
es o
r re
latio
nshi
ps re
pres
ente
d in
sym
bolic
fo
rm
• Id
entif
y va
riabl
es a
nd c
onst
ants
in
give
n fo
rmul
ae a
nd e
quat
ions
Wha
t is
diffe
rent
to th
e in
term
edia
te P
hase
?
This
is a
n in
trodu
ctio
n to
form
al a
lgeb
raic
lang
uage
and
is n
ew in
the
Sen
ior
Pha
se. T
he u
se o
f sym
bolic
lang
uage
hel
ps to
dev
elop
an
unde
rsta
ndin
g of
va
riabl
es.
alg
ebra
ic e
xpre
ssio
ns a
re d
one
agai
n in
ter
m 4
, whe
re ru
les
and
rela
tions
hips
can
incl
ude
inte
gers
.
Lear
ners
hav
e op
portu
nitie
s to
writ
e an
d in
terp
ret a
lgeb
raic
exp
ress
ions
whe
n th
ey
writ
e ge
nera
l rul
es to
des
crib
e re
latio
nshi
ps b
etw
een
num
bers
in n
umbe
r pat
tern
s,
and
whe
n th
ey fi
nd in
put a
nd o
utpu
t val
ues
for g
iven
rule
s in
flow
dia
gram
s, ta
bles
an
d fo
rmul
ae.
exam
ples
a)
Wha
t doe
s th
e ru
le 2
x n
–1
mea
n fo
r the
follo
win
g nu
mbe
r seq
uenc
e: 1
; 3; 5
; 7;
9;..
..
Her
e le
arne
rs s
houl
d re
cogn
ize
that
2 x
n –
1 re
pres
ents
the
gene
ral t
erm
in th
is
sequ
ence
, whe
re n
repr
esen
ts th
e po
sitio
n of
the
term
in th
e se
quen
ce. T
hus
it is
the
rule
that
can
be
used
to fi
nd a
ny te
rm in
the
give
n se
quen
ce.
b)
The
rela
tions
hip
betw
een
a bo
y’s
age
(x y
rs o
ld) a
nd h
is m
othe
r’s a
ge is
giv
en
as 2
5 +
x. H
ow c
an th
is re
latio
nshi
p be
use
d to
find
the
mot
her’s
age
whe
n th
e bo
y is
11
year
s ol
d?
Her
e le
arne
rs s
houl
d re
cogn
ize
that
to fi
nd th
e m
othe
r’s a
ge, t
hey
shou
ld
subs
titut
e th
e bo
y’s
give
n ag
e in
to th
e ru
le 2
5 +
x. T
hey
shou
ld a
lso
reco
gniz
e th
at th
e gi
ven
rule
mea
ns th
e m
othe
r is
25 y
ears
old
er th
an th
e bo
y.
See
furth
er e
xam
ples
giv
en fo
r fun
ctio
ns a
nd re
latio
nshi
ps.
3 ho
urs
MATHEMATICS GRADES 7-9
64 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.4
alg
ebra
ic
equa
tions
num
ber s
ente
nces
• W
rite
num
ber s
ente
nces
to d
escr
ibe
prob
lem
situ
atio
ns
• A
naly
se a
nd in
terp
ret n
umbe
r se
nten
ces
that
des
crib
e a
give
n si
tuat
ion
• S
olve
and
com
plet
e nu
mbe
r se
nten
ces
by:
-in
spec
tion
-tri
al a
nd im
prov
emen
t
• Id
entif
y va
riabl
es a
nd c
onst
ants
in
give
n fo
rmul
ae o
r equ
atio
ns
• D
eter
min
e th
e nu
mer
ical
val
ue o
f an
expr
essi
on b
y su
bstit
utio
n.
Wha
t is
diffe
rent
to th
e in
term
edia
te P
hase
? Th
e nu
mbe
r se
nten
ces
that
lear
ners
can
sol
ve a
re e
xten
ded
to in
clud
e nu
mbe
r se
nten
ces
with
inte
gers
, squ
are
num
bers
and
cub
ic n
umbe
rs.
Num
ber s
ente
nces
are
use
d he
re a
s a
mor
e fa
mili
ar te
rm fo
r Gra
de 7
lear
ners
than
eq
uatio
ns.
How
ever
, th
e te
rm e
quat
ion
will
be
used
ins
tead
of
num
ber
sent
ence
s in
lat
er
grad
es.
alg
ebra
ic e
quat
ions
are
don
e ag
ain
in t
erm
4, w
here
num
ber
sent
ence
s ca
n in
clud
e in
tege
rs.
Lear
ners
hav
e op
portu
nitie
s to
writ
e, s
olve
and
com
plet
e nu
mbe
r sen
tenc
es w
hen
they
writ
e ge
nera
l ru
les
to d
escr
ibe
rela
tions
hips
bet
wee
n nu
mbe
rs i
n nu
mbe
r pa
ttern
s, a
nd w
hen
they
find
inpu
t and
out
put v
alue
s fo
r giv
en ru
les
in fl
ow d
iagr
ams,
ta
bles
and
form
ulae
.
Rat
her
than
use
form
al a
lgeb
raic
pro
cess
es, l
earn
ers
solv
e nu
mbe
r se
nten
ces
by
insp
ectio
n or
det
erm
ine
the
num
eric
al v
alue
of e
xpre
ssio
ns b
y su
bstit
utio
n.
In th
is p
hase
, it i
s us
eful
whe
n so
lvin
g eq
uatio
ns to
beg
in to
spe
cify
whe
ther
x is
a
natu
ral n
umbe
r, in
tege
r or
rat
iona
l num
ber.
This
bui
lds
lear
ners
’ aw
aren
ess
of th
e do
mai
n of
x.
exam
ples
a)
Sol
ve x
if x
+ 4
= 7
, whe
re x
is a
nat
ural
num
ber.
(Wha
t mus
t be
adde
d to
4 to
gi
ve 7
?)
b)
Sol
ve x
if x
+ 4
= –
7, w
here
x is
an
inte
ger.
(Wha
t mus
t be
adde
d to
4 to
giv
e –7
?)
c)
Sol
ve x
if 2
x =
30, w
here
x is
a n
atur
al n
umbe
r. (W
hat m
ust b
e m
ultip
lied
by 2
to
giv
e 30
?)
d)
Writ
e a
num
ber s
ente
nce
to fi
nd th
e ar
ea o
f a re
ctan
gle
with
leng
th 4
,5 c
m a
nd
brea
dth
2 cm
.
e)
If y
= x2 +
1, c
alcu
late
y w
hen
x =
3
3 ho
urs
MATHEMATICS GRADES 7-9
65CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.4
alg
ebra
ic
equa
tions
num
ber s
ente
nces
• W
rite
num
ber s
ente
nces
to d
escr
ibe
prob
lem
situ
atio
ns
• A
naly
se a
nd in
terp
ret n
umbe
r se
nten
ces
that
des
crib
e a
give
n si
tuat
ion
• S
olve
and
com
plet
e nu
mbe
r se
nten
ces
by:
-in
spec
tion
-tri
al a
nd im
prov
emen
t
• Id
entif
y va
riabl
es a
nd c
onst
ants
in
give
n fo
rmul
ae o
r equ
atio
ns
• D
eter
min
e th
e nu
mer
ical
val
ue o
f an
expr
essi
on b
y su
bstit
utio
n.
Wha
t is
diffe
rent
to th
e in
term
edia
te P
hase
? Th
e nu
mbe
r se
nten
ces
that
lear
ners
can
sol
ve a
re e
xten
ded
to in
clud
e nu
mbe
r se
nten
ces
with
inte
gers
, squ
are
num
bers
and
cub
ic n
umbe
rs.
Num
ber s
ente
nces
are
use
d he
re a
s a
mor
e fa
mili
ar te
rm fo
r Gra
de 7
lear
ners
than
eq
uatio
ns.
How
ever
, th
e te
rm e
quat
ion
will
be
used
ins
tead
of
num
ber
sent
ence
s in
lat
er
grad
es.
alg
ebra
ic e
quat
ions
are
don
e ag
ain
in t
erm
4, w
here
num
ber
sent
ence
s ca
n in
clud
e in
tege
rs.
Lear
ners
hav
e op
portu
nitie
s to
writ
e, s
olve
and
com
plet
e nu
mbe
r sen
tenc
es w
hen
they
writ
e ge
nera
l ru
les
to d
escr
ibe
rela
tions
hips
bet
wee
n nu
mbe
rs i
n nu
mbe
r pa
ttern
s, a
nd w
hen
they
find
inpu
t and
out
put v
alue
s fo
r giv
en ru
les
in fl
ow d
iagr
ams,
ta
bles
and
form
ulae
.
Rat
her
than
use
form
al a
lgeb
raic
pro
cess
es, l
earn
ers
solv
e nu
mbe
r se
nten
ces
by
insp
ectio
n or
det
erm
ine
the
num
eric
al v
alue
of e
xpre
ssio
ns b
y su
bstit
utio
n.
In th
is p
hase
, it i
s us
eful
whe
n so
lvin
g eq
uatio
ns to
beg
in to
spe
cify
whe
ther
x is
a
natu
ral n
umbe
r, in
tege
r or
rat
iona
l num
ber.
This
bui
lds
lear
ners
’ aw
aren
ess
of th
e do
mai
n of
x.
exam
ples
a)
Sol
ve x
if x
+ 4
= 7
, whe
re x
is a
nat
ural
num
ber.
(Wha
t mus
t be
adde
d to
4 to
gi
ve 7
?)
b)
Sol
ve x
if x
+ 4
= –
7, w
here
x is
an
inte
ger.
(Wha
t mus
t be
adde
d to
4 to
giv
e –7
?)
c)
Sol
ve x
if 2
x =
30, w
here
x is
a n
atur
al n
umbe
r. (W
hat m
ust b
e m
ultip
lied
by 2
to
giv
e 30
?)
d)
Writ
e a
num
ber s
ente
nce
to fi
nd th
e ar
ea o
f a re
ctan
gle
with
leng
th 4
,5 c
m a
nd
brea
dth
2 cm
.
e)
If y
= x2 +
1, c
alcu
late
y w
hen
x =
3
3 ho
urs
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.5
Gra
phs
inte
rpre
ting
grap
hs
• A
naly
se a
nd in
terp
ret g
loba
l gra
phs
of p
robl
em s
ituat
ions
, with
spe
cial
fo
cus
on th
e fo
llow
ing
trend
s an
d fe
atur
es:
-lin
ear o
r non
-line
ar
-co
nsta
nt, i
ncre
asin
g or
dec
reas
ing
dra
win
g gr
aphs
• D
raw
glo
bal g
raph
s fro
m g
iven
de
scrip
tions
of a
pro
blem
situ
atio
n,
iden
tifyi
ng fe
atur
es li
sted
abo
ve
Wha
t is
diffe
rent
to th
e in
term
edia
te P
hase
?
In th
e In
term
edia
te P
hase
lear
ners
enc
ount
ered
gra
phs
in th
e fo
rm o
f dat
a ba
r gr
aphs
and
pie
cha
rts. T
his
mea
ns th
ey d
o ha
ve s
ome
expe
rienc
e re
adin
g an
d in
terp
retin
g gr
aphs
. How
ever
, in
the
Sen
ior P
hase
, the
y ar
e in
trodu
ced
to li
ne
grap
hs th
at s
how
func
tiona
l rel
atio
nshi
ps d
escr
ibed
in te
rms
of d
epen
dent
and
in
depe
nden
t var
iabl
es.
In G
rade
7, t
he fo
cus
is o
n dr
awin
g, a
naly
sing
and
inte
rpre
ting
glob
al g
raph
s on
ly.
That
is, l
earn
ers
do n
ot h
ave
to p
lot p
oint
s to
dra
w g
raph
s an
d th
ey fo
cus
on th
e fe
atur
es o
f the
glo
bal r
elat
ions
hip
show
n in
the
grap
h.
exam
ples
of c
onte
xts
for g
loba
l gra
phs
incl
ude:
• th
e re
latio
nshi
p be
twee
n tim
e an
d di
stan
ce tr
avel
led
• th
e re
latio
nshi
p be
twee
n te
mpe
ratu
re a
nd ti
me
over
whi
ch it
is m
easu
red
• th
e re
latio
nshi
p be
twee
n ra
infa
ll an
d tim
e ov
er w
hich
it is
mea
sure
d, e
tc.
6 ho
urs
spac
e an
d sh
ape
(geo
met
ry)
3.4
tran
sfor
ma-
tion
G
eom
etry
tran
sfor
mat
ions
• R
ecog
nize
, des
crib
e an
d pe
rform
tra
nsla
tions
, refl
ectio
ns a
nd ro
tatio
ns
with
geo
met
ric fi
gure
s an
d sh
apes
on
squa
red
pape
r
• Id
entif
y an
d dr
aw li
nes
of s
ymm
etry
in
geo
met
ric fi
gure
s
enla
rgem
ents
and
redu
ctio
ns
• D
raw
enl
arge
men
ts a
nd re
duct
ions
of
geom
etric
figu
res
on s
quar
ed p
aper
an
d co
mpa
re th
em in
term
s of
sha
pe
and
size
Wha
t is
diffe
rent
to G
rade
6
Lear
ners
in G
rade
7 h
ave
to d
o tra
nsfo
rmat
ions
on
squa
red
pape
r.
Focu
s of
tran
sfor
mat
ions
• U
sing
squ
ared
pap
er fo
r tra
nsfo
rmat
ions
allo
ws
lear
ners
to m
ore
accu
rate
ly
perfo
rm tr
ansf
orm
atio
ns a
nd to
com
pare
the
shap
e an
d si
ze o
f figu
res.
• Le
arne
rs s
houl
d re
cogn
ize
that
tran
slat
ions
, refl
ectio
ns a
nd ro
tatio
ns o
nly
chan
ge th
e po
sitio
n of
the
figur
e, a
nd n
ot it
s sh
ape
or s
ize.
• Th
ey s
houl
d re
cogn
ize
that
the
abov
e tra
nsfo
rmat
ions
pro
duce
con
grue
nt
figur
es.
• Le
arne
rs s
houl
d re
cogn
ize
that
enl
arge
men
ts a
nd re
duct
ions
cha
nge
the
size
of
figur
es b
y in
crea
sing
or d
ecre
asin
g th
e le
ngth
of s
ides
, but
kee
ping
the
angl
es
the
sam
e, p
rodu
cing
sim
ilar r
athe
r tha
n co
ngru
ent fi
gure
s.
• Le
arne
rs s
houl
d al
so b
e ab
le to
wor
k ou
t the
fact
or o
f enl
arge
men
t or r
educ
tion.
9 ho
urs
MATHEMATICS GRADES 7-9
66 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
3.2
Geo
met
ry o
f 3d
obj
ects
Cla
ssify
ing
3d o
bjec
ts
• D
escr
ibe,
sor
t and
com
pare
po
lyhe
dra
in te
rms
of
-sh
ape
and
num
ber o
f fac
es
-nu
mbe
r of v
ertic
es
-nu
mbe
r of e
dges
Bui
ldin
g 3d
mod
el
• R
evis
e us
ing
nets
to c
reat
e m
odel
s of
ge
omet
ric s
olid
s, in
clud
ing:
-cu
bes
-pr
ism
s
Wha
t is
diffe
rent
to G
rade
6?
• M
ost o
f thi
s w
ork
cons
olid
ates
wha
t has
bee
n do
ne in
Gra
de 6
.
Poly
hedr
a
Exa
mpl
es o
f sor
ting
or g
roup
ing
cate
gorie
s:
• cu
bes
(onl
y sq
uare
face
s)
• re
ctan
gula
r pris
ms
(onl
y re
ctan
gula
r fac
es)
• tri
angu
lar p
rism
s (o
nly
trian
gula
r and
rect
angu
lar f
aces
)
• py
ram
ids
(squ
are
and
trian
gula
r fac
es)
• cy
linde
rs (c
ircul
ar a
nd re
ctan
gula
r fac
es).
usi
ng a
nd c
onst
ruct
ing
nets
• U
sing
and
con
stru
ctin
g ne
ts a
re u
sefu
l con
text
s fo
r exp
lorin
g or
con
solid
atin
g pr
oper
ties
of p
olyh
edra
.
• Le
arne
rs s
houl
d re
cogn
ize
the
nets
of d
iffer
ent s
olid
s.
• Le
arne
rs s
houl
d dr
aw s
ketc
hes
of th
e ne
ts u
sing
thei
r kno
wle
dge
of s
hape
and
nu
mbe
r of f
aces
of t
he s
olid
s, b
efor
e dr
awin
g an
d cu
tting
out
the
nets
to b
uild
m
odel
s.
• Th
e co
nstru
ctio
n of
net
s is
bas
ed o
n th
e nu
mbe
r and
sha
pe o
f fac
es o
f the
so
lids,
and
do
not r
equi
re m
easu
ring
of in
tern
al a
ngle
s of
pol
ygon
s.
• Le
arne
rs h
ave
to w
ork
out t
he re
lativ
e po
sitio
n of
the
face
s of
the
nets
, and
us
e tri
al a
nd e
rror
to m
atch
up
the
edge
s an
d ve
rtice
s, in
ord
er to
bui
ld th
e 3D
ob
ject
.
9 ho
urs
rev
isio
n/a
sses
smen
t:A
t thi
s st
age
lear
ners
sho
uld
have
bee
n as
sess
ed o
n:
• nu
mer
ic a
nd g
eom
etric
pat
tern
s
• fu
nctio
ns a
nd re
latio
nshi
ps
• al
gebr
aic
expr
essi
ons
• al
gebr
aic
equa
tions
• gr
aphs
• tra
nsfo
rmat
ion
geom
etry
• ge
omet
ry o
f 3D
obj
ects
6 ho
urs
MATHEMATICS GRADES 7-9
67CAPS
Gr
ad
e 7
– te
rm
4
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.3
inte
gers
Cou
ntin
g, o
rder
ing
and
com
parin
g in
tege
rs
• C
ount
forw
ards
and
bac
kwar
ds in
in
tege
rs fo
r any
inte
rval
• R
ecog
nize
, ord
er a
nd c
ompa
re
inte
gers
Cal
cula
tions
with
inte
gers
• A
dd a
nd s
ubtra
ct w
ith in
tege
rs
Prop
ertie
s of
inte
gers
• R
ecog
nize
and
use
com
mut
ativ
e an
d as
soci
ativ
e pr
oper
ties
of a
dditi
on a
nd
mul
tiplic
atio
n fo
r int
eger
s
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
addi
tion
and
subt
ract
ion
of in
tege
rs
Wha
t is
diffe
rent
to G
rade
6?
Inte
gers
are
new
num
bers
intro
duce
d in
Gra
de 7
.
Cou
ntin
g, o
rder
ing
and
com
parin
g in
tege
rs
• C
ount
ing
shou
ld n
ot o
nly
be th
ough
t of a
s ve
rbal
cou
ntin
g. L
earn
ers
can
coun
t us
ing:
-st
ruct
ured
, sem
i-stru
ctur
ed o
r em
pty
num
ber l
ines
-ch
ain
diag
ram
s fo
r cou
ntin
g
• Le
arne
rs s
houl
d be
giv
en a
rang
e of
exe
rcis
es s
uch
as:
-ar
rang
e gi
ven
num
bers
from
the
smal
lest
to th
e bi
gges
t: or
big
gest
to s
mal
lest
-fil
l in
mis
sing
num
bers
in
♦a
sequ
ence
♦on
a n
umbe
r grid
♦on
a n
umbe
r lin
e
♦fil
l in
<, =
or >
exa
mpl
e: –
425
* –
450
Cal
cula
tions
usi
ng in
tege
rs
• S
tart
calc
ulat
ions
usi
ng in
tege
rs in
sm
all n
umbe
r ran
ges.
• D
evel
op a
n un
ders
tand
ing
that
sub
tract
ing
an in
tege
r is
the
sam
e as
add
ing
its
addi
tive
inve
rse.
•ex
ampl
e:
7 –
4 =
7 +
(– 4
) = 3
or
–7
– 4
= –7
+ (–
4) =
–11
So
too,
7 –
(– 4
) = 7
+ (+
4) =
11
or
–7
– (–
4) =
–7
+ (+
4) =
–3
Her
e th
e us
e of
bra
cket
s ar
ound
the
inte
gers
are
use
ful.
Prop
ertie
s of
inte
gers
• Le
arne
rs s
houl
d in
vest
igat
e th
e pr
oper
ties
for o
pera
tions
usi
ng w
hole
num
bers
on
the
set o
f int
eger
s.
• Th
ese
prop
ertie
s sh
ould
ser
ve a
s m
otiv
atio
n fo
r the
ope
ratio
ns th
ey c
an p
erfo
rm
usin
g in
tege
rs.
• Le
arne
rs s
houl
d se
e th
at th
e co
mm
utat
ive
prop
erty
for a
dditi
on h
olds
for
inte
gers
e.g
8 +
(–3)
= (–
3) +
8 =
5
• Le
arne
rs s
houl
d se
e th
at th
ey c
an s
till u
se s
ubtra
ctio
n to
che
ck a
dditi
on o
r vic
e ve
rsa.
exa
mpl
e: If
8 +
(–3)
= 5
, the
n 5
– 8
= –
3 an
d 5
–(–3
) = 8
9 ho
urs
MATHEMATICS GRADES 7-9
68 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.3
inte
gers
• Le
arne
rs s
houl
d se
e th
at th
e as
soci
ativ
e pr
oper
ty fo
r add
ition
hol
ds fo
r int
eger
s.
exam
ple:
[(–6
) + 4
] + (–
1) =
(–6)
+ [4
+ (–
1)] =
–3
• Le
arne
rs s
houl
d on
ly e
xplo
re th
e di
strib
utiv
e pr
oper
ty o
nce
they
can
mul
tiply
w
ith in
tege
rs
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.1
num
eric
and
ge
omet
ric
patte
rns
inve
stig
ate
and
exte
nd p
atte
rns
• In
vest
igat
e an
d ex
tend
num
eric
an
d ge
omet
ric p
atte
rns
look
ing
for
rela
tions
hips
bet
wee
n nu
mbe
rs,
incl
udin
g pa
ttern
s:
-re
pres
ente
d in
phy
sica
l or
diag
ram
fo
rm
-no
t lim
ited
to s
eque
nces
invo
lvin
g a
cons
tant
diff
eren
ce o
r rat
io
-of
lear
ner’s
ow
n cr
eatio
n
-re
pres
ente
d in
tabl
es
• D
escr
ibe
and
just
ify th
e ge
nera
l rul
es
for o
bser
ved
rela
tions
hips
bet
wee
n nu
mbe
rs in
ow
n w
ords
The
focu
s of
num
eric
pat
tern
s in
this
term
sho
uld
be o
n pr
actis
ing
oper
atio
ns w
ith
inte
gers
.
see
addi
tiona
l not
es in
ter
m 3
.
3 ho
urs
2.2
Func
tions
an
d re
latio
nshi
ps
inpu
t and
out
put v
alue
s•
Det
erm
ine
inpu
t val
ues,
out
put
valu
es o
r rul
es fo
r pat
tern
s an
d re
latio
nshi
ps u
sing
:
-flo
w d
iagr
ams
-ta
bles
-fo
rmul
ae
equi
vale
nt fo
rms
• D
eter
min
e, in
terp
ret a
nd ju
stify
eq
uiva
lenc
e of
diff
eren
t des
crip
tions
of
the
sam
e re
latio
nshi
p or
rule
pr
esen
ted:
-ve
rbal
ly
-in
flow
dia
gram
s
-in
tabl
es
-by
form
ulae
-by
num
ber s
ente
nces
Func
tions
and
rela
tions
hips
in th
is te
rm s
houl
d in
clud
e in
tege
rs a
s in
put o
r out
put
valu
es, a
s w
ell a
s us
ing
inte
gers
in th
e ru
les
for p
atte
rns
and
rela
tions
hips
.
see
addi
tiona
l not
es in
ter
ms
2 &
3.
3 ho
urs
MATHEMATICS GRADES 7-9
69CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.3
alg
ebra
ic
expr
essi
ons
alg
ebra
ic la
ngua
ge
• R
ecog
nize
and
inte
rpre
t rul
es o
r re
latio
nshi
ps re
pres
ente
d in
sym
bolic
fo
rm
• Id
entif
y va
riabl
es a
nd c
onst
ants
in
form
ulae
and
equ
atio
ns
Alg
ebra
ic e
xpre
ssio
ns s
houl
d in
clud
e in
tege
rs in
the
rule
s or
rela
tions
hips
repr
e-se
nted
in s
ymbo
lic fo
rm.
see
addi
tiona
l not
es in
ter
m 3
.
3 ho
urs
2.4
alg
ebra
ic
equa
tions
num
ber s
ente
nces
• W
rite
num
ber s
ente
nces
to d
escr
ibe
prob
lem
situ
atio
ns
• A
naly
se a
nd in
terp
ret n
umbe
r se
nten
ces
that
des
crib
e a
give
n si
tuat
ion
• S
olve
and
com
plet
e nu
mbe
r se
nten
ces
by:
-in
spec
tion
-tri
al a
nd im
prov
emen
t
• Id
entif
y va
riabl
es a
nd c
onst
ants
in
give
n fo
rmul
ae o
r equ
atio
ns
• D
eter
min
e th
e nu
mer
ical
val
ue o
f an
expr
essi
on b
y su
bstit
utio
n.
Num
ber s
ente
nces
sho
uld
incl
ude
inte
gers
.
see
addi
tiona
l not
es in
ter
m 3
.
4 ho
urs
MATHEMATICS GRADES 7-9
70 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
dat
a H
an
dli
nG
5.1
Col
lect
, or
gani
ze a
nd
sum
mar
ize
data
Col
lect
dat
a
• P
ose
ques
tions
rela
ting
to s
ocia
l, ec
onom
ic, a
nd e
nviro
nmen
tal i
ssue
s in
ow
n en
viro
nmen
t
• S
elec
t app
ropr
iate
sou
rces
for
the
colle
ctio
n of
dat
a (in
clud
ing
peer
s, fa
mily
, new
spap
ers,
boo
ks,
mag
azin
es)
• D
istin
guis
h be
twee
n sa
mpl
es a
nd
popu
latio
ns
• D
esig
n an
d us
e si
mpl
e qu
estio
nnai
res
to a
nsw
er q
uest
ions
:
-w
ith y
es/n
o ty
pe re
spon
ses
-w
ith m
ultip
le c
hoic
e re
spon
ses.
org
aniz
e an
d su
mm
ariz
e da
ta
• O
rgan
ize
(incl
udin
g gr
oupi
ng w
here
ap
prop
riate
) and
reco
rd d
ata
usin
g
-ta
lly m
arks
-ta
bles
-st
em-a
nd-le
af d
ispl
ays
Wha
t is
diffe
rent
to G
rade
6?
The
follo
win
g ar
e ne
w in
Gra
de 7
• sa
mpl
es a
nd p
opul
atio
ns
• m
ultip
le c
hoic
e qu
estio
nnai
res
• st
em-a
nd-le
af d
ispl
ays
• gr
oupi
ng d
ata
in in
terv
als
• m
ean
• ra
nge
• hi
stog
ram
s
• sc
ales
on
grap
hs
dat
a se
ts a
nd c
onte
xts
Lear
ners
sho
uld
be e
xpos
ed to
a v
arie
ty o
f con
text
s th
at d
eal w
ith s
ocia
l and
en
viro
nmen
tal i
ssue
s, a
nd s
houl
d w
ork
with
giv
en d
ata
sets
, rep
rese
nted
in
a va
riety
of w
ays,
that
incl
ude
big
num
ber r
ange
s, p
erce
ntag
es a
nd d
ecim
al
fract
ions
. Lea
rner
s sh
ould
then
pra
ctis
e or
gani
zing
and
sum
mar
izin
g th
is d
ata,
an
alys
ing
and
inte
rpre
ting
the
data
, and
writ
ing
a re
port
abou
t the
dat
a.
Com
plet
e a
data
cyc
le
Lear
ners
sho
uld
com
plet
e at
leas
t one
dat
a cy
cle
for t
he y
ear,
star
ting
with
po
sing
thei
r ow
n qu
estio
ns, s
elec
ting
the
sour
ces
and
met
hod
for c
olle
ctin
g da
ta,
reco
rdin
g th
e da
ta, o
rgan
izin
g th
e da
ta, r
epre
sent
ing
the
data
, the
n an
alys
ing,
su
mm
ariz
ing,
inte
rpre
ting
and
repo
rting
the
data
. Cha
lleng
e le
arne
rs to
thin
k ab
out
wha
t kin
ds o
f que
stio
ns a
nd d
ata
need
to b
e co
llect
ed to
be
repr
esen
ted
in a
hi
stog
ram
, pie
cha
rt, o
r bar
gra
ph.
tim
e fo
r co
llect
ing
and
orga
nizi
ng
data
: 4 h
ours
MATHEMATICS GRADES 7-9
71CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
dat
a H
an
dli
nG
5.1
Col
lect
, or
gani
ze a
nd
sum
mar
ize
data
• G
roup
dat
a in
to in
terv
als
• S
umm
ariz
e an
d di
stin
guis
h be
twee
n un
grou
ped
num
eric
al d
ata
by
dete
rmin
ing:
-m
ean
-m
edia
n
-m
ode
• Id
entif
y th
e la
rges
t and
sm
alle
st
scor
es in
a d
ata
set a
nd d
eter
min
e th
e di
ffere
nce
betw
een
them
in o
rder
to
det
erm
ine
the
spre
ad o
f the
dat
a (r
ange
).
rep
rese
ntin
g da
ta
• D
raw
ing
pie
char
ts to
repr
esen
t dat
a do
not
hav
e to
be
accu
rate
ly d
raw
n w
ith a
co
mpa
ss a
nd p
rotra
ctor
, etc
. Lea
rner
s ca
n us
e an
y ro
und
obje
ct to
dra
w a
circ
le,
then
div
ide
the
circ
le in
to h
alve
s an
d qu
arte
rs a
nd e
ight
hs if
nee
ded,
as
a gu
ide
to e
stim
ate
the
prop
ortio
ns o
f the
circ
le th
at n
eed
to b
e sh
own
to re
pres
ent t
he
data
. Wha
t is
impo
rtant
is th
at th
e va
lues
or p
erce
ntag
es a
ssoc
iate
d w
ith th
e da
ta, a
re s
how
n pr
opor
tiona
lly o
n th
e pi
e ch
art.
• D
raw
ing,
read
ing
and
inte
rpre
ting
pie
char
ts is
a u
sefu
l con
text
to re
-vis
it eq
uiva
lenc
e be
twee
n fra
ctio
ns a
nd p
erce
ntag
es, e
.g. 2
5% o
f the
dat
a is
re
pres
ente
d by
a 1 4
sec
tor o
f the
circ
le.
• It
is a
lso
a co
ntex
t in
whi
ch le
arne
rs c
an fi
nd p
erce
ntag
es o
f who
le n
umbe
rs e
.g.
if 25
% o
f 300
lear
ners
like
rugb
y, h
ow m
any
(act
ual n
umbe
r) le
arne
rs li
ke ru
gby?
• H
isto
gram
s ar
e us
ed to
repr
esen
t gro
uped
dat
a sh
own
in in
terv
als
on th
e ho
rizon
tal a
xis
of th
e gr
aph.
Poi
nt o
ut th
e di
ffere
nces
bet
wee
n hi
stog
ram
s an
d ba
r gra
phs,
in p
artic
ular
bar
gra
phs
that
repr
esen
t dis
cret
e da
ta (e
.g. f
avou
rite
spor
ts) c
ompa
red
to h
isto
gram
s th
at s
how
cat
egor
ies
in c
onse
cutiv
e, n
on-
over
lapp
ing
inte
rval
s, (e
.g. t
est s
core
s ou
t of 1
00 s
how
n in
inte
rval
s of
10)
. The
ba
rs o
n ba
r gra
phs
do n
ot h
ave
to to
uch
each
oth
er, w
hile
in a
his
togr
am th
ey
have
to to
uch
sinc
e th
ey s
how
con
secu
tive
inte
rval
s.
dev
elop
ing
criti
cal a
naly
sis
skill
s
• Le
arne
rs s
houl
d co
mpa
re th
e sa
me
data
repr
esen
ted
in d
iffer
ent w
ays
e.g.
in a
pi
e ch
art o
r a b
ar g
raph
or a
tabl
e, a
nd d
iscu
ss w
hat i
nfor
mat
ion
is s
how
n an
d w
hat i
s hi
dden
; the
y sh
ould
eva
luat
e w
hat f
orm
of r
epre
sent
atio
n w
orks
bes
t for
th
e gi
ven
data
.
• Le
arne
rs s
houl
d co
mpa
re g
raph
s on
the
sam
e to
pic
but w
here
dat
a ha
s be
en
colle
cted
from
diff
eren
t gro
ups
of p
eopl
e, a
t diff
eren
t tim
es, i
n di
ffere
nt p
lace
s or
in d
iffer
ent w
ays.
Her
e le
arne
rs s
houl
d di
scus
s di
ffere
nces
bet
wee
n th
e da
ta
with
an
awar
enes
s of
bia
s re
late
d to
the
impa
ct o
f dat
a so
urce
s an
d m
etho
ds o
f da
ta c
olle
ctio
n on
the
inte
rpre
tatio
n of
the
data
.
• Le
arne
rs s
houl
d co
mpa
re d
iffer
ent w
ays
of s
umm
aris
ing
the
sam
e da
ta s
ets,
de
velo
ping
an
awar
enes
s of
how
dat
a re
porti
ng c
an b
e m
anip
ulat
ed; e
valu
atin
g w
hich
sum
mar
y st
atis
tics
best
repr
esen
t the
dat
a.
• Le
arne
rs s
houl
d co
mpa
re g
raph
s of
the
sam
e da
ta, w
here
the
scal
es o
f th
e gr
aphs
are
diff
eren
t. H
ere
lear
ners
sho
uld
disc
uss
diffe
renc
es w
ith a
n aw
aren
ess
of h
ow re
pres
enta
tion
of d
ata
can
be m
anip
ulat
ed; t
hey
shou
ld
eval
uate
whi
ch fo
rm o
f rep
rese
ntat
ion
wor
ks b
est f
or th
e gi
ven
data
.
• Le
arne
rs s
houl
d w
rite
repo
rts o
n th
e da
ta in
sho
rt pa
ragr
aphs
.
tim
e fo
r re
pres
entin
g da
ta: 3
hou
rs
tim
e fo
r an
alys
ing,
in
terp
retin
g an
d re
port
ing
data
: 3,5
ho
urs
MATHEMATICS GRADES 7-9
72 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
5.2
rep
rese
ntin
g da
ta
rep
rese
nt d
ata
• D
raw
a v
arie
ty o
f gra
phs
by h
and/
tech
nolo
gy to
dis
play
and
inte
rpre
t da
ta (g
roup
ed a
nd u
ngro
uped
) in
clud
ing:
-ba
r gra
phs
and
doub
le b
ar g
raph
s -
hist
ogra
ms
with
giv
en in
terv
als
-pi
e ch
arts
5.3
inte
rpre
t, an
alys
e an
d re
port
dat
a
inte
rpre
t dat
a•
Crit
ical
ly re
ad a
nd in
terp
ret d
ata
repr
esen
ted
in:
-w
ords
-ba
r gra
phs
-do
uble
bar
gra
phs
-pi
e ch
arts
-hi
stog
ram
sa
naly
se d
ata
• C
ritic
ally
ana
lyse
dat
a by
ans
wer
ing
ques
tions
rela
ted
to:
-da
ta c
ateg
orie
s, in
clud
ing
data
in
terv
als
-da
ta s
ourc
es a
nd c
onte
xts
-ce
ntra
l ten
denc
ies
(mea
n, m
ode,
m
edia
n) -
scal
es u
sed
on g
raph
sr
epor
t dat
a•
Sum
mar
ize
data
in s
hort
para
grap
hs
that
incl
ude
-dr
awin
g co
nclu
sion
s ab
out t
he d
ata
-m
akin
g pr
edic
tions
bas
ed o
n th
e da
ta
-id
entif
ying
sou
rces
of e
rror
and
bi
as in
the
data
-ch
oosi
ng a
ppro
pria
te s
umm
ary
stat
istic
s fo
r the
dat
a (m
ean,
m
edia
n, m
ode)
MATHEMATICS GRADES 7-9
73CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
5.2
rep
rese
ntin
g da
ta
rep
rese
nt d
ata
• D
raw
a v
arie
ty o
f gra
phs
by h
and/
tech
nolo
gy to
dis
play
and
inte
rpre
t da
ta (g
roup
ed a
nd u
ngro
uped
) in
clud
ing:
-ba
r gra
phs
and
doub
le b
ar g
raph
s -
hist
ogra
ms
with
giv
en in
terv
als
-pi
e ch
arts
5.3
inte
rpre
t, an
alys
e an
d re
port
dat
a
inte
rpre
t dat
a•
Crit
ical
ly re
ad a
nd in
terp
ret d
ata
repr
esen
ted
in:
-w
ords
-ba
r gra
phs
-do
uble
bar
gra
phs
-pi
e ch
arts
-hi
stog
ram
sa
naly
se d
ata
• C
ritic
ally
ana
lyse
dat
a by
ans
wer
ing
ques
tions
rela
ted
to:
-da
ta c
ateg
orie
s, in
clud
ing
data
in
terv
als
-da
ta s
ourc
es a
nd c
onte
xts
-ce
ntra
l ten
denc
ies
(mea
n, m
ode,
m
edia
n) -
scal
es u
sed
on g
raph
sr
epor
t dat
a•
Sum
mar
ize
data
in s
hort
para
grap
hs
that
incl
ude
-dr
awin
g co
nclu
sion
s ab
out t
he d
ata
-m
akin
g pr
edic
tions
bas
ed o
n th
e da
ta
-id
entif
ying
sou
rces
of e
rror
and
bi
as in
the
data
-ch
oosi
ng a
ppro
pria
te s
umm
ary
stat
istic
s fo
r the
dat
a (m
ean,
m
edia
n, m
ode)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
5.4
Prob
abili
ty
Prob
abili
ty
Per
form
sim
ple
expe
rimen
ts w
here
the
poss
ible
out
com
es a
re e
qual
ly li
kely
an
d
• lis
t the
pos
sibl
e ou
tcom
es b
ased
on
the
cond
ition
s of
the
activ
ity
• de
term
ine
the
prob
abili
ty o
f eac
h po
ssib
le o
utco
me,
usi
ng th
e de
finiti
on
of p
roba
bilit
y
Prob
abili
ty e
xper
imen
tsIn
the
Inte
rmed
iate
Pha
se le
arne
rs d
id e
xper
imen
ts w
ith c
oins
, dic
e an
d sp
inne
rs.
In th
is g
rade
exp
erim
ents
can
be
done
with
oth
er o
bjec
ts, l
ike,
diff
eren
t col
oure
d bu
ttons
in a
bag
; cho
osin
g sp
ecifi
c ca
rds
from
a d
eck
of c
ards
, etc
.
exam
ple
If yo
u to
ss a
coi
n th
ere
are
two
poss
ible
out
com
es (h
ead
or ta
il). T
he p
roba
bilit
y of
a h
ead
is 1 2
whi
ch is
equ
ival
ent t
o 50
% (s
ince
it is
one
out
of t
wo
poss
ible
ou
tcom
es)
4,5
hour
s
rev
isio
n/a
sses
smen
t:A
t thi
s st
age
lear
ners
sho
uld
have
bee
n as
sess
ed o
n:
• ad
ding
and
sub
tract
ing
with
inte
gers
• co
llect
ing,
org
aniz
ing,
repr
esen
ting,
ana
lysi
ng, s
umm
ariz
ing,
inte
rpre
ting
and
repo
rting
dat
a
• pr
obab
ility
tota
l tim
e fo
r re
visi
on/
asse
ssm
ent
for t
he te
rm8
hour
s
MATHEMATICS GRADES 7-9
74 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
time alloCation Per term: Grade 8
term 1 term 2 term 3 term 4
topic time topic time topic time topic time
Whole numbers 6 hours
Algebraic expressions
9 hours Common fractions 7
hoursFunctions and relationships
6 hours
Integers 9 hours
Algebraic equations
3 hours Decimal fractions 6
hoursAlgebraic equations
3 hours
Exponents 9 hours
Construction of Geometric figures
8 hours
Theorem of Pythagoras
5 hours Graphs 9
hours
Numeric and geometric patterns
4,5 hours
Geometry of 2D shapes
8 hours
Area and perimeter of 2D shapes
5 hours Transformation
geometry6
hours
Functions and relationships
3 hours
Geometry of straight lines
9 hours
Surface area and volume of 3D objects
5 hours Geometry of 3D
objects7
hours
Algebraic expressions
4,5 hours
Collect, organize and summarize data
4 hours Probability
4,5 hours
Algebraic equations
3 hours Represent data 3
hours
Interpret, analyse and report data
3,5 hours
revision/assessment
6 hours
revision/assessment
8 hours
revision/assessment
6,5 hours
revision/assessment
9,5 hours
total: 45 hours total: 45 hours total: 45 hours total: 45 hours
MATHEMATICS GRADES 7-9
75CAPS
3.3.2Clarifi
catio
nofcon
tentfo
rGrade8
Gr
ad
e 8
– te
rm
1
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.1
Who
le
num
bers
men
tal c
alcu
latio
ns
Rev
ise:
• m
ultip
licat
ion
of w
hole
num
bers
to a
t le
ast 1
2 x
12
ord
erin
g an
d co
mpa
ring
who
le
num
bers
Rev
ise
Prim
e nu
mbe
rs to
at l
east
100
Prop
ertie
s of
who
le n
umbe
rs
• R
evis
e:
-Th
e co
mm
utat
ive;
ass
ocia
tive;
di
strib
utiv
e pr
oper
ties
of w
hole
nu
mbe
rs
-0
in te
rms
of it
s ad
ditiv
e pr
oper
ty
(iden
tity
elem
ent f
or a
dditi
on)
-1
in te
rms
of it
s m
ultip
licat
ive
prop
erty
(ide
ntify
ele
men
t for
m
ultip
licat
ion)
-R
ecog
nise
the
divi
sion
pro
perty
of
0, w
here
by a
ny n
umbe
r div
ided
by
0 is
und
efine
d
Wha
t is
diffe
rent
to G
rade
7?
In G
rade
8 le
arne
rs c
onso
lidat
e nu
mbe
r kno
wle
dge
and
calc
ulat
ion
tech
niqu
es fo
r w
hole
num
bers
, dev
elop
ed in
the
Inte
rmed
iate
Pha
se a
nd G
rade
7
Prop
ertie
s of
who
le n
umbe
rs
• R
evis
ing
the
prop
ertie
s of
who
le n
umbe
rs s
houl
d be
the
star
ting
poin
t for
wor
k w
ith w
hole
num
bers
. The
pro
perti
es o
f num
bers
sho
uld
prov
ide
the
mot
ivat
ion
for
why
and
how
ope
ratio
ns w
ith n
umbe
rs w
ork.
• W
hen
lear
ners
are
intro
duce
d to
new
num
bers
, suc
h as
inte
gers
for e
xam
ple,
th
ey c
an a
gain
exp
lore
how
the
prop
ertie
s of
num
bers
wor
k fo
r the
new
set
of
num
bers
.
• Le
arne
rs a
lso
have
to a
pply
the
prop
ertie
s of
num
bers
in a
lgeb
ra, w
hen
they
w
ork
with
var
iabl
es in
pla
ce o
f num
bers
.
• Le
arne
rs s
houl
d kn
ow a
nd b
e ab
le to
use
the
follo
win
g pr
oper
ties:
-Th
e co
mm
utat
ive
prop
erty
of a
dditi
on a
nd m
ultip
licat
ion:
♦a
+ b
= b
+ a
♦a
x b
= b
x a
-Th
e as
soci
ativ
e (g
roup
ing)
pro
perty
of a
dditi
on a
nd m
ultip
licat
ion:
♦(a
+ b
) + c
= a
+ (b
+ c
)
♦(a
x b
) x c
= a
x (b
x c
)
-Th
e di
strib
utiv
e pr
oper
ty o
f mul
tiplic
atio
n ov
er a
dditi
on a
nd s
ubtra
ctio
n:
♦a(
b +
c) =
(a x
b) +
(a x
c)
♦a(
b –
c) =
(a x
b) –
(a x
c)
-A
dditi
on a
nd s
ubtra
ctio
n as
inve
rse
oper
atio
ns
-m
ultip
licat
ion
and
divi
sion
as
inve
rse
oper
atio
ns
-0
is th
e id
entit
y el
emen
t for
add
ition
: t +
0 =
t
-1
is th
e id
entit
y el
emen
t for
mul
tiplic
atio
n: t
x 1
= t
6 ho
urs
MATHEMATICS GRADES 7-9
76 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.1
Who
le
num
bers
Cal
cula
tions
usi
ng w
hole
num
bers
Rev
ise:
• C
alcu
latio
ns u
sing
all
four
ope
ratio
ns
on w
hole
num
bers
, est
imat
ing
and
usin
g ca
lcul
ator
s w
here
app
ropr
iate
Cal
cula
tion
tech
niqu
es
• U
se a
rang
e of
stra
tegi
es to
per
form
an
d ch
eck
writ
ten
and
men
tal
calc
ulat
ions
with
who
le n
umbe
rs
incl
udin
g:
-es
timat
ion
-ad
ding
, sub
tract
ing
and
mul
tiply
ing
in c
olum
ns
-lo
ng d
ivis
ion
-ro
undi
ng o
ff an
d co
mpe
nsat
ing
-us
ing
a ca
lcul
ator
mul
tiple
s an
d fa
ctor
s
Rev
ise:
-P
rime
fact
ors
of n
umbe
rs to
at l
east
3-
digi
t who
le n
umbe
rs
-LC
m a
nd H
CF
of n
umbe
rs to
at
leas
t 3-d
igit
who
le n
umbe
rs, b
y in
spec
tion
or fa
ctor
isat
ion
illus
trat
ing
the
prop
ertie
s w
ith w
hole
num
bers
a)
33 +
99
= 99
+ 3
3 =
132
b)
51 +
(19
+ 46
) = (5
1 +
19) +
46
= 11
6
c)
4(12
+ 9
) = (4
x 1
2) +
(4 x
9) =
48
+ 36
= 8
4
d)
(9 x
64)
+ (9
x 3
6) =
9(6
4 +
36) =
9 x
100
= 9
00
e)
if 33
+ 9
9 =
132,
then
132
– 9
9 =
33 a
d 13
2 –
33 =
99
f) if
20 x
5 =
110
, the
n 11
0 ÷
20 =
5 a
nd 1
10 ÷
5 =
20
Cal
cula
tions
with
who
le n
umbe
rs
• Le
arne
rs s
houl
d co
ntin
ue to
do
cont
ext f
ree
calc
ulat
ions
and
sol
ve p
robl
ems
in
cont
exts
usi
ng w
hole
num
bers
, int
eger
s an
d fra
ctio
ns
• Le
arne
rs s
houl
d be
com
e m
ore
confi
dent
in a
nd m
ore
inde
pend
ent a
t m
athe
mat
ics,
if th
ey h
ave
tech
niqu
es
-to
che
ck th
eir s
olut
ions
them
selv
es, e
.g. u
sing
inve
rse
oper
atio
ns; u
sing
ca
lcul
ator
s
-to
judg
e th
e re
ason
able
ness
of t
heir
solu
tions
e.g
. est
imat
e by
roun
ding
off;
es
timat
e by
dou
blin
g or
hal
ving
;
• A
ddin
g, s
ubtra
ctin
g an
d m
ultip
lyin
g in
col
umns
, and
long
div
isio
n, s
houl
d on
ly b
e us
ed to
pra
ctic
e nu
mbe
r fac
ts a
nd c
alcu
latio
n te
chni
ques
, and
hen
ce s
houl
d be
do
ne w
ith fa
mili
ar a
nd s
mal
ler n
umbe
r ran
ges.
For
big
and
unw
ield
y ca
lcul
atio
ns,
lear
ners
sho
uld
be e
ncou
rage
d to
use
a c
alcu
lato
r.
mul
tiple
s an
d fa
ctor
s
• Le
arne
rs s
houl
d co
ntin
ue p
ract
isin
g fin
ding
mul
tiple
s an
d fa
ctor
s of
who
le
num
bers
. Thi
s is
esp
ecia
lly im
porta
nt w
hen
lear
ners
do
calc
ulat
ions
with
fra
ctio
ns. T
hey
use
this
kno
wle
dge
to fi
nd th
e LC
M fo
r den
omin
ator
s th
at a
re
diffe
rent
from
eac
h ot
her,
and
also
whe
n th
ey s
impl
ify fr
actio
ns o
r hav
e to
find
eq
uiva
lent
frac
tions
.
• Fa
ctor
isin
g w
hole
num
bers
lays
the
foun
datio
n fo
r fac
toris
atio
n of
alg
ebra
ic
expr
essi
ons.
• U
sing
the
defin
ition
of p
rime
num
bers
, em
phas
ise
that
1 is
not
cla
ssifi
ed a
s a
prim
e nu
mbe
r
MATHEMATICS GRADES 7-9
77CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, o
pera
tions
and
r
elat
ions
hips
1.1
Who
le
num
bers
solv
ing
prob
lem
s•
Sol
ve p
robl
ems
invo
lvin
g w
hole
nu
mbe
rs, i
nclu
ding
:
-C
ompa
ring
two
or m
ore
quan
titie
s of
the
sam
e ki
nd (r
atio
)
-C
ompa
ring
two
quan
titie
s of
di
ffere
nt k
inds
(rat
e)
-S
harin
g in
a g
iven
ratio
whe
re th
e w
hole
is g
iven
-In
crea
sing
or d
ecre
asin
g of
a
num
ber i
n a
give
n ra
tio
• S
olve
pro
blem
s th
at in
volv
e w
hole
nu
mbe
rs, p
erce
ntag
es a
nd d
ecim
al
fract
ions
in fi
nanc
ial c
onte
xts
such
as:
-P
rofit
, los
s, d
isco
unt a
nd V
AT
-B
udge
ts
-A
ccou
nts
-Lo
ans
-S
impl
e in
tere
st
-H
ire P
urch
ase
-E
xcha
nge
rate
s
exam
ples
a)
LCM
of 6
and
18
is 1
8LC
M o
f 6 a
nd 7
is 4
2b)
Th
e fa
ctor
s of
24
are
1, 2
, 3, 4
, 6,1
2 an
d 24
by
insp
ectio
n.A
nd, t
he p
rime
fact
ors
of 2
4 ar
e 2
and
3c)
Th
e fa
ctor
s of
140
are
1, 2
, 5, 7
, 10,
14,
28,
35,
70
and
140
d)
Det
erm
ine
the
HC
F of
120
; 300
and
900
. Le
arne
rs d
o th
is b
y fin
ding
the
prim
e fa
ctor
s of
the
num
bers
firs
t.12
0 =
5 x
3 x
23 Ini
tially
lear
ners
may
writ
e th
is a
s: 5
x 3
x 2
x 2
x 2
300
= 52 x
3 x
22
900
= 52 x
32 x
23
HC
F =
5 x
3 x
22 = 6
0 (M
ultip
ly th
e co
mm
on p
rime
fact
ors
of th
e th
ree
num
bers
)so
lvin
g pr
oble
ms
• S
olvi
ng p
robl
ems
in c
onte
xts
shou
ld ta
ke a
ccou
nt o
f the
num
ber r
ange
s le
arne
rs
are
fam
iliar
with
.
• C
onte
xts
invo
lvin
g ra
tio a
nd ra
te s
houl
d in
clud
e sp
eed,
dis
tanc
e an
d tim
e pr
oble
ms.
• In
fina
ncia
l con
text
s, le
arne
rs a
re n
ot e
xpec
ted
to u
se fo
rmul
ae fo
r cal
cula
ting
sim
ple
inte
rest
.
MATHEMATICS GRADES 7-9
78 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
1.3
inte
gers
Cou
ntin
g, o
rder
ing
and
com
parin
g in
tege
rs
• R
evis
e:
-co
untin
g fo
rwar
ds a
nd b
ackw
ards
in
inte
gers
for a
ny in
terv
al
-re
cogn
isin
g, o
rder
ing
and
com
parin
g in
tege
rs
Cal
cula
tions
with
inte
gers
• R
evis
e ad
ditio
n an
d su
btra
ctio
n w
ith
inte
gers
• m
ultip
ly a
nd d
ivid
e w
ith in
tege
rs
• P
erfo
rm c
alcu
latio
ns in
volv
ing
all f
our
oper
atio
ns w
ith in
tege
rs
• P
erfo
rm c
alcu
latio
ns in
volv
ing
all f
our
oper
atio
ns w
ith n
umbe
rs th
at in
volv
e th
e sq
uare
s, c
ubes
, squ
are
root
s an
d cu
be ro
ots
of in
tege
rs
Wha
t is
diffe
rent
to G
rade
7?
• m
ultip
ly a
nd d
ivid
e w
ith in
tege
rs
• A
ll fo
ur o
pera
tions
with
inte
gers
• A
ll fo
ur o
pera
tions
with
squ
ares
, cub
es, s
quar
e an
d cu
be ro
ots
of in
tege
rs
In G
rade
8 le
arne
rs c
onso
lidat
e nu
mbe
r kno
wle
dge
and
calc
ulat
ion
tech
niqu
es fo
r in
tege
rs, d
evel
oped
in G
rade
7.
Cou
ntin
g, o
rder
ing
and
com
parin
g in
tege
rs
• Le
arne
rs s
houl
d co
ntin
ue p
ract
isin
g co
untin
g, o
rder
ing
and
com
parin
g in
tege
rs.
Cou
ntin
g sh
ould
not
onl
y be
thou
ght o
f as
verb
al c
ount
ing.
Lea
rner
s ca
n co
unt
usin
g:
-st
ruct
ured
, sem
i-stru
ctur
ed o
r em
pty
num
ber l
ines
-ch
ain
diag
ram
s fo
r cou
ntin
g
• Le
arne
rs s
houl
d be
giv
en a
rang
e of
exe
rcis
es
• A
rran
ge g
iven
num
bers
from
the
smal
lest
to th
e bi
gges
t: or
big
gest
to s
mal
lest
• Fi
ll in
mis
sing
num
bers
in
-a
sequ
ence
-on
a n
umbe
r grid
-on
a n
umbe
r lin
e
-fil
l in
<, =
or >
e.g
. – 4
25 *
– 4
50;
Cal
cula
tions
usi
ng in
tege
rs
• S
tart
calc
ulat
ions
with
inte
gers
usi
ng s
mal
l num
ber r
ange
s.
• D
evel
op a
n un
ders
tand
ing
that
sub
tract
ing
an in
tege
r is
the
sam
e as
add
ing
its
addi
tive
inve
rse.
exam
ple:
7 –
4 =
7 +
(– 4
) = 3
OR
–7
– 4
= –7
+ (–
4) =
–11
So
too,
7 –
(– 4
) = 7
+ (+
4) =
11
OR
–7
– (–
4) =
–7
+ (+
4) =
– 3
. Her
e th
e us
e of
br
acke
ts a
roun
d th
e in
tege
rs a
re u
sefu
l.
• A
usef
ul s
trate
gy is
to u
se re
peat
ed a
dditi
on a
nd n
umbe
r pat
tern
s to
sho
w
lear
ners
the
reas
onab
lene
ss o
f rul
es fo
r the
resu
ltant
sig
n fo
r mul
tiplic
atio
n w
ith
inte
gers
.
Tota
l tim
e fo
r In
tege
rs:
9 ho
urs
MATHEMATICS GRADES 7-9
79CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
1.3
inte
gers
exam
ple:
a)
Rep
eate
d ad
ditio
n of
(–3)
: (–3
) + (–
3) +
(–3)
= –
9 =
3 x
(–3)
b)
Rep
eate
d ad
ditio
n of
(–2)
: (–2
) + (–
2) +
(–2)
+ (–
2) =
–8
= 4
x (–
2)
c)
Cou
ntin
g do
wn
in in
terv
als
of 3
from
9:
3 x
3 =
9
3 x
2 =
6
3 x
1 =
3
3 x
0 =
0
3 x
–1 =
–3
3 x
–2 =
?
3 x
–3 =
?
Hen
ce th
e ru
le: a
pos
itive
inte
ger x
a n
egat
ive
inte
ger =
a n
egat
ive
inte
ger
d)
Usi
ng th
e ru
le th
at a
pos
itive
inte
ger x
a n
egat
ive
inte
ger =
a n
egat
ive
inte
ger,
esta
blis
hed
from
exa
mpl
es a
bove
, the
follo
win
g pa
ttern
can
be
used
:
–1 x
3 =
–3
–1 x
2 =
–2
–1 x
1 =
–1
–1 x
0 =
0
–1 x
–1
= 1
–1 x
–2
= ?
–1 x
–3
= ?
Hen
ce th
e ru
le: a
neg
ativ
e in
tege
r x a
neg
ativ
e in
tege
r = a
pos
itive
inte
ger
• U
se th
e in
vers
e op
erat
ion
for m
ultip
licat
ion
and
divi
sion
to d
evel
op a
rule
for t
he
resu
ltant
sig
n fo
r div
isio
n w
ith in
tege
rs.
exam
ple:
a)
If 4
x (–
2) =
–8,
then
–8
÷ 4
= –2
and
–8
÷ (–
2) =
4
b)
If (–
1) x
(–3)
= 3
, the
n 3
÷ (–
1) =
–3
and
3 ÷
(–3)
= –
1
Hen
ce th
e ru
les:
div
isio
n of
a p
ositi
ve a
nd n
egat
ive
inte
ger e
qual
s a
nega
tive
inte
ger a
nd d
ivis
ion
of tw
o ne
gativ
e in
tege
rs e
qual
a p
ositi
ve in
tege
r.
MATHEMATICS GRADES 7-9
80 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
1.3
inte
gers
Prop
ertie
s of
inte
gers
• R
ecog
nize
and
use
com
mut
ativ
e,
asso
ciat
ive
and
dist
ribut
ive
prop
ertie
s of
add
ition
and
mul
tiplic
atio
n fo
r in
tege
rs
• R
ecog
nize
and
use
add
itive
and
m
ultip
licat
ive
inve
rses
for i
nteg
ers
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
mul
tiple
ope
ratio
ns w
ith in
tege
rs
• Fi
ndin
g th
e sq
uare
s, c
ubes
, squ
are
root
s an
d cu
be ro
ots
of in
tege
rs a
re a
lso
oppo
rtuni
ties
to c
heck
that
lear
ners
kno
w th
e ru
les
for r
esul
tant
sig
ns w
hen
mul
tiply
ing
inte
gers
.
• Th
eref
ore,
mak
e su
re th
at le
arne
rs u
nder
stan
d w
hy y
ou c
anno
t find
the
squa
re
root
of a
neg
ativ
e in
tege
r, an
d th
at th
e sq
uare
of a
neg
ativ
e in
tege
r is
alw
ays
posi
tive.
exam
ple:
a)
(–5)
2 = (–
5) x
(–5)
= 2
5
b)
(–4)
3 = (–
4) x
(–4)
x (–
4) =
–64
c)
3–2
7√
= –
3 be
caus
e –3
x –
3 x–
3 =
–27
Prop
ertie
s of
inte
gers
• Le
arne
rs s
houl
d in
vest
igat
e th
e pr
oper
ties
for o
pera
tions
with
who
le n
umbe
rs o
n th
e se
t of i
nteg
ers.
• Th
ese
prop
ertie
s sh
ould
ser
ve a
s m
otiv
atio
n fo
r the
ope
ratio
ns th
ey c
an p
erfo
rm
with
inte
gers
.
• Le
arne
rs s
houl
d se
e th
at th
e co
mm
utat
ive
prop
erty
for a
dditi
on a
nd m
ultip
licat
ion
hold
s fo
r int
eger
s, e
.g.
8 +
(–3)
= (–
3) +
8 =
5;
8 x
(–3)
= (–
3) x
8 =
–24
• Le
arne
rs s
houl
d se
e th
at th
ey c
an s
till u
se s
ubtra
ctio
n to
che
ck a
dditi
on o
r vic
e ve
rsa,
e.g
. if 8
+ (–
3) =
5, t
hen
5 –
8 =
–3 a
nd 5
–(–
3) =
8
• Le
arne
rs s
houl
d se
e th
at th
e as
soci
ativ
e pr
oper
ty fo
r add
ition
hol
ds fo
r int
eger
s,
e.g.
[(–6
) + 4
] + (–
1) =
(–6)
+ [4
+ (–
1)] =
–3
• Le
arne
rs s
houl
d se
e th
at th
e in
vers
e op
erat
ion
for m
ultip
licat
ion
and
divi
sion
ho
lds
for i
nteg
ers,
e.g
. if 5
x (–
6) =
–30
, the
n –3
0 ÷
5 =
–6 a
nd –
30 ÷
(–6)
= 5
• Le
arne
rs s
houl
d de
velo
p th
e ru
les,
thro
ugh
patte
rnin
g, fo
r res
ulta
nt s
igns
whe
n m
ultip
lyin
g an
d di
vidi
ng in
tege
rs:
(+5)
x (+
5) =
(+25
);
(–5)
x (–
5) =
(+25
);
(–5)
x (+
5) =
(–25
);
(+25
) ÷ (+
5) =
(+5)
;
(–25
) ÷ (–
5) =
(+5)
;
(–25
) ÷ (+
5) =
(–5)
;
MATHEMATICS GRADES 7-9
81CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
1.2
expo
nent
sm
enta
l cal
cula
tions
• R
evis
e:
-S
quar
es to
at l
east
122 a
nd th
eir
squa
re ro
ots
-C
ubes
to a
t lea
st 6
3 and
thei
r cub
e ro
ots
Com
parin
g an
d re
pres
entin
g nu
mbe
rs in
exp
onen
tial f
orm
• R
evis
e co
mpa
re a
nd re
pres
ent w
hole
nu
mbe
rs in
exp
onen
tial f
orm
• C
ompa
re a
nd re
pres
ent i
nteg
ers
in
expo
nent
ial f
orm
• C
ompa
re a
nd re
pres
ent n
umbe
rs in
sc
ient
ific
nota
tion,
lim
ited
to p
ositi
ve
expo
nent
s
Wha
t is
diffe
rent
to G
rade
7?
• In
tege
rs a
nd ra
tiona
l num
bers
in e
xpon
entia
l for
m
• S
cien
tific
nota
tion
of n
umbe
rs
Com
parin
g an
d re
pres
entin
g nu
mbe
rs in
exp
onen
tial f
orm
• Le
arne
rs n
eed
to u
nder
stan
d th
at in
the
expo
nent
ial f
orm
ab ,
the
num
ber i
s re
ad
as ‘a
to th
e po
wer
of b
, whe
re a
is c
alle
d th
e ba
se a
nd b
is c
alle
d th
e ex
pone
nt o
r in
dex
and
b in
dica
tes
the
num
ber o
f fac
tors
that
are
mul
tiplie
d.
exam
ple:
a3 =
a x
a x
a;
a5 =
a x
a x
a x
a x
a
Lear
ners
can
repr
esen
t any
num
ber i
n ex
pone
ntia
l for
m, w
ithou
t nee
ding
to
com
pute
the
valu
e. e
xam
ple:
50
x 50
x 5
0 x
50 x
50
x 50
x 5
0 =
507
• m
ake
sure
lear
ners
und
erst
and
that
squ
are
root
s an
d cu
be ro
ots
are
the
inve
rse
oper
atio
ns o
f squ
arin
g an
d cu
bing
num
bers
. exa
mpl
e: 3
2 =
9 th
eref
ore
√9 =
3
• M
ake
sure
lear
ners
und
erst
and
that
any
num
ber r
aise
d to
the
pow
er 1
is e
qual
to
that
par
ticul
ar n
umbe
r
exam
ple:
m1 =
m
• U
sing
pat
tern
s an
d th
eir k
now
ledg
e of
mul
tiplic
atio
n w
ith in
tege
rs, l
earn
ers
shou
ld a
ntic
ipat
e th
e re
sulta
nt s
ign
of a
n in
tege
r rai
sed
to a
n od
d or
eve
n po
wer
e.
g. (–
15)4 w
ill b
e po
sitiv
e, w
hile
(–15
)3 will
be
nega
tive
• To
avo
id c
omm
on m
isco
ncep
tions
, em
phas
ize
the
follo
win
g
-12
2 = 1
2 x
12 a
nd n
ot 1
2 x
2
-13 m
eans
1 x
1 x
1 a
nd n
ot 1
x 3
-10
01 =
100
-81
√ =
9 b
ecau
se 9
2 =
81
-3
27√
= 3
bec
ause
33 =
27
-th
e sq
uare
of 9
= 8
1, w
here
as th
e sq
uare
root
of 9
= 3
• Le
arne
rs s
houl
d us
e th
eir k
now
ledg
e of
repr
esen
ting
num
bers
in e
xpon
entia
l fo
rm w
hen
sim
plify
ing
and
expa
ndin
g al
gebr
aic
expr
essi
ons
and
solv
ing
alge
brai
c eq
uatio
ns.
Tota
l tim
e fo
r ex
pone
nts:
9 ho
urs
MATHEMATICS GRADES 7-9
82 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
1.2
expo
nent
sC
alcu
latio
ns u
sing
num
bers
in
expo
nent
ial f
orm
• E
stab
lish
gene
ral l
aws
of e
xpon
ents
, lim
ited
to:
-na
tura
l num
ber e
xpon
ents
♦am
x a
n = a
m+n
♦am
÷ a
n = a
m–n
, if m
> n
♦(a
m)n =
am
x n
♦(a
x t)
n = a
n x
tn
♦a0 =
1
• R
ecog
nize
and
use
the
appr
opria
te
law
s of
ope
ratio
ns u
sing
num
bers
in
volv
ing
expo
nent
s an
d sq
uare
and
cu
be ro
ots
• P
erfo
rm c
alcu
latio
ns in
volv
ing
all f
our
oper
atio
ns w
ith n
umbe
rs th
at in
volv
e sq
uare
s, c
ubes
, squ
are
root
s an
d cu
be ro
ots
of in
tege
rs
• C
alcu
late
the
squa
res,
cub
es, s
quar
e ro
ots
and
cube
root
s of
ratio
nal
num
bers
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
num
bers
in e
xpon
entia
l for
m
law
s of
exp
onen
ts
• Th
e la
ws
of e
xpon
ents
sho
uld
be in
trodu
ced
thro
ugh
a ra
nge
of n
umer
ic
exam
ples
firs
t, th
en v
aria
bles
can
be
used
. In
othe
r wor
ds, t
he n
umbe
rs a
re
repl
aced
with
lette
rs, b
ut th
e ru
les
wor
k th
e sa
me.
• Th
e fo
llow
ing
law
s of
exp
onen
ts s
houl
d be
intro
duce
d, w
here
m a
nd n
are
nat
ural
nu
mbe
rs a
nd a
and
t ar
e no
t equ
al to
0:
am x
an =
am
+n
exam
ple
a)
23 x 2
4 = 2
3+4 =
27
b)
x3 x x
4 = x
3+4 =
x7
am ÷
an =
am
–n if
m >
n
exam
ple:
a)
35 ÷ 3
2 = 3
3 = 2
7
b)
x5 ÷ x
3 = x
2
(am)n =
am
n
exam
ple:
a)
(23 )2 =
26 =
64
b)
(x3 )2 =
x6
(a x
t)n =
an x
tn
exam
ple:
(3x2 )3 =
33 . x
6 = 2
7x6
a0 = 1
exam
ples
: (37
)0 = 1
; (4x
2 )0 = 1
;
• m
ake
sure
lear
ners
und
erst
and
thes
e la
ws
read
ing
from
bot
h si
des
of th
e eq
ual
sign
i.e.
if th
e LH
S =
RH
S, t
hen
the
RH
S =
LH
S.
• Th
e la
w a
0 = 1
can
be
deriv
ed b
y us
ing
the
law
of e
xpon
ents
for d
ivis
ion
in a
few
ex
ampl
es. a
4 ÷
a4 =
a x
a x
a x
a a
x a
x a
x a =
1 th
eref
ore
a4–4 = a0 =
1
• Le
arne
rs s
houl
d be
abl
e to
use
the
law
s of
exp
onen
ts in
cal
cula
tions
and
fo
r sol
ving
sim
ple
expo
nent
ial e
quat
ions
as
wel
l as
expa
ndin
g or
sim
plify
ing
alge
brai
c ex
pres
sion
s.
MATHEMATICS GRADES 7-9
83CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
1.2
expo
nent
s•
Look
out
for t
he fo
llow
ing
com
mon
mis
conc
eptio
ns w
here
:
-le
arne
rs m
ultip
ly u
nlik
e ba
ses
and
add
the
expo
nent
.
exam
ple:
xm x
yn =
(xy)
m+n
-le
arne
rs m
ultip
ly li
ke b
ases
and
add
the
expo
nent
s
exam
ple:
25 x 2
7 = 4
12 in
stea
d of
the
corr
ect a
nsw
er 2
12.
-le
arne
rs f
orge
t, fo
r ex
ampl
e, t
hat
whe
n sq
uarin
g a
bino
mia
l the
re is
a m
iddl
e te
rm
exam
ple:
(x +
y)m
= x
m +
ym
-le
arne
rs c
onfu
se a
ddin
g th
e ex
pone
nts
and
addi
ng th
e te
rms
exam
ple:
xm +
xn =
xm
+n o
r xm
n
Cal
cula
tions
usi
ng n
umbe
rs in
exp
onen
tial f
orm
• K
now
ing
the
rule
s of
ope
ratio
ns fo
r cal
cula
tions
invo
lvin
g ex
pone
nts
are
impo
rtant
, e.g
.
a)
(7 –
4)3
= 33 a
nd n
ot
73 –
43
b)
16 +
9
√ =
25
√ a
nd n
ot
the
16√
+
9√
• Le
arne
rs c
an a
lso
do s
impl
e ca
lcul
atio
ns w
here
the
num
erat
or a
nd d
enom
inat
or
of a
frac
tion
are
writ
ten
in e
xpon
entia
l for
m, e
.g. 23 22
= 2
x 2
x 2
2 x
2 =
8 4 =
2
• Le
arne
rs c
an a
lso
find
squa
res,
cub
es, s
quar
e ro
ots
and
cube
root
s of
dec
imal
an
d co
mm
on fr
actio
ns b
y in
spec
tion.
exam
ples
a)
(0,7
)2 = 0
,49
b)
(0,1
)3 = 0
,001
c)
0,09
√
= 0
,3
d)
(3 4)2 =
32 42 =
9 16
e) √
9 25 =
9
√ 25√
= 3 5
MATHEMATICS GRADES 7-9
84 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
1.2
expo
nent
sSc
ientificno
tatio
n
• W
hen
writ
ing
num
bers
in s
cien
tific
nota
tion,
lear
ners
hav
e to
und
erst
and
the
rela
tions
hip
betw
een
the
num
ber o
f dec
imal
pla
ces
and
the
inde
x of
10
exam
ples
:
a)
25 =
2,5
x 1
01
b)
250
= 2,
5 x
102
c)
2 50
0 =
2,5
x 10
3
• S
cien
tific
nota
tion
limite
d to
pos
itive
exp
onen
ts, i
nclu
des
writ
ing
very
larg
e nu
mbe
rs in
sci
entifi
c no
tatio
n.
exam
ple:
25
mill
ion
= 2,
5 x
107
• Le
arne
rs p
ract
ise
writ
ing
larg
e nu
mbe
rs in
sci
entifi
c no
tatio
n, th
ey w
ill re
aliz
e th
ey h
ave
enco
unte
red
thes
e in
Nat
ural
Sci
ence
. It i
s us
eful
to re
fer t
o th
ese
cont
exts
whe
n ta
lkin
g ab
out s
cien
tific
nota
tion.
MATHEMATICS GRADES 7-9
85CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.1
num
eric
and
ge
omet
ric
patte
rns
inve
stig
ate
and
exte
nd p
atte
rns
• In
vest
igat
e an
d ex
tend
num
eric
an
d ge
omet
ric p
atte
rns
look
ing
for
rela
tions
hips
bet
wee
n nu
mbe
rs,
incl
udin
g pa
ttern
s:
-re
pres
ente
d in
phy
sica
l or
diag
ram
fo
rm
-no
t lim
ited
to s
eque
nces
invo
lvin
g a
cons
tant
diff
eren
ce o
r rat
io
-of
lear
ner’s
ow
n cr
eatio
n
-re
pres
ente
d in
tabl
es
-re
pres
ente
d al
gebr
aica
lly
• D
escr
ibe
and
just
ify th
e ge
nera
l rul
es
for o
bser
ved
rela
tions
hips
bet
wee
n nu
mbe
rs in
ow
n w
ords
or i
n al
gebr
aic
lang
uage
Wha
t is
diffe
rent
to G
rade
7?
• Th
e ra
nge
of n
umbe
r pat
tern
s ar
e ex
tend
ed to
incl
ude
patte
rns
with
mul
tiplic
atio
n an
d di
visi
on w
ith in
tege
rs, n
umbe
rs in
exp
onen
tial f
orm
• A
s le
arne
rs b
ecom
e us
ed to
des
crib
ing
patte
rns
in th
eir o
wn
wor
ds, t
heir
desc
riptio
ns s
houl
d be
com
e m
ore
prec
ise
and
effic
ient
with
the
use
of a
lgeb
raic
la
ngua
ge to
des
crib
e ge
nera
l rul
es o
f pat
tern
s
• It
is u
sefu
l als
o to
intro
duce
the
lang
uage
of ‘
term
in a
seq
uenc
e’ in
ord
er to
di
stin
guis
h th
e te
rm fr
om th
e po
sitio
n of
a te
rm in
a s
eque
nce
• In
vest
igat
ing
num
ber p
atte
rns
is a
n op
portu
nity
to g
ener
aliz
e –
to g
ive
gene
ral
alge
brai
c de
scrip
tions
of t
he re
latio
nshi
p be
twee
n te
rms
and
thei
r pos
ition
in a
se
quen
ce a
nd to
just
ify s
olut
ions
.
Kin
ds o
f num
eric
pat
tern
s
• G
iven
a s
eque
nce
of n
umbe
rs, l
earn
ers
have
to id
entif
y a
patte
rn o
r rel
atio
nshi
p be
twee
n co
nsec
utiv
e te
rms
in o
rder
to e
xten
d th
e pa
ttern
.
exam
ples
Pro
vide
a ru
le to
des
crib
e th
e re
latio
nshi
p be
twee
n th
e nu
mbe
rs in
the
sequ
ence
s be
low
. Use
this
rule
to p
rovi
de th
e ne
xt th
ree
num
bers
in th
e se
quen
ce:
a)
–3; –
7; –
11; –
15; .
.. ...
Her
e le
arne
rs s
houl
d id
entif
y th
e co
nsta
nt d
iffer
ence
bet
wee
n co
nsec
utiv
e te
rms
in o
rder
to e
xten
d th
e pa
ttern
. Thi
s pa
ttern
can
be
desc
ribed
in le
arne
rs’
own
wor
ds a
s ‘a
ddin
g –4
’ or ‘
coun
ting
in –
4s’ o
r ‘ad
d –4
to th
e pr
evio
us
num
ber i
n th
e pa
ttern
’.
b)
2; –
4; 8
; –16
; 32
... ..
.
Her
e le
arne
rs s
houl
d id
entif
y th
e co
nsta
nt ra
tio b
etw
een
cons
ecut
ive
term
s.
This
pat
tern
can
be
desc
ribed
in le
arne
rs’ o
wn
wor
ds a
s ‘m
ultip
ly th
e pr
evio
us
num
ber b
y –2
’.
c)
1; 2
; 4; 7
; 11;
16
... ..
.
This
pat
tern
has
nei
ther
a c
onst
ant d
iffer
ence
nor
con
stan
t rat
io. T
his
patte
rn
can
be d
escr
ibed
in le
arne
rs’ o
wn
wor
ds a
s ‘in
crea
se th
e di
ffere
nce
betw
een
cons
ecut
ive
term
s by
1 e
ach
time’
or ‘
add
1 m
ore
than
was
add
ed to
get
the
prev
ious
term
’. U
sing
this
rule
, the
nex
t 3 te
rms
will
be
22; 2
9; 3
7.
• G
iven
a s
eque
nce
of n
umbe
rs, l
earn
ers
have
to id
entif
y a
patte
rn o
r rel
atio
nshi
p be
twee
n th
e te
rm a
nd it
s po
sitio
n in
the
sequ
ence
. Thi
s en
able
s le
arne
rs to
pr
edic
t a te
rm in
a s
eque
nce
base
d on
the
posi
tion
of th
at te
rm in
the
sequ
ence
. It
is u
sefu
l for
lear
ners
to re
pres
ent t
hese
seq
uenc
es in
tabl
es s
o th
at th
ey c
an
cons
ider
the
posi
tion
of th
e te
rm.
Tota
l tim
e fo
r N
umer
ic a
nd
geom
etric
pa
ttern
s:
4,5
hour
s
MATHEMATICS GRADES 7-9
86 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.1
num
eric
and
ge
omet
ric
patte
rns
exam
ples
a)
Pro
vide
a ru
le to
des
crib
e th
e re
latio
nshi
p be
twee
n th
e nu
mbe
rs in
this
se
quen
ce: 1
; 8; 2
7; 6
4; ..
. .. U
se th
is ru
le to
find
the
10th
term
in th
is s
eque
nce.
Firs
tly,
lear
ners
hav
e to
und
erst
and
that
the
‘10
th t
erm
’ ref
ers
to p
ositi
on i
n th
e nu
mbe
r se
quen
ce.
They
hav
e to
find
a r
ule
in o
rder
to
dete
rmin
e th
e 10
th t
erm
, ra
ther
than
con
tinui
ng th
e se
quen
ce to
the
tent
h te
rm.
exam
ple
b)
This
seq
uenc
e ca
n be
re-p
rese
nted
in th
e fo
llow
ing
tabl
e:
Pos
ition
in s
eque
nce
12
34
10
Term
18
2764
?
Lear
ners
hav
e to
reco
gniz
e th
at e
ach
term
in th
e bo
ttom
row
is o
btai
ned
by c
ubin
g th
e po
sitio
n nu
mbe
r in
the
top
row
. Thu
s th
e 10
th te
rm w
ill b
e 10
cub
ed o
r 103 ,
whi
ch is
. Usi
ng th
e sa
me
rule
, lea
rner
s ca
n al
so b
e as
ked
wha
t ter
m n
umbe
r or
posi
tion
will
512
be?
If th
e te
rm is
obt
aine
d by
cub
ing
the
posi
tion
num
ber o
f the
te
rm, t
hen
the
posi
tion
num
ber c
an b
e ob
tain
ed b
y fin
ding
the
cube
root
of t
he
term
. Hen
ce, 5
12 w
ill b
e th
e 8th
term
in th
e se
quen
ce s
ince
351
2 √
= 8
c)
Pro
vide
a ru
le to
des
crib
e th
e re
latio
nshi
p be
twee
n th
e nu
mbe
rs in
this
se
quen
ce: 4
; 7; 1
0; 1
3; ..
. Use
this
rule
to fi
nd th
e 20
th te
rm in
this
seq
uenc
e.
If le
arne
rs c
onsi
der o
nly
the
rela
tions
hip
betw
een
cons
ecut
ive
term
s, th
en th
ey
have
to c
ontin
ue th
e pa
ttern
(‘ad
d 3
to p
revi
ous
num
ber’)
to th
e 20
th te
rm to
fin
d th
e an
swer
. How
ever
, if t
hey
look
for a
rela
tions
hip
or ru
le b
etw
een
the
term
an
d th
e po
sitio
n of
the
term
, the
y ca
n pr
edic
t the
ans
wer
with
out c
ontin
uing
the
patte
rn. U
sing
num
ber s
ente
nces
can
be
usef
ul to
find
the
rule
:
1st t
erm
: 4 =
3(1
) + 1
2nd
term
: 7 =
3(2
) + 1
3rd
term
: 10
= 3(
3) +
1
4th
term
: 13
= 3(
4) +
1
The
num
ber i
n th
e br
acke
ts c
orre
spon
ds to
the
posi
tion
of th
e te
rm. H
ence
, the
20
th te
rm w
ill b
e: 3
(20)
+ 1
= 6
1
The
rule
in le
arne
rs’ o
wn
wor
ds c
an b
e w
ritte
n as
‘3 ti
mes
the
posi
tion
of th
e te
rm
+1’ o
r 3n
+ 1
whe
re n
is th
e po
sitio
n of
the
term
.
• Th
ese
type
s of
num
eric
pat
tern
s de
velo
p an
und
erst
andi
ng o
f fun
ctio
nal
rela
tions
hips
, in
whi
ch y
ou h
ave
a de
pend
ent v
aria
ble
(pos
ition
of t
he te
rm) a
nd
inde
pend
ent v
aria
ble
(the
term
itse
lf), a
nd w
here
you
hav
e a
uniq
ue o
utpu
t for
an
y gi
ven
inpu
t val
ue.
MATHEMATICS GRADES 7-9
87CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.1
num
eric
and
ge
omet
ric
patte
rns
Kin
ds o
f geo
met
ric p
atte
rns
• G
eom
etric
pat
tern
s ar
e nu
mbe
r pat
tern
s re
pres
ente
d di
agra
mm
atic
ally.
The
di
agra
mm
atic
repr
esen
tatio
n re
veal
s th
e st
ruct
ure
of th
e nu
mbe
r pat
tern
.
• H
ence
, rep
rese
ntin
g th
e nu
mbe
r pat
tern
s in
tabl
es m
akes
it e
asie
r for
lear
ners
to
desc
ribe
the
gene
ral r
ule
for t
he p
atte
rn.
exam
ple
Con
side
r thi
s pa
ttern
for b
uild
ing
hexa
gons
with
mat
chst
icks
. How
man
y m
atch
stic
ks w
ill b
e us
ed to
bui
ld th
e 10
th h
exag
on?
The
rule
for t
he p
atte
rn is
con
tain
ed in
the
stru
ctur
e (c
onst
ruct
ion)
of t
he
succ
essi
ve h
exag
onal
sha
pes:
(1) a
dd 1
mat
chst
ick
per s
ide
(2) t
here
are
6 s
ides
(3) a
dd 6
mat
chst
icks
per
hex
agon
as
you
proc
eed
from
a g
iven
hex
agon
to th
e ne
xt o
ne.
So,
for t
he 2
nd h
exag
on, y
ou h
ave
2 x
6 m
atch
es; f
or th
e 3r
d he
xago
n yo
u ha
ve
3 x
6 m
atch
es: U
sing
this
pat
tern
for b
uild
ing
hexa
gons
, the
10t
h he
xago
n w
ill h
ave
10 x
6 m
atch
es.
Lear
ners
can
als
o us
e a
tabl
e to
reco
rd th
e nu
mbe
r of m
atch
es u
sed
for e
ach
hexa
gon.
Thi
s w
ay th
ey c
an lo
ok a
t the
num
ber p
atte
rn re
late
d to
the
num
ber o
f m
atch
es u
sed
for e
ach
new
hex
agon
.
Posi
tion
of h
exag
on in
pat
tern
12
34
56
10
num
ber o
f mat
ches
612
18
des
crib
ing
patte
rns
• It
does
not
mat
ter i
f lea
rner
s ar
e al
read
y fa
mili
ar w
ith a
par
ticul
ar p
atte
rn. T
heir
desc
riptio
ns o
f the
sam
e pa
ttern
can
be
diffe
rent
whe
n th
ey e
ncou
nter
it a
t di
ffere
nt s
tage
s of
thei
r mat
hem
atic
al d
evel
opm
ent.
MATHEMATICS GRADES 7-9
88 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.1
num
eric
and
ge
omet
ric
patte
rns
exam
ple
The
rule
for t
he s
eque
nce:
can
be
desc
ribed
in th
e fo
llow
ing
way
s:a)
ad
d 3
to th
e pr
evio
us te
rm
b)
3 x
the
posi
tion
of th
e te
rm +
1c)
3(
n) +
1, w
here
n is
the
posi
tion
of th
e te
rmd)
3(
n) +
1, w
here
n w
here
is a
nat
ural
num
ber
2.2
Func
tions
an
d re
latio
nshi
ps
inpu
t and
out
put v
alue
s•
Det
erm
ine
inpu
t val
ues,
out
put v
alue
s or
rule
s fo
r pat
tern
s an
d re
latio
nshi
ps
usin
g:
-flo
w d
iagr
ams
-ta
bles
-fo
rmul
ae -
equa
tions
equi
vale
nt fo
rms
• D
eter
min
e, in
terp
ret a
nd ju
stify
eq
uiva
lenc
e of
diff
eren
t des
crip
tions
of
the
sam
e re
latio
nshi
p or
rule
pr
esen
ted:
-ve
rbal
ly -
in fl
ow d
iagr
ams
-in
tabl
es -
by fo
rmul
ae -
by e
quat
ions
Wha
t is
diffe
rent
to G
rade
7?
• Fi
ndin
g in
put o
r out
put v
alue
s us
ing
give
n eq
uatio
ns•
The
rule
s an
d nu
mbe
r pat
tern
s fo
r whi
ch le
arne
rs h
ave
to fi
nd in
put a
nd o
utpu
t va
lues
are
ext
ende
d to
incl
ude
patte
rns
with
mul
tiplic
atio
n an
d di
visi
on o
f in
tege
rs a
nd n
umbe
rs in
exp
onen
tial f
orm
• In
this
pha
se, i
t is
usef
ul to
beg
in to
spe
cify
whe
ther
the
inpu
t val
ues
are
natu
ral
num
bers
, or i
nteg
ers
or ra
tiona
l num
bers
. Thi
s bu
ilds
lear
ners
’ aw
aren
ess
of th
e do
mai
n of
inpu
t val
ues.
Hen
ce, t
o fin
d ou
tput
val
ues,
lear
ners
sho
uld
be g
iven
th
e ru
le/fo
rmul
a as
wel
l as
the
dom
ain
of th
e in
put v
alue
s.Fu
nctio
ns a
nd re
latio
nshi
ps w
ill b
e do
ne a
gain
in t
erm
4. i
n te
rm 1
the
focu
s of
Fun
ctio
ns a
nd re
latio
nshi
ps is
on
prac
tisin
g op
erat
ions
with
inte
gers
, or
includ
ingintegersinth
erulesforfi
ndingou
tputvalues.
Not
e th
at w
hen
lear
ners
find
inpu
t or o
utpu
t val
ues
for g
iven
rule
s, th
ey a
re a
ctua
lly
findi
ng th
e nu
mer
ical
val
ue o
f alg
ebra
ic e
xpre
ssio
ns u
sing
sub
stitu
tion.
Flow
dia
gram
s ar
e re
pres
enta
tions
of f
unct
iona
l rel
atio
nshi
ps. H
ence
, whe
n us
ing
flow
dia
gram
s, th
e co
rres
pond
ence
bet
wee
n in
put a
nd o
utpu
t val
ues
shou
ld b
e cl
ear i
n its
repr
esen
tatio
nal f
orm
i.e.
the
first
inpu
t pro
duce
s th
e fir
st o
utpu
t, th
e se
cond
inpu
t pro
duce
s th
e se
cond
out
put,
etc.
exam
ples
a)
Use
the
give
n ru
le to
cal
cula
te th
e va
lues
of t
for e
ach
valu
e of
p, w
here
p is
a
natu
ral n
umbe
r.
t
p
Rule
0 -3
-5
-7
-9
t =
p x
3 +
1
In th
is k
ind
of fl
ow d
iagr
am, l
earn
ers
can
also
be
aske
d to
find
the
valu
e of
p fo
r a
give
n t v
alue
.
Tim
e fo
r Fu
nctio
ns
and
Rel
a-tio
nshi
ps in
th
is te
rm:
3 ho
urs
MATHEMATICS GRADES 7-9
89CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.1
num
eric
and
ge
omet
ric
patte
rns
exam
ple
The
rule
for t
he s
eque
nce:
can
be
desc
ribed
in th
e fo
llow
ing
way
s:a)
ad
d 3
to th
e pr
evio
us te
rm
b)
3 x
the
posi
tion
of th
e te
rm +
1c)
3(
n) +
1, w
here
n is
the
posi
tion
of th
e te
rmd)
3(
n) +
1, w
here
n w
here
is a
nat
ural
num
ber
2.2
Func
tions
an
d re
latio
nshi
ps
inpu
t and
out
put v
alue
s•
Det
erm
ine
inpu
t val
ues,
out
put v
alue
s or
rule
s fo
r pat
tern
s an
d re
latio
nshi
ps
usin
g:
-flo
w d
iagr
ams
-ta
bles
-fo
rmul
ae -
equa
tions
equi
vale
nt fo
rms
• D
eter
min
e, in
terp
ret a
nd ju
stify
eq
uiva
lenc
e of
diff
eren
t des
crip
tions
of
the
sam
e re
latio
nshi
p or
rule
pr
esen
ted:
-ve
rbal
ly -
in fl
ow d
iagr
ams
-in
tabl
es -
by fo
rmul
ae -
by e
quat
ions
Wha
t is
diffe
rent
to G
rade
7?
• Fi
ndin
g in
put o
r out
put v
alue
s us
ing
give
n eq
uatio
ns•
The
rule
s an
d nu
mbe
r pat
tern
s fo
r whi
ch le
arne
rs h
ave
to fi
nd in
put a
nd o
utpu
t va
lues
are
ext
ende
d to
incl
ude
patte
rns
with
mul
tiplic
atio
n an
d di
visi
on o
f in
tege
rs a
nd n
umbe
rs in
exp
onen
tial f
orm
• In
this
pha
se, i
t is
usef
ul to
beg
in to
spe
cify
whe
ther
the
inpu
t val
ues
are
natu
ral
num
bers
, or i
nteg
ers
or ra
tiona
l num
bers
. Thi
s bu
ilds
lear
ners
’ aw
aren
ess
of th
e do
mai
n of
inpu
t val
ues.
Hen
ce, t
o fin
d ou
tput
val
ues,
lear
ners
sho
uld
be g
iven
th
e ru
le/fo
rmul
a as
wel
l as
the
dom
ain
of th
e in
put v
alue
s.Fu
nctio
ns a
nd re
latio
nshi
ps w
ill b
e do
ne a
gain
in t
erm
4. i
n te
rm 1
the
focu
s of
Fun
ctio
ns a
nd re
latio
nshi
ps is
on
prac
tisin
g op
erat
ions
with
inte
gers
, or
includ
ingintegersinth
erulesforfi
ndingou
tputvalues.
Not
e th
at w
hen
lear
ners
find
inpu
t or o
utpu
t val
ues
for g
iven
rule
s, th
ey a
re a
ctua
lly
findi
ng th
e nu
mer
ical
val
ue o
f alg
ebra
ic e
xpre
ssio
ns u
sing
sub
stitu
tion.
Flow
dia
gram
s ar
e re
pres
enta
tions
of f
unct
iona
l rel
atio
nshi
ps. H
ence
, whe
n us
ing
flow
dia
gram
s, th
e co
rres
pond
ence
bet
wee
n in
put a
nd o
utpu
t val
ues
shou
ld b
e cl
ear i
n its
repr
esen
tatio
nal f
orm
i.e.
the
first
inpu
t pro
duce
s th
e fir
st o
utpu
t, th
e se
cond
inpu
t pro
duce
s th
e se
cond
out
put,
etc.
exam
ples
a)
Use
the
give
n ru
le to
cal
cula
te th
e va
lues
of t
for e
ach
valu
e of
p, w
here
p is
a
natu
ral n
umbe
r.
t
p
Rule
0 -3
-5
-7
-9
t =
p x
3 +
1
In th
is k
ind
of fl
ow d
iagr
am, l
earn
ers
can
also
be
aske
d to
find
the
valu
e of
p fo
r a
give
n t v
alue
.
Tim
e fo
r Fu
nctio
ns
and
Rel
a-tio
nshi
ps in
th
is te
rm:
3 ho
urs
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.2
Func
tions
an
d re
latio
nshi
ps
b)
Find
the
rule
for c
alcu
latin
g th
e ou
tput
val
ue fo
r eve
ry g
iven
inpu
t val
ue in
the
flow
dia
gram
bel
ow.
t
p
Rule
0 3 5 7 9
-3
-9
-21
-27
-15
In fl
ow d
iagr
ams
such
as
thes
e, m
ore
than
one
rule
mig
ht b
e po
ssib
le to
des
crib
e th
e re
latio
nshi
p be
twee
n in
put a
nd o
utpu
t val
ues.
The
rule
s ar
e ac
cept
able
if th
ey m
atch
th
e gi
ven
inpu
t val
ues
to th
e co
rres
pond
ing
outp
ut v
alue
s.
c)
If th
e ru
le fo
r find
ing
y in
the
tabl
e be
low
is: y
= –
3x –
1, fi
nd y
for t
he g
iven
x
valu
es:
x0
12
510
5010
0
y
b)
Des
crib
e th
e re
latio
nshi
p be
twee
n th
e nu
mbe
rs in
the
top
row
and
bot
tom
row
in
the
tabl
e. T
hen
writ
e do
wn
the
valu
e of
and
x–2
–10
12
12n
y–5
–4–3
–2–1
m34
In ta
bles
suc
h as
thes
e, m
ore
than
one
rule
mig
ht b
e po
ssib
le to
des
crib
e th
e re
latio
nshi
p be
twee
n x
and
y va
lues
. The
rule
s ar
e ac
cept
able
if th
ey m
atch
the
give
n in
put v
alue
s to
the
corr
espo
ndin
g ou
tput
val
ues.
For
exa
mpl
e, th
e ru
le
y =
x –3
des
crib
es th
e re
latio
nshi
p be
twee
n th
e x
valu
es a
nd g
iven
y v
alue
s. T
o fin
d m
and
n, l
earn
ers
have
to s
ubst
itute
the
corr
espo
ndin
g va
lues
for x
or y
in th
e ru
le
and
solv
e th
e eq
uatio
n by
insp
ectio
n.
MATHEMATICS GRADES 7-9
90 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.3
alg
ebra
icex
pres
sion
s
alg
ebra
ic la
ngua
ge
• R
evis
e th
e fo
llow
ing
done
in G
rade
7:
-re
cogn
ize
and
inte
rpre
t rul
es
or re
latio
nshi
ps re
pres
ente
d in
sy
mbo
lic fo
rm
-id
entif
y va
riabl
es a
nd c
onst
ants
in
give
n fo
rmul
ae a
nd e
quat
ions
• R
ecog
nize
and
iden
tify
conv
entio
ns
for w
ritin
g al
gebr
aic
expr
essi
ons
• Id
entif
y an
d cl
assi
fy li
ke a
nd u
nlik
e te
rms
in a
lgeb
raic
exp
ress
ions
• R
ecog
nize
and
iden
tify
coef
ficie
nts
and
expo
nent
s in
alg
ebra
ic
expr
essi
ons
expa
nd a
nd s
impl
ify a
lgeb
raic
ex
pres
sion
s
Use
com
mut
ativ
e, a
ssoc
iativ
e an
d di
strib
utiv
e la
ws
for r
atio
nal n
umbe
rs
and
law
s of
exp
onen
ts to
:
• A
dd a
nd s
ubtra
ct li
ke te
rms
in
alge
brai
c ex
pres
sion
s
• D
eter
min
e th
e sq
uare
s, c
ubes
, sq
uare
root
s an
d cu
be ro
ots
of s
ingl
e al
gebr
aic
term
s or
like
alg
ebra
ic te
rms
• D
eter
min
e th
e nu
mer
ical
val
ue o
f al
gebr
aic
expr
essi
ons
by s
ubst
itutio
n
Wha
t is
diffe
rent
to G
rade
7?
• In
trodu
ctio
n to
con
vent
ions
of a
lgeb
raic
lang
uage
• M
anip
ulat
ing
alge
brai
c ex
pres
sion
s
alg
ebra
ic e
xpre
ssio
ns a
re d
one
agai
n in
ter
m 2
, whe
re th
e fo
cus
is m
ore
fully
on
man
ipul
atin
g al
gebr
aic
expr
essi
ons.
in th
is te
rm th
e fo
cus
is o
n in
terp
retin
g al
gebr
aic
expr
essi
ons
and
intr
oduc
ing
conv
entio
ns o
f alg
ebra
ic
lang
uage
thro
ugh
addi
ng a
nd s
ubtr
actin
g lik
e te
rms.
Lear
ners
hav
e op
portu
nitie
s to
writ
e an
d in
terp
ret a
lgeb
raic
exp
ress
ions
whe
n th
ey
writ
e ge
nera
l rul
es to
des
crib
e re
latio
nshi
ps b
etw
een
num
bers
in n
umbe
r pat
tern
s,
and
whe
n th
ey fi
nd in
put o
r out
put v
alue
s fo
r giv
en ru
les
in fl
ow d
iagr
ams,
tabl
es,
form
ulae
and
equ
atio
ns.
exam
ples
of i
nter
pret
ing
alge
brai
c ex
pres
sion
s
a)
Wha
t doe
s th
e ru
le 2
n mea
n fo
r the
follo
win
g nu
mbe
r seq
uenc
e:
2; 4
; 8; 1
6; 3
2...
Her
e le
arne
rs s
houl
d re
cogn
ize
that
2n re
pres
ents
the
gene
ral t
erm
in th
is
sequ
ence
, whe
re n
repr
esen
ts th
e po
sitio
n of
the
term
in th
e se
quen
ce. T
hus,
it
is th
e ru
le th
at c
an b
e us
ed to
find
any
term
in th
e gi
ven
sequ
ence
.
b)
The
rela
tions
hip
betw
een
a bo
y’s
age
(x yr
s ol
d) a
nd h
is m
othe
r’s a
ge is
giv
en
as 2
5 +
x. H
ow c
an th
is re
latio
nshi
p be
use
d to
find
the
mot
her’s
age
whe
n th
e bo
y is
11
year
s ol
d? H
ere
lear
ners
sho
uld
reco
gniz
e th
at to
find
the
mot
her’s
ag
e, th
ey m
ust s
ubst
itute
the
boy’
s gi
ven
age
into
the
rule
25
+ x.
The
y sh
ould
al
so re
cogn
ize
that
the
give
n ru
le m
eans
the
mot
her i
s 25
yea
rs o
lder
than
the
boy.
See
furth
er e
xam
ples
giv
en fo
r fun
ctio
ns a
nd re
latio
nshi
ps, a
s w
ell a
s no
tes
in
Term
2.
Tim
e fo
r al
gebr
aic
expr
essi
ons
in th
is te
rm:
4,5
hour
s
MATHEMATICS GRADES 7-9
91CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.3
alg
ebra
icex
pres
sion
s
alg
ebra
ic la
ngua
ge
• R
evis
e th
e fo
llow
ing
done
in G
rade
7:
-re
cogn
ize
and
inte
rpre
t rul
es
or re
latio
nshi
ps re
pres
ente
d in
sy
mbo
lic fo
rm
-id
entif
y va
riabl
es a
nd c
onst
ants
in
give
n fo
rmul
ae a
nd e
quat
ions
• R
ecog
nize
and
iden
tify
conv
entio
ns
for w
ritin
g al
gebr
aic
expr
essi
ons
• Id
entif
y an
d cl
assi
fy li
ke a
nd u
nlik
e te
rms
in a
lgeb
raic
exp
ress
ions
• R
ecog
nize
and
iden
tify
coef
ficie
nts
and
expo
nent
s in
alg
ebra
ic
expr
essi
ons
expa
nd a
nd s
impl
ify a
lgeb
raic
ex
pres
sion
s
Use
com
mut
ativ
e, a
ssoc
iativ
e an
d di
strib
utiv
e la
ws
for r
atio
nal n
umbe
rs
and
law
s of
exp
onen
ts to
:
• A
dd a
nd s
ubtra
ct li
ke te
rms
in
alge
brai
c ex
pres
sion
s
• D
eter
min
e th
e sq
uare
s, c
ubes
, sq
uare
root
s an
d cu
be ro
ots
of s
ingl
e al
gebr
aic
term
s or
like
alg
ebra
ic te
rms
• D
eter
min
e th
e nu
mer
ical
val
ue o
f al
gebr
aic
expr
essi
ons
by s
ubst
itutio
n
Wha
t is
diffe
rent
to G
rade
7?
• In
trodu
ctio
n to
con
vent
ions
of a
lgeb
raic
lang
uage
• M
anip
ulat
ing
alge
brai
c ex
pres
sion
s
alg
ebra
ic e
xpre
ssio
ns a
re d
one
agai
n in
ter
m 2
, whe
re th
e fo
cus
is m
ore
fully
on
man
ipul
atin
g al
gebr
aic
expr
essi
ons.
in th
is te
rm th
e fo
cus
is o
n in
terp
retin
g al
gebr
aic
expr
essi
ons
and
intr
oduc
ing
conv
entio
ns o
f alg
ebra
ic
lang
uage
thro
ugh
addi
ng a
nd s
ubtr
actin
g lik
e te
rms.
Lear
ners
hav
e op
portu
nitie
s to
writ
e an
d in
terp
ret a
lgeb
raic
exp
ress
ions
whe
n th
ey
writ
e ge
nera
l rul
es to
des
crib
e re
latio
nshi
ps b
etw
een
num
bers
in n
umbe
r pat
tern
s,
and
whe
n th
ey fi
nd in
put o
r out
put v
alue
s fo
r giv
en ru
les
in fl
ow d
iagr
ams,
tabl
es,
form
ulae
and
equ
atio
ns.
exam
ples
of i
nter
pret
ing
alge
brai
c ex
pres
sion
s
a)
Wha
t doe
s th
e ru
le 2
n mea
n fo
r the
follo
win
g nu
mbe
r seq
uenc
e:
2; 4
; 8; 1
6; 3
2...
Her
e le
arne
rs s
houl
d re
cogn
ize
that
2n re
pres
ents
the
gene
ral t
erm
in th
is
sequ
ence
, whe
re n
repr
esen
ts th
e po
sitio
n of
the
term
in th
e se
quen
ce. T
hus,
it
is th
e ru
le th
at c
an b
e us
ed to
find
any
term
in th
e gi
ven
sequ
ence
.
b)
The
rela
tions
hip
betw
een
a bo
y’s
age
(x yr
s ol
d) a
nd h
is m
othe
r’s a
ge is
giv
en
as 2
5 +
x. H
ow c
an th
is re
latio
nshi
p be
use
d to
find
the
mot
her’s
age
whe
n th
e bo
y is
11
year
s ol
d? H
ere
lear
ners
sho
uld
reco
gniz
e th
at to
find
the
mot
her’s
ag
e, th
ey m
ust s
ubst
itute
the
boy’
s gi
ven
age
into
the
rule
25
+ x.
The
y sh
ould
al
so re
cogn
ize
that
the
give
n ru
le m
eans
the
mot
her i
s 25
yea
rs o
lder
than
the
boy.
See
furth
er e
xam
ples
giv
en fo
r fun
ctio
ns a
nd re
latio
nshi
ps, a
s w
ell a
s no
tes
in
Term
2.
Tim
e fo
r al
gebr
aic
expr
essi
ons
in th
is te
rm:
4,5
hour
s
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.4
alg
ebra
iceq
uatio
ns
equa
tions
• R
evis
e th
e fo
llow
ing
done
in G
rade
7:
-se
t up
equa
tions
to d
escr
ibe
prob
lem
situ
atio
ns
-an
alys
e an
d in
terp
ret e
quat
ions
that
de
scrib
e a
give
n si
tuat
ion
-so
lve
equa
tions
by
insp
ectio
n
-de
term
ine
the
num
eric
al v
alue
of a
n ex
pres
sion
by
subs
titut
ion.
-id
entif
y va
riabl
es a
nd c
onst
ants
in
give
n fo
rmul
ae o
r equ
atio
ns
• E
xten
d so
lvin
g eq
uatio
ns to
incl
ude:
-U
sing
add
itive
and
mul
tiplic
ativ
e in
vers
es
-U
sing
law
s of
exp
onen
ts
• U
se s
ubst
itutio
n in
equ
atio
ns to
ge
nera
te ta
bles
of o
rder
ed p
airs
Wha
t is
diffe
rent
to G
rade
7?
Up
to a
nd in
clud
ing
Gra
de 7
lear
ners
use
the
term
'num
bers
sen
tenc
es'.
From
G
rade
8 th
e te
rm 'e
quat
ions
' is
used
.
Sol
ving
equ
atio
ns u
sing
add
itive
and
mul
tiplic
ativ
e in
vers
es a
s w
ell a
s la
ws
of
expo
nent
s
alg
ebra
ic e
quat
ions
are
don
e ag
ain
in t
erm
2 a
nd t
erm
4. i
n th
is te
rm th
e fo
cus
is o
n so
lvin
g eq
uatio
ns th
at in
volv
e m
ultip
licat
ion
and
divi
sion
of
inte
gers
and
num
bers
in e
xpon
entia
l for
m, b
y in
spec
tion
only
. Le
arne
rs h
ave
oppo
rtuni
ties
to w
rite
and
solv
e eq
uatio
ns w
hen
they
writ
e ge
nera
l ru
les
to d
escr
ibe
rela
tions
hips
bet
wee
n nu
mbe
rs in
num
ber p
atte
rns,
and
whe
n th
ey fi
nd in
put o
r out
put v
alue
s fo
r giv
en ru
les
in fl
ow d
iagr
ams,
tabl
es a
nd
form
ulae
.
See
furth
er n
otes
in T
erm
2.
Tim
e fo
r A
lgeb
raic
eq
uatio
ns in
th
is te
rm:
3 ho
urs
rev
isio
n/a
sses
smen
t:A
t thi
s st
age
lear
ners
sho
uld
have
bee
n as
sess
ed o
n:
• ca
lcul
atin
g an
d so
lvin
g pr
oble
ms
with
who
le n
umbe
rs a
nd in
tege
rs
• re
pres
entin
g, a
nd c
alcu
latin
g w
ith, n
umbe
rs in
exp
onen
tial f
orm
• nu
mer
ic a
nd g
eom
etric
pat
tern
s
• fu
nctio
ns a
nd re
latio
nshi
ps
• al
gebr
aic
expr
essi
ons
• al
gebr
aic
equa
tions
Tota
l tim
e fo
r rev
isio
n/as
sess
men
t fo
r the
term
6 ho
urs
MATHEMATICS GRADES 7-9
92 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 8
– te
rm
2
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.3
alg
ebra
icex
pres
sion
sa
lgeb
raic
lang
uage
• R
evis
e th
e fo
llow
ing
done
in G
rade
7:
-re
cogn
ize
and
inte
rpre
t rul
es
or re
latio
nshi
ps re
pres
ente
d in
sy
mbo
lic fo
rm
-id
entif
y va
riabl
es a
nd c
onst
ants
in
give
n fo
rmul
ae a
nd e
quat
ions
• R
ecog
nize
and
iden
tify
conv
entio
ns
for w
ritin
g al
gebr
aic
expr
essi
ons
• Id
entif
y an
d cl
assi
fy li
ke a
nd u
nlik
e te
rms
in a
lgeb
raic
exp
ress
ions
• R
ecog
nize
and
iden
tify
coef
ficie
nts
and
expo
nent
s in
alg
ebra
ic
expr
essi
ons
expa
nd a
nd s
impl
ify a
lgeb
raic
ex
pres
sion
s
Use
com
mut
ativ
e, a
ssoc
iativ
e an
d di
strib
utiv
e la
ws
for r
atio
nal n
umbe
rs
and
law
s of
exp
onen
ts to
:
• A
dd a
nd s
ubtra
ct li
ke te
rms
in
alge
brai
c ex
pres
sion
s
• m
ultip
ly in
tege
rs a
nd m
onom
ials
by:
-m
onom
ials
-bi
nom
ials
-tri
nom
ials
•r
evis
e th
e fo
llow
ing
done
in t
erm
1
alg
ebra
ic e
xpre
ssio
ns w
ere
also
don
e in
ter
m 1
. in
this
term
the
focu
s is
on
exp
andi
ng a
nd s
impl
ifyin
g al
gebr
aic
expr
essi
ons.
Lear
ners
hav
e op
portu
nitie
s to
writ
e an
d in
terp
ret a
lgeb
raic
exp
ress
ions
whe
n th
ey w
rite
gene
ral r
ules
to d
escr
ibe
rela
tions
hips
bet
wee
n nu
mbe
rs in
num
ber
patte
rns,
and
whe
n th
ey fi
nd in
put o
r out
put v
alue
s fo
r giv
en ru
les
in fl
ow
diag
ram
s, ta
bles
, for
mul
ae a
nd e
quat
ions
.
exam
ples
of i
nter
pret
ing
alge
brai
c ex
pres
sion
s
a)
Wha
t doe
s th
e ru
le 2
n mea
n fo
r the
follo
win
g nu
mbe
r seq
uenc
e:
2; 4
; 8; 1
6; 3
2....
Her
e le
arne
rs s
houl
d re
cogn
ize
that
2n re
pres
ents
the
gene
ral t
erm
in th
is
sequ
ence
, whe
re n
repr
esen
ts th
e po
sitio
n of
the
term
in th
e se
quen
ce.
Thus
, it i
s th
e ru
le th
at c
an b
e us
ed to
find
any
term
in th
e gi
ven
sequ
ence
.
b)
The
rela
tions
hip
betw
een
a bo
y’s
age
(x y
rs o
ld) a
nd h
is m
othe
r’s a
ge is
gi
ven
as 2
5 +
x. H
ow c
an th
is re
latio
nshi
p be
use
d to
find
the
mot
her’s
age
w
hen
the
boy
is 1
1 ye
ars
old?
Her
e le
arne
rs s
houl
d re
cogn
ize
that
to fi
nd th
e m
othe
r’s a
ge, t
hey
have
to
subs
titut
e th
e bo
y’s
give
n ag
e in
to th
e ru
le 2
5 +
x. T
hey
shou
ld a
lso
reco
gniz
e th
at th
e gi
ven
rule
mea
ns th
e m
othe
r is
25 y
ears
old
er th
an th
e bo
y.
See
furth
er e
xam
ples
giv
en fo
r fun
ctio
ns a
nd re
latio
nshi
ps.
•m
anip
ulat
ing
alge
brai
c ex
pres
sion
s
-m
ake
sure
lear
ners
und
erst
and
that
the
rul
e fo
r op
erat
ing
with
inte
gers
and
ra
tiona
l num
bers
, inc
ludi
ng la
ws
of e
xpon
ents
, app
lies
equa
lly w
hen
num
bers
ar
e re
plac
ed w
ith v
aria
bles
. The
var
iabl
es a
re n
umbe
rs o
f a g
iven
type
(e.
g.
who
le n
umbe
rs, i
nteg
ers
or ra
tiona
l num
bers
) in
gene
raliz
ed fo
rm.
-W
hen
mul
tiply
ing
or d
ivid
ing
expr
essi
ons,
mak
e su
re le
arne
rs u
nder
stan
d ho
w
the
dist
ribut
ive
rule
wor
ks.
-Th
e as
soci
ativ
e ru
le a
llow
s fo
r gro
upin
g of
like
term
s w
hen
addi
ng.
Tim
e fo
r al
gebr
aic
expr
essi
ons
in
this
term
:
9 ho
urs
MATHEMATICS GRADES 7-9
93CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.3
alg
ebra
icex
pres
sion
s
• D
ivid
e th
e fo
llow
ing
by in
tege
rs o
r m
onom
ials
:
-m
onom
ials
-bi
nom
ials
-tri
nom
ials
• S
impl
ify a
lgeb
raic
exp
ress
ions
in
volv
ing
the
abov
e op
erat
ions
• D
eter
min
e th
e sq
uare
s, c
ubes
, sq
uare
root
s an
d cu
be ro
ots
of s
ingl
e al
gebr
aic
term
s or
like
alg
ebra
ic
term
s
• D
eter
min
e th
e nu
mer
ical
val
ue o
f al
gebr
aic
expr
essi
ons
by s
ubst
itutio
n
Look
out
for t
he fo
llow
ing
com
mon
mis
conc
eptio
ns:
•x
+ x
= 2x
and
no
t x2 .
Not
e th
e co
nven
tion
is to
writ
e 2x
rath
er th
an x
2
•x2 +
x2 =
2x2 a
nd
no
t 2x
4
•a
+ b
= a
+ b
an
d n
ot
ab
• (–
2x2 )3 =
–8x
6 an
d n
ot
– 6x
5
• –x
(3x
+ 1)
= –
3x2 –
x a
nd
no
t –
3x2 +
1
•6x
2 + 1
x2
= 6
+ 1 x2 a
nd
no
t 6
+ 1
• If
x =
2 th
en –
3x2 =
–3(
2)2 =
–3
x 4
= –1
2 a
nd
no
t (–
6)2
• If
x =
–2 th
en –
x2 – x
= –
(–2)
2 – 2
= –
4 +
2 =
–2 a
nd
no
t 4
+ 2
= 6
• 25
x2 – 9
x2√
=
16x2
√ =
4x
an
d n
ot
5x –
3x
= 2x
exam
ples
a)
Sim
plify
: 2(5
+ x
– x
2 ) –
x(3x
+ 1
) [m
ultip
ly in
tege
r or m
onom
ial b
y po
lyno
mia
l]
b)
If x
= –2
det
erm
ine
the
num
eric
al v
alue
of 3
x2 – 4
x +
5 [u
sing
sub
stitu
tion]
c)
Sim
plify
: 6x3 +
2x2 +
4
2x2
, x ≠
0 [d
ivid
e tri
nom
ial b
y m
onom
ial;
rem
inde
r tha
t de
nom
inat
or c
anno
t be
0]
d)
Sim
plify
: 8x3 –
(–x2 )(
2x)
–x2
, x ≠0
[cal
cula
tions
invo
lvin
g m
ultip
le o
pera
tions
; rem
ind
lear
ners
that
den
omin
ator
can
not b
e 0]
e)
Det
erm
ine:
36
x4 √
[squ
are
root
of m
onom
ial]
It m
ight
hel
p to
rem
ind
lear
ners
that
thes
e va
riabl
es (o
r x in
this
cas
e) re
pres
ent
num
bers
of a
par
ticul
ar ty
pe –
thes
e m
ay b
e ra
tiona
l, or
inte
gers
, or p
erha
ps
who
le n
umbe
rs; s
uch
a re
min
der a
lso
then
impl
ies
that
all
the
asso
ciat
ed ru
les
or
prop
ertie
s of
thes
e nu
mbe
rs a
pply
her
e. In
the
abov
e ex
ampl
e, if
x is
an
inte
ger,
then
x =
a o
r x =
–a
beca
use
a4 = (–
a)4
MATHEMATICS GRADES 7-9
94 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.4
alg
ebra
iceq
uatio
ns
equa
tions
• R
evis
e th
e fo
llow
ing
done
in G
rade
7:
-S
et u
p eq
uatio
ns to
des
crib
e pr
oble
m s
ituat
ions
-A
naly
se a
nd in
terp
ret e
quat
ions
th
at d
escr
ibe
a gi
ven
situ
atio
n
-S
olve
equ
atio
ns b
y in
spec
tion
-D
eter
min
e th
e nu
mer
ical
val
ue o
f an
exp
ress
ion
by s
ubst
itutio
n.
-Id
entif
y va
riabl
es a
nd c
onst
ants
in
give
n fo
rmul
ae a
nd e
quat
ions
• E
xten
d so
lvin
g eq
uatio
ns to
incl
ude:
-U
sing
add
itive
and
mul
tiplic
ativ
e in
vers
es
-U
sing
law
s of
exp
onen
ts
-U
se s
ubst
itutio
n in
equ
atio
ns to
ge
nera
te ta
bles
of o
rder
ed p
airs
Wha
t is
diffe
rent
to G
rade
7?
• S
olvi
ng e
quat
ions
usi
ng a
dditi
ve a
nd m
ultip
licat
ive
inve
rses
as
wel
l as
law
s of
ex
pone
nts
alg
ebra
ic e
quat
ions
wer
e al
so d
one
in t
erm
1. i
n th
is te
rm th
e fo
cus
is o
n so
lvin
g eq
uatio
ns u
sing
add
itive
and
mul
tiplic
ativ
e in
vers
es a
s w
ell a
s th
e la
ws
of e
xpon
ents
. alg
ebra
ic e
quat
ions
are
don
e ag
ain
in t
erm
4.
Lear
ners
hav
e op
portu
nitie
s to
writ
e an
d so
lve
equa
tions
whe
n th
ey w
rite
gene
ral
rule
s to
des
crib
e re
latio
nshi
ps b
etw
een
num
bers
in n
umbe
r pat
tern
s, a
nd w
hen
they
find
inpu
t or o
utpu
t val
ues
for g
iven
rule
s in
flow
dia
gram
s, ta
bles
and
fo
rmul
ae.
exam
ples
of e
quat
ions
a)
Sol
ve x
if x
+ 6
= –
9
To s
olve
the
equa
tion:
add
–6
to b
oth
side
s of
the
equa
tion
x +
6 –
6 =
– 9
– 6,
ther
efor
e x
= –1
5
b)
Sol
ve x
if –
2x =
8
To s
olve
the
equa
tion;
div
ide
both
sid
es o
f the
equ
atio
n by
–2:
–2x
–2 =
8
–2
x =
–4
c)
Sol
ve x
if –
x =
–5
To s
olve
the
equa
tion;
div
ide
both
sid
es o
f the
equ
atio
n by
–1
x –1 =
–5
–1 ,
ther
efor
e x
= 5
d)
Sol
ve x
if 3
x +
1 =
7
To s
olve
the
equa
tion
requ
ires
two
step
s:
Add
–1
to b
oth
side
s of
the
equa
tion:
3x +
1 –
1 =
7 –
1, t
here
fore
3x
= 6
Then
div
ide
both
sid
es o
f the
equ
atio
n by
33x
3
= 6 3
, the
refo
re x
= 2
e)
Pro
vide
an
equa
tion
to fi
nd th
e ar
ea o
f a re
ctan
gle
with
leng
th 2
x cm
and
wid
th
2x +
1 c
m.
f) If
the
area
of a
rect
angl
e is
(4x2 –
6x)
cm
2 , an
d its
wid
th is
2x
cm, w
hat w
ill b
e its
leng
th in
term
s of
x?
g)
If y
= x3
+ 1,
cal
cula
te y
whe
n x
= 4
h)
Than
di is
6 y
ears
old
er th
an S
ophi
e. In
3 y
ears
tim
e Th
andi
will
be
twic
e as
old
as
Sop
hie.
How
old
is T
hand
i now
?
Tim
e fo
r al
gebr
aic
equa
tions
in
this
term
:
3 ho
urs
MATHEMATICS GRADES 7-9
95CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
spac
e an
d sh
ape
(geo
met
ry)
3.5
Con
stru
ctio
n of
ge
omet
ric
figures
Con
stru
ctio
ns
• A
ccur
atel
y co
nstru
ct g
eom
etric
fig
ures
app
ropr
iate
ly u
sing
a
com
pass
, rul
er a
nd p
rotra
ctor
, in
clud
ing:
-B
isec
ting
lines
and
ang
les
-P
erpe
ndic
ular
line
s at
a g
iven
poi
nt
or fr
om a
giv
en p
oint
-Tr
iang
les
-Q
uadr
ilate
rals
• C
onst
ruct
ang
les
of 3
0°, 4
5° a
nd 6
0°
and
thei
r mul
tiple
s w
ithou
t usi
ng a
pr
otra
ctor
inve
stig
atin
g pr
oper
ties
of g
eom
etric
fig
ures
• B
y co
nstru
ctio
n, in
vest
igat
e th
e an
gles
in a
tria
ngle
, foc
usin
g on
:
-th
e su
m o
f the
inte
rior a
ngle
s of
tri
angl
es
-th
e si
ze o
f ang
les
in a
n eq
uila
tera
l tri
angl
e
-th
e si
des
and
base
ang
les
of a
n is
ocel
es tr
iang
le
• B
y co
nstru
ctio
n, in
vest
igat
e si
des
and
angl
es in
qua
drila
tera
ls, f
ocus
ing
on:
-th
e su
m o
f the
inte
rior a
ngle
s of
qu
adril
ater
als
-th
e si
des
and
oppo
site
ang
les
of
para
llelo
gram
s
Wha
t is
diffe
rent
to G
rade
7?
• A
ll th
e co
nstru
ctio
ns a
re n
ew. I
n G
rade
7 le
arne
rs o
nly
cons
truct
ed a
ngle
s,
perp
endi
cula
r and
par
alle
l lin
es
• U
sing
con
stru
ctio
ns to
exp
lore
pro
perti
es o
f tria
ngle
s an
d qu
adril
ater
als
Con
stru
ctio
ns
• C
onst
ruct
ions
pro
vide
a u
sefu
l con
text
to e
xplo
re o
r con
solid
ate
know
ledg
e of
an
gles
and
sha
pes
• m
ake
sure
lear
ners
are
com
pete
nt a
nd c
omfo
rtabl
e w
ith th
e us
e of
a c
ompa
ss
and
know
how
to m
easu
re a
nd re
ad a
ngle
siz
es o
n a
prot
ract
or
• R
evis
e th
e co
nstru
ctio
ns o
f ang
les
if ne
cess
ary
befo
re p
roce
edin
g w
ith th
e ne
w
cons
truct
ions
• S
tart
with
the
cons
truct
ions
of l
ines
, so
that
lear
ners
can
firs
t exp
lore
ang
le
rela
tions
hips
on
stra
ight
line
s.
• W
hen
cons
truct
ing
trian
gles
lear
ners
sho
uld
draw
on
know
n pr
oper
ties
and
cons
truct
ion
of c
ircle
s.
• C
onst
ruct
ion
of s
peci
al a
ngle
s w
ithou
t pro
tract
ors
are
done
by:
-bi
sect
ing
a rig
ht a
ngle
to g
et 4
5°
-dr
awin
g an
equ
ilate
ral t
riang
le to
get
60°
-bi
sect
ing
the
angl
es o
f an
equi
late
ral t
riang
le to
get
30°
Tota
l Tim
e fo
r co
nstru
ctio
ns
of g
eom
etric
fig
ures
:
8 ho
urs
MATHEMATICS GRADES 7-9
96 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
spac
e an
d sh
ape
(geo
met
ry)
3.1
Geo
met
ry o
f 2d
sha
pes
Cla
ssify
ing
2d s
hape
s
• Id
entif
y an
d w
rite
clea
r defi
nitio
ns o
f tri
angl
es in
term
s of
thei
r sid
es a
nd
angl
es, d
istin
gush
ing
betw
een:
-eq
uila
tera
l tria
ngle
s
-is
osce
les
trian
gles
-rig
ht-a
ngle
d tri
angl
es
• Id
entif
y an
d w
rite
clea
r defi
nito
ns o
f qu
adril
ater
als
in te
rms
of th
eir s
ides
an
d an
gles
, dis
tingu
ishi
ng b
etw
een:
-pa
ralle
logr
am
-re
ctan
gle
-sq
uare
-rh
ombu
s
-tra
pezi
um
-ki
te
Wha
t is
diffe
rent
to G
rade
7?
• N
ew p
rope
rties
in te
rms
of a
ngle
s of
tria
ngle
s
• W
rite
clea
r defi
nitio
ns o
f the
pro
perti
es o
f tria
ngle
s an
d qu
adril
ater
als
• U
se d
efini
tions
to s
olve
geo
met
ric p
robl
ems
• In
vest
igat
e co
nditi
ons
for 2
D s
hape
s to
be
cong
ruen
t or
sim
ilar
tria
ngle
s
• C
onst
ruct
ions
ser
ve a
s a
usef
ul c
onte
xt fo
r exp
lorin
g pr
oper
ties
of tr
iang
les.
S
ee n
otes
on
Con
stru
ctio
ns a
bove
.
• P
rope
rties
of t
riang
les
lear
ners
sho
uld
know
:
-th
e su
m o
f the
inte
rior a
ngle
s of
tria
ngle
s =
180°
-an
equ
ilate
ral t
riang
le h
as a
ll si
des
equa
l and
all
inte
rior a
ngle
s =
60°
-an
isos
cele
s tri
angl
e ha
s at
leas
t tw
o eq
ual s
ides
and
its
base
ang
les
are
equa
l
-a
right
-ang
led
trian
gle
has
one
angl
e th
at is
a ri
ght-a
ngle
-th
e si
de o
ppos
ite th
e rig
ht-a
ngle
in a
righ
t-ang
led
trian
gle,
is c
alle
d th
e hy
pote
nuse
-in
a ri
ght-a
ngle
d tri
angl
e, th
e sq
uare
of t
he h
ypot
enus
e is
equ
al to
the
sum
of
the
squa
res
of th
e ot
her t
wo
side
s (T
heor
em o
f Pyt
hago
ras)
.
Qua
drila
tera
ls
• C
onst
ruct
ions
ser
ve a
s a
usef
ul c
onte
xt fo
r exp
lorin
g pr
oper
ties
of tr
iang
les.
S
ee n
otes
on
Con
stru
ctio
ns a
bove
.
• Th
e cl
assi
ficat
ion
of q
uadr
ilate
rals
sho
uld
incl
ude
the
reco
gniti
on th
at:
-re
ctan
gles
and
rhom
bi a
re s
peci
al k
inds
of p
aral
lelo
gram
s
-a
squa
re is
a s
peci
al k
ind
of re
ctan
gle
and
rhom
bus.
• P
rope
rties
of q
uadr
ilate
rals
lear
ners
sho
uld
know
:
-th
e su
m o
f the
inte
rior a
ngle
s of
qua
drila
tera
ls =
360
°
-th
e op
posi
te s
ides
of p
aral
lelo
gram
s ar
e pa
ralle
l and
equ
al
-th
e op
posi
te a
ngle
s of
par
alle
logr
ams
are
equa
l
-th
e op
posi
te a
ngle
s of
a rh
ombu
s ar
e eq
ual
-th
e op
posi
te s
ides
of a
rhom
bus
are
para
llel a
nd e
qual
-th
e si
ze o
f eac
h an
gle
of re
ctan
gles
and
squ
ares
is 9
0°
-a
trape
zium
has
one
pai
r of o
ppos
ite s
ides
par
alle
l
Tota
l tim
e fo
r ge
omet
ry o
f 2D
sha
pes
8 ho
urs.
MATHEMATICS GRADES 7-9
97CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
spac
e an
d sh
ape
(geo
met
ry)
3.1
Geo
met
ry o
f 2d
sha
pes
Cla
ssify
ing
2d s
hape
s
• Id
entif
y an
d w
rite
clea
r defi
nitio
ns o
f tri
angl
es in
term
s of
thei
r sid
es a
nd
angl
es, d
istin
gush
ing
betw
een:
-eq
uila
tera
l tria
ngle
s
-is
osce
les
trian
gles
-rig
ht-a
ngle
d tri
angl
es
• Id
entif
y an
d w
rite
clea
r defi
nito
ns o
f qu
adril
ater
als
in te
rms
of th
eir s
ides
an
d an
gles
, dis
tingu
ishi
ng b
etw
een:
-pa
ralle
logr
am
-re
ctan
gle
-sq
uare
-rh
ombu
s
-tra
pezi
um
-ki
te
Wha
t is
diffe
rent
to G
rade
7?
• N
ew p
rope
rties
in te
rms
of a
ngle
s of
tria
ngle
s
• W
rite
clea
r defi
nitio
ns o
f the
pro
perti
es o
f tria
ngle
s an
d qu
adril
ater
als
• U
se d
efini
tions
to s
olve
geo
met
ric p
robl
ems
• In
vest
igat
e co
nditi
ons
for 2
D s
hape
s to
be
cong
ruen
t or
sim
ilar
tria
ngle
s
• C
onst
ruct
ions
ser
ve a
s a
usef
ul c
onte
xt fo
r exp
lorin
g pr
oper
ties
of tr
iang
les.
S
ee n
otes
on
Con
stru
ctio
ns a
bove
.
• P
rope
rties
of t
riang
les
lear
ners
sho
uld
know
:
-th
e su
m o
f the
inte
rior a
ngle
s of
tria
ngle
s =
180°
-an
equ
ilate
ral t
riang
le h
as a
ll si
des
equa
l and
all
inte
rior a
ngle
s =
60°
-an
isos
cele
s tri
angl
e ha
s at
leas
t tw
o eq
ual s
ides
and
its
base
ang
les
are
equa
l
-a
right
-ang
led
trian
gle
has
one
angl
e th
at is
a ri
ght-a
ngle
-th
e si
de o
ppos
ite th
e rig
ht-a
ngle
in a
righ
t-ang
led
trian
gle,
is c
alle
d th
e hy
pote
nuse
-in
a ri
ght-a
ngle
d tri
angl
e, th
e sq
uare
of t
he h
ypot
enus
e is
equ
al to
the
sum
of
the
squa
res
of th
e ot
her t
wo
side
s (T
heor
em o
f Pyt
hago
ras)
.
Qua
drila
tera
ls
• C
onst
ruct
ions
ser
ve a
s a
usef
ul c
onte
xt fo
r exp
lorin
g pr
oper
ties
of tr
iang
les.
S
ee n
otes
on
Con
stru
ctio
ns a
bove
.
• Th
e cl
assi
ficat
ion
of q
uadr
ilate
rals
sho
uld
incl
ude
the
reco
gniti
on th
at:
-re
ctan
gles
and
rhom
bi a
re s
peci
al k
inds
of p
aral
lelo
gram
s
-a
squa
re is
a s
peci
al k
ind
of re
ctan
gle
and
rhom
bus.
• P
rope
rties
of q
uadr
ilate
rals
lear
ners
sho
uld
know
:
-th
e su
m o
f the
inte
rior a
ngle
s of
qua
drila
tera
ls =
360
°
-th
e op
posi
te s
ides
of p
aral
lelo
gram
s ar
e pa
ralle
l and
equ
al
-th
e op
posi
te a
ngle
s of
par
alle
logr
ams
are
equa
l
-th
e op
posi
te a
ngle
s of
a rh
ombu
s ar
e eq
ual
-th
e op
posi
te s
ides
of a
rhom
bus
are
para
llel a
nd e
qual
-th
e si
ze o
f eac
h an
gle
of re
ctan
gles
and
squ
ares
is 9
0°
-a
trape
zium
has
one
pai
r of o
ppos
ite s
ides
par
alle
l
Tota
l tim
e fo
r ge
omet
ry o
f 2D
sha
pes
8 ho
urs.
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
spac
e an
d sh
ape
(geo
met
ry)
3.1
Geo
met
ry o
f 2d
sha
pes
sim
ilar a
nd c
ongr
uent
2-d
sha
pes
• Id
entif
y an
d de
scrib
e th
e pr
oper
ties
of c
ongr
uent
sha
pes
• Id
entif
y an
d de
scrib
e th
e pr
oper
ties
of s
imila
r sha
pes
solv
ing
prob
lem
s
• S
olve
geo
met
ric p
robl
ems
invo
lvin
g un
know
n si
des
and
angl
es in
tri
angl
es a
nd q
uadr
ilate
rals
, usi
ng
know
n pr
oper
ties
and
defin
ition
s.
• a
kite
has
two
pairs
of a
djac
ent s
ides
equ
al
sim
ilarit
y an
d co
ngru
ency
• Th
is c
an b
e ex
plor
ed w
ith a
ny 2
-D s
hape
• Le
arne
rs s
houl
d re
cogn
ise
that
two
or m
ore
figur
es a
re c
ongr
uent
if th
ey a
re
equa
l in
all r
espe
cts
i.e c
orre
spon
ding
ang
les
and
side
s ar
e eq
ual
• Le
arne
rs s
houl
d re
cogn
ise
that
two
or m
ore
figur
es a
re s
imila
r if t
hey
have
. co
rres
pond
ing
angl
es e
qual
and
the
ir si
des
are
prop
ortio
nally
long
er o
r sho
rter.
S
ee e
xam
ples
bel
ow.
• N
ote
that
in G
rade
9 le
arne
rs w
ill fo
cus
on th
e sp
ecia
l cas
es o
f sim
ilarit
y an
d co
ngru
ence
in tr
iang
les.
• S
imiil
ar fi
gure
s ar
e fu
rther
exp
lore
d w
hen
doin
g en
larg
emen
ts a
nd re
duct
ions
. R
efer
to “C
larifi
catio
n N
otes
” und
er 3
.3 T
rans
form
atio
n G
eom
etry
.
exam
ples
:
• C
ompa
ring
squa
res
to o
ther
rect
angl
es, l
earn
ers
can
asce
rtain
that
hav
ing
corr
espo
ndin
g an
gles
equ
al d
oes
not n
eces
saril
y im
ply
that
the
side
s w
ill b
e of
pro
porti
onal
leng
th. H
ence
hav
ing
equa
l ang
les
alon
e, is
not
a s
uffic
ient
co
nditi
on fo
r figu
res
to b
e si
mila
r.
• C
ompa
ring
rhom
bii w
ith s
ides
pro
porti
onal
, lea
rner
s ca
n as
certa
in th
at h
avin
g si
des
prop
ortio
nal d
oes
not n
eces
saril
y im
ply
that
the
corr
espo
ndin
g an
gles
will
be
equ
al. S
o on
ly h
avin
g si
des
of p
ropo
rtion
al le
ngth
is n
ot a
suf
ficie
nt c
ondi
tion
for s
imila
rity
solv
ing
prob
lem
s
• Le
arne
rs c
an s
olve
geo
met
ric p
robl
ems
to fi
nd u
nkno
wn
side
s an
d an
gles
in
tria
ngle
s an
d qu
adril
ater
als,
usi
ng k
now
n de
finiti
ons
as w
ell a
s an
gle
rela
tions
hips
on
stra
ight
line
s (s
ee n
otes
on
Geo
met
ry o
f Stra
ight
line
s.)
• Fo
r rig
ht-a
ngle
d tri
angl
es, l
earn
ers
can
also
use
the
Theo
rem
of P
ytha
gora
s to
fin
d un
know
n le
ngth
s.
• Le
arne
rs s
houl
d gi
ve re
ason
s an
d ju
stify
thei
r sol
utio
ns fo
r eve
ry w
ritte
n st
atem
ent.
• N
ote
that
sol
ving
geo
met
ric p
robl
ems
is a
n op
portu
nity
to p
ract
ise
solv
ing
equa
tions
.
MATHEMATICS GRADES 7-9
98 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
spac
e an
d sh
ape
(geo
met
ry)
3.1
Geo
met
ry o
f 2d
sha
pes
exam
ple:
Â1,
Â2,
Â3 an
d ar
e th
ree
angl
es o
n a
stra
ight
line
. Â2 =
75°,
Â3 =
55°.
W
hat i
s th
e si
ze o
f Â1?
Lear
ners
can
find
Â1 b
y so
lvin
g th
e fo
llow
ing
equa
tion:
Â1 +
75°
+ 55
° =
180°
(bec
ause
the
sum
of a
ngle
s on
a s
traig
ht li
ne =
180
°)Â
1 =
180°
– 1
30°(
add
–55°
and
–75
° to
bot
h si
des
of th
e eq
uatio
n)Â
1 =
50°
3.3
Geo
met
ry o
f st
raig
ht li
nes
ang
le re
latio
nshi
ps•
Rec
ogni
se a
nd d
escr
ibe
pairs
of
angl
es fo
rmed
by:
-pe
rpen
dicu
lar l
ines
-in
ters
ectin
g lin
es -
para
llel l
ines
cut
by
a tra
nsve
rsal
solv
ing
prob
lem
s•
Sol
ve g
eom
etric
pro
blem
s us
ing
the
rela
tions
hips
bet
wee
n pa
irs o
f ang
les
desc
ribed
abo
ve
Wha
t is
diffe
rent
to G
rade
7?
• In
Gra
de 7
lear
ners
onl
y de
fined
line
seg
men
t, ra
y, s
traig
ht li
ne, p
aral
lel l
ines
an
d pe
rpen
dicu
lar l
ines
ang
le re
latio
nshi
ps le
arne
rs s
houl
d kn
ow:
• th
e su
m o
f the
ang
les
on a
stra
ight
line
is 1
80°
• If
lines
are
per
pend
icul
ar, t
hen
adja
cent
sup
plem
enta
ry a
ngle
s ar
e ea
ch e
qual
to
90°.
• If
lines
inte
rsec
t, th
en v
ertic
ally
opp
osite
ang
les
are
equa
l.•
if pa
ralle
l lin
es a
re c
ut b
y a
trans
vers
al, t
hen
corr
espo
ndin
g an
gles
are
equ
al•
if pa
ralle
l lin
es c
ut b
y a
trans
vers
al, t
hen
alte
rnat
e an
gles
are
equ
al•
if pa
ralle
l lin
es c
ut b
y a
trans
vers
al, t
hen
co-in
terio
r ang
les
are
supp
lem
enta
ryTh
e ab
ove
angl
es h
ave
to b
e id
entifi
ed a
nd n
amed
by
lear
ner
solv
ing
prob
lem
s•
Lear
ners
can
sol
ve g
eom
etric
pro
blem
s to
find
unk
now
n an
gles
usi
ng th
e an
gle
rela
tions
hips
abo
ve, a
s w
ell a
s ot
her k
now
n pr
oper
ties
of tr
iang
les
and
quad
rilat
eral
s.
• Le
arne
rs s
houl
d gi
ve re
ason
s an
d ju
stify
thei
r sol
utio
ns fo
r eve
ry w
ritte
n st
atem
ent.
• N
ote
that
sol
ving
geo
met
ric p
robl
ems
is a
n op
portu
nity
to p
ract
ise
solv
ing
equa
tions
. exa
mpl
e:Â
, B a
nd Ĉ
are
thre
e an
gles
on
a st
raig
ht li
ne. Â
= 5
5°, B
= 7
5°. W
hat i
s th
e si
ze
of Ĉ?
Lear
ners
can
find
Ĉb
y so
lvin
g th
e fo
llow
ing
equa
tion:
55
° +
75°
+ Ĉ
= 1
80°
(be
caus
e th
e su
m o
f ang
les
on a
stra
ight
line
= 1
80°)
Ĉ =
180
° –
130°
(
add
–55°
and
–75
° to
bot
h si
des
of th
e eq
uatio
n)Ĉ
= 5
0°
Tota
l tim
e fo
r ge
omet
ry o
f st
raig
ht li
nes:
9 ho
urs
MATHEMATICS GRADES 7-9
99CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
spac
e an
d sh
ape
(geo
met
ry)
3.1
Geo
met
ry o
f 2d
sha
pes
exam
ple:
Â1,
Â2,
Â3 an
d ar
e th
ree
angl
es o
n a
stra
ight
line
. Â2 =
75°,
Â3 =
55°.
W
hat i
s th
e si
ze o
f Â1?
Lear
ners
can
find
Â1 b
y so
lvin
g th
e fo
llow
ing
equa
tion:
Â1 +
75°
+ 55
° =
180°
(bec
ause
the
sum
of a
ngle
s on
a s
traig
ht li
ne =
180
°)Â
1 =
180°
– 1
30°(
add
–55°
and
–75
° to
bot
h si
des
of th
e eq
uatio
n)Â
1 =
50°
3.3
Geo
met
ry o
f st
raig
ht li
nes
ang
le re
latio
nshi
ps•
Rec
ogni
se a
nd d
escr
ibe
pairs
of
angl
es fo
rmed
by:
-pe
rpen
dicu
lar l
ines
-in
ters
ectin
g lin
es -
para
llel l
ines
cut
by
a tra
nsve
rsal
solv
ing
prob
lem
s•
Sol
ve g
eom
etric
pro
blem
s us
ing
the
rela
tions
hips
bet
wee
n pa
irs o
f ang
les
desc
ribed
abo
ve
Wha
t is
diffe
rent
to G
rade
7?
• In
Gra
de 7
lear
ners
onl
y de
fined
line
seg
men
t, ra
y, s
traig
ht li
ne, p
aral
lel l
ines
an
d pe
rpen
dicu
lar l
ines
ang
le re
latio
nshi
ps le
arne
rs s
houl
d kn
ow:
• th
e su
m o
f the
ang
les
on a
stra
ight
line
is 1
80°
• If
lines
are
per
pend
icul
ar, t
hen
adja
cent
sup
plem
enta
ry a
ngle
s ar
e ea
ch e
qual
to
90°.
• If
lines
inte
rsec
t, th
en v
ertic
ally
opp
osite
ang
les
are
equa
l.•
if pa
ralle
l lin
es a
re c
ut b
y a
trans
vers
al, t
hen
corr
espo
ndin
g an
gles
are
equ
al•
if pa
ralle
l lin
es c
ut b
y a
trans
vers
al, t
hen
alte
rnat
e an
gles
are
equ
al•
if pa
ralle
l lin
es c
ut b
y a
trans
vers
al, t
hen
co-in
terio
r ang
les
are
supp
lem
enta
ryTh
e ab
ove
angl
es h
ave
to b
e id
entifi
ed a
nd n
amed
by
lear
ner
solv
ing
prob
lem
s•
Lear
ners
can
sol
ve g
eom
etric
pro
blem
s to
find
unk
now
n an
gles
usi
ng th
e an
gle
rela
tions
hips
abo
ve, a
s w
ell a
s ot
her k
now
n pr
oper
ties
of tr
iang
les
and
quad
rilat
eral
s.
• Le
arne
rs s
houl
d gi
ve re
ason
s an
d ju
stify
thei
r sol
utio
ns fo
r eve
ry w
ritte
n st
atem
ent.
• N
ote
that
sol
ving
geo
met
ric p
robl
ems
is a
n op
portu
nity
to p
ract
ise
solv
ing
equa
tions
. exa
mpl
e:Â
, B a
nd Ĉ
are
thre
e an
gles
on
a st
raig
ht li
ne. Â
= 5
5°, B
= 7
5°. W
hat i
s th
e si
ze
of Ĉ?
Lear
ners
can
find
Ĉb
y so
lvin
g th
e fo
llow
ing
equa
tion:
55
° +
75°
+ Ĉ
= 1
80°
(be
caus
e th
e su
m o
f ang
les
on a
stra
ight
line
= 1
80°)
Ĉ =
180
° –
130°
(
add
–55°
and
–75
° to
bot
h si
des
of th
e eq
uatio
n)Ĉ
= 5
0°
Tota
l tim
e fo
r ge
omet
ry o
f st
raig
ht li
nes:
9 ho
urs
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
rev
isio
n/a
sses
smen
t:A
t thi
s st
age
lear
ners
sho
uld
have
bee
n as
sess
ed o
n:
• al
gebr
aic
expr
essi
ons
• al
gebr
aic
equa
tions
• co
nstru
ctin
g ge
omet
ric o
bjec
ts
• ge
omet
ry o
f 2D
sha
pes
• ge
omet
ry o
f stra
ight
line
s
Tota
l tim
e fo
r rev
isio
n/as
sess
men
t fo
r the
term
8 ho
urs
MATHEMATICS GRADES 7-9
100 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 8
– te
rm
3
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, op
erat
ions
and
re
latio
nshi
ps
1.4
Com
mon
fr
actio
ns
Cal
cula
tions
usi
ng fr
actio
ns
• R
evis
e:
-ad
ditio
n an
d su
btra
ctio
n of
co
mm
on fr
actio
ns, i
nclu
ding
mix
ed
num
bers
-fin
ding
frac
tions
of w
hole
num
bers
-m
ultip
licat
ion
of c
omm
on fr
actio
ns,
incl
udin
g m
ixed
num
bers
• D
ivid
e w
hole
num
bers
and
com
mon
fra
ctio
ns b
y co
mm
on fr
actio
ns
• C
alcu
late
the
squa
res,
cub
es, s
quar
e ro
ots
and
cube
root
s of
com
mon
fra
ctio
ns
Cal
cula
tion
tech
niqu
es
• R
evis
e:
-C
onve
rt m
ixed
num
bers
to
com
mon
frac
tions
in o
rder
to
perfo
rm c
alcu
latio
ns w
ith th
em
-U
se k
now
ledg
e of
mul
tiple
s an
d fa
ctor
s to
writ
e fra
ctio
ns in
the
sim
ples
t for
m b
efor
e or
afte
r ca
lcul
atio
ns
-U
se k
now
ledg
e of
equ
ival
ent
fract
ions
to a
dd a
nd s
ubtra
ct
com
mon
frac
tions
• U
se k
now
ledg
e of
reci
proc
al
rela
tions
hips
to d
ivid
e co
mm
on
fract
ions
Wha
t is
diffe
rent
to G
rade
7?
• D
ivid
e by
com
mon
frac
tions
• S
quar
es, c
ubes
, squ
are
root
s an
d cu
be ro
ots
of c
omm
on fr
actio
ns
In G
rade
8 le
arne
rs c
onso
lidat
e nu
mbe
r kno
wle
dge
and
calc
ulat
ion
tech
niqu
es fo
r co
mm
on fr
actio
ns, d
evel
oped
in G
rade
7.
Cal
cula
tions
usi
ng fr
actio
ns
• Le
arne
rs s
houl
d co
ntin
ue to
do
cont
ext f
ree
calc
ulat
ions
and
sol
ve p
robl
ems
in
cont
exts
.
-B
y G
rade
8 le
arne
rs s
houl
d be
com
forta
ble
conv
ertin
g m
ixed
num
bers
to
com
mon
frac
tions
for c
alcu
latio
ns.
exam
ple
51 2 =
11 2;
61 3 =
19 3
-To
sim
plify
frac
tions
, lea
rner
s us
e kn
owle
dge
of c
omm
on fa
ctor
s i.e
. wha
t can
di
vide
equ
ally
into
the
num
erat
or a
nd d
enom
inat
or o
f a fr
actio
n. E
mph
asiz
e th
at
whe
n si
mpl
ifyin
g, th
e fra
ctio
ns m
ust r
emai
n eq
uiva
lent
.
add
ition
and
sub
trac
tion
• LC
ms
have
to b
e fo
und
whe
n ad
ding
and
sub
tract
ing
fract
ions
with
diff
eren
t de
nom
inat
ors.
Her
e le
arne
rs u
se k
now
ledg
e of
com
mon
mul
tiple
s to
find
the
LCM
i.e.
wha
t num
ber c
an b
oth
deno
min
ator
s be
div
ided
into
.
mul
tiplic
atio
n
• Fo
r mul
tiplic
atio
n of
frac
tions
, lea
rner
s sh
ould
be
enco
urag
ed to
sim
plify
fra
ctio
ns b
y di
vidi
ng n
umer
ator
s an
d de
nom
inat
ors
by c
omm
on fa
ctor
s.
• Le
arne
rs s
houl
d no
te th
e di
ffere
nce
betw
een
addi
ng o
r sub
tract
ing
fract
ions
, an
d m
ultip
lyin
g fra
ctio
ns
exam
ples
3
4 +
2
5 =
15 20 +
8 20 =
23 20 =
13 20
(usi
ng L
CM
and
equ
ival
ent f
ract
ions
)3
4 x
2
5 =
3 10 (d
ivid
e 2
and
4 by
com
mon
fact
or 2
)
• Le
arne
rs s
houl
d re
cogn
ize
that
find
ing
a ‘fr
actio
n of
a w
hole
num
ber’
or ‘fi
ndin
g a
fract
ion
of a
frac
tion’
mea
ns m
ultip
lyin
g th
e fra
ctio
n an
d th
e w
hole
num
ber o
r th
e fra
ctio
n w
ith th
e fra
ctio
n.
Tota
l tim
e fo
r com
mon
fra
ctio
ns:
7 ho
urs
MATHEMATICS GRADES 7-9
101CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, op
erat
ions
and
re
latio
nshi
ps
1.4
Com
mon
fr
actio
ns
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
com
mon
frac
tions
and
mix
ed
num
bers
, inc
ludi
ng g
roup
ing,
sha
ring
and
findi
ng fr
actio
ns o
f who
le
num
bers
• W
hen
lear
ners
find
frac
tions
of w
hole
num
bers
, the
exa
mpl
es c
an b
e ch
osen
to
resu
lt ei
ther
in w
hole
num
bers
or f
ract
ions
or b
oth.
• Le
arne
rs s
houl
d al
so u
se th
e co
nven
tion
of w
ritin
g th
e w
hole
num
ber a
s a
fract
ion
over
whe
n m
ultip
lyin
g.
exam
ples
Find
4 5 o
f 20
= 4 5
x 20 1
= 80 5
= 1
6
Find
2 3 o
f 5 6
= 2 3
x 5 6
= 10 18
= 5 9
div
isio
n
• Th
e te
chni
que
of ‘i
nver
t and
mul
tiply
’ app
lies
to d
ivis
ion
in g
ener
al a
nd n
ot ju
st
to d
ivis
ion
by fr
actio
ns. H
ence
, a u
sefu
l way
of m
akin
g le
arne
rs c
omfo
rtabl
e w
ith
divi
sion
by
fract
ions
is to
sta
rt w
ith e
xam
ples
of d
ivis
ion
by w
hole
num
bers
.
• Le
arne
rs h
ave
to u
nder
stan
d th
at d
ivid
ing
by a
num
ber i
s th
e sa
me
as
mul
tiply
ing
by th
e re
cipr
ocal
of t
he n
umbe
r i.e
. the
reci
proc
al o
f n is
1 n
exam
ples
:
a)
10 ÷
5 is
the
sam
e as
10
x 1 5
= 2
(mul
tiply
by
the
reci
proc
al o
f 5)
b)
10 ÷
1 5 =
10
x 5
= 50
(mul
tiply
by
the
reci
proc
al o
f 1 5
)
This
can
als
o be
exp
lain
ed b
y us
ing
diag
ram
mod
els
for f
ract
ions
and
ask
ing,
ho
w m
any
times
doe
s 1 5
fit i
nto
10?
We
know
that
5 fi
fths
fit in
to 1
who
le, s
o (5
x
10) fi
fths
will
fit i
nto
10 w
hole
s. H
ence
, 10
÷1 5
= 5
0
c)
20 ÷
4 is
the
sam
e as
20
x 1 4
= 5
(mul
tiply
by
the
reci
proc
al o
f 4)
d)
20 ÷
1 4 =
20
x 4
= 80
(mul
tiply
by
the
reci
proc
al o
f 1 4
)
This
can
als
o be
exp
lain
ed b
y us
ing
diag
ram
mod
els
for f
ract
ions
and
ask
ing,
ho
w m
any
times
doe
s 1 4
fit i
nto
20?
We
know
that
4 q
uarte
rs fi
t int
o 1
who
le,
so (4
x 2
0) q
uarte
rs w
ill fi
t int
o 20
who
les.
Hen
ce, 2
0 ÷
1 4 =
80
e)
Onc
e le
arne
rs h
ave
done
a fe
w o
f the
abo
ve e
xam
ples
, the
y ca
n us
e th
e te
chni
que
of m
ultip
lyin
g by
the
reci
proc
al to
div
ide
fract
ions
by
fract
ions
:3 4
÷ 1 2
= 3 4
x 2 1
= 6 4
= 3 2
= 1
1 2(m
ultip
ly b
y th
e re
cipr
ocal
of
1 2)
squa
res,
cub
es, s
quar
e ro
ots
and
cube
root
s
• K
now
ing
the
rule
s of
ope
ratio
ns fo
r cal
cula
ting
squa
res,
cub
es, s
quar
e ro
ots
and
cube
root
s of
com
mon
frac
tions
is im
porta
nt
MATHEMATICS GRADES 7-9
102 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, op
erat
ions
and
re
latio
nshi
ps
1.4
Com
mon
fr
actio
ns
Perc
enta
ges
• R
evis
e: -
findi
ng p
erce
ntag
es o
f who
le
num
bers
-ca
lcul
atin
g th
e pe
rcen
tage
of p
art
of a
who
le
-ca
lcul
atin
g pe
rcen
tage
incr
ease
or
decr
ease
•
Cal
cula
te a
mou
nts
if gi
ven
perc
enta
ge in
crea
se o
r dec
reas
e•
Sol
ve p
robl
ems
in c
onte
xts
invo
lvin
g pe
rcen
tage
s
equi
vale
nt fo
rms
• R
evis
e eq
uiva
lent
form
s be
twee
n:
-co
mm
on fr
actio
ns (f
ract
ions
whe
re
one
deno
min
ator
is a
mul
tiple
of
the
othe
r)
-co
mm
on fr
actio
n an
d de
cim
al
fract
ion
form
s of
the
sam
e nu
mbe
r
-co
mm
on fr
actio
n, d
ecim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r
exam
ples
:a)
(3 4
)2 = 32 42
= 9 16
b) √16
25
=
25√
16√
= 4 5
• O
nce
lear
ners
are
com
forta
ble
doin
g al
l the
ope
ratio
ns w
ith fr
actio
ns,
calc
ulat
ions
do
not h
ave
to b
e re
stric
ted
to p
ositi
ve fr
actio
ns.
Cal
cula
tion
usin
g pe
rcen
tage
s•
Lear
ners
sho
uld
cont
inue
to d
o co
ntex
t fre
e ca
lcul
atio
ns a
nd s
olve
pro
blem
s in
co
ntex
ts.
• W
hen
doin
g ca
lcul
atio
ns u
sing
per
cent
ages
, lea
rner
s ha
ve to
use
the
equi
vale
nt
com
mon
frac
tion
form
, whi
ch is
a fr
actio
n w
ith d
enom
inat
or 1
00.
• Le
arne
rs s
houl
d be
com
e fa
mili
ar w
ith th
e eq
uiva
lent
frac
tion
and
deci
mal
form
s of
com
mon
per
cent
ages
eg.
25%
is e
quiv
alen
t to
1 4or
0,2
5; 5
0% is
equ
ival
ent t
o 1 2
or 0
,5; 6
0% is
equ
ival
ent t
o 3 5
or 0
,6.
• To
cal
cula
te p
erce
ntag
e of
par
t of a
who
le, o
r per
cent
age
incr
ease
or d
ecre
ase,
le
arne
rs h
ave
to le
arn
the
stra
tegy
of m
ultip
lyin
g by
1 100 .
It is
use
ful f
or le
arne
rs
to le
arn
to u
se c
alcu
lato
rs fo
r som
e of
thes
e ca
lcul
atio
ns w
here
the
fract
ions
are
no
t eas
ily s
impl
ified
. •
Whe
n us
ing
calc
ulat
ors,
lear
ners
can
use
the
equi
vale
nt d
ecim
al fr
actio
n fo
rm
for p
erce
ntag
es to
do
the
calc
ulat
ions
.ex
ampl
es:
a)
Cal
cula
te o
f 60%
of R
105
Am
ount
= 60
10
0 x R
105
= R
63b)
W
hat p
erce
ntag
e is
40c
of R
3,20
?
Per
cent
age
= 40
32
0 x 10
0 1 =
100 8 =
12,
5%c)
C
alcu
late
the
perc
enta
ge in
crea
se if
the
pric
e of
a b
us ti
cket
of R
60 is
in
crea
sed
to R
84.
Am
ount
incr
ease
d =
R24
. The
refo
re p
erce
ntag
e in
crea
se =
24
60 x
100 1 =
40%
d)
Cal
cula
te th
e pe
rcen
tage
dec
reas
e if
the
pric
e of
pet
rol g
oes
dow
n fro
m 2
0 ce
nts
a lit
re to
18
cent
s a
litre
.
Am
ount
dec
reas
ed =
2 c
ents
. The
refo
re p
erce
ntag
e de
crea
se =
2 20 x
100 1 =
10%
e)
Cal
cula
te h
ow m
uch
a ca
r will
cos
t if i
ts o
rigin
al p
rice
of R
150
000
is re
duce
d by
15%
Cal
cula
tion
invo
lves
find
ing
15%
of R
150
000
and
then
sub
tract
ing
that
am
ount
fro
m th
e or
igin
al p
rice.
i.e.
15
100 x
R15
0 00
0 1
= R
22 5
00H
ence
new
pric
e of
car
= R
150
000
– R
22 5
00 =
R12
7 50
0
Or
85
100 x
R15
0 00
0 1
= R
127
500
MATHEMATICS GRADES 7-9
103CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
1.5
dec
imal
fr
actio
ns
ord
erin
g an
d co
mpa
ring
deci
mal
fr
actio
ns
• R
evis
e:
-O
rder
ing,
com
parin
g an
d pl
ace
valu
e of
dec
imal
frac
tions
to a
t le
ast 3
dec
imal
pla
ces
-R
ound
ing
off d
ecim
al fr
actio
ns to
at
leas
t 2 d
ecim
al p
lace
Cal
cula
tions
with
dec
imal
frac
tions
• R
evis
e:
-ad
ditio
n, s
ubtra
ctio
n an
d m
ultip
licat
ion
of d
ecim
al fr
actio
ns
to a
t lea
st 3
dec
imal
pla
ces
-di
visi
on o
f dec
imal
frac
tions
by
who
le n
umbe
rs
• E
xten
d m
ultip
licat
ion
to 'm
ultip
licat
ion
by d
ecim
al fr
actio
ns' n
ot li
mite
d to
on
e de
cim
al p
lace
Wha
t is
diffe
rent
to G
rade
7?
• m
ultip
licat
ion
by d
ecim
al fr
actio
ns n
ot li
mite
d to
one
dec
imal
pla
ce
• D
ivis
ion
of d
ecim
al fr
actio
ns b
y de
cim
al fr
actio
ns
• S
quar
es, c
ubes
, squ
are
root
s an
d cu
be ro
ots
of d
ecim
al fr
actio
ns
In G
rade
8 le
arne
rs c
onso
lidat
e nu
mbe
r kno
wle
dge
and
calc
ulat
ion
tech
niqu
es fo
r de
cim
al fr
actio
ns, d
evel
oped
in G
rade
7.
ord
erin
g, c
ount
ing
and
com
parin
g de
cim
al fr
actio
ns
• Le
arne
rs s
houl
d co
ntin
ue to
pra
ctis
e co
untin
g, o
rder
ing
and
com
parin
g de
cim
al
fract
ions
. Cou
ntin
g sh
ould
not
onl
y be
thou
ght o
f as
verb
al c
ount
ing.
Lea
rner
s ca
n co
unt i
n de
cim
al in
terv
als
usin
g:
-st
ruct
ured
, sem
i-stru
ctur
ed o
r em
pty
num
ber l
ines
-ch
ain
diag
ram
s fo
r cou
ntin
g
• Le
arne
rs s
houl
d be
giv
en a
rang
e of
exe
rcis
es
• A
rran
ge g
iven
num
bers
from
the
smal
lest
to th
e bi
gges
t: or
big
gest
to s
mal
lest
.
• Fi
ll in
mis
sing
num
bers
in
-a
sequ
ence
-on
a n
umbe
r grid
-on
a n
umbe
r lin
e
-fil
l in
<, =
or >
e.g
. 0,4
* 0
,04
* 0,
004
• C
ount
ing
exer
cise
s in
cha
in d
iagr
ams
can
be c
heck
ed u
sing
cal
cula
tors
and
le
arne
rs c
an e
xpla
in a
ny d
iffer
ence
s be
twee
n th
eir a
nsw
ers
and
thos
e sh
own
by
the
calc
ulat
or.
Cal
cula
ting
usin
g de
cim
al fr
actio
ns
• Le
arne
rs s
houl
d co
ntin
ue to
do
cont
ext f
ree
calc
ulat
ions
and
sol
ve p
robl
ems
in
cont
exts
.
• Le
arne
rs s
houl
d es
timat
e th
eir a
nsw
ers
befo
re c
alcu
latin
g, e
spec
ially
with
m
ultip
licat
ion
and
divi
sion
by
deci
mal
frac
tions
. The
y sh
ould
be
able
to ju
dge
the
reas
onab
lene
ss o
f ans
wer
s in
resp
ect o
f how
man
y de
cim
al p
lace
s an
d al
so
chec
k th
eir o
wn
answ
ers.
• m
ultip
licat
ion
by d
ecim
al fr
actio
ns s
houl
d st
art w
ith fa
mili
ar n
umbe
rs th
at
lear
ners
can
cal
cula
te b
y in
spec
tion,
so
that
lear
ners
get
a s
ense
of h
ow
deci
mal
pla
ces
are
affe
cted
by
mul
tiplic
atio
n.
Tota
l tim
e fo
r dec
imal
fra
ctio
ns:
6 ho
urs
MATHEMATICS GRADES 7-9
104 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
1.5
dec
imal
fr
actio
ns
• E
xten
d di
visi
on to
'div
isio
n of
dec
imal
fra
ctio
ns b
y de
cim
al fr
actio
ns'
• C
alcu
late
the
squa
res,
cub
es, s
quar
e ro
ots
and
cube
root
s of
dec
imal
fra
ctio
ns
Cal
cula
tion
tech
niqu
es
• U
se k
now
ledg
e of
pla
ce v
alue
to
estim
ate
the
num
ber o
f dec
imal
pl
aces
in th
e re
sult
befo
re p
erfo
rmin
g ca
lcul
atio
ns
• U
se ro
undi
ng o
ff an
d a
calc
ulat
or to
ch
eck
resu
lts w
here
app
ropr
iate
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
invo
lvin
g de
cim
al fr
actio
ns
equi
vale
nt fo
rms
• R
evis
e eq
uiva
lent
form
s be
twee
n:
-co
mm
on fr
actio
n an
d de
cim
al
fract
ion
form
s of
the
sam
e nu
mbe
r
-co
mm
on fr
actio
n, d
ecim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r
exam
ples
:
a)
3 x
2 =
6
0,3
x 2
= 0,
6
0,3
x 0,
2 =
0,06
0,3
x 0,
02 =
0,0
06
0,03
x 0
,02
= 0,
0006
etc
b)
15 x
3 =
45
1,5
x 3
= 4,
5
0,15
x 3
= 0
,45
0,15
x 0
,3 =
0,0
45
0,01
5 x
0,3
= 0,
0045
etc
• Fo
r div
isio
n by
dec
imal
frac
tions
with
out c
alcu
lato
rs, l
earn
ers
have
to u
se
thei
r kno
wle
dge
of m
ultip
licat
ion
by 1
0 or
mul
tiple
s of
10
to m
ake
the
divi
sor a
w
hole
num
ber.
Hen
ce s
tart
with
fam
iliar
num
bers
that
lear
ners
can
cal
cula
te b
y in
spec
tion,
so
that
lear
ners
get
a s
ense
of h
ow d
ecim
al p
lace
s ar
e af
fect
ed b
y di
visi
on.
exam
ples
:
a)
54 ÷
6 =
9
54 ÷
0,6
= 5
40 ÷
6 =
90
(mul
tiply
bot
h nu
mbe
rs b
y 10
to m
ake
the
deci
mal
frac
tion
a w
hole
num
ber)
54 ÷
0,0
6 =
5 40
0 ÷
6 =
900
(mul
tiply
bot
h nu
mbe
rs b
y 10
0 to
mak
e th
e de
cim
al fr
actio
n a
who
le n
umbe
r)
0,54
÷ 0
,06
= 54
÷ 6
= 9
(mul
tiply
bot
h nu
mbe
rs b
y 10
0 to
mak
e th
e de
cim
al fr
actio
n a
who
le n
umbe
r)
b)
125
÷ 5
= 25
125
÷ 0,
5 =
1 25
0 ÷
5 =
250
(mul
tiply
bot
h nu
mbe
rs b
y 10
to m
ake
the
deci
mal
frac
tion
a w
hole
num
ber)
125
÷ 0,
05 =
12
500
÷ 5
= 2
500
(mul
tiply
bot
h nu
mbe
rs b
y 10
0 to
mak
e th
e de
cim
al fr
actio
n a
who
le n
umbe
r)
1,25
÷ 0
,05
= 12
5 ÷
5 =
25
(mul
tiply
bot
h nu
mbe
rs b
y 10
0 to
mak
e th
e de
cim
al fr
actio
n a
who
le n
umbe
r
MATHEMATICS GRADES 7-9
105CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
1.5
dec
imal
fr
actio
ns
• Fo
r big
ger a
nd u
nfam
iliar
dec
imal
frac
tions
, lea
rner
s sh
ould
use
cal
cula
tors
for
mul
tiplic
atio
n an
d di
visi
on, b
ut s
till j
udge
the
reas
onab
lene
ss o
f the
ir so
lutio
ns.
• S
imila
rly, fi
ndin
g sq
uare
s, c
ubes
, squ
are
root
s an
d cu
be ro
ots
for d
ecim
al
fract
ions
sho
uld
star
t with
fam
iliar
num
bers
that
lear
ners
can
cal
cula
te b
y in
spec
tion.
exam
ples
:
a)
42 = 1
6
(0,4
)2 = 0
,4 x
0,4
= 0
,16
(0,0
4)2 =
0,0
4 x
0,04
= 0
,001
6
b)
(0,1
)3 = 0
,1 x
0,1
x 0
,1 =
0,0
01
c)
0,04
√
= 0
,2
• O
nce
lear
ners
are
com
forta
ble
with
all
the
oper
atio
ns u
sing
dec
imal
frac
tions
, ca
lcul
atio
ns s
houl
d no
t be
rest
ricte
d to
pos
itive
dec
imal
frac
tions
.
mea
sure
men
t4.
3
the
theo
rem
of
Pyth
agor
as
dev
elop
an
d us
e th
e th
eore
m
of
Pyth
agor
as
• In
vest
igat
e th
e re
latio
nshi
p be
twee
n th
e le
ngth
s of
the
side
s of
a ri
ght-
angl
ed tr
iang
le to
dev
elop
the
Theo
rem
of P
ytha
gora
s
• D
eter
min
e w
heth
er a
tria
ngle
is a
rig
ht-a
ngle
d tri
angl
e or
not
if th
e le
ngth
of t
he th
ree
side
s of
the
trian
gle
are
know
n
• U
se th
e Th
eore
m o
f Pyt
hago
ras
to
calc
ulat
e a
mis
sing
leng
th in
a ri
ght-
angl
ed tr
iang
le, l
eavi
ng ir
ratio
nal
answ
ers
in s
urd
form
• Th
e th
eore
m o
f Pyt
hago
ras
is n
ew in
Gra
de 8
.
• It
is im
porta
nt th
at le
arne
rs u
nder
stan
d th
at th
e Th
eore
m o
f Pyt
hago
ras
appl
ies
only
to ri
ght-a
ngle
d tri
angl
es.
• Th
e Th
eore
m o
f Pyt
hago
ras
is b
asic
ally
a fo
rmul
a to
cal
cula
te u
nkno
wn
leng
th
of s
ides
in ri
ght-a
ngle
d tri
angl
es.
• In
the
FET
phas
e, th
e Th
eore
m o
f Pyt
hago
ras
is c
ruci
al to
the
furth
er s
tudy
of
Geo
met
ry a
nd T
rigon
omet
ry
exam
ples
of s
olvi
ng p
robl
ems
usin
g th
e th
eore
m o
f Pyt
hago
ras:
• In
∆A
BC
, ∠B
= 9
0o , A
C =
4 c
m, B
C =
2 c
m. C
alcu
late
the
leng
th o
f AB
with
out
usin
g a
calc
ulat
or. L
eave
the
answ
er in
the
sim
ples
t sur
d fo
rm.
Tota
l tim
e fo
r th
e Th
eore
m
of P
ytha
gora
s:
5 ho
urs
MATHEMATICS GRADES 7-9
106 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
4.1
are
a an
d pe
rimet
er o
f 2d
sha
pes
are
a an
d pe
rimet
er
• U
se a
ppro
pria
te fo
rmul
ae to
cal
cula
te
perim
eter
and
are
a of
:
-sq
uare
s
-re
ctan
gles
-tri
angl
es
-ci
rcle
s
• C
alcu
late
the
area
s of
pol
ygon
s,
to a
t lea
st 2
dec
imal
pla
ces,
by
deco
mpo
sing
them
into
rect
angl
es
and/
or tr
iang
les
• U
se a
nd d
escr
ibe
the
rela
tions
hip
betw
een
the
radi
us, d
iam
eter
an
d ci
rcum
fere
nce
of a
circ
le in
ca
lcul
atio
ns
• U
se a
nd d
escr
ibe
the
rela
tions
hip
betw
een
the
radi
us a
nd a
rea
of a
ci
rcle
in c
alcu
latio
ns
Cal
cula
tions
and
sol
ving
pro
blem
s
• S
olve
pro
blem
s, w
ith o
r with
out a
ca
lcul
ator
, inv
olvi
ng p
erim
eter
and
ar
ea o
f pol
ygon
s an
d ci
rcle
s
• C
alcu
late
to a
t lea
st 2
dec
imal
pla
ces
• U
se a
nd d
escr
ibe
the
mea
ning
of
the
irrat
iona
l num
ber P
i (π)
in
calc
ulat
ions
invo
lvin
g ci
rcle
s
• U
se a
nd c
onve
rt be
twee
n ap
prop
riate
S
I uni
ts, i
nclu
ding
:
-m
m2
↔ cm
2 ↔
m2
↔ km
2
Wha
t is
diffe
rent
to G
rade
7?
• A
reas
of p
olyg
ons
by d
ecom
posi
tion
• C
ircum
fere
nce
and
area
of a
circ
le
•Fo
rmul
ae le
arne
rs s
houl
d kn
ow a
nd u
se:
-pe
rimet
er o
f a s
quar
e =
4s
-pe
rimet
er o
f a re
ctan
gle
= 2(
l + b
) or 2
l + 2
b
-ar
ea o
f a s
quar
e =
l2
-ar
ea o
f a re
ctan
gle
= l x
b
-ar
ea o
f a tr
iang
le =
1 2 (b
x h)
-di
amet
er o
f a c
ircle
: d =
2r
-ci
rcum
fere
nce
of c
ircle
: c =
πd
or 2
πr
-ar
ea o
f a c
ircle
: A =
πr2
solv
ing
equa
tions
usi
ng fo
rmul
ae
• Th
e us
e of
form
ulae
pro
vide
s a
cont
ext t
o pr
actis
e so
lvin
g eq
uatio
ns b
y in
spec
tion
or u
sing
add
itive
or m
ultip
licat
ive
inve
rses
.
exam
ples
:
1. I
f the
per
imet
er o
f a s
quar
e is
32
cm, w
hat i
s th
e le
ngth
of e
ach
side
? Le
arne
rs s
houl
d w
rite
this
as:
4s =
32
and
solv
e by
ask
ing:
4 ti
mes
wha
t will
be
32 O
R s
ayin
g s
= 32
4
?
2. If
the
area
of a
rect
angl
e is
200
cm
2 , an
d its
leng
th is
50
cm, w
hat i
s its
wid
th?
Lear
ners
sho
uld
writ
e th
is a
s:
50 x
b =
200
and
sol
ve b
y in
spec
tion
by a
skin
g: 5
0 tim
es w
hat w
ill b
e 20
0 O
R
sayi
ng b
= 20
0 50
?
For a
reas
of t
riang
les:
• m
ake
sure
lear
ners
kno
w th
at th
e he
ight
of a
tria
ngle
is a
line
seg
men
t dra
wn
from
any
ver
tex
perp
endi
cula
r to
the
oppo
site
sid
e.
Tota
l tim
e fo
r are
a an
d pe
rimet
er:
5 ho
urs.
MATHEMATICS GRADES 7-9
107CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
4.1
are
a an
d pe
rimet
er o
f 2d
sha
pes
are
a an
d pe
rimet
er
• U
se a
ppro
pria
te fo
rmul
ae to
cal
cula
te
perim
eter
and
are
a of
:
-sq
uare
s
-re
ctan
gles
-tri
angl
es
-ci
rcle
s
• C
alcu
late
the
area
s of
pol
ygon
s,
to a
t lea
st 2
dec
imal
pla
ces,
by
deco
mpo
sing
them
into
rect
angl
es
and/
or tr
iang
les
• U
se a
nd d
escr
ibe
the
rela
tions
hip
betw
een
the
radi
us, d
iam
eter
an
d ci
rcum
fere
nce
of a
circ
le in
ca
lcul
atio
ns
• U
se a
nd d
escr
ibe
the
rela
tions
hip
betw
een
the
radi
us a
nd a
rea
of a
ci
rcle
in c
alcu
latio
ns
Cal
cula
tions
and
sol
ving
pro
blem
s
• S
olve
pro
blem
s, w
ith o
r with
out a
ca
lcul
ator
, inv
olvi
ng p
erim
eter
and
ar
ea o
f pol
ygon
s an
d ci
rcle
s
• C
alcu
late
to a
t lea
st 2
dec
imal
pla
ces
• U
se a
nd d
escr
ibe
the
mea
ning
of
the
irrat
iona
l num
ber P
i (π)
in
calc
ulat
ions
invo
lvin
g ci
rcle
s
• U
se a
nd c
onve
rt be
twee
n ap
prop
riate
S
I uni
ts, i
nclu
ding
:
-m
m2
↔ cm
2 ↔
m2
↔ km
2
Wha
t is
diffe
rent
to G
rade
7?
• A
reas
of p
olyg
ons
by d
ecom
posi
tion
• C
ircum
fere
nce
and
area
of a
circ
le
•Fo
rmul
ae le
arne
rs s
houl
d kn
ow a
nd u
se:
-pe
rimet
er o
f a s
quar
e =
4s
-pe
rimet
er o
f a re
ctan
gle
= 2(
l + b
) or 2
l + 2
b
-ar
ea o
f a s
quar
e =
l2
-ar
ea o
f a re
ctan
gle
= l x
b
-ar
ea o
f a tr
iang
le =
1 2 (b
x h)
-di
amet
er o
f a c
ircle
: d =
2r
-ci
rcum
fere
nce
of c
ircle
: c =
πd
or 2
πr
-ar
ea o
f a c
ircle
: A =
πr2
solv
ing
equa
tions
usi
ng fo
rmul
ae
• Th
e us
e of
form
ulae
pro
vide
s a
cont
ext t
o pr
actis
e so
lvin
g eq
uatio
ns b
y in
spec
tion
or u
sing
add
itive
or m
ultip
licat
ive
inve
rses
.
exam
ples
:
1. I
f the
per
imet
er o
f a s
quar
e is
32
cm, w
hat i
s th
e le
ngth
of e
ach
side
? Le
arne
rs s
houl
d w
rite
this
as:
4s =
32
and
solv
e by
ask
ing:
4 ti
mes
wha
t will
be
32 O
R s
ayin
g s
= 32
4
?
2. If
the
area
of a
rect
angl
e is
200
cm
2 , an
d its
leng
th is
50
cm, w
hat i
s its
wid
th?
Lear
ners
sho
uld
writ
e th
is a
s:
50 x
b =
200
and
sol
ve b
y in
spec
tion
by a
skin
g: 5
0 tim
es w
hat w
ill b
e 20
0 O
R
sayi
ng b
= 20
0 50
?
For a
reas
of t
riang
les:
• m
ake
sure
lear
ners
kno
w th
at th
e he
ight
of a
tria
ngle
is a
line
seg
men
t dra
wn
from
any
ver
tex
perp
endi
cula
r to
the
oppo
site
sid
e.
Tota
l tim
e fo
r are
a an
d pe
rimet
er:
5 ho
urs.
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
4.1
are
a an
d Pe
rimet
er o
f 2d
sha
pes
exam
ple:
AD
is th
e he
ight
ont
o ba
se B
C o
f ∆A
BC
.
A D
B C
A D B
C
• P
oint
out
that
eve
ry tr
iang
le h
as b
ases
, eac
h w
ith a
rela
ted
heig
ht o
r alti
tude
.
•Fo
r con
vers
ions
, not
e:
-If
1cm
= 1
0 m
m th
en 1
cm
2 = 1
00 m
m2
-If
1m =
100
cm
then
1 m
2 = 1
0 00
0 cm
2
Circ
les
• m
ake
sure
lear
ners
can
iden
tify
the
cent
re, r
adiu
s, d
iam
eter
and
circ
umfe
renc
e of
the
circ
le.
• S
pend
tim
e in
vest
igat
ing
the
rela
tions
hip
betw
een
radi
us, c
ircum
fere
nce
and
diam
eter
, so
that
lear
ners
dev
elop
a s
ense
of w
here
the
irrat
iona
l num
ber P
i (π)
is
der
ived
from
.
• D
evel
op a
n un
ders
tand
ing
of π
, mak
ing
sure
lear
ners
und
erst
and
that
:
-π
repr
esen
ts th
e va
lue
of th
e ci
rcum
fere
nce
divi
ded
by th
e di
amet
er, f
or a
ny
circ
le
-π
is a
n irr
atio
nal n
umbe
r an
d is
giv
en a
s 3,
141
592
654
corr
ect t
o 9
deci
mal
pl
aces
on
the
calc
ulat
or
-22
7
or 3
,14
are
appr
oxim
ate
ratio
nal v
alue
s of
π in
eve
ryda
y us
e.
MATHEMATICS GRADES 7-9
108 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
4.2
surf
ace
area
an
d vo
lum
e of
3d
obj
ects
surf
ace
area
and
vol
ume
• U
se a
ppro
pria
te fo
rmul
ae to
cal
cula
te
the
surfa
ce a
rea,
vol
ume
and
capa
city
of:
-cu
bes
-re
ctan
gula
r pris
ms
-tri
angu
lar p
rism
s
• D
escr
ibe
the
inte
rrel
atio
nshi
p be
twee
n su
rface
are
a an
d vo
lum
e of
th
e ob
ject
s m
entio
ned
abov
e
Cal
cula
tions
and
sol
ving
pro
blem
s
• S
olve
pro
blem
s, w
ith o
r with
out a
ca
lcul
ator
, inv
olvi
ng s
urfa
ce a
rea,
vo
lum
e an
d ca
paci
ty
• U
se a
nd c
onve
rt be
twee
n ap
prop
riate
S
I uni
ts, i
nclu
ding
:
-m
m2
↔ cm
2 ↔
m2
↔ km
2
-m
m3
↔ cm
3 ↔
m3
-m
l (cm
3 ) ↔
l ↔ kl
Wha
t is
diffe
rent
to G
rade
7?
• S
urfa
ce a
rea
and
volu
me
of tr
iang
ular
pris
ms
•Fo
rmul
ae le
arne
rs s
houl
d kn
ow a
nd u
se:
-th
e vo
lum
e of
a p
rism
= th
e ar
ea o
f the
bas
e x
the
heig
ht
-th
e su
rface
are
a of
a p
rism
= th
e su
m o
f the
are
a of
all
its fa
ces
-th
e vo
lum
e of
a c
ube
= l3
-th
e vo
lum
e of
a re
ctan
gula
r pris
m =
l x
b x
h
-th
e vo
lum
e of
a tr
iang
ular
pris
m =
(1 2b x
h) x
hei
ght o
f pris
m
• Fo
r con
vers
ions
, not
e:
-if
1 cm
= 1
0 m
m th
en 1
cm
3 = 1
000
mm
3 and
-if
1 m
= 1
00 c
m th
en 1
m3 =
1 0
00 0
00 c
m3 o
r 106
cm3
-an
obj
ect w
ith a
vol
ume
of 1
cm
3 w
ill d
ispl
ace
exac
tly 1
ml o
f wat
er
-an
obj
ect w
ith a
vol
ume
of 1
m3 w
ill d
ispl
ace
exac
tly 1
kl o
f wat
er.
• E
mph
asiz
e th
at th
e am
ount
of s
pace
insi
de a
pris
m is
cal
led
its c
apac
ity; a
nd
the
amou
nt o
f spa
ce o
ccup
ied
by a
pris
m is
cal
led
its v
olum
e.
• In
vest
igat
e th
e ne
ts o
f cub
es a
nd re
ctan
gula
r pris
ms
in o
rder
to d
educ
e fo
rmul
ae fo
r cal
cula
ting
thei
r sur
face
are
as.
exam
ple
of s
olvi
ng p
robl
ems
invo
lvin
g su
rfac
e ar
ea a
nd v
olum
e:
• C
alcu
late
the
volu
me
and
surfa
ce a
rea
of th
e pr
ism
if A
B =
8 c
m, B
C =
6 c
m a
nd
CF
= 16
cm
.A D
C F
EB
Tota
l tim
e fo
r su
rface
are
a an
d vo
lum
e:
5 ho
urs
MATHEMATICS GRADES 7-9
109CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
dat
a ha
ndlin
g5.
1C
olle
ct,
orga
nize
an
d su
mm
ariz
eda
ta
Col
lect
dat
a•
Pos
e qu
estio
ns re
latin
g to
soc
ial,
econ
omic
, and
env
ironm
enta
l iss
ues
• S
elec
t app
ropr
iate
sou
rces
for
the
colle
ctio
n of
dat
a (in
clud
ing
peer
s, fa
mily
, new
spap
ers,
boo
ks,
mag
azin
es)
• D
istin
guis
h be
twee
n sa
mpl
es a
nd
popu
latio
ns, a
nd s
ugge
st a
ppro
pria
te
sam
ples
for i
nves
tigat
ion
• D
esig
n an
d us
e si
mpl
e qu
estio
nnai
res
to a
nsw
er q
uest
ions
w
ith m
ultip
le c
hoic
e re
spon
ses
org
aniz
e an
d su
mm
ariz
e da
ta•
Org
aniz
e (in
clud
ing
grou
ping
whe
re
appr
opria
te) a
nd re
cord
dat
a us
ing
-ta
lly m
arks
-ta
bles
-st
em-a
nd-le
af d
ispl
ays
• G
roup
dat
a in
to in
terv
als
• S
umm
ariz
e da
ta u
sing
mea
sure
s of
ce
ntra
l ten
denc
y, in
clud
ing:
-m
ean
-m
edia
n -
mod
e
•
Sum
mar
ize
data
usi
ng m
easu
res
of
disp
ersi
on, i
nclu
ding
: -
rang
e -
extre
mes
Wha
t is
diffe
rent
to G
rade
7?
The
follo
win
g ar
e ne
w in
Gra
de 8
• ex
trem
es
• br
oken
line
gra
phs
• di
sper
sion
of d
ata
• er
ror a
nd b
ias
in d
ata
dat
a se
ts a
nd c
onte
xts
Lear
ners
sho
uld
be e
xpos
ed to
a v
arie
ty o
f con
text
s th
at d
eal w
ith s
ocia
l and
en
viro
nmen
tal i
ssue
s, a
nd s
houl
d w
ork
with
giv
en d
ata
sets
, rep
rese
nted
in
a va
riety
of w
ays,
that
incl
ude
big
num
ber r
ange
s, p
erce
ntag
es a
nd d
ecim
al
fract
ions
. Lea
rner
s sh
ould
then
pra
ctis
e or
gani
zing
and
sum
mar
izin
g th
is d
ata,
an
alys
ing
and
inte
rpre
ting
the
data
, and
writ
ing
a re
port
abou
t the
dat
a.
Com
plet
e a
data
cyc
leLe
arne
rs s
houl
d co
mpl
ete
at le
ast o
ne d
ata
cycl
e fo
r the
yea
r, st
artin
g w
ith p
osin
g th
eir o
wn
ques
tions
, sel
ectin
g th
e so
urce
s an
d m
etho
d fo
r col
lect
ing,
reco
rdin
g,
orga
nizi
ng, r
epre
sent
ing,
ana
lysi
ng, s
umm
ariz
ing,
inte
rpre
ting
and
repo
rting
the
data
. Cha
lleng
e le
arne
rs to
thin
k ab
out w
hat k
inds
of q
uest
ions
and
dat
a ne
ed to
be
col
lect
ed to
be
repr
esen
ted
on a
his
togr
am, a
pie
cha
rt, a
bar
gra
ph, o
r a li
ne
grap
h.
Tota
l tim
e fo
r co
llect
ing
and
orga
nizi
ng
data
:
4 ho
urs.
MATHEMATICS GRADES 7-9
110 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
5.5
rep
rese
nt
data
rep
rese
nt d
ata
• D
raw
a v
arie
ty o
f gra
phs
by h
and/
tech
nolo
gy to
dis
play
and
inte
rpre
t da
ta in
clud
ing:
-ba
r gra
phs
and
doub
le b
ar g
raph
s
-hi
stog
ram
s w
ith
give
n an
d ow
n in
terv
als
-pi
e ch
arts
-br
oken
-line
gra
phs
rep
rese
ntin
g da
ta
• D
raw
ing
pie
char
ts to
repr
esen
t dat
a do
not
hav
e to
be
accu
rate
ly d
raw
n w
ith a
co
mpa
ss a
nd p
rotra
ctor
, etc
. Lea
rner
s ca
n us
e an
y ro
und
obje
ct to
dra
w a
circ
le,
then
div
ide
the
circ
le in
to h
alve
s an
d qu
arte
rs a
nd e
ight
hs if
nee
ded,
as
a gu
ide
to e
stim
ate
the
prop
ortio
ns o
f the
circ
le th
at n
eed
to b
e sh
own
to re
pres
ent t
he
data
. Wha
t is
impo
rtant
is th
at th
e va
lues
or p
erce
ntag
es a
ssoc
iate
d w
ith th
e da
ta a
re s
how
n pr
opor
tiona
lly o
n th
e pi
e ch
art.
• D
raw
ing,
read
ing
and
inte
rpre
ting
pie
char
ts is
a u
sefu
l con
text
to re
-vis
it eq
uiva
lenc
e be
twee
n fra
ctio
ns a
nd p
erce
ntag
es, e
.g. 2
5% o
f the
dat
a is
re
pres
ente
d by
a 1 4 s
ecto
r of t
he c
ircle
.
• It
is a
con
text
in w
hich
lear
ners
can
find
per
cent
ages
of w
hole
num
bers
e.g
. if
25%
of 3
00 le
arne
rs li
ke ru
gby,
how
man
y (a
ctua
l num
ber)
lear
ners
like
rugb
y?
• H
isto
gram
s ar
e us
ed to
repr
esen
t gro
uped
dat
a sh
own
in in
terv
als
on th
e ho
rizon
tal a
xis
of th
e gr
aph.
Poi
nt o
ut th
e di
ffere
nces
bet
wee
n hi
stog
ram
s an
d ba
r gra
phs,
in p
artic
ular
bar
gra
phs
that
repr
esen
t dis
cret
e da
ta e
.g. f
avou
rite
spor
ts, c
ompa
red
to h
isto
gram
s th
at s
how
cat
egor
ies
in c
onse
cutiv
e, n
on-
over
lapp
ing
inte
rval
s, e
.g. t
est s
core
s ou
t of 1
00 s
how
n in
inte
rval
s of
10.
The
ba
rs o
n ba
r gra
phs
do n
ot h
ave
to to
uch
each
oth
er, w
hile
in a
his
togr
am th
ey
have
to to
uch
sinc
e th
ey s
how
con
secu
tive
inte
rval
s.
• B
roke
n-lin
e gr
aphs
refe
r to
data
gra
phs
that
repr
esen
t dat
a po
ints
join
ed b
y a
line
and
are
not t
he s
ame
as s
traig
ht li
ne g
raph
s th
at a
re d
raw
n us
ing
the
equa
tion
of th
e lin
e.
• B
roke
n-lin
e gr
aphs
are
use
d to
repr
esen
t dat
a th
at c
hang
es c
ontin
uous
ly o
ver
time,
e.g
. ave
rage
dai
ly te
mpe
ratu
re fo
r a m
onth
. Eac
h da
y’s
tem
pera
ture
is
repr
esen
ted
with
a p
oint
on
the
grap
h, a
nd o
nce
the
who
le m
onth
has
bee
n pl
otte
d, th
e po
ints
are
join
ed to
sho
w a
bro
ken-
line
grap
h.
• B
roke
n-lin
e gr
aphs
are
use
ful t
o re
ad ‘t
rend
s’ a
nd p
atte
rns
in th
e da
ta, f
or
pred
ictiv
e pu
rpos
es e
.g. w
ill th
e te
mpe
ratu
res
go u
p or
dow
n in
the
next
mon
th.
Tota
l tim
e fo
r re
pres
entin
g da
ta:
3 ho
urs
MATHEMATICS GRADES 7-9
111CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
5.6
inte
rpre
t, an
alys
e an
d re
port
dat
a
inte
rpre
t dat
a
• C
ritic
ally
read
and
inte
rpre
t dat
a re
pres
ente
d in
:
-w
ords
-ba
r gra
phs
-do
uble
bar
gra
phs
-pi
e ch
arts
-hi
stog
ram
s
-br
oken
-line
gra
phs
ana
lyse
dat
a
• C
ritic
ally
ana
lyse
dat
a by
ans
wer
ing
ques
tions
rela
ted
to:
-da
ta c
ateg
orie
s, in
clud
ing
data
in
terv
als
-da
ta s
ourc
es a
nd c
onte
xts
-ce
ntra
l ten
denc
ies
– (m
ean,
mod
e,
med
ian)
-sc
ales
use
d on
gra
phs
-sa
mpl
es a
nd p
opul
atio
ns
-di
sper
sion
of d
ata
-er
ror a
nd b
ias
in th
e da
ta
rep
ort d
ata
• S
umm
ariz
e da
ta in
sho
rt pa
ragr
aphs
th
at in
clud
e
-dr
awin
g co
nclu
sion
s ab
out t
he d
ata
-m
akin
g pr
edic
tions
bas
ed o
n th
e da
ta
-id
entif
ying
sou
rces
of e
rror
and
bi
as in
the
data
-ch
oosi
ng a
ppro
pria
te s
umm
ary
stat
istic
s fo
r the
dat
a (m
ean,
m
edia
n, m
ode,
rang
e)
-th
e ro
le o
f ext
rem
es in
the
data
dev
elop
ing
criti
cal a
naly
sis
skill
s
• Le
arne
rs s
houl
d co
mpa
re th
e sa
me
data
repr
esen
ted
in d
iffer
ent w
ays
e.g.
in a
pi
e ch
art o
r a b
ar g
raph
or a
tabl
e, a
nd d
iscu
ss w
hat i
nfor
mat
ion
is s
how
n an
d w
hat i
s hi
dden
; the
y sh
ould
eva
luat
e w
hat f
orm
of r
epre
sent
atio
n w
orks
bes
t for
th
e gi
ven
data
.
• Le
arne
rs s
houl
d co
mpa
re g
raph
s on
the
sam
e to
pic
but w
here
dat
a ha
s be
en
colle
cted
from
diff
eren
t gro
ups
of p
eopl
e, a
t diff
eren
t tim
es, i
n di
ffere
nt p
lace
s or
in d
iffer
ent w
ays.
Her
e le
arne
rs s
houl
d di
scus
s di
ffere
nces
bet
wee
n th
e da
ta
with
an
awar
enes
s of
bia
s re
late
d to
the
impa
ct o
f dat
a so
urce
s an
d m
etho
ds o
f da
ta c
olle
ctio
n on
the
inte
rpre
tatio
n of
the
data
.
• Le
arne
rs s
houl
d co
mpa
re d
iffer
ent w
ays
of s
umm
ariz
ing
the
sam
e da
ta s
ets,
de
velo
ping
an
awar
enes
s of
how
dat
a re
porti
ng c
an b
e m
anip
ulat
ed; t
hey
shou
ld e
valu
ate
whi
ch s
umm
ary
stat
istic
s be
st re
pres
ent t
he d
ata.
• Le
arne
rs s
houl
d co
mpa
re g
raph
s of
the
sam
e da
ta, w
here
the
scal
es o
f th
e gr
aphs
are
diff
eren
t. H
ere
lear
ners
sho
uld
disc
uss
diffe
renc
es w
ith a
n aw
aren
ess
of h
ow re
pres
enta
tion
of d
ata
can
be m
anip
ulat
ed; t
hey
shou
ld
eval
uate
whi
ch fo
rm o
f rep
rese
ntat
ion
wor
ks b
est f
or th
e gi
ven
data
.
• Le
arne
rs s
houl
d co
mpa
re d
ata
on th
e sa
me
topi
c, w
here
one
set
of d
ata
has
extre
mes
, and
dis
cuss
diff
eren
ces
with
an
awar
enes
s of
the
effe
ct o
f the
ex
trem
es o
n th
e in
terp
reta
tion
of th
e da
ta, i
n pa
rticu
lar,
extre
mes
affe
ct th
e ra
nge.
• Le
arne
rs s
houl
d w
rite
repo
rts o
n th
e da
ta in
sho
rt pa
ragr
aphs
.
Tota
l tim
e fo
r an
alys
ing,
in
terp
retin
g an
d su
mm
aris
ing
data
:
3,5
hour
s
MATHEMATICS GRADES 7-9
112 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
rev
isio
n/a
sses
smen
t:A
t thi
s st
age
lear
ners
sho
uld
have
bee
n as
sess
ed o
n:
• ca
lcul
atin
g an
d so
lvin
g pr
oble
ms
with
com
mon
frac
tions
and
dec
imal
frac
tions
• th
e Th
eore
m o
f Pyt
hago
ras
• ar
ea a
nd p
erim
eter
of 2
D s
hape
s
• su
rface
are
a an
d vo
lum
e of
3D
obj
ects
Tota
l tim
e fo
r rev
isio
n/as
sess
men
t fo
r the
term
6,5
hour
s.
MATHEMATICS GRADES 7-9
113CAPS
Gr
ad
e 8
– te
rm
4
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.2
Func
tions
and
re
latio
nshi
ps
inpu
t and
out
put v
alue
s•
Det
erm
ine
inpu
t val
ues,
out
put
valu
es o
r rul
es fo
r pat
tern
s an
d re
latio
nshi
ps u
sing
: -
flow
dia
gram
s -
tabl
es -
form
ulae
-eq
uatio
nseq
uiva
lent
form
s•
Det
erm
ine,
inte
rpre
t and
just
ify
equi
vale
nce
of d
iffer
ent d
escr
iptio
ns
of th
e sa
me
rela
tions
hip
or ru
le
pres
ente
d: -
verb
ally
-in
flow
dia
gram
s -
in ta
bles
-by
form
ulae
-by
equ
atio
ns
Func
tions
and
rela
tions
hips
wer
e al
so d
one
in T
erm
1. I
n th
is te
rm th
e fo
cus
is o
n us
ing
form
ulae
to fi
nd o
utpu
t val
ues
from
giv
en in
put v
alue
s, a
s w
ell a
s eq
uiva
lent
form
s of
des
crip
tions
of t
he s
ame
rela
tions
hip.
see
furt
her n
otes
and
exa
mpl
es in
ter
m 1
. ex
ampl
eU
se th
e fo
rmul
a fo
r the
are
a of
a re
ctan
gle:
A =
l x
b to
cal
cula
te th
e fo
llow
ing:
a)
The
area
, if t
he le
ngth
is 4
,5 c
m a
nd th
e w
idth
is 2
,5 c
m
b)
The
leng
th, i
f the
are
a is
240
cm
2 and
the
wid
th is
4 c
mc)
Th
e w
idth
, if t
he a
rea
is 1
4 cm
2 and
the
leng
th is
3,5
cm
Lear
ners
can
writ
e th
ese
as n
umbe
r sen
tenc
es, a
nd s
olve
by
insp
ectio
n.
Tim
e fo
r Fu
nctio
ns a
nd
Rel
atio
nshi
ps
in th
is te
rm:
6 ho
urs
2.4
alg
ebra
iceq
uatio
ns
equa
tions
• R
evis
e th
e fo
llow
ing
done
in G
rade
7:
-se
t up
equa
tions
to d
escr
ibe
prob
lem
situ
atio
ns -
anal
yse
and
inte
rpre
t equ
atio
ns
that
des
crib
e a
give
n si
tuat
ion
-so
lve
equa
tions
by
insp
ectio
n -
dete
rmin
e th
e nu
mer
ical
val
ue o
f an
exp
ress
ion
by s
ubst
itutio
n -
Iden
tify
varia
bles
and
con
stan
ts in
gi
ven
form
ulae
or e
quat
ions
• E
xten
d so
lvin
g eq
uatio
ns to
incl
ude:
-us
ing
addi
tive
and
mul
tiplic
ativ
e in
vers
es
-us
ing
law
s of
exp
onen
ts
• U
se s
ubst
itutio
n in
equ
atio
ns to
ge
nera
te ta
bles
of o
rder
ed p
airs
Alg
ebra
ic e
quat
ions
wer
e al
so d
one
in T
erm
s 1
and
2. In
this
term
the
focu
s is
on
usi
ng s
ubst
itutio
n in
equ
atio
ns to
gen
erat
e ta
bles
of o
rder
ed p
airs
.se
e fu
rthe
r not
es a
nd e
xam
ples
in t
erm
s 1
and
2.ex
ampl
es o
f gen
erat
ing
orde
red
pairs
a)
Com
plet
e th
e ta
ble
belo
w fo
r x a
nd y
val
ues
for t
he e
quat
ion:
y =
–3x
+ 2
x–3
–10
y–4
–10
b)
Com
plet
e th
e ta
ble
belo
w fo
r x a
nd y
val
ues
for t
he e
quat
ion:
y =
x2 –
2
x–3
–20
y–2
2
Tim
e fo
r A
lgeb
raic
eq
uatio
ns in
th
is te
rm:
3 ho
urs
MATHEMATICS GRADES 7-9
114 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.5
G
raph
s
inte
rpre
ting
grap
hs
• R
evis
e th
e fo
llow
ing
done
in G
rade
7:
-A
naly
se a
nd in
terp
ret g
loba
l gra
phs
of p
robl
em s
ituat
ions
, with
a s
peci
al
focu
s on
the
fol
low
ing
trend
s an
d fe
atur
es:
♦lin
ear o
r non
-line
ar
♦co
nsta
nt, i
ncre
asin
g or
de
crea
sing
• E
xten
d th
e fo
cus
on fe
atur
es o
f gr
aphs
to in
clud
e:
-m
axim
um o
r min
imum
-di
scre
te o
r con
tinuo
us
dra
win
g gr
aphs
• D
raw
glo
bal g
raph
s fro
m g
iven
de
scrip
tions
of a
pro
blem
situ
atio
n,
iden
tifyi
ng fe
atur
es li
sted
abo
ve
• U
se ta
bles
of o
rder
ed p
airs
to p
lot
poin
ts a
nd d
raw
gra
phs
on th
e C
arte
sian
pla
ne
Wha
t is
diffe
rent
to G
rade
7?
• N
ew fe
atur
es o
f glo
bal g
raph
s: m
axim
um a
nd m
inim
um; d
iscr
ete
and
cont
inuo
us
• P
lotti
ng p
oint
s to
dra
w g
raph
s
Exa
mpl
es o
f con
text
s fo
r glo
bal g
raph
s in
clud
e:
• th
e re
latio
nshi
p be
twee
n tim
e an
d di
stan
ce tr
avel
led
• th
e re
latio
nshi
p be
twee
n te
mpe
ratu
re a
nd ti
me
over
whi
ch it
is m
easu
red
• th
e re
latio
nshi
p be
twee
n ra
infa
ll an
d tim
e ov
er w
hich
it is
mea
sure
d, e
tc.
exam
ples
of d
raw
ing
grap
hs b
y pl
ottin
g po
ints
a)
Com
plet
e th
e ta
ble
of o
rder
ed p
airs
bel
ow fo
r the
equ
atio
n: y
= x
+ 3
x–4
–3–2
–1 0
12
34
y
Now
, plo
t the
abo
ve c
o-or
dina
te p
oint
s on
the
Car
tesi
an p
lane
. Joi
n po
ints
to
form
a g
raph
.
b)
Com
plet
e th
e ta
ble
of o
rder
ed p
airs
bel
ow fo
r the
equ
atio
n: y
= x
2 + 3
x–4
–3–2
–1 0
12
34
y
Now
, plo
t the
abo
ve c
o-or
dina
te p
oint
s on
the
Car
tesi
an p
lane
. Joi
n po
ints
to
form
a g
raph
.
Tota
l tim
e fo
r gr
aphs
:
9 ho
urs
MATHEMATICS GRADES 7-9
115CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
spac
e an
d sh
ape
(Geo
met
ry)
3.4
tran
sfor
mat
ion
Geo
met
ry
tran
sfor
mat
ions
• R
ecog
nize
, des
crib
e an
d pe
rform
tra
nsfo
rmat
ions
with
poi
nts
on a
co
ordi
nate
pla
ne, f
ocus
ing
on:
-re
flect
ing
a po
int i
n th
e y-
axis
or
x-a
xis
-tra
nsla
ting
a po
int w
ithin
and
ac
ross
qua
dran
ts
• R
ecog
nize
, des
crib
e an
d pe
rform
tra
nsfo
rmat
ions
with
tria
ngle
s on
a
co-o
rdin
ate
plan
e, fo
cusi
ng o
n th
e co
-ord
inat
es o
f the
ver
tices
whe
n:
-re
flect
ing
a tri
angl
e in
the
x-a
xis
or
y-ax
is
-tra
nsla
ting
a tri
angl
e w
ithin
and
ac
ross
qua
dran
ts
-ro
tatin
g a
trian
gle
arou
nd th
e or
igin
enla
rgem
ents
and
redu
ctio
ns•
Use
pro
porti
on to
des
crib
e th
e ef
fect
of
enl
arge
men
t or r
educ
tion
on a
rea
and
perim
eter
of g
eom
etric
figu
res
Wha
t is
diffe
rent
to G
rade
7?
• Tr
ansf
orm
atio
ns a
re d
one
on a
co-
ordi
nate
pla
ne
• C
o-or
dina
tes
of p
oint
s an
d ve
rtice
s
Co-
ordi
nate
pla
ne•
Doi
ng tr
ansf
orm
atio
ns o
n th
e co
-ord
inat
e pl
ane
is a
n op
portu
nity
to p
ract
ise
plot
ting
poin
ts w
ith o
rder
ed p
airs
, and
link
s up
with
dra
win
g al
gebr
aic
grap
hs.
• L
earn
ers
have
to le
arn
how
to p
lot p
oint
s on
the
co-o
rdin
ate
plan
e an
d re
ad
the
co-o
rdin
ates
of p
oint
s of
f the
x-a
xis
and
y-ax
is. T
his
is a
lso
done
with
al
gebr
aic
grap
hs.
• Le
arne
rs h
ave
to k
now
the
conv
entio
n fo
r writ
ing
orde
red
pairs
(x;y
)
• P
oint
out
the
diffe
renc
es b
etw
een
the
axes
in th
e fo
ur q
uadr
ants
.
Focu
s of
tran
sfor
mat
ions
• D
oing
tran
sfor
mat
ions
on
a co
-ord
inat
e pl
ane
focu
ses
atte
ntio
n on
the
co-
ordi
nate
s of
poi
nts
and
verti
ces
of s
hape
s.
• Le
arne
rs s
houl
d re
cogn
ize
that
tran
slat
ions
, refl
ectio
ns a
nd ro
tatio
ns o
nly
chan
ge th
e po
sitio
n of
the
figur
e, a
nd n
ot it
s sh
ape
or s
ize.
• Le
arne
rs s
houl
d re
cogn
ize
that
the
abov
e tra
nsfo
rmat
ions
pro
duce
con
grue
nt
figur
es.
• Le
arne
rs d
o no
t hav
e to
lear
n ge
nera
l rul
es fo
r the
tran
sfor
mat
ions
at t
his
stag
e, b
ut s
houl
d ex
plor
e th
e w
ay th
e co
-ord
inat
es o
f poi
nts
chan
ge w
hen
perfo
rmin
g di
ffere
nt tr
ansf
orm
atio
ns w
ith li
nes
or s
hape
s.
• Le
arne
rs s
houl
d re
cogn
ize
that
enl
arge
men
ts a
nd re
duct
ions
cha
nge
the
size
of
figu
res
by in
crea
sing
or d
ecre
asin
g th
e le
ngth
of s
ides
, but
kee
ping
the
angl
es th
e sa
me,
pro
duce
s si
mila
r rat
her t
han
cong
ruen
t figu
res.
• Le
arne
rs s
houl
d al
so b
e ab
le to
wor
k ou
t the
fact
or o
f enl
arge
men
t or
redu
ctio
n of
a fi
gure
.ex
ampl
es o
f tra
nsfo
rmat
ion
prob
lem
s•
Plo
t poi
nt A
(4;3
) and
A',
its im
age,
afte
r refl
ectio
n in
:
a)
the
x-a
xis
b)
the
y-a
xis.
• W
rite
dow
n th
e co
-ord
inat
es o
f T' i
f T(–
2;3)
is tr
ansl
ated
4 u
nits
dow
nwar
ds.
• Th
e pe
rimet
er o
f squ
are
AB
CD
= 4
8cm
a)
Writ
e do
wn
the
perim
eter
of t
he s
quar
e if
the
leng
th o
f eac
h si
de is
do
uble
d.
b)
Will
the
area
of t
he e
nlar
ged
squa
re b
e tw
ice
or fo
ur ti
mes
that
of t
he
orig
inal
squ
are?
Tota
l tim
e fo
r Tr
ansf
orm
a-tio
ns:
6 ho
urs
MATHEMATICS GRADES 7-9
116 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
3.2
Geo
met
ry o
f 3d
ob
ject
s
Cla
ssify
ing
3d o
bjec
ts
• D
escr
ibe,
nam
e an
d co
mpa
re th
e 5
Pla
toni
c so
lids
in te
rms
of th
e sh
ape
and
num
ber o
f fac
es, t
he n
umbe
r of
verti
ces
and
the
num
ber o
f edg
es
Bui
ldin
g 3d
mod
els
• R
evis
e us
ing
nets
to m
ake
mod
els
of
geom
etric
sol
ids,
incl
udin
g:
-cu
bes
-pr
ism
s
-py
ram
ids
Wha
t is
diffe
rent
to G
rade
7?
• N
amin
g an
d co
mpa
ring
Pla
toni
c so
lids
• N
ets
of p
yram
ids
Plat
onic
sol
ids
• P
lato
nic
solid
s ar
e a
spec
ial g
roup
of p
olyh
edra
that
hav
e fa
ces
that
are
co
ngru
ent r
egul
ar p
olyg
ons.
• Th
ere
are
only
5 P
lato
nic
solid
s:
-Te
trahe
dron
-H
exah
edro
n (c
ube)
-O
ctah
edro
n
-D
odec
ahed
ron
-Ic
osah
edro
ns
• Th
e na
me
of e
ach
Pla
toni
c so
lid is
der
ived
from
its
num
ber o
f fac
es.
• P
lato
nic
solid
s pr
ovid
e an
inte
rest
ing
cont
ext i
n w
hich
to in
vest
igat
e th
e re
latio
nshi
p be
twee
n th
e nu
mbe
r of f
aces
, ver
tices
and
edg
es. B
y lis
ting
thes
e pr
oper
ties
for a
ll th
e P
lato
nic
solid
s, le
arne
rs c
an in
vest
igat
e th
e pa
ttern
that
em
erge
s, to
com
e up
with
the
gene
ral r
ule:
V –
E +
F =
2, w
here
V =
num
ber
of v
ertic
es; E
= n
umbe
r of e
dges
; F =
num
ber o
f fac
es
usi
ng a
nd c
onst
ruct
ing
nets
• U
sing
and
con
stru
ctin
g ne
ts a
re u
sefu
l con
text
s fo
r exp
lorin
g or
con
solid
atin
g pr
oper
ties
of p
olyh
edra
.
• Le
arne
rs s
houl
d re
cogn
ize
the
nets
of d
iffer
ent s
olid
s.
• Le
arne
rs s
houl
d m
ake
sket
ches
of t
he n
ets
usin
g th
eir k
now
ledg
e of
the
shap
e an
d nu
mbe
r of f
aces
of t
he s
olid
s, b
efor
e dr
awin
g an
d cu
tting
out
the
nets
to b
uild
mod
els.
• S
ince
lear
ners
hav
e m
ore
know
ledg
e ab
out t
he s
ize
of a
ngle
s in
equ
ilate
ral
trian
gles
, and
can
mea
sure
ang
les,
thei
r con
stru
ctio
ns o
f net
s sh
ould
be
mor
e ac
cura
te.
• Le
arne
rs h
ave
to w
ork
out t
he re
lativ
e po
sitio
n of
face
s of
the
nets
in o
rder
to
build
the
3D m
odel
.
Tota
l tim
e fo
r ge
omet
ry o
f 3D
obj
ects
:
7 ho
urs
MATHEMATICS GRADES 7-9
117CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
dat
a ha
ndlin
g5.
4 P
roba
bilit
yPr
obab
ility
• C
onsi
der a
sim
ple
situ
atio
n (w
ith
equa
lly li
kely
out
com
es) t
hat c
an b
e de
scrib
ed u
sing
pro
babi
lity
and:
-lis
t all
the
poss
ible
out
com
es
-de
term
ine
the
prob
abili
ty o
f eac
h po
ssib
le o
utco
me
usin
g th
e de
finiti
on o
f pro
babi
lity
-pr
edic
t, w
ith re
ason
s, th
e re
lativ
e fre
quen
cy o
f the
pos
sibl
e ou
tcom
es
for a
ser
ies
of tr
ials
bas
ed o
n pr
obab
ility
-co
mpa
re re
lativ
e fre
quen
cy w
ith
prob
abili
ty a
nd e
xpla
in p
ossi
ble
diffe
renc
es
Prob
abili
ty e
xper
imen
tsIn
the
Inte
rmed
iate
Pha
se a
nd G
rade
7 le
arne
rs d
id p
roba
bilit
y ex
perim
ents
with
co
ins,
dic
e an
d sp
inne
rs. I
n G
rade
8 d
oing
act
ual t
rials
of e
xper
imen
ts b
ecom
e le
ss im
porta
nt, a
nd le
arne
rs s
houl
d co
nsid
er p
roba
bilit
y fo
r hyp
othe
tical
eve
nts
e.g.
the
prob
abili
ty o
f whi
te a
s a
succ
essf
ul o
utco
me
on a
roul
ette
tabl
e, o
r the
pr
obab
ility
of g
ettin
g a
Coc
a C
ola
at th
e sh
op if
you
kno
w w
hat t
he to
tal n
umbe
r of
drin
ks is
that
they
sto
ck a
nd h
ow m
any
cans
of C
oca
Col
a th
ey h
ave.
Com
parin
g re
lativ
e fr
eque
ncy
and
prob
abili
ty
• Th
e re
lativ
e fre
quen
cy is
the
obse
rved
num
ber o
f suc
cess
ful o
utco
mes
for a
fin
ite s
ampl
e of
tria
ls.
• Fo
r exa
mpl
e, if
you
toss
a c
oin
50 ti
mes
, the
resu
lts a
re 2
7 he
ads
and
23 ta
ils.
Defi
ne a
hea
d as
a s
ucce
ssfu
l out
com
e. T
he re
lativ
e fre
quen
cy o
f hea
ds is
: 27
50
= 5
4%
• Th
e pr
obab
ility
of a
hea
d is
50%
(one
of t
wo
likel
y ou
tcom
es).
The
diffe
renc
e be
twee
n th
e re
lativ
e fre
quen
cy o
f 54%
and
the
prob
abili
ty o
f 50%
is d
ue to
sm
all s
ampl
e si
ze.
• Th
e m
ore
trial
s yo
u do
, the
clo
ser t
he re
lativ
e fre
quen
cy g
ets
to th
e pr
obab
ility
. Th
is c
an b
e co
mpa
red
in c
lass
by
com
bini
ng re
sults
from
tria
ls d
one
in g
roup
s or
pai
rs.
Tota
l tim
e fo
r pr
obab
ility
:
4,5
hour
s
rev
isio
n/a
sses
smen
t:A
t thi
s st
age
lear
ners
sho
uld
have
bee
n as
sess
ed o
n:
• fu
nctio
ns a
nd re
latio
nshi
ps
• al
gebr
aic
equa
tions
• gr
aphs
• tra
nsfo
rmat
ion
geom
etry
• ge
omet
ry o
f 3D
obj
ects
• pr
obab
ility
Tota
l tim
e fo
r rev
isio
n/as
sess
men
t fo
r the
term
9, 5
hou
rs
MATHEMATICS GRADES 7-9
118 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
time alloCation Per term: Grade 9
term 1 term 2 term 3 term 4
topic time topic time topic time topic time
Whole numbers 4,5 hours
Construction of geometric figures
9 hours
Functions and relationships
5 hours
Transformation geometry
9 hours
Integers 4,5 hours
Geometry of 2D shapes
9 hours
Algebraic expressions
9 hours
Geometry of 3D objects
9 hours
Common fractions 4,5 hours
Geometry of straight-lines
9 hours
Algebraic equations
9 hours
Collect, organize and summarize data
4 hours
Decimal fractions 4,5 hours
Theorem of Pythagoras
5 hours Graphs 12
hours Represent data 3 hours
Exponents 5 hours
Area and Perimeter of 2D shapes
5 hours
Surface Area and volume of 3D objects
5 hours
Interpret, analyse and report data
3,5 hours
Numeric and geometric patterns
4,5 hours Probability 4,5
hours
Functions and relationships
4 hours
Algebraic expressions
4,5 hours
Algebraic equations
4 hours
revision/assessment
5 hours
revision/assessment
8 hours
revision/assessment
5 hours
revision/assessment
12 hours
total: 45 hours total: 45 hours total: 45 hours total: 45 hours
MATHEMATICS GRADES 7-9
119CAPS
3.3.3Clarifi
catio
nofcon
tentfo
rGrade9
Gr
ad
e 9
– te
rm
1
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, op
erat
ions
and
re
latio
nshi
ps
1.1
Who
le
num
bers
Prop
ertie
s of
num
bers
• D
escr
ibe
the
real
num
ber s
yste
m
by re
cogn
isin
g, d
efini
ng a
nd
dist
ingu
ishi
ng p
rope
rties
of:
-na
tura
l num
bers
-w
hole
num
bers
-in
tege
rs
-ra
tiona
l num
bers
-irr
atio
nal n
umbe
rs
Cal
cula
tions
usi
ng w
hole
num
bers
Rev
ise:
• C
alcu
latio
ns u
sing
all
four
ope
ratio
ns
on w
hole
num
bers
, est
imat
ing
and
usin
g ca
lcul
ator
s w
here
app
ropr
iate
Cal
cula
tion
tech
niqu
es
Use
a ra
nge
of s
trate
gies
to p
erfo
rm
and
chec
k w
ritte
n an
d m
enta
l ca
lcul
atio
ns o
f who
le n
umbe
rs
incl
udin
g:
• es
timat
ion
• ad
ding
, sub
tract
ing
and
mul
tiply
ing
in
colu
mns
• lo
ng d
ivis
ion
• ro
undi
ng o
ff an
d co
mpe
nsat
ing
• us
ing
a ca
lcul
ator
mul
tiple
s an
d fa
ctor
s
Use
prim
e fa
ctor
isat
ion
of n
umbe
rs to
fin
d LC
M a
nd H
CF
Wha
t is
diffe
rent
to G
rade
8?
In G
rade
9 le
arne
rs c
onso
lidat
e nu
mbe
r kno
wle
dge
and
calc
ulat
ion
tech
niqu
es fo
r w
hole
num
bers
, dev
elop
ed in
Gra
de 8
.
• Th
e fo
cus
in G
rade
9 s
houl
d be
on
deve
lopi
ng a
n un
ders
tand
ing
of d
iffer
ent
num
ber s
yste
ms
and
the
prop
ertie
s of
ope
ratio
ns th
at a
pply
for d
iffer
ent n
umbe
r sy
stem
s.
• Th
e co
ntex
ts fo
r sol
ving
pro
blem
s sh
ould
be
mor
e co
mpl
ex a
nd v
arie
d, in
volv
ing
who
le n
umbe
rs, i
nteg
ers
and
ratio
nal n
umbe
rs. F
inan
cial
con
text
s ar
e es
peci
ally
ric
h in
this
rega
rd.
• Le
arne
rs s
houl
d be
giv
en a
cle
ar in
dica
tion
of w
hen
the
use
of c
alcu
lato
rs is
pe
rmis
sibl
e or
not
. Cal
cula
tors
sho
uld
be u
sed
rout
inel
y fo
r cal
cula
tions
with
big
nu
mbe
rs a
nd w
here
kno
wle
dge
of n
umbe
r fac
ts o
r con
cept
s ar
e no
t exp
licitl
y as
sess
ed. H
owev
er, g
uard
aga
inst
lear
ners
bec
omin
g de
pend
ent o
n ca
lcul
ator
s fo
r all
calc
ulat
ions
. Cal
cula
tors
rem
ain
a us
eful
tool
for c
heck
ing
solu
tions
.
• C
ompe
tenc
y in
find
ing
mul
tiple
s an
d fa
ctor
s, a
nd p
rime
fact
oris
atio
n of
who
le
num
bers
, rem
ains
impo
rtant
for d
evel
opin
g co
mpe
tenc
y in
fact
oris
ing
alge
brai
c ex
pres
sion
s an
d so
lvin
g al
gebr
aic
equa
tions
.
Prop
ertie
s of
num
bers
• B
y di
stin
guis
hing
the
prop
ertie
s of
diff
eren
t num
ber s
yste
ms,
lear
ners
sho
uld
reco
gniz
e th
at n
atur
al n
umbe
rs is
a s
ubse
t of w
hole
num
bers
, whi
ch in
turn
is
a su
bset
of i
nteg
ers,
whi
ch in
turn
is a
sub
set o
f rat
iona
l num
bers
. All
of th
ese
num
bers
form
par
t of t
he re
al n
umbe
r sys
tem
.
• N
ote
that
0 m
ay s
omet
imes
be
incl
uded
in th
e se
t of n
atur
al n
umbe
rs.
• Le
arne
rs s
houl
d re
cogn
ize
the
follo
win
g di
stin
guis
hing
feat
ures
of t
he n
umbe
r sy
stem
s:
-in
tege
rs e
xten
d th
e na
tura
l and
who
le n
umbe
r sys
tem
s by
incl
udin
g th
e op
erat
ion
a –
b, w
here
a <
b.
-ra
tiona
l num
bers
ext
end
the
set o
f int
eger
s by
incl
udin
g th
e op
erat
ion
a b w
here
a <
b
-ra
tiona
l num
bers
are
defi
ned
as n
umbe
rs th
at c
an b
e w
ritte
n in
the
form
a b w
here
a a
nd b
are
inte
gers
and
b ≠
0
-si
nce
inte
gers
are
a s
ubse
t of r
atio
nal n
umbe
rs, e
very
inte
ger,
can
be
expr
esse
d as
a ra
tiona
l num
ber a b
Tota
l tim
e fo
r who
le
num
bers
4, 5
hou
rs.
MATHEMATICS GRADES 7-9
120 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, op
erat
ions
and
re
latio
nshi
ps
1.1
Who
le
num
bers
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
-ra
tio a
nd ra
te
-di
rect
and
indi
rect
pro
porti
on
-irr
atio
nal n
umbe
rs a
re n
umbe
rs th
at c
anno
t be
expr
esse
d as
ratio
nal
num
bers
in th
e fo
rm a b
-Pi
(π) i
s an
irra
tiona
l num
ber,
even
thou
gh w
e us
e 22
7
or 3
,14
as ra
tiona
l nu
mbe
r app
roxi
mat
ions
for π
in c
alcu
latio
ns
rat
io a
nd ra
te p
robl
ems
• In
clud
e pr
oble
ms
invo
lvin
g sp
eed,
dis
tanc
e an
d tim
e. L
earn
ers
shou
ld b
e fa
mili
ar w
ith th
e fo
llow
ing
form
ulae
for t
hese
cal
cula
tions
:
a)
spee
d =
dist
ance
tim
e
b)
dist
ance
= s
peed
x ti
me
c)
time
= di
stan
ce
spee
d
• S
peed
is u
sual
ly g
iven
as
cons
tant
spe
ed o
r ave
rage
spe
ed.
• M
ake
sure
lear
ners
reco
gniz
e an
d ar
e ab
le to
con
vert
corr
ectly
bet
wee
n un
its
for t
ime
and
dist
ance
.
exam
ples
a)
A ca
r tra
velli
ng a
t a c
onst
ant s
peed
trav
els
60 k
m in
18
min
utes
. How
far,
trave
lling
at t
he s
ame
cons
tant
spe
ed, w
ill th
e ca
r tra
vel i
n 1
hour
12
min
utes
?
b)
A ca
r tra
velli
ng a
t an
aver
age
spee
d of
100
km
/h c
over
s a
certa
in d
ista
nce
in
3 ho
urs
20 m
inut
es. A
t wha
t con
stan
t spe
ed m
ust t
he c
ar tr
avel
to c
over
the
sam
e di
stan
ce in
2 h
ours
40
min
utes
?
dire
ct a
nd in
dire
ct p
ropo
rtio
n
Lear
ners
sho
uld
be fa
mili
ar w
ith th
e fo
llow
ing
rela
tions
hips
:
• x
is d
irect
ly p
ropo
rtion
al to
y if
x y = c
onst
ant
• x
and
y ar
e di
rect
ly p
ropo
tiona
l if,
as th
e va
lue
of x
incr
ease
s th
e va
lue
of y
in
crea
ses
in th
e sa
me
prop
ortio
n, a
nd a
s th
e va
lue
of x
dec
reas
es th
e va
lue
of y
de
crea
ses
in th
e sa
me
prop
ortio
n
• Th
e di
rect
pro
porti
onal
rela
tions
hip
is re
pres
ente
d by
a s
traig
ht li
ne g
raph
• x
is in
dire
ctly
or i
nver
sely
pro
porti
onal
to y
if x
x y
= a
con
stan
t. In
oth
er w
ords
y
= c x
• x
and
y ar
e in
dire
ctly
pro
potio
nal i
f, as
the
valu
e of
x in
crea
ses
the
valu
e of
y
decr
ease
s an
d as
the
valu
e of
x d
ecre
ases
the
valu
e of
y in
crea
ses
• an
indi
rect
pro
porti
onal
rela
tions
hip
is re
pres
ente
d by
a n
on-li
near
cur
ve
MATHEMATICS GRADES 7-9
121CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
num
bers
, op
erat
ions
and
re
latio
nshi
ps
1.1
Who
le
num
bers
• S
olve
pro
blem
s th
at in
volv
e w
hole
nu
mbe
rs, p
erce
ntag
es a
nd d
ecim
al
fract
ions
in fi
nanc
ial c
onte
xts
such
as
:
-pr
ofit,
loss
, dis
coun
t and
VAT
-bu
dget
s
-ac
coun
ts a
nd lo
ans
-si
mpl
e in
tere
st a
nd h
ire p
urch
ase
-ex
chan
ge ra
tes
and
com
mis
sion
-re
ntal
s
-co
mpo
und
inte
rest
Fina
ncia
l con
text
s
• O
nce
lear
ners
hav
e do
ne s
uffic
ient
cal
cula
tions
for s
impl
e an
d co
mpo
und
inte
rest
thro
ugh
repe
ated
cal
cula
tions
, the
y co
uld
use
give
n fo
rmul
ae fo
r the
se
calc
ulat
ions
.
exam
ples
a)
Cal
cula
te th
e si
mpl
e in
tere
st o
n R
600
at 7
% p
.a fo
r 3 y
ears
usi
ng th
e fo
rmul
a SI
= P.
n.r
100 o
r SI =
P.n
.i fo
r i =
r
10
0 .
b)
R80
0 in
vest
ed a
t r%
per
ann
um s
impl
e in
tere
st fo
r a p
erio
d of
3 y
ears
yi
elds
R16
8. C
alcu
late
the
valu
e of
r
c)
How
long
will
it ta
ke fo
r R3
000
inve
sted
at 6
% p
er a
nnum
sim
ple
inte
rest
to
grow
to R
4 26
0?
d)
Tem
oso
borr
owed
R50
0 fro
m th
e ba
nk fo
r 3 y
ears
at 8
% p
.a. c
ompo
und
inte
rest
. With
out u
sing
a fo
rmul
a, c
alcu
late
how
muc
h Te
mos
o ow
es th
e ba
nk a
t the
end
of t
hree
yea
rs.
e)
Use
the
form
ula
A =
P(1
+
r
100 )n to
cal
cula
te th
e co
mpo
und
inte
rest
on
a lo
an o
f R3
450
at 6
,5%
per
ann
um fo
r 5 y
ears
.
1.3
inte
gers
Cal
cula
tions
with
inte
gers
• R
evis
e:
-pe
rform
cal
cula
tions
invo
lvin
g al
l fo
ur o
pera
tions
with
inte
gers
-pe
rform
cal
cula
tions
invo
lvin
g al
l fo
ur o
pera
tions
with
num
bers
that
in
volv
e th
e sq
uare
s, c
ubes
, squ
are
root
s an
d cu
be ro
ots
of in
tege
rs
Prop
ertie
s of
inte
gers
• R
evis
e:
-co
mm
utat
ive,
ass
ocia
tive
and
dist
ribut
ive
prop
ertie
s of
add
ition
an
d m
ultip
licat
ion
for i
nteg
ers
-ad
ditiv
e an
d m
ultip
licat
ive
inve
rses
fo
r int
eger
s
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
mul
tiple
ope
ratio
ns w
ith in
tege
rs
Wha
t is
diffe
rent
to G
rade
8?
In G
rade
9 le
arne
rs c
onso
lidat
e nu
mbe
r kno
wle
dge
and
calc
ulat
ion
tech
niqu
es fo
r in
tege
rs, d
evel
oped
in G
rade
8.
In G
rade
9, l
earn
ers
wor
k w
ith in
tege
rs m
ostly
as
coef
ficie
nts
in a
lgeb
raic
ex
pres
sion
s an
d eq
uatio
ns. T
hey
are
expe
cted
to b
e co
mpe
tent
in p
erfo
rmin
g al
l fo
ur o
pera
tions
with
inte
gers
and
usi
ng th
e pr
oper
ties
of in
tege
rs a
ppro
pria
tely
w
here
nec
essa
ry.
Tota
l tim
e fo
r In
tege
rs:
4,5
hour
s
MATHEMATICS GRADES 7-9
122 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
1.4
Com
mon
fr
actio
ns
Cal
cula
tions
usi
ng fr
actio
ns
• A
ll fo
ur o
pera
tions
with
com
mon
fra
ctio
ns a
nd m
ixed
num
bers
• A
ll fo
ur o
pera
tions
, with
num
bers
that
in
volv
e th
e sq
uare
s, c
ubes
, squ
are
root
s an
d cu
be ro
ots
of c
omm
on
fract
ions
Cal
cula
tion
tech
niqu
es
• R
evis
e:
-C
onve
rt m
ixed
num
bers
to
com
mon
frac
tions
in o
rder
to
perfo
rm c
alcu
latio
ns w
ith th
em
-U
se k
now
ledg
e of
mul
tiple
s an
d fa
ctor
s to
writ
e fra
ctio
ns in
the
sim
ples
t for
m b
efor
e or
afte
r ca
lcul
atio
ns
-U
se k
now
ledg
e of
equ
ival
ent
fract
ions
to a
dd a
nd s
ubtra
ct
com
mon
frac
tions
-U
se k
now
ledg
e of
reci
proc
al
rela
tions
hips
to d
ivid
e co
mm
on
fract
ions
solv
ing
prob
lem
s
Sol
ve p
robl
ems
in c
onte
xts
invo
lvin
g co
mm
on fr
actio
ns, m
ixed
num
bers
and
pe
rcen
tage
s
equi
vale
nt fo
rms
• R
evis
e eq
uiva
lent
form
s be
twee
n:
-co
mm
on fr
actio
ns w
here
one
de
nom
inat
or is
a m
ultip
le o
f an
othe
r
-co
mm
on fr
actio
n an
d de
cim
al
fract
ion
form
s of
the
sam
e nu
mbe
r
-co
mm
on fr
actio
n, d
ecim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r
Wha
t is
diffe
rent
to G
rade
8?
In G
rade
9 le
arne
rs c
onso
lidat
e nu
mbe
r kno
wle
dge
and
calc
ulat
ion
tech
niqu
es fo
r co
mm
on fr
actio
ns, d
evel
oped
in G
rade
8.
In G
rade
9, l
earn
ers
wor
k w
ith c
omm
on fr
actio
ns m
ostly
as
coef
ficie
nts
in a
lgeb
ra-
ic e
xpre
ssio
ns a
nd e
quat
ions
. The
y ar
e ex
pect
ed to
be
com
pete
nt in
per
form
ing
mul
tiple
ope
ratio
ns u
sing
com
mon
frac
tions
and
mix
ed n
umbe
rs, a
pply
ing
prop
er-
ties
of ra
tiona
l num
bers
app
ropr
iate
ly. T
hey
are
also
exp
ecte
d to
reco
gniz
e an
d us
e eq
uiva
lent
form
s fo
r com
mon
frac
tions
app
ropr
iate
ly in
cal
cula
tions
and
whe
n si
mpl
ifyin
g al
gebr
aic
fract
ions
.
Tota
l tim
e fo
r com
mon
fra
ctio
ns:
4,5
hour
s
MATHEMATICS GRADES 7-9
123CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
1.5
dec
imal
fr
actio
ns
Cal
cula
tions
with
dec
imal
frac
tions
• m
ultip
le o
pera
tions
with
dec
imal
fra
ctio
ns, u
sing
a c
alcu
lato
r whe
re
appr
opria
te
• m
ultip
le o
pera
tions
, with
or w
ithou
t br
acke
ts, w
ith n
umbe
rs th
at in
volv
e th
e sq
uare
s, c
ubes
, squ
are
root
s an
d cu
be ro
ots
of d
ecim
al fr
actio
ns
Cal
cula
tion
tech
niqu
es
• U
se k
now
ledg
e of
pla
ce v
alue
s to
es
timat
e th
e nu
mbe
r of d
ecim
al
plac
es in
the
resu
lt be
fore
per
form
ing
calc
ulat
ions
• U
se ro
undi
ng o
ff an
d a
calc
ulat
or to
ch
eck
resu
lts w
here
app
ropr
iate
solv
ing
prob
lem
s
Sol
ve p
robl
ems
in c
onte
xt in
volv
ing
deci
mal
frac
tions
equi
vale
nt fo
rms
• R
evis
e eq
uiva
lent
form
s be
twee
n:
-co
mm
on fr
actio
n an
d de
cim
al
fract
ion
form
s of
the
sam
e nu
mbe
r
-co
mm
on fr
actio
n, d
ecim
al fr
actio
n an
d pe
rcen
tage
form
s of
the
sam
e nu
mbe
r
Wha
t is
diffe
rent
to G
rade
8?
In G
rade
9 le
arne
rs c
onso
lidat
e nu
mbe
r kno
wle
dge
and
calc
ulat
ion
tech
niqu
es fo
r de
cim
al fr
actio
ns, d
evel
oped
in G
rade
8.
In G
rade
9, l
earn
ers
wor
k w
ith d
ecim
al fr
actio
ns m
ostly
as
coef
ficie
nts
in a
lgeb
raic
ex
pres
sion
s an
d eq
uatio
ns. T
hey
are
expe
cted
to b
e co
mpe
tent
in p
erfo
rmin
g m
ultip
le o
pera
tions
usi
ng d
ecim
al fr
actio
ns a
nd m
ixed
num
bers
, app
lyin
g pr
oper
-tie
s of
ratio
nal n
umbe
rs a
ppro
pria
tely.
The
y ar
e al
so e
xpec
ted
to re
cogn
ize
and
use
equi
vale
nt fo
rms
for d
ecim
al fr
actio
ns a
ppro
pria
tely
in c
alcu
latio
ns.
Tota
l tim
e fo
r dec
imal
fra
ctio
ns:
4,5
hour
s
MATHEMATICS GRADES 7-9
124 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
1.2
expo
nent
sC
ompa
ring
and
repr
esen
ting
num
bers
in e
xpon
entia
l for
m
• R
evis
e:
-co
mpa
re a
nd r
epre
sent
inte
gers
in
expo
nent
ial f
orm
-co
mpa
re a
nd re
pres
ent n
umbe
rs in
sc
ient
ific
nota
tion
• E
xten
d sc
ient
ific
nota
tion
to in
clud
e ne
gativ
e ex
pone
nts
Cal
cula
tions
usi
ng n
umbe
rs in
ex
pone
ntia
l for
m
• R
evis
e th
e fo
llow
ing
gene
ral l
aws
of
expo
nent
s:
-am
x a
n = a
m +
n
-am
÷ a
n = a
m -
n , if
m>n
-(a
m)n =
am
x n
-(a
x t)
n = a
n x
t n
-a0 =
1
• E
xten
d th
e ge
nera
l law
s of
exp
onen
ts
to in
clud
e:
-in
tege
r exp
onen
ts
-a–m
=
1 am
• P
erfo
rm c
alcu
latio
ns in
volv
ing
all
four
ope
ratio
ns u
sing
num
bers
in
expo
nent
ial f
orm
solv
ing
prob
lem
s
• S
olve
pro
blem
s in
con
text
s in
volv
ing
num
bers
in e
xpon
entia
l for
m,
incl
udin
g sc
ient
ific
nota
tion
Wha
t is
diffe
rent
to G
rade
8?
• A
dditi
onal
law
s of
exp
onen
ts in
volv
ing
inte
ger e
xpon
ents
• S
cien
tific
nota
tion
for n
umbe
rs, i
nclu
ding
neg
ativ
e ex
pone
nts
In G
rade
9 le
arne
rs c
onso
lidat
e nu
mbe
r kno
wle
dge
and
calc
ulat
ion
tech
niqu
es fo
r ex
pone
nts,
dev
elop
ed in
Gra
de 8
.
law
s of
exp
onen
ts
• Th
e la
ws
of e
xpon
ents
sho
uld
be in
trodu
ced
thro
ugh
a ra
nge
of n
umer
ic
exam
ples
firs
t, th
en v
aria
bles
can
be
used
.
• Th
e fo
llow
ing
law
s of
exp
onen
ts s
houl
d be
kno
wn,
whe
re m
and
n a
re in
tege
rs
and
a an
d t a
re n
ot e
qual
to 0
:
am x
an =
am
+nam
÷ a
n = a
m -
n
exam
ples
exam
ples
a)
23 x 2
4 = 2
3+4 =
27 =
128
a) 3
5 ÷ 3
2 = 3
3 = 2
7
b)
x3 x x
4 = x
3+4 =
x7
b) x
5 ÷ x
3 = x
2
(am)n =
am
x n
(a x
t)n =
an x
t n
exam
ples
exam
ples
a)
(23 )2 =
26 =
64
a) (
3x2 )3 =
33 x
6 = 2
7x6
a0 = 1
a–m =
1 am
exam
ples
exam
ples
a)
(37)
0 = 1
a)
5–3
= 1 53
= 1 75
b)
(4x2 )0 =
1
b) 7
3 ÷ 7
5 = 7
–2 =
1 72 =
1 49
• m
ake
sure
lear
ners
und
erst
and
thes
e la
ws
read
ing
from
bot
h si
des
of th
e eq
ual
sign
i.e.
if th
e LH
S =
RH
S, t
hen
the
RH
S =
LH
S
Tota
l tim
e fo
r ex
pone
nts:
5 ho
urs
MATHEMATICS GRADES 7-9
125CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
• Th
e la
w a
0 = 1
can
be
deriv
ed b
y us
ing
the
law
of e
xpon
ents
for d
ivis
ion
in a
few
ex
ampl
es e
.g. a
4 ÷
a4 =
a x
a x
a x
a a
x a
x a
x a =
1, t
here
fore
a4–
4 = a0 =
1
• Le
arne
rs s
houl
d be
abl
e to
use
the
law
s of
exp
onen
ts in
cal
cula
tions
and
for
solv
ing
sim
ple
expo
nent
ial e
quat
ions
as
wel
l as
expa
ndin
g an
d si
mpl
ifyin
g al
gebr
aic
expr
essi
ons.
• Lo
ok o
ut fo
r the
follo
win
g co
mm
on m
isco
ncep
tions
whe
re:
-Le
arne
rs m
ultip
ly u
nlik
e ba
ses
and
add
the
expo
nent
s
Exa
mpl
e: x
m x
yn =
(xy)
m +
n
25 x
27 = 4
9 inst
ead
of th
e co
rrec
t ans
wer
29
-Le
arne
rs fo
rget
the
mid
dle
term
of t
he b
inom
ial e
.g. (
x +
y)m
= x
m +
ym
-Le
arne
rs c
onfu
se a
ddin
g th
e ex
pone
nts
and
addi
ng th
e te
rms,
e.g
. xm
+ x
n =
xm +
n
-Le
arne
rs c
onfu
se th
e ex
pone
nt o
f the
var
iabl
e an
d th
e co
effic
ient
e.g
. 2x
–3 =
1
2x3 i
nste
ad o
f the
cor
rect
ans
wer
2 1
x2
Cal
cula
tions
and
sim
ple
equa
tions
usi
ng n
umbe
rs in
exp
onen
tial f
orm
• Th
e ca
lcul
atio
ns a
nd e
quat
ions
sho
uld
prov
ide
oppo
rtuni
ties
to a
pply
the
law
s of
ex
pone
nts
and
shou
ld n
ot b
e un
duly
com
plex
.
exam
ples
a)
Cal
cula
te: 2
–1 x
63 x
3–2
b)
Sim
plify
: (–2
x2 )(–2
x)–2
c)
Sol
ve x
: 3x =
9
d)
Sol
ve x
: 2x =
1 4
e)
5x+1 =
1
Scientificno
tatio
n
• W
hen
writ
ing
num
bers
in s
cien
tific
nota
tion,
lear
ners
hav
e to
und
erst
and
the
rela
tions
hip
betw
een
the
num
ber o
f dec
imal
pla
ces
and
the
inde
x of
10.
exam
ple:
25
= 2,
5 x
101 ;
and
250
= 2,
5 x
102
• S
cien
tific
nota
tion
that
ext
ends
to n
egat
ive
expo
nent
s in
clud
es w
ritin
g ve
ry s
mal
l nu
mbe
rs in
sci
entifi
c no
tatio
n.
MATHEMATICS GRADES 7-9
126 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
1.2
expo
nent
sex
ampl
e: 2
5 m
illio
nth
= 2,
5 x
10–5
• Le
arne
rs p
ract
ise
writ
ing
smal
l and
larg
e nu
mbe
rs in
sci
entifi
c no
tatio
n, w
hich
th
ey m
ight
alre
ady
have
enc
ount
ered
in N
atur
al S
cien
ce. I
t is
usef
ul to
refe
r to
thes
e co
ntex
ts w
hen
disc
ussi
ng s
cien
tific
nota
tion.
• C
alcu
latio
ns c
an b
e do
ne w
ith o
r with
out a
cal
cula
tor.
exam
ples
a)
Cal
cula
te: 2
,6 x
105 x
9 x
107
with
out u
sing
a c
alcu
lato
r and
giv
e an
swer
in
scie
ntifi
c no
tatio
n.
b)
Writ
e in
sci
entifi
c no
tatio
n: 0
,000
53
c)
Cal
cula
te: 5
,8 x
10–4
+ 2
,3 x
10–5
with
out u
sing
a c
alcu
lato
r.
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.1
num
eric
and
ge
omet
ric
patte
rns
inve
stig
ate
and
exte
nd p
atte
rns
• In
vest
igat
e an
d ex
tend
num
eric
an
d ge
omet
ric p
atte
rns
look
ing
for
rela
tions
hips
bet
wee
n nu
mbe
rs
incl
udin
g pa
ttern
s:
-re
pres
ente
d in
phy
sica
l or
diag
ram
fo
rm
-no
t lim
ited
to s
eque
nces
invo
lvin
g a
cons
tant
diff
eren
ce o
r rat
io
-of
lear
ner’s
ow
n cr
eatio
n
-re
pres
ente
d in
tabl
es
-re
pres
ente
d al
gebr
aica
lly
• D
escr
ibe
and
just
ify th
e ge
nera
l rul
es
for o
bser
ved
rela
tions
hips
bet
wee
n nu
mbe
rs in
ow
n w
ords
or i
n al
gebr
aic
lang
uage
Wha
t is
diffe
rent
to G
rade
8?
Lear
ners
con
solid
ate
wor
k in
volv
ing
num
eric
and
geo
met
ric p
atte
rns
done
in
Gra
de 8
.
• In
vest
igat
ing
num
ber p
atte
rns
is a
n op
portu
nity
to g
ener
aliz
e –
to g
ive
gene
ral
alge
brai
c de
scrip
tions
of t
he re
latio
nshi
p be
twee
n te
rms
and
thie
r pos
ition
in a
se
quen
ce a
nd to
just
ify s
olut
ions
.
Kin
ds o
f num
eric
pat
tern
s
• G
iven
a s
eque
nce
of n
umbe
rs, l
earn
ers
have
to id
entif
y a
patte
rn o
r re
latio
nshi
p be
twee
n co
nsec
utiv
e te
rms
in o
rder
to e
xten
d th
e pa
ttern
.
exam
ples
Pro
vide
a ru
le to
des
crib
e th
e re
latio
nshi
p be
twee
n th
e nu
mbe
rs in
the
sequ
ence
s be
low
. Use
this
rule
to g
ive
the
next
thre
e nu
mbe
rs in
the
sequ
ence
:
a)
–1; –
1,5;
–2;
–2,
5 ...
...
Her
e le
arne
rs s
houl
d id
entif
y th
e co
nsta
nt d
iffer
ence
bet
wee
n co
nsec
utiv
e te
rms
in o
rder
to e
xten
d th
e pa
ttern
. Thi
s pa
ttern
can
be
desc
ribed
in
lear
ners
’ ow
n w
ords
as
‘add
ing
–0,5
’ or ‘
coun
ting
in –
0,5s
’ or
‘add
–0,
5 to
th
e pr
evio
us n
umbe
r in
the
patte
rn’.
b)
2; –
1; 0
,5; –
0,25
; 0,
125
... ..
.
Her
e le
arne
rs s
houl
d id
entif
y th
e co
nsta
nt ra
tio b
etw
een
cons
ecut
ive
term
s. T
his
patte
rn c
an b
e de
scrib
ed in
lear
ners
’ ow
n w
ords
as
‘mul
tiply
the
prev
ious
num
ber b
y –0
,5 ’.
Tota
l tim
e fo
r nu
mer
ic a
nd
geom
etric
pa
ttern
s
4, 5
hou
rs
MATHEMATICS GRADES 7-9
127CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.1
num
eric
and
ge
omet
ric
patte
rns
c)
1; 0
; –2;
–5;
–9;
–14
... .
This
pat
tern
has
nei
ther
a c
onst
ant d
iffer
ence
nor
con
stan
t rat
io. T
his
patte
rn c
an b
e de
scrib
ed in
lear
ners
’ ow
n w
ords
as
‘sub
tract
1 m
ore
than
w
as s
ubtra
cted
to g
et th
e pr
evio
us te
rm’.
Usi
ng th
is ru
le, t
he n
ext 3
term
s w
ill b
e –2
0, –
27, –
35
• G
iven
a s
eque
nce
of n
umbe
rs, l
earn
ers
have
to id
entif
y a
patte
rn o
r re
latio
nshi
p be
twee
n th
e te
rm a
nd it
s po
sitio
n in
the
sequ
ence
. Thi
s en
able
s le
arne
rs to
pre
dict
a te
rm in
a s
eque
nce
base
d on
the
posi
tion
of th
at
term
in th
e se
quen
ce. I
t is
usef
ul fo
r lea
rner
s to
repr
esen
t the
se s
eque
nces
in
tabl
es s
o th
at th
ey c
an c
onsi
der t
he p
ositi
on o
f the
term
.
exam
ples
a)
Pro
vide
a ru
le to
des
crib
e th
e re
latio
nshi
p be
twee
n th
e nu
mbe
rs in
this
se
quen
ce:
2; 5
; 10;
17
... .
Use
you
r rul
e to
find
the
10th
term
in th
is
sequ
ence
.
Firs
tly, l
earn
ers
have
to u
nder
stan
d th
at th
e ‘1
0th
term
’ ref
ers
to p
ositi
on 1
0 in
th
e nu
mbe
r seq
uenc
e. T
hey
have
to fi
nd a
rule
in o
rder
to d
eter
min
e th
e 10
th
term
, rat
her t
han
cont
inui
ng th
e se
quen
ce u
p to
the
tent
h te
rm.
This
seq
uenc
e ca
n be
repr
esen
ted
in th
e fo
llow
ing
tabl
e:
Pos
ition
in s
eque
nce
12
34
10
Term
25
1017
?
Lear
ners
hav
e to
reco
gniz
e th
at e
ach
term
in th
e bo
ttom
row
is o
btai
ned
by s
quar
ing
the
posi
tion
num
ber i
n th
e to
p ro
w a
nd a
ddin
g. T
hus
the
10th
te
rm w
ill b
e '1
0 sq
uare
d +1
’ or 1
02 + 1
whi
ch is
101
. Usi
ng th
e sa
me
rule
, le
arne
rs c
an a
lso
be a
sked
wha
t ter
m n
umbe
r or p
ositi
on w
ill b
e 62
6? If
the
term
is o
btai
ned
by s
quar
ing
the
posi
tion
num
ber o
f the
term
and
add
ing
1,
then
the
posi
tion
num
ber c
an b
e ob
tain
ed b
y su
btra
ctin
g, th
en fi
ndin
g th
e sq
uare
root
of t
he te
rm. H
ence
, 626
will
be
the
25th
term
in th
e se
quen
ce
sinc
e 62
6 –
1 =
625
and
625
√ =
25.
b)
Pro
vide
a ru
le to
des
crib
e th
e re
latio
nshi
p be
twee
n th
e nu
mbe
rs in
this
se
quen
ce: –
2; –
5;–8
; –11
... .
Use
this
rule
to fi
nd th
e 20
th te
rm in
this
se
quen
ce.
If le
arne
rs c
onsi
der o
nly
the
rela
tions
hip
betw
een
cons
ecut
ive
term
s, th
en
they
can
con
tinue
the
patte
rn (‘
add
-3 to
pre
viou
s nu
mbe
r’) u
p to
the
20th
te
rm to
find
the
answ
er. H
owev
er, i
f the
y lo
ok fo
r a re
latio
nshi
p or
rule
be
twee
n th
e te
rm a
nd th
e po
sitio
n of
the
term
, the
y ca
n pr
edic
t the
ans
wer
w
ithou
t con
tinui
ng th
e pa
ttern
. Usi
ng n
umbe
r sen
tenc
es c
an b
e us
eful
to
find
the
rule
:
MATHEMATICS GRADES 7-9
128 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.1
num
eric
and
ge
omet
ric
patte
rns
1st t
erm
: –2
= –3
(1) +
1
2nd
term
: –5
= –3
(2) +
1
3rd
term
: –8
= –3
(3) +
1
4th
term
: –11
= –
3(4)
+ 1
The
num
ber i
n th
e br
acke
ts c
orre
spon
ds to
the
posi
tion
of th
e te
rm. H
ence
, th
e 20
th te
rm w
ill b
e: –
3(20
) + 1
= –
59
The
rule
in le
arne
rs’ o
wn
wor
ds c
an b
e w
ritte
n as
–3
x th
e po
sitio
n of
the
term
+ 1
’ or –
3n +
1, w
here
n is
the
posi
tion
of th
e te
rm.
• Th
ese
type
s of
num
eric
pat
tern
s de
velo
p an
und
erst
andi
ng o
f fun
ctio
nal
rela
tions
hips
, in
whi
ch th
ere
is a
dep
ende
nt v
aria
ble
(pos
ition
of t
he te
rm) a
nd
an in
depe
nden
t var
iabl
e (th
e te
rm it
self)
, and
whe
re y
ou h
ave
a un
ique
out
put
for a
ny g
iven
inpu
t val
ue.
Kin
ds o
f geo
met
ric p
atte
rns
• G
eom
etric
pat
tern
s ar
e nu
mbe
r pat
tern
s re
pres
ente
d di
agra
mm
atic
ally.
The
di
agra
mm
atic
repr
esen
tatio
n re
veal
s th
e st
ruct
ure
of th
e nu
mbe
r pat
tern
.
• H
ence
, rep
rese
ntin
g th
e nu
mbe
r pat
tern
s in
tabl
es, m
akes
it e
asie
r for
lear
ners
to
des
crib
e th
e ge
nera
l rul
e fo
r the
pat
tern
.
exam
ple
Con
side
r th
is p
atte
rn f
or b
uild
ing
hexa
gons
usi
ng m
atch
stic
ks.
How
man
y m
atch
stic
ks w
ill b
e us
ed t
o bu
ild t
he 1
0th
hexa
gon?
Pro
vide
an
expr
essi
on t
o de
scrib
e th
e ge
nera
l ter
m fo
r thi
s nu
mbe
r seq
uenc
e.
The
rule
for t
he p
atte
rn is
con
tain
ed in
the
stru
ctur
e (c
onst
ruct
ion)
of t
he
succ
essi
ve h
exag
onal
sha
pes:
(1)
add
on 1
mat
chst
ick
per s
ide
(2)
ther
e ar
e 6
side
s, s
o
(3)
add
on 6
mat
chst
icks
per
hex
agon
as
you
proc
eed
from
a g
iven
hex
agon
to
the
next
one
.
So,
for t
he 2
nd h
exag
on, y
ou h
ave
2 x
6 m
atch
es; f
or th
e 3r
d he
xago
n yo
u ha
ve
3 x
6 m
atch
es. U
sing
this
pat
tern
for b
uild
ing
hexa
gons
, the
10t
h he
xago
n w
ill
have
10
x 6m
atch
es.
MATHEMATICS GRADES 7-9
129CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns a
nd
alge
bra
2.1
num
eric
and
ge
omet
ric
patte
rns
Lear
ners
can
als
o us
e a
tabl
e to
reco
rd th
e nu
mbe
r of m
atch
es u
sed
for e
ach
hexa
gon.
Thi
s w
ay th
e nu
mbe
r pat
tern
is re
late
d to
the
num
ber o
f mat
ches
use
d fo
r eac
h ne
w h
exag
on.
Posi
tion
of h
exag
on in
pat
tern
12
34
56
10
num
ber o
f mat
ches
612
18
The
nth te
rm fo
r thi
s se
quen
ce c
an b
e w
ritte
n as
6n
or 6
+ (n
– 1
)6
2.2
Func
tions
an
d re
latio
nshi
ps
inpu
t and
out
put v
alue
s
• D
eter
min
e in
put v
alue
s, o
utpu
t va
lues
or r
ules
for p
atte
rns
and
rela
tions
hips
usi
ng:
-flo
w d
iagr
ams
-ta
bles
-fo
rmul
ae
-eq
uatio
ns
equi
vale
nt fo
rms
• D
eter
min
e, in
terp
ret a
nd ju
stify
eq
uiva
lenc
e of
diff
eren
t des
crip
tions
of
the
sam
e re
latio
nshi
p or
rule
pr
esen
ted:
-ve
rbal
ly
-in
flow
dia
gram
s
-in
tabl
es
-by
form
ulae
-by
equ
atio
ns
-by
gra
phs
on a
Car
tesi
an p
lane
Wha
t is
diffe
rent
to G
rade
8?
Lear
ners
con
solid
ate
wor
k w
ith in
put a
nd o
utpu
t val
ues
done
in G
rade
8. T
hey
shou
ld c
ontin
ue to
find
inpu
t or o
utpu
t val
ues
in fl
ow d
iagr
ams,
tabl
es, f
orm
ulae
an
d eq
uatio
ns.
Func
tions
and
rela
tions
hips
are
don
e ag
ain
in t
erm
3.
In th
is p
hase
, it i
s us
eful
to s
tart
spec
ifyin
g w
heth
er th
e in
put v
alue
s ar
e na
tura
l nu
mbe
rs, o
r int
eger
s or
ratio
nal n
umbe
rs. T
his
build
s le
arne
rs’ a
war
enes
s of
the
dom
ain
of in
put v
alue
s. H
ence
, to
find
outp
ut v
alue
s, le
arne
rs s
houl
d be
giv
en th
e ru
le/fo
rmul
a as
wel
l as
the
dom
ain
of th
e in
put v
alue
s.
Lear
ners
sho
uld
begi
n to
reco
gniz
e eq
uiva
lent
repr
esen
tatio
ns o
f the
sam
e re
la-
tions
hips
sho
wn
as a
n eq
uatio
n, a
set
of o
rder
ed p
airs
in a
tabl
e or
on
a gr
aph.
exam
ples
a)
If th
e ru
le fo
r find
ing
in th
e ta
ble
belo
w is
: y =
1 2 x +
1, d
eter
min
e th
e va
lues
of y
fo
r the
giv
en x
val
ues:
x0
12
410
5010
0
y
b)
Des
crib
e th
e re
latio
nshi
p be
twee
n th
e nu
mbe
rs in
the
top
row
and
thos
e in
the
botto
m ro
w in
the
tabl
e. T
hen
writ
e do
wn
the
valu
e of
m a
nd n
x–2
–10
12
12n
y–7
–5–3
–11
m27
In ta
bles
suc
h as
thes
e, m
ore
than
one
rule
mig
ht b
e po
ssib
le to
des
crib
e th
e re
latio
nshi
p be
twee
n x
and
y va
lues
. The
rule
s ar
e ac
cept
able
if th
ey m
atch
the
give
n in
put v
alue
s to
the
corr
espo
ndin
g ou
tput
val
ues.
For
exa
mpl
e, th
e ru
le
y =
2x –
3 d
escr
ibes
the
rela
tions
hip
betw
een
the
give
n va
lues
for x
and
y. T
o fin
d m
and
n, l
earn
ers
have
to s
ubst
itute
the
corr
espo
ndin
g va
lues
for x
or y
into
the
rule
and
sol
ve th
e eq
uatio
n by
insp
ectio
n.
MATHEMATICS GRADES 7-9
130 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.3
alg
ebra
ic
expr
essi
ons
alg
ebra
ic la
ngua
ge
• R
evis
e th
e fo
llow
ing
done
in G
rade
8:
-R
ecog
nize
and
iden
tify
conv
entio
ns
for w
ritin
g al
gebr
aic
expr
essi
ons
-Id
entif
y an
d cl
assi
fy li
ke a
nd u
nlik
e te
rms
in a
lgeb
raic
exp
ress
ions
-R
ecog
nize
and
iden
tify
coef
ficie
nts
and
expo
nent
s in
alg
ebra
ic
expr
essi
ons
• R
ecog
nize
and
diff
eren
tiate
bet
wee
n m
onom
ials
, bin
omia
ls a
nd tr
inom
ials
expa
nd a
nd s
impl
ify a
lgeb
raic
ex
pres
sion
s
• R
evis
e th
e fo
llow
ing
done
in G
rade
8,
usi
ng th
e co
mm
utat
ive,
ass
ocia
tive
and
dist
ribut
ive
law
s fo
r rat
iona
l nu
mbe
rs a
nd la
ws
of e
xpon
ents
to:
-ad
d an
d su
btra
ct li
ke te
rms
in
alge
brai
c ex
pres
sion
s
-m
ultip
ly in
tege
rs a
nd m
onom
ials
by
: ♦m
onom
ials
♦bi
nom
ials
♦tri
nom
ials
-di
vide
the
follo
win
g by
inte
gers
or
mon
omia
ls:
♦m
onom
ials
♦bi
nom
ials
♦tri
nom
ials
-S
impl
ify a
lgeb
raic
exp
ress
ions
in
volv
ing
the
abov
e op
erat
ions
Wha
t is
diffe
rent
to G
rade
8?
• A
lgeb
raic
man
ipul
atio
ns w
hich
incl
ude:
-m
ultip
ly in
tege
rs a
nd m
onom
ials
by
poly
nom
ials
-di
vide
pol
ynom
ials
by
inte
gers
or m
onom
ials
-th
e pr
oduc
t of t
wo
bino
mia
ls
-th
e sq
uare
of a
bin
omia
l
alg
ebra
ic e
xpre
ssio
ns a
re d
one
agai
n in
ter
m 3
. in
this
term
the
focu
s is
on
expa
ndin
g an
d si
mpl
ifyin
g al
gebr
aic
expr
essi
ons.
in t
erm
3 th
e fo
cus
is o
n fa
ctor
izin
g ex
pres
sion
s.
man
ipul
atin
g al
gebr
aic
expr
essi
ons
• m
ake
sure
lear
ners
und
erst
and
that
the
rule
s fo
r ope
ratin
g w
ith in
tege
rs a
nd
ratio
nal n
umbe
rs, i
nclu
ding
law
s of
exp
onen
ts, a
pply
equ
ally
whe
n nu
mbe
rs a
re
repl
aced
with
var
iabl
es. T
he v
aria
bles
are
num
bers
of a
giv
en ty
pe (e
.g. i
nteg
ers
or ra
tiona
l num
bers
) in
gene
raliz
ed fo
rm.
• W
hen
mul
tiply
ing
or d
ivid
ing
expr
essi
ons,
mak
e su
re le
arne
rs u
nder
stan
d ho
w
the
dist
ribut
ive
rule
wor
ks.
• Th
e as
soci
ativ
e ru
le a
llow
s fo
r gro
upin
g of
like
term
s w
hen
addi
ng.
Look
out
for t
he fo
llow
ing
com
mon
mis
conc
eptio
ns:
•x
+ x
= 2
x an
d n
ot
x2 . N
ote
the
conv
entio
n is
to w
rite
2x ra
ther
than
x2
•x2 +
x2 =
2x2
and
no
t 2x
4
•a
+b =
a +
b a
nd n
ot
ab
•(–
2x2 )
3 =
–8x
6 an
d n
ot
–6x5
•-x
(3x +
1) =
–3x
2 –
1 and
no
t –3
x2 +
1
•6x
2 +
11
x2 x2
= 6
+
and
no
t 6 +
1
• If
x =
2 then
–3x
2 =
–3(2
)2 =
3 x
4 =
12 a
nd n
ot
(–6)
2
• If
x =
–2 th
en –
x2 –
x =
–(–2
)2 –
(–2)
= –4
+ 2
= –
2 an
d n
ot
4 +
2 =
6
•25
x2 –9
x2 =
16x2
= 4x
and
no
t 5x
– 3
x =
2x√
√
•(x
+ 2
)2 =
x2 +
4x +
4 a
nd n
ot
x2 +
4
Tim
e fo
r al
gebr
aic
expr
essi
ons
in
this
term
:
4,5
hour
s
MATHEMATICS GRADES 7-9
131CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.3
alg
ebra
ic
expr
essi
ons
-D
eter
min
e th
e sq
uare
s, c
ubes
, sq
uare
root
s an
d cu
be ro
ots
of
sing
le a
lgeb
raic
term
s or
like
al
gebr
aic
term
s
-D
eter
min
e th
e nu
mer
ical
val
ue
of a
lgeb
raic
exp
ress
ions
by
subs
titut
ion
• E
xten
d th
e ab
ove
alge
brai
c m
anip
ulat
ions
to in
clud
e:
-m
ultip
ly in
tege
rs a
nd m
onom
ials
by
poly
nom
ials
-di
vide
pol
ynom
ials
by
inte
gers
or
mon
omia
ls
-th
e pr
oduc
t of t
wo
bino
mia
ls
-th
e sq
uare
of a
bin
omia
l
Fact
oriz
e al
gebr
aic
expr
essi
ons
• Fa
ctor
ize
alge
brai
c ex
pres
sion
s th
at
invo
lve:
-co
mm
on fa
ctor
s
-di
ffere
nce
of tw
o sq
uare
s
-tri
nom
ials
of t
he fo
rm:
♦x2 +
bx
+ c
♦ax
2 + b
x +
c, w
here
a is
a c
omm
on
fact
or
• S
impl
ify a
lgeb
raic
exp
ress
ions
that
in
volv
e th
e ab
ove
fact
oris
atio
n pr
oces
ses
• S
impl
ify a
lgeb
raic
frac
tions
usi
ng
fact
oris
atio
n
exam
ples
of e
xpan
ding
and
sim
plify
ing
expr
essi
ons
a)
Sim
plify
: –3(
x3 + 2
x2 – x
) – x
2 (3x
+ 1)
[mul
tiply
inte
ger a
nd m
onom
ial b
y po
lyno
mia
l]
b)
Det
erm
ine/
expa
nd: (
x +
2)(x
– 3
) [m
ultip
ly b
inom
ial b
y bi
nom
ial]
c)
Det
erm
ine/
expa
nd: (
x +
2)(x
– 2
) [m
ultip
ly b
inom
ial b
y bi
nom
ial]
d)
Det
erm
ine/
expa
nd: (
x +
3)2 [
mul
tiply
out
a p
erfe
ct s
quar
e]
e)
Sim
plify
: 2(x
– 3
)2 –3(
x +
1)(2
x –
5) [m
ultip
le c
alcu
latio
ns in
volv
ing
prod
uct o
f bi
nom
ials
]
f) If
x =
–2 d
eter
min
e th
e nu
mer
ical
val
ue o
f 3x2 –
4x
+ 5
[usi
ng s
ubst
itutio
n]
g)
Sim
plify
: 6x4 –
8x3
– 2x
2 +
42x
2 fo
r x ≠
0 fo
r [d
ivid
e po
lyno
mia
l by
mon
omia
l; re
min
d le
arne
rs th
at d
enom
inat
or c
anno
t be
0]
h)
Sim
plify
: 8x
3 –
(–x3 )(
2x)
-x2
for x
≠ 0
for
[ca
lcul
atio
ns in
volv
ing
mul
tiple
op
erat
ions
; rem
ind
lear
ners
that
den
omin
ator
can
not b
e ]
i) D
eter
min
e:
36x4
√ [s
quar
e ro
ot o
f mon
omia
l]
It m
ight
hel
p to
rem
ind
lear
ners
that
thes
e va
riabl
es (o
r x in
this
cas
e) re
pres
ent
num
bers
of a
par
ticul
ar ty
pe –
thes
e m
ay b
e ra
tiona
l, or
inte
gers
, or p
erha
ps
who
le n
umbe
rs; s
uch
a re
min
der a
lso
then
impl
ies
that
all
the
asso
ciat
ed ru
les
or p
rope
rties
of t
hese
num
bers
app
ly h
ere.
So,
in th
e ab
ove
exam
ple,
if x
is a
n in
tege
r, th
en x
= a
or x
= –
a be
caus
e a4 =
(–a)
4
MATHEMATICS GRADES 7-9
132 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.4
alg
ebra
ic
equa
tions
equa
tions
• R
evis
e th
e fo
llow
ing
done
in G
rade
8:
-S
et u
p eq
uatio
ns to
des
crib
e pr
oble
m s
ituat
ions
-A
naly
se a
nd in
terp
ret e
quat
ions
th
at d
escr
ibe
a gi
ven
situ
atio
n
-S
olve
equ
atio
ns b
y:
♦in
spec
tion
♦us
ing
addi
tive
and
mul
tiplic
ativ
e in
vers
es
♦us
ing
law
s of
exp
onen
ts
-D
eter
min
e th
e nu
mer
ical
val
ue o
f an
exp
ress
ion
by s
ubst
itutio
n.
-U
se s
ubst
itutio
n in
equ
atio
ns to
ge
nera
te ta
bles
of o
rder
ed p
airs
• E
xten
d so
lvin
g eq
uatio
ns to
incl
ude:
-us
ing
fact
oris
atio
n
-eq
uatio
ns o
f the
form
: a p
rodu
ct o
f fa
ctor
s =
0
Wha
t is
diffe
rent
to G
rade
8?
• S
olvi
ng e
quat
ions
usi
ng fa
ctor
izat
ion
• S
olvi
ng e
quat
ions
of t
he fo
rm: a
pro
duct
of f
acto
rs =
0
alg
ebra
ic e
quat
ions
are
don
e ag
ain
in t
erm
3. i
n th
is te
rm th
e fo
cus
is o
n co
nsol
idat
ing
solv
ing
equa
tions
usi
ng a
dditi
ve a
nd m
ultip
licat
ive
inve
rses
an
d th
e la
ws
of e
xpon
ents
. in
term
3, t
he fo
cus
is o
n so
lvin
g eq
uatio
ns a
fter
fact
oriz
ing
as w
ell a
s ge
nera
ting
tabl
es o
f ord
ered
pai
rs fo
r lin
ear e
quat
ions
. Le
arne
rs h
ave
oppo
rtuni
ties
to w
rite
and
solv
e eq
uatio
ns w
hen
they
writ
e ge
nera
l ru
les
to d
escr
ibe
rela
tions
hips
bet
wee
n nu
mbe
rs in
num
ber p
atte
rns,
and
whe
n th
ey fi
nd in
put o
r out
put v
alue
s fo
r giv
en ru
les
in fl
ow d
iagr
ams,
tabl
es a
nd
form
ulae
.
In G
rade
9, l
earn
ers
can
be g
iven
equ
atio
ns w
here
they
hav
e to
exp
and,
sim
plify
or
fact
oriz
e ex
pres
sion
s fir
st, b
efor
e so
lvin
g th
e eq
uatio
n.
For e
quat
ions
of t
he fo
rm: a
pro
duct
of t
wo
fact
ors
= 0,
lear
ners
hav
e to
un
ders
tand
that
if th
e pr
oduc
t of t
wo
fact
ors
equa
ls 0
, the
n at
leas
t one
of t
he
fact
ors
mus
t be
equa
l to
0. H
ence
to s
olve
the
equa
tion,
eac
h fa
ctor
mus
t be
writ
ten
as a
n eq
uatio
n eq
ual t
o 0,
and
ther
efor
e m
ore
than
one
sol
utio
n fo
r x is
po
ssib
le.
Whe
n w
orki
ng w
ith a
lgeb
raic
frac
tions
, lea
rner
s m
ust b
e re
min
ded
that
the
deno
min
ator
can
not e
qual
0, s
o an
y va
lue
of x
that
mak
es th
e de
nom
inat
or 0
ca
nnot
be
a so
lutio
n to
the
equa
tion.
exam
ples
of e
quat
ions
a)
Sol
ve: x
if
3(x –
2) =
x +
2
3x
– 6
= x
+ 2
(e
xpan
d LH
S fi
rst)
3x
– x
– 6
= x
– x
+ 2
(add
–x
to b
oth
side
s of
the
equa
tion)
th
eref
ore
2x –
6 =
2
2x
– 6
+ 6
= 2
+ 6
(add
6 to
bot
h si
des
of th
e eq
uatio
n)
th
eref
ore
2x =
8
2x
2 =
8 2 (d
ivid
e bo
th s
ides
of t
he e
quat
ion
by 2
)
x
= 4
b)
Sol
ve x
if (x
– 1
)(x
+ 3)
= 0
x –
1= 0
or x
+ 3
= 0
(at l
east
one
fact
or m
ust b
e eq
ual t
o 0)
Thus
x =
1 (a
dd –
1 to
bot
h si
des
of th
e eq
uatio
n) o
r x =
–3
(add
–3
to b
oth
side
s of
the
equa
tion)
Tim
e fo
r al
gebr
aic
equa
tions
in
this
term
:
4 ho
urs
MATHEMATICS GRADES 7-9
133CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.4
alg
ebra
ic
equa
tions
c)
Sol
ve x
if x 3 +
2x –
14
= 1
4x +
3(2
x –
1) =
12
(mul
tiply
eac
h te
rm o
n bo
th s
ides
of t
he e
quat
ion
by th
e LC
M, 1
2)
4x +
6x
–3 =
12
(exp
and
expr
essi
on o
n LH
S)
10x
= 15
(add
3 to
bot
h si
des
of th
e eq
uatio
n, a
nd a
dd li
ke te
rms
to th
e LH
S)
x =
2 3 (di
vide
bot
h si
des
of th
e eq
uatio
n by
10)
d)
If y
= 2x
2 + 4
x +
3, c
alcu
late
y w
hen
x =
–2
e)
Than
di is
6 y
ears
old
er th
an S
ophi
e. In
3 y
ears
tim
e Th
andi
will
be
twic
e as
old
as
Sop
hie.
How
old
is T
hand
i now
?
rev
isio
n/a
sses
smen
t:A
t thi
s st
age
lear
ners
sho
uld
have
bee
n as
sess
ed o
n:
• th
e pr
oper
ties
of d
iffer
ent n
umbe
r sys
tem
s
• ca
lcul
atin
g an
d so
lvin
g pr
oble
ms
with
who
le n
umbe
rs, i
nteg
ers,
com
mon
frac
tions
and
dec
imal
frac
tions
, num
bers
in e
xpon
entia
l for
m
• nu
mer
ic a
nd g
eom
etric
pat
tern
s
• fu
nctio
ns a
nd re
latio
nshi
ps
• al
gebr
aic
expr
essi
ons
• al
gebr
aic
equa
tions
Tota
l tim
e fo
r rev
isio
n/as
sess
men
t fo
r the
term
7 ho
urs
MATHEMATICS GRADES 7-9
134 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Gr
ad
e 9
– te
rm
2
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
spac
e an
d sh
ape
(geo
met
ry)
3.5
Con
stru
ctio
n of
geo
met
ric
figures
Con
stru
ctio
ns
• A
ccur
atel
y co
nstru
ct g
eom
etric
fig
ures
app
ropr
iate
ly u
sing
a
com
pass
, rul
er a
nd p
rotra
ctor
, in
clud
ing
bise
ctin
g an
gles
of a
tri
angl
e
• C
onst
ruct
ang
les
of 4
5°, 3
0°, 6
0°an
d an
d th
eir m
ultip
les
with
out u
sing
a
prot
ract
or
inve
stig
atin
g pr
oper
ties
of g
eom
etric
fig
ures
• B
y co
nstru
ctio
n, in
vest
igat
e th
e an
gles
in a
tria
ngle
, foc
usin
g on
the
rela
tions
hip
betw
een
the
exte
rior
angl
e of
a tr
iang
le a
nd it
s in
terio
r an
gles
• B
y co
nstru
ctio
n, e
xplo
re th
e m
inim
um
cond
ition
s fo
r tw
o tri
angl
es to
be
cong
ruen
t
• B
y co
nstru
ctio
n, in
vest
igat
e si
des,
ang
les
and
diag
onal
s in
qu
adril
ater
als,
focu
sing
on
the
diag
onal
s of
rect
angl
es, s
quar
es,
para
llelo
gram
s, rh
ombi
and
kite
s
• B
y co
nstru
ctio
n ex
plor
e th
e su
m o
f th
e in
terio
r ang
les
of p
olyg
ons
Wha
t is
diffe
rent
to G
rade
8?
• B
isec
ting
angl
es in
a tr
iang
le
• C
onst
ruct
ing
30°
with
out a
pro
tract
or
• In
vest
igat
ion
of n
ew p
rope
rties
of t
riang
les,
qua
drila
tera
ls a
nd p
olyg
ons
Con
stru
ctio
ns
• C
onst
ruct
ions
pro
vide
a u
sefu
l con
text
to e
xplo
re o
r con
solid
ate
know
ledg
e of
an
gles
and
sha
pes.
• m
ake
sure
lear
ners
are
com
pete
nt a
nd c
omfo
rtabl
e in
the
use
of a
com
pass
and
kn
ow h
ow to
mea
sure
and
read
ang
le s
izes
on
a pr
otra
ctor
• R
evis
e th
e co
nstru
ctio
ns o
f ang
les
if ne
cess
ary,
bef
ore
proc
eedi
ng w
ith th
e ne
w
cons
truct
ions
.
• S
tart
with
the
cons
truct
ions
of l
ines
, so
that
lear
ners
can
firs
t exp
lore
ang
le
rela
tions
hips
on
stra
ight
line
s.
• W
hen
cons
truct
ing
trian
gles
lear
ners
sho
uld
draw
on
know
n pr
oper
ties
and
cons
truct
ion
of c
ircle
s.
• C
onst
ruct
ion
of s
peci
al a
ngle
s w
ithou
t pro
tract
ors
are
done
by:
-bi
sect
ing
a rig
ht-a
ngle
to g
et 4
5°
-dr
awin
g an
equ
ilate
ral t
riang
le to
get
60°
-bi
sect
ing
the
angl
es o
f an
equi
late
ral t
riang
le to
get
30°
Tota
l tim
e fo
r co
nstru
ctio
ns
of g
eom
etric
fig
ures
:
9 ho
urs
MATHEMATICS GRADES 7-9
135CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
spac
e an
d sh
ape
(geo
met
ry)
3.1
Geo
met
ry o
f 2d
sha
pes
Cla
ssify
ing
2d s
hape
s
• R
evis
e pr
oper
ties
and
defin
ition
s of
tri
angl
es in
term
s of
thei
r sid
es a
nd
angl
es, d
istin
guis
hing
bet
wee
n:
-eq
uila
tera
l tria
ngle
s
-is
osce
les
trian
gles
-rig
ht-a
ngle
d tri
angl
es
• R
evis
e an
d w
rite
clea
r defi
nitio
ns o
f qu
adril
ater
als
in te
rms
of th
eir s
ides
, an
gles
and
dia
gona
ls, d
istin
guis
hing
be
twee
n:
-pa
ralle
logr
am
-re
ctan
gle
-sq
uare
-rh
ombu
s
-tra
pezi
um
-ki
te
Wha
t is
diffe
rent
to G
rade
8?
• P
rope
rties
of d
iago
nals
of q
uadr
ilate
rals
• m
inim
um c
ondi
tions
for c
ongr
uent
and
sim
ilar t
riang
les
• Tr
iang
les
• C
onst
ruct
ions
ser
ve a
s a
usef
ul c
onte
xt fo
r exp
lorin
g pr
oper
ties
of tr
iang
les.
S
ee 3
.5 C
onst
ruct
ion
of G
eom
etric
figu
res.
• P
rope
rties
of t
riang
les
lear
ners
sho
uld
know
:
-th
e su
m o
f the
inte
rior a
ngle
s of
tria
ngle
s =
180°
-an
equ
ilate
ral t
riang
le h
as a
ll si
des
equa
l and
all
inte
rior a
ngle
s =
60°
-an
isos
cele
s tri
angl
e ha
s at
leas
t tw
o eq
ual s
ides
and
its
base
ang
les
are
equa
l
-a
right
-ang
led
trian
gle
has
one
angl
e th
at is
a ri
ght-a
ngle
-th
e si
de o
ppos
ite th
e rig
ht-a
ngle
in a
righ
t-ang
led
trian
gle,
is c
alle
d th
e hy
pote
nuse
-in
a ri
ght-a
ngle
d tri
angl
e, th
e sq
uare
of t
he h
ypot
enus
e is
equ
al to
the
sum
of
the
squa
res
of th
e ot
her t
wo
side
s (T
heor
em o
f Pyt
hago
ras)
.
-th
e ex
terio
r ang
le o
f a tr
iang
le =
the
sum
of t
he o
ppos
ite tw
o in
terio
r ang
les
Qua
drila
tera
ls
• C
onst
ruct
ions
ser
ve a
s a
usef
ul c
onte
xt fo
r exp
lorin
g pr
oper
ties
of tr
iang
les.
S
ee n
otes
on
cons
truct
ions
abo
ve.
• Th
e cl
assi
ficat
ion
of q
uadr
ilate
rals
sho
uld
incl
ude
the
reco
gniti
on th
at:
-re
ctan
gles
and
rhom
bi a
re s
peci
al k
inds
of p
aral
lelo
gram
s
-a
squa
re is
a s
peci
al k
ind
of re
ctan
gle
and
rhom
bus.
Prop
ertie
s of
qua
drila
tera
ls le
arne
rs s
houl
d kn
ow:
• th
e su
m o
f the
inte
rior a
ngle
s of
qua
drila
tera
ls =
360
°
• th
e op
posi
te s
ides
of p
aral
lelo
gram
s ar
e pa
ralle
l and
equ
al
• th
e op
posi
te a
ngle
s of
par
alle
logr
ams
are
equa
l
• th
e op
posi
te a
ngle
s of
a rh
ombu
s ar
e eq
ual
• th
e op
posi
te s
ides
of a
rhom
bus
are
para
llel a
nd e
qual
• th
e si
ze o
f eac
h an
gle
of re
ctan
gles
and
squ
ares
is 9
0°
• a
trape
zium
has
one
pai
r of o
ppos
ite s
ides
par
alle
l
Tota
l tim
e fo
r ge
omet
ry o
f 2D
sha
pes
9 ho
urs
MATHEMATICS GRADES 7-9
136 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
spac
e an
d sh
ape
(geo
met
ry)
3.1
Geo
met
ry o
f 2d
sha
pes
sim
ilar a
nd c
ongr
uent
tria
ngle
s
• Th
roug
h in
vest
igat
ion,
est
ablis
h th
e m
inim
um c
ondi
tions
for c
ongr
uent
tri
angl
es
• Th
roug
h in
vest
igat
ion,
est
ablis
h th
e m
inim
um c
ondi
tions
for s
imila
r tri
angl
es
solv
ing
prob
lem
s
Sol
ve g
eom
etric
pro
blem
s in
volv
ing
unkn
own
side
s an
d an
gles
in
trian
gles
and
qua
drila
tera
ls, u
sing
kn
own
prop
ertie
s of
tria
ngle
s an
d qu
adril
ater
als,
as
wel
l as
prop
ertie
s of
co
ngru
ent a
nd s
imila
r tria
ngle
s.
• a
kite
has
two
pairs
of a
djac
ent s
ides
equ
al
• th
e di
agon
als
of a
squ
are,
rect
angl
e, p
aral
lelo
gram
and
rhom
bus
bise
ct e
ach
othe
r
• th
e di
agon
als
of a
squ
are,
rhom
bus
and
kite
are
per
pend
icul
ar
Con
grue
nt tr
iang
les
• C
onst
ruct
ions
are
a u
sefu
l con
text
for e
stab
lishi
ng th
e m
inim
um c
ondi
tions
for
two
trian
gles
to b
e co
ngru
ent.
See
not
es o
n C
onst
ruct
ions
abo
ve.
• C
ondi
tions
for t
wo
trian
gles
to b
e co
ngru
ent:
-th
ree
corr
espo
ndin
g si
des
are
equa
l (S
,S,S
)
-tw
o co
rres
pond
ing
side
s an
d th
e in
clud
ed a
ngle
are
equ
al (S
,A,S
)
-tw
o co
rres
pond
ing
angl
es a
nd a
cor
resp
ondi
ng s
ide
are
equa
l (A
,A,S
)
-rig
ht-a
ngle
, hyp
oten
use
and
one
othe
r cor
resp
ondi
ng s
ide
are
equa
l (R
,H,S
)
sim
ilar t
riang
les
• C
onst
ruct
ions
are
a u
sefu
l con
text
for e
stab
lishi
ng th
e m
inim
um c
ondi
tions
for
two
trian
gles
to b
e si
mila
r. S
ee n
otes
on
Con
stru
ctio
ns a
bove
.
• C
ondi
tion
for t
wo
trian
gles
to b
e si
mila
r: co
rres
pond
ing
angl
es a
re e
qual
and
co
rres
pond
ing
side
s ar
e pr
opor
tiona
l
solv
ing
prob
lem
s
• Le
arne
rs c
an s
olve
geo
met
ric p
robl
ems
to fi
nd u
nkno
wn
side
s an
d an
gles
in
tria
ngle
s an
d qu
adril
ater
als,
usi
ng k
now
n de
finiti
ons
as w
ell a
s an
gle
rela
tions
hips
on
stra
ight
line
s.
• Fo
r rig
ht-a
ngle
d tri
angl
es, l
earn
ers
can
also
use
the
Theo
rem
of P
ytha
gora
s to
fin
d un
know
n le
ngth
s.
• Le
arne
rs s
houl
d gi
ve re
ason
s an
d ju
stify
thei
r sol
utio
ns fo
r eve
ry w
ritte
n st
atem
ent.
• N
ote
that
sol
ving
geo
met
ric p
robl
ems
is a
n op
portu
nity
to p
ract
ise
solv
ing
equa
tions
.
exam
ple:
In ∆
AB
C, Â
= x
, ang
le B
= 5
0° a
nd a
ngle
Ĉ =
80°
. Wha
t is
the
size
of Â
?
Lear
ners
can
sol
ve x
in th
e fo
llow
ing
equa
tion:
x +
50°
+ 80
° =
180°
(bec
ause
the
sum
of t
he a
ngle
s in
a tr
iang
le =
180
°)
x =
180°
– 1
30°
(add
–50
° an
d –8
0° to
bot
h si
des
of th
e eq
uatio
n)
x =
50°,
hen
ce Â
= 5
0°
MATHEMATICS GRADES 7-9
137CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
spac
e an
d sh
ape
(geo
met
ry)
3.1
Geo
met
ry o
f 2d
sha
pes
sim
ilar a
nd c
ongr
uent
tria
ngle
s
• Th
roug
h in
vest
igat
ion,
est
ablis
h th
e m
inim
um c
ondi
tions
for c
ongr
uent
tri
angl
es
• Th
roug
h in
vest
igat
ion,
est
ablis
h th
e m
inim
um c
ondi
tions
for s
imila
r tri
angl
es
solv
ing
prob
lem
s
Sol
ve g
eom
etric
pro
blem
s in
volv
ing
unkn
own
side
s an
d an
gles
in
trian
gles
and
qua
drila
tera
ls, u
sing
kn
own
prop
ertie
s of
tria
ngle
s an
d qu
adril
ater
als,
as
wel
l as
prop
ertie
s of
co
ngru
ent a
nd s
imila
r tria
ngle
s.
• a
kite
has
two
pairs
of a
djac
ent s
ides
equ
al
• th
e di
agon
als
of a
squ
are,
rect
angl
e, p
aral
lelo
gram
and
rhom
bus
bise
ct e
ach
othe
r
• th
e di
agon
als
of a
squ
are,
rhom
bus
and
kite
are
per
pend
icul
ar
Con
grue
nt tr
iang
les
• C
onst
ruct
ions
are
a u
sefu
l con
text
for e
stab
lishi
ng th
e m
inim
um c
ondi
tions
for
two
trian
gles
to b
e co
ngru
ent.
See
not
es o
n C
onst
ruct
ions
abo
ve.
• C
ondi
tions
for t
wo
trian
gles
to b
e co
ngru
ent:
-th
ree
corr
espo
ndin
g si
des
are
equa
l (S
,S,S
)
-tw
o co
rres
pond
ing
side
s an
d th
e in
clud
ed a
ngle
are
equ
al (S
,A,S
)
-tw
o co
rres
pond
ing
angl
es a
nd a
cor
resp
ondi
ng s
ide
are
equa
l (A
,A,S
)
-rig
ht-a
ngle
, hyp
oten
use
and
one
othe
r cor
resp
ondi
ng s
ide
are
equa
l (R
,H,S
)
sim
ilar t
riang
les
• C
onst
ruct
ions
are
a u
sefu
l con
text
for e
stab
lishi
ng th
e m
inim
um c
ondi
tions
for
two
trian
gles
to b
e si
mila
r. S
ee n
otes
on
Con
stru
ctio
ns a
bove
.
• C
ondi
tion
for t
wo
trian
gles
to b
e si
mila
r: co
rres
pond
ing
angl
es a
re e
qual
and
co
rres
pond
ing
side
s ar
e pr
opor
tiona
l
solv
ing
prob
lem
s
• Le
arne
rs c
an s
olve
geo
met
ric p
robl
ems
to fi
nd u
nkno
wn
side
s an
d an
gles
in
tria
ngle
s an
d qu
adril
ater
als,
usi
ng k
now
n de
finiti
ons
as w
ell a
s an
gle
rela
tions
hips
on
stra
ight
line
s.
• Fo
r rig
ht-a
ngle
d tri
angl
es, l
earn
ers
can
also
use
the
Theo
rem
of P
ytha
gora
s to
fin
d un
know
n le
ngth
s.
• Le
arne
rs s
houl
d gi
ve re
ason
s an
d ju
stify
thei
r sol
utio
ns fo
r eve
ry w
ritte
n st
atem
ent.
• N
ote
that
sol
ving
geo
met
ric p
robl
ems
is a
n op
portu
nity
to p
ract
ise
solv
ing
equa
tions
.
exam
ple:
In ∆
AB
C, Â
= x
, ang
le B
= 5
0° a
nd a
ngle
Ĉ =
80°
. Wha
t is
the
size
of Â
?
Lear
ners
can
sol
ve x
in th
e fo
llow
ing
equa
tion:
x +
50°
+ 80
° =
180°
(bec
ause
the
sum
of t
he a
ngle
s in
a tr
iang
le =
180
°)
x =
180°
– 1
30°
(add
–50
° an
d –8
0° to
bot
h si
des
of th
e eq
uatio
n)
x =
50°,
hen
ce Â
= 5
0°
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
3.3
Geo
met
ry o
f st
raig
ht li
nes
ang
le re
latio
nshi
ps
• R
evis
e an
d w
rite
clea
r des
crip
tions
of
the
rela
tions
hip
betw
een
angl
es
form
ed b
y:
-pe
rpen
dicu
lar l
ines
-in
ters
ectin
g lin
es
-pa
ralle
l lin
es c
ut b
y a
trans
vers
al
solv
ing
prob
lem
s
Sol
ve g
eom
etric
pro
blem
s us
ing
the
rela
tions
hips
bet
wee
n pa
irs o
f ang
les
desc
ribed
abo
ve.
Wha
t is
diffe
rent
to G
rade
8?
Lear
ners
revi
se a
nd w
rite
clea
r des
crip
tions
of a
ngle
rela
tions
hips
on
stra
ight
line
s
ang
le re
latio
nshi
ps le
arne
rs s
houl
d kn
ow:
• th
e su
m o
f the
ang
les
on a
stra
ight
line
is 1
80°
• If
lines
are
per
pend
icul
ar li
nes,
then
adj
acen
t sup
plem
enta
ry a
ngle
s ar
e ea
ch
equa
l to
90°
.•
If lin
es in
ters
ect,
then
ver
tical
ly o
ppos
ite a
ngle
s ar
e eq
ual.
• if
para
llel l
ines
are
cut
by
a tra
nsve
rsal
, the
n co
rres
pond
ing
angl
es a
re e
qual
• if
para
llel l
ines
cut
by
a tra
nsve
rsal
, the
n al
tern
ate
angl
es a
re e
qual
• if
para
llel l
ines
cut
by
a tra
nsve
rsal
, the
n co
-inte
rior a
ngle
s ar
e su
pple
men
tary
The
abov
e an
gles
hav
e to
be
iden
tified
and
nam
ed b
y le
arne
rs.
solv
ing
prob
lem
s
• Le
arne
rs c
an s
olve
geo
met
ric p
robl
ems
to fi
nd u
nkno
wn
angl
es u
sing
the
angl
e re
latio
nshi
ps a
bove
, as
wel
l as
othe
r kno
wn
prop
ertie
s of
tria
ngle
s an
d qu
adril
ater
als.
• Le
arne
rs s
houl
d gi
ve re
ason
s an
d ju
stify
thei
r sol
utio
ns fo
r eve
ry w
ritte
n st
atem
ent.
• N
ote
that
sol
ving
geo
met
ric p
robl
ems
is a
n op
portu
nity
to p
ract
ise
solv
ing
equa
tions
.
exam
ple:
B1 a
nd B
2 are
two
angl
es o
n a
stra
ight
line
. B1 =
35°
. Wha
t is
the
size
of B
2 ?
Lear
ners
can
find
B2 b
y so
lvin
g th
e fo
llow
ing
equa
tion:
35°
+ B
2 =
180°
(bec
ause
the
sum
of a
ngle
s on
a s
traig
ht li
ne
180°
)
B2
= 18
0° –
35°
(add
–35
° to
bot
h si
des
of th
e eq
uatio
n)
B2 =
145
°
Tota
l tim
e fo
r ge
omet
ry o
f st
raig
ht li
nes
9 ho
urs
MATHEMATICS GRADES 7-9
138 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
mea
sure
men
t4.
3
the
theo
rem
of
Py
thag
oras
solv
e pr
oble
ms
usin
g th
e th
eore
m
of P
ytha
gora
s
Use
the
Theo
rem
of P
ytha
gora
s to
so
lve
prob
lem
s in
volv
ing
unkn
own
leng
ths
in g
eom
etric
figu
res
that
con
-ta
in ri
ght-a
ngle
d tri
angl
es
• Th
e Th
eore
m o
f Pyt
hago
ras
was
intro
duce
d in
Gra
de 8
• It
is im
porta
nt th
at le
arne
rs u
nder
stan
d th
at th
e Th
eore
m o
f Pyt
hago
ras
appl
ies
only
to ri
ght-a
ngle
d tri
angl
es.
• Th
e Th
eore
m o
f Pyt
hago
ras
is b
asic
ally
a fo
rmul
a to
cal
cula
te u
nkno
wn
leng
th
of s
ides
in ri
ght-a
ngle
d tri
angl
es.
• In
par
ticul
ar, t
he T
heor
em o
f Pyt
hago
ras
can
be th
e fir
st s
tep
in c
alcu
latio
ns o
f pe
rimet
ers
or a
reas
of c
ompo
site
figu
res,
whe
n on
e of
the
figur
es is
a ri
ght-
angl
ed tr
iang
le w
ith a
n un
know
n le
ngth
. See
exa
mpl
e be
low
.
• In
the
FET
phas
e, th
e Th
eore
m o
f Pyt
hago
ras
is c
ruci
al to
the
furth
er s
tudy
of
Geo
met
ry a
nd T
rigon
omet
ry.
exam
ples
of s
olvi
ng p
robl
ems
usin
g th
e th
eore
m o
f Pyt
hago
ras:
AB
CD
is a
rect
angl
e w
here
BD
= 1
5 cm
and
BC
= 9
cm
.
Det
erm
ine
the:
a)
perim
eter
of A
BC
D
b)
area
of A
BC
D
15
cm
9
cm
A B C
D
Tota
l tim
e fo
r th
e Th
eore
m
of P
ytha
gora
s:
5 ho
urs
MATHEMATICS GRADES 7-9
139CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
mea
sure
men
t4.
1
are
a an
d pe
rimet
er o
f 2d
sha
pes
are
a an
d pe
rimet
er
• U
se a
ppro
pria
te fo
rmul
ae a
nd
conv
ersi
ons
betw
een
SI u
nits
, to
sol
ve p
robl
ems
and
calc
ulat
e pe
rimet
er a
nd a
rea
of:
-po
lygo
ns
-ci
rcle
s
• In
vest
igat
e ho
w d
oubl
ing
any
or a
ll of
th
e di
men
sion
s of
a 2
D fi
gure
affe
cts
its p
erim
eter
and
its
area
Wha
t is
diffe
rent
to G
rade
8?
• Th
e ca
lcul
atio
ns a
re th
e sa
me
as in
Gra
de 8
, but
lear
ners
can
find
per
imet
ers
and
area
s of
mor
e co
mpo
site
and
com
plex
figu
res
• P
olyg
ons
can
incl
ude
trape
zium
s, p
aral
lelo
gram
s, rh
ombi
and
kite
s
•Fo
rmul
ae le
arne
rs s
houl
d kn
ow a
nd u
se:
Per
imet
er o
f a s
quar
e:P
= 4s
Per
imet
er o
f a re
ctan
gle:
P =
2(l +
b) o
r P =
2l +
2b
Are
a of
a s
quar
e:A
= l2
Are
a of
a re
ctan
gle:
A
= le
ngth
x b
read
th
Are
a of
a rh
ombu
s:A
= le
ngth
x h
eigh
t
Are
a of
a k
ite:
A =
1 2 (di
agon
al1 x
dia
gona
l 2
Are
a of
a p
aral
lelo
gram
:A
= ba
se x
hei
ght
Are
a of
a tr
apez
ium
A =
1 2 (su
m o
f par
alle
l sid
es) x
hei
ght
Are
a of
a tr
iang
le:
A =
1 2 (b
x h)
Dia
met
er o
f a c
ircle
: d
= 2r
Circ
umfe
renc
e of
circ
le:
c =
πd o
r c =
2πr
Are
a of
a c
ircle
: A
= πr
2
solv
ing
equa
tions
usi
ng fo
rmul
ae
The
use
of fo
rmul
ae p
rovi
des
a co
ntex
t to
prac
tise
solv
ing
equa
tions
by
insp
ectio
n or
usi
ng a
dditi
ve o
r mul
tiplic
ativ
e in
vers
es.
exam
ple:
a)
If th
e pe
rimet
er o
f a s
quar
e is
32
cm, w
hat i
s th
e le
ngth
of e
ach
side
? Le
arne
rs
shou
ld w
rite
this
as:
4s
= 3
2 an
d so
lve
by a
skin
g: 4
tim
es w
hat w
ill b
e 32
? or
say
ing
s= 32
4
.
b)
If th
e ar
ea o
f a re
ctan
gle
is 2
00 c
m2 ,
and
its le
ngth
is 5
0 cm
, wha
t is
its w
idth
? Le
arne
rs s
houl
d w
rite
this
as:
50
x b
= 2
00 a
nd s
olve
by
insp
ectio
n by
ask
ing:
50
times
wha
t will
be
200?
or
sayi
ng b
= 20
0 50
Tota
l tim
e fo
r Are
a an
d P
erim
eter
5 ho
urs
MATHEMATICS GRADES 7-9
140 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
mea
sure
men
t4.
1
are
a an
d pe
rimet
er o
f 2d
sha
pes
For a
reas
of t
riang
les:
• m
ake
sure
lear
ners
kno
w th
at th
e he
ight
of a
tria
ngle
is a
line
seg
men
t dra
wn
from
any
ver
tex
perp
endi
cula
r to
the
oppo
site
sid
e.
exam
ple:
AD
is th
e he
ight
ont
o ba
se B
C o
f ∆A
BC
.
A D
B C
A D B
C
• P
oint
out
that
eve
ry tr
iang
le h
as 3
bas
es, e
ach
with
a re
late
d he
ight
or a
ltitu
de.
•Fo
r con
vers
ions
:
-If
1 cm
= 1
0 cm
then
1 c
m2 =
100
mm
2
-If
1 cm
= 1
00 c
m th
en 1
m2 =
10
000
cm2
rev
isio
n/a
sses
smen
t:A
t thi
s st
age
lear
ners
sho
uld
have
bee
n as
sess
ed o
n:
• co
nstru
ctin
g ge
omet
ric o
bjec
ts
• ge
omet
ry o
f 2D
sha
pes
• ge
omet
ry o
f stra
ight
line
s
• th
e Th
eore
m o
f Pyt
hago
ras
• ar
ea a
nd p
erim
eter
of 2
D s
hape
s
Tota
l tim
e fo
r rev
isio
n/as
sess
men
t fo
r the
term
8 ho
urs
MATHEMATICS GRADES 7-9
141CAPS
Gr
ad
e 9
– te
rm
3
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns &
al
gebr
a
2.2
Fu
nctio
ns
and
re
latio
nshi
ps
inpu
t and
out
put v
alue
s
• D
eter
min
e in
put v
alue
s, o
utpu
t va
lues
or r
ules
for p
atte
rns
and
rela
tions
hips
usi
ng:
-flo
w d
iagr
ams
-ta
bles
-fo
rmul
ae
-eq
uatio
ns
equi
vale
nt fo
rms
• D
eter
min
e, in
terp
ret a
nd ju
stify
eq
uiva
lenc
e of
diff
eren
t des
crip
tions
of
the
sam
e re
latio
nshi
p or
rule
pr
esen
ted:
-ve
rbal
ly
-in
flow
dia
gram
s
-in
tabl
es
-by
form
ulae
-by
equ
atio
ns
-by
gra
phs
on a
Car
tesi
an p
lane
Func
tions
and
rela
tions
hips
wer
e al
so d
one
in T
erm
1. T
he fo
cus
in th
is te
rm is
on
findi
ng o
utpu
t val
ues
for g
iven
equ
atio
ns, a
nd re
cogn
isin
g eq
uiva
lent
form
s be
-tw
een
diffe
rent
des
crip
tions
of t
he s
ame
rela
tions
hip.
see
addi
tiona
l not
es a
nd e
xam
ples
in t
erm
1.
Tim
e fo
r Fu
nctio
ns a
nd
rela
tions
hips
in
this
term
:
5 ho
urs
MATHEMATICS GRADES 7-9
142 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns &
al
gebr
a
2.3
alg
ebra
icex
pres
sion
s
alg
ebra
ic la
ngua
ge
• R
evis
e th
e fo
llow
ing
done
in G
rade
8:
-re
cogn
ize
and
iden
tify
conv
entio
ns
for w
ritin
g al
gebr
aic
expr
essi
ons
-id
entif
y an
d cl
assi
fy li
ke a
nd u
nlik
e te
rms
in a
lgeb
raic
exp
ress
ions
-re
cogn
ize
and
iden
tify
coef
ficie
nts
and
expo
nent
s in
alg
ebra
ic
expr
essi
ons
• R
ecog
nize
and
diff
eren
tiate
bet
wee
n m
onom
ials
, bin
omia
ls a
nd tr
inom
ials
expa
nd a
nd s
impl
ify a
lgeb
raic
ex
pres
sion
s
• R
evis
e th
e fo
llow
ing
done
in G
rade
8,
usi
ng th
e co
mm
utat
ive,
ass
ocia
tive
and
dstri
butiv
e la
ws
for r
atio
nal
num
bers
and
law
s of
exp
onen
ts to
:
-ad
d an
d su
btra
ct li
ke te
rms
in
alge
brai
c ex
pres
sion
s
-m
ultip
ly in
tege
rs a
nd m
onom
ials
by
: ♦m
onom
ials
♦bi
nom
ials
♦tri
nom
ials
-di
vide
the
follo
win
g by
inte
gers
or
mon
omia
ls:
♦m
onom
ials
♦bi
nom
ials
♦tri
nom
ials
-si
mpl
ify a
lgeb
raic
exp
ress
ions
in
volv
ing
the
abov
e op
erat
ions
-de
term
ine
the
squa
res,
cub
es,
squa
re ro
ots
and
cube
root
s of
si
ngle
alg
ebra
ic te
rms
or li
ke
alge
brai
c te
rms
Alg
ebra
ic e
xpre
ssio
ns w
ere
also
don
e in
Ter
m 1
. The
focu
s in
this
term
is o
n fa
ctor
izin
g ex
pres
sion
s.
see
addi
tiona
l not
es a
nd e
xam
ples
in t
erm
1.
Fact
oriz
ing
expr
essi
ons
• M
ake
sure
lear
ners
und
erst
and
that
fact
oriz
ing
is th
e re
vers
e of
exp
andi
ng a
n ex
pres
sion
thro
ugh
mul
tiplic
atio
n e.
g.
Exp
and:
2x
(x +
3) =
2x2 +
6
Fact
oriz
e:
2x2 +
6 =
2x(
x +
3)
• N
ote
that
1 a
nd –
1 ar
e co
mm
on fa
ctor
s of
eve
ry e
xpre
ssio
n e.
g.
Exp
and:
a
– 4b
= 1
(a –
4b)
Fact
oriz
e:
4b –
a =
1(a
– 4
b)
exam
ples
of e
xpre
ssio
ns w
ith c
omm
on fa
ctor
s th
at c
an b
e fa
ctor
ized
a)
6a4 –
4a2
b)
ax –
bx
+ 2a
– 2
b
c)
2x(a
– b
) – 3
(a –
b)
d)
2x(a
– b
) – 3
(b –
a)
e)
(a +
b)2 –
5(a
+ b
)
exam
ples
of e
xpre
ssio
ns w
ith a
diff
eren
ce o
f tw
o sq
uare
s th
at c
an b
e fa
ctor
ized
a)
25a2 =
1
b)
a4 – b
4
c)
9(a
+ b)
2 – 1
d)
3x 3 –
27
exam
ples
of a
lgeb
raic
frac
tions
that
can
be
fact
oriz
ed
a)
2x +
6y
x +
3y
b)
3x –
3y
6x –
6y
c)
9a2 –
13a
+ 1
Tota
l tim
e fo
r alg
ebra
ic
expr
essi
ons:
9 ho
urs
MATHEMATICS GRADES 7-9
143CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
Patte
rns,
fu
nctio
ns &
al
gebr
a
2.3
alg
ebra
icex
pres
sion
s
-de
term
ine
the
num
eric
al v
alue
of
alg
ebra
ic e
xpre
ssio
ns b
y su
bstit
utio
n
• E
xten
d th
e ab
ove
alge
brai
c m
anip
ulat
ions
to in
clud
e:
-m
ultip
ly in
tege
rs a
nd m
onom
ials
by
poly
nom
ials
-di
vide
pol
ynom
ials
by
inte
gers
or
mon
omia
ls
-th
e pr
oduc
t of t
wo
bino
mia
ls
-th
e sq
uare
of a
bin
omia
l
Fact
oriz
e al
gebr
aic
expr
essi
ons
• Fa
ctor
ize
alge
brai
c ex
pres
sion
s th
at
invo
lve:
-co
mm
on fa
ctor
s
-di
ffere
nce
of tw
o sq
uare
s
-tri
nom
ials
of t
he fo
rm:
♦x2 +
bx
+ c
♦ax
2 + b
x +
c, w
here
a is
a c
omm
on
fact
or
• S
impl
ify a
lgeb
raic
exp
ress
ions
that
in
volv
e th
e ab
ove
fact
oris
atio
n pr
oces
ses
• S
impl
ify a
lgeb
raic
frac
tions
usi
ng
fact
oris
atio
n
exam
ples
of t
rinom
ials
that
can
be
fact
oriz
ed
a)
x2 + 5
x +
6
b)
x2 – 5
x +
6
c)
x2 – x
– 6
d)
x2 – 6
x +
9
e)
2x2 +
10x
+ 1
2
MATHEMATICS GRADES 7-9
144 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.4
alg
ebra
iceq
uatio
ns
equa
tions
• R
evis
e th
e fo
llow
ing
done
in G
rade
8:
-se
t up
equa
tions
to d
escr
ibe
prob
lem
situ
atio
ns
-an
alys
e an
d in
terp
ret e
quat
ions
th
at d
escr
ibe
a gi
ven
situ
atio
n
-so
lve
equa
tions
by:
♦in
spec
tion
♦us
ing
addi
tive
and
mul
tiplic
ativ
e in
vers
es
♦us
ing
law
s of
exp
onen
ts
-de
term
ine
the
num
eric
al v
alue
of
an e
xpre
ssio
n by
sub
stitu
tion.
-us
e su
bstit
utio
n in
equ
atio
ns to
ge
nera
te ta
bles
of o
rder
ed p
airs
• E
xten
d so
lvin
g eq
uatio
ns to
incl
ude:
-us
ing
fact
oris
atio
n
-eq
uatio
ns o
f the
form
: a p
rodu
ct o
f fa
ctor
s =
0
Alg
ebra
ic e
quat
ions
wer
e do
ne in
Ter
m 1
. The
focu
s in
this
term
is o
n so
lvin
g eq
uatio
ns u
sing
fact
oriz
atio
n, a
nd e
quat
ions
with
a p
rodu
ct o
f fac
tors
. Thi
s te
rm
also
focu
ses
on u
sing
equ
atio
ns to
gen
erat
e ta
bles
of o
rder
ed p
airs
.
see
addi
tiona
l not
es a
nd e
xam
ples
in t
erm
1.
exam
ples
of e
quat
ions
a)
Sol
ve x
if
x2 – 3
x =
0
x(
x –
3) =
0 (f
acto
rize
LHS
)
x
= 0
or
x –
3 =
0 (a
t lea
st o
ne fa
ctor
= 0
)
Th
eref
ore,
x =
0 o
r x
= 3
(add
3 to
bot
h si
des
of th
e se
cond
equ
atio
n)
b)
Sol
ve x
if
x2 – 2
5 =
0
(x
+ 5
)(x
– 5)
= 0
(fac
toriz
e th
e di
ffere
nce
of tw
o sq
uare
s on
LH
S)
x +
5 =
0 or
x –
5 =
0 (a
t lea
st o
ne fa
ctor
= 0
)
Th
eref
ore,
x =
– 5
(add
– 5
to b
oth
side
s of
the
equa
tion)
or
x =
5 (a
dd 5
to
both
sid
es o
f the
equ
atio
n)
c)
Writ
e an
equ
atio
n to
find
the
volu
me
of a
rect
angu
lar p
rism
with
leng
th 2
x cm
; w
idth
(2x
+ 1)
cm
and
hei
ght (
2x +
3) c
m
d)
If y
= 2x
2 +
4x +
3, c
alcu
late
y w
hen
x =
–2
e)
Than
di is
6 y
ears
old
er th
an S
ophi
e. In
3 y
ears
' tim
e Th
andi
will
be
twic
e as
old
as
Sop
hie.
How
old
is T
hand
i now
?
exam
ples
of g
ener
atin
g or
dere
d pa
irs
a)
Com
plet
e th
e ta
ble
belo
w fo
r x a
nd y
val
ues
for t
he e
quat
ion:
y =
2x2
– 3
x–2
–10
12
y
b)
Com
plet
e th
e ta
ble
belo
w fo
r x a
nd y
val
ues
for t
he e
quat
ion:
y =
x2 –
2
x–3
–20
y–2
2
Tim
e fo
r al
gebr
aic
equa
tions
in
this
term
:
9 ho
urs
MATHEMATICS GRADES 7-9
145CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
2.5
Gra
phs
inte
rpre
ting
grap
hs
• R
evis
e th
e fo
llow
ing
done
in G
rade
8:
-an
alys
e an
d in
terp
ret g
loba
l gr
aphs
of p
robl
em s
ituat
ions
, with
a
spec
ial f
ocus
on
the
follo
win
g tre
nds
and
feat
ures
:
♦lin
ear o
r non
-line
ar
♦co
nsta
nt, i
ncre
asin
g or
de
crea
sing
♦m
axim
um o
r min
imum
♦di
scre
te o
r con
tinuo
us
• E
xten
d th
e ab
ove
with
spe
cial
focu
s on
the
follo
win
g fe
atur
es o
f lin
ear
grap
hs:
-x-
inte
rcep
t and
y-in
terc
ept
-gr
adie
nt
dra
win
g gr
aphs
• R
evis
e th
e fo
llow
ing
done
in G
rade
8:
-dr
aw g
loba
l gra
phs
from
giv
en
desc
riptio
ns o
f a p
robl
em s
ituat
ion,
id
entif
ying
feat
ures
list
ed a
bove
.
-us
e ta
bles
of o
rder
ed p
airs
to p
lot
poin
ts a
nd d
raw
gra
phs
on th
e C
arte
sian
pla
ne
• E
xten
d th
e ab
ove
with
a s
peci
al
focu
s on
:
-dr
awin
g lin
ear g
raph
s fro
m g
iven
eq
uatio
ns
-de
term
ine
equa
tions
from
giv
en
linea
r gra
phs
Wha
t is
diffe
rent
to G
rade
8?
• x-
inte
rcep
t, y-
inte
rcep
t and
gra
dien
t of l
inea
r gra
phs
• D
raw
line
ar g
raph
s fro
m g
iven
equ
atio
ns
• D
eter
min
e eq
uatio
ns o
f lin
ear g
raph
s
Lear
ners
sho
uld
cont
inue
to a
naly
se a
nd in
terp
ret g
raph
s of
pro
blem
situ
atio
ns.
inve
stig
atin
g lin
ear g
raph
s
• To
ske
tch
linea
r gra
phs
from
giv
en e
quat
ions
, lea
rner
s sh
ould
firs
t dra
w u
p a
tabl
e of
ord
ered
pai
rs, t
hat i
nclu
des
the
inte
rcep
t poi
nts
(x; 0
) and
(0; y
), an
d th
en p
lotti
ng th
e po
ints
.
• Le
arne
rs s
houl
d in
vest
igat
e gr
adie
nts
by c
ompa
ring
vert
ical
cha
nge
hori
zont
al c
hang
e b
etw
een
any
two
poin
ts o
n a
stra
ight
line
gra
ph.
• Le
arne
rs s
houl
d al
so in
vest
igat
e th
e re
latio
nshi
p be
twee
n th
e va
lue
of th
e gr
adie
nt a
nd th
e co
effic
ient
of x
in th
e eq
uatio
n of
a s
traig
ht li
ne g
raph
.
• Le
arne
rs s
houl
d co
mpa
re y
-inte
rcep
ts o
f lin
ear g
raph
s to
the
valu
e of
the
cons
tant
in th
e eq
uatio
n of
the
stra
ight
line
gra
ph.
exam
ples
of l
inea
r gra
phs
a)
Ske
tch
and
com
pare
the
grap
hs o
f: y
= 4
and
x =
4
b)
Ske
tch
and
com
pare
the
grap
hs o
f: y
= x
and
y =
–x
c)
Ske
tch
and
com
pare
the
grap
hs o
f: y
= 2x
; y =
2x
+ 1;
y =
2x
– 1
d)
Ske
tch
and
com
pare
the
grap
hs o
f: y
= 3x
; y =
4x;
y =
5x
e)
Ske
tch
the
grap
hs o
f: y
= –3
x +
2; u
sing
the
tabl
e m
etho
d
f) D
eter
min
e th
e eq
uatio
n of
the
stra
ight
line
pas
sing
thro
ugh
the
follo
win
g po
ints
:
x–4
–3–2
–10
12
34
y–1
01
23
45
67
Tota
l tim
e fo
r gr
aphs
:
12 h
ours
MATHEMATICS GRADES 7-9
146 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
mea
sure
men
t4.
2
surf
ace
area
an
d vo
lum
e of
3d
obj
ects
surf
ace
area
and
vol
ume
• U
se a
ppro
pria
te fo
rmul
ae a
nd
conv
ersi
ons
betw
een
SI u
nits
to
solv
e pr
oble
ms
and
calc
ulat
e th
e su
rface
are
a, v
olum
e an
d ca
paci
ty o
f:
-cu
bes
-re
ctan
gula
r pris
ms
-tri
angu
lar p
rism
s
-cy
linde
rs
• In
vest
igat
e ho
w d
oubl
ing
any
or a
ll th
e di
men
sion
s of
righ
t pris
ms
and
cylin
ders
affe
cts
the
volu
me
Wha
t is
diffe
rent
to G
rade
8?
• S
urfa
ce a
rea
and
volu
me
of c
ylin
ders
•Fo
rmul
ae le
arne
rs s
houl
d kn
ow a
nd u
se:
-th
e vo
lum
e of
a p
rism
= th
e ar
ea o
f the
bas
e x
the
heig
ht
-th
e su
rface
are
a of
a p
rism
= th
e su
m o
f the
are
a of
all
its fa
ces
-th
e vo
lum
e of
a c
ube
= l3
-th
e vo
lum
e of
a re
ctan
gula
r pris
m =
l x
b x
h
-th
e vo
lum
e of
a tr
iang
ular
pris
m =
(1 2
b x
h) x
hei
ght o
f the
pris
m
-th
e vo
lum
e of
a c
ylin
der =
(πr2
) x th
e he
ight
of t
he c
ylin
der
•Fo
r con
vers
ions
, not
e:
-if
1 cm
= 1
0 m
m th
en 1
cm
3 = 1
000
mm
3 ; an
d
- if
1 m
= 1
00 c
m th
en 1
m3 =
1 0
00 0
00 o
r 106
cm3
-an
obj
ect w
ith a
vol
ume
of 1
cm
3 will
dis
plac
e ex
actly
1 m
l of w
ater
; and
-an
obj
ect w
ith a
vol
ume
of 1
m3 w
ill d
ispl
ace
exac
tly 1
kl o
f wat
er.
exam
ples
of s
olvi
ng p
robl
ems
invo
lvin
g su
rfac
e ar
ea a
nd v
olum
e of
cy
linde
rs
• C
alcu
late
the
volu
me
of a
cyl
inde
r, w
ithou
t usi
ng a
cal
cula
tor i
f its
dia
met
er is
28
cm
, its
hei
ght i
s 30
cm
andπ=
22 7
• C
alcu
late
the
surfa
ce a
rea
of a
cyl
inde
r, co
rrec
t to
2 de
cim
al p
lace
s, if
its
heig
ht
is 6
5 cm
and
the
circ
umfe
renc
e of
its
base
is 4
7,6
cm.
Tota
l tim
e fo
r su
rface
are
a an
d vo
lum
e:
5 ho
urs
rev
isio
n/a
sses
smen
t:A
t thi
s st
age
lear
ners
sho
uld
have
bee
n as
sess
ed o
n:
• fu
nctio
ns a
nd re
latio
nshi
ps
• al
gebr
aic
expr
essi
ons
• A
lgeb
raic
equ
atio
ns
• gr
aphs
• vo
lum
e an
d su
rface
are
a
Tota
l tim
e fo
r rev
isio
n/as
sess
men
t fo
r the
term
5 ho
urs
MATHEMATICS GRADES 7-9
147CAPS
Gr
ad
e 9
– te
rm
4
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
spac
e an
d sh
ape
(geo
met
ry)
3.4
tran
sfor
ma-
tion
G
eom
etry
tran
sfor
mat
ions
• R
ecog
nize
, des
crib
e an
d pe
rform
tra
nsfo
rmat
ions
with
poi
nts,
line
se
gmen
ts a
nd s
impl
e ge
omet
ric
figur
es o
n a
co-o
rdin
ate
plan
e,
focu
sing
on:
-re
flect
ion
in th
e y-
axis
or x
-axi
s
-tra
nsla
tion
with
in a
nd a
cros
s qu
adra
nts
-re
flect
ion
in th
e lin
e y
= x
• Id
entif
y w
hat t
he tr
ansf
orm
atio
n of
a
poin
t is,
if g
iven
the
co-o
rdin
ates
of
its im
age
enla
rgem
ents
and
redu
ctio
ns•
Use
pro
porti
on to
des
crib
e th
e ef
fect
of
enl
arge
men
t or r
educ
tion
on a
rea
and
perim
eter
of g
eom
etric
figu
res
• In
vest
igat
e th
e co
-ord
inat
es o
f the
ve
rtice
s of
figu
res
that
hav
e be
en
enla
rged
or r
educ
ed b
y a
give
n sc
ale
fact
or
Wha
t is
diffe
rent
to G
rade
8?
• R
eflec
tion
in th
e lin
e y
= x
• Id
entif
y tra
nsfo
rmat
ions
from
co-
ordi
nate
poi
nts
of th
e im
age
• C
o-or
dina
tes
of v
ertic
es
Co-
ordi
nate
pla
ne•
Doi
ng tr
ansf
orm
atio
ns o
n th
e co
-ord
inat
e pl
ane
is a
n op
portu
nity
to p
ract
ise
read
ing
and
plot
ting
poin
ts w
ith o
rder
ed p
airs
, and
link
s to
dra
win
g al
gebr
aic
grap
hs.
• m
ake
sure
lear
ners
kno
w h
ow to
plo
t poi
nts
on th
e co
-ord
inat
e pl
ane
and
can
read
the
co-o
rdin
ates
of p
oint
s of
f the
x-a
xis
and
y-ax
is.
• M
ake
sure
lear
ners
kno
w th
e co
nven
tion
for w
ritin
g or
dere
d pa
irs (x
; y)
• P
oint
out
the
diffe
renc
es b
etw
een
the
axes
in th
e fo
ur q
uadr
ants
.
Focu
s of
tran
sfor
mat
ions
• D
oing
tran
sfor
mat
ions
on
a co
-ord
inat
e pl
ane
focu
ses
atte
ntio
n on
the
co-
ordi
nate
s of
poi
nts
and
verti
ces
of s
hape
s.
• Le
arne
rs s
houl
d re
cogn
ize
that
tran
slat
ions
, refl
ectio
ns a
nd ro
tatio
ns o
nly
chan
ge th
e po
sitio
n of
the
figur
e, a
nd n
ot it
s sh
ape
or s
ize.
• Le
arne
rs s
houl
d re
cogn
ize
that
the
abov
e tra
nsfo
rmat
ions
pro
duce
con
grue
nt
figur
es.
• Le
arne
rs s
houl
d be
gin
to s
ee p
atte
rns
in te
rms
of th
e co
-ord
inat
e po
ints
, for
the
diffe
rent
tran
sfor
mat
ions
, suc
h as
:
-fo
r tra
nsla
tions
to th
e rig
ht o
r lef
t, th
e x–
valu
e ch
ange
s an
d y–
valu
e st
ays
the
sam
e
-fo
r tra
nsla
tions
up
or d
own,
the
y–va
lue
chan
ges
and
the
x–va
lue
stay
s th
e sa
me
-fo
r refl
ectio
ns in
the
y–a
xis,
the
x–va
lue
chan
ges
sign
and
the
y–va
lue
stay
s th
e sa
me
-fo
r refl
ectio
ns in
the
x–a
xis,
the
y–va
lue
chan
ges
sign
and
the
x–va
lue
stay
s th
e sa
me
-fo
r refl
ectio
ns in
the
line
y =
x, th
e x–
valu
e an
d y–
valu
e ar
e in
terc
hang
ed.
• Le
arne
rs s
houl
d re
cogn
ize
that
enl
arge
men
ts a
nd re
duct
ions
cha
nge
the
size
of
figur
es b
y in
crea
sing
or d
ecre
asin
g th
e le
ngth
of s
ides
, but
kee
ping
the
angl
es
the
sam
e, p
rodu
ces
sim
ilar r
athe
r tha
n co
ngru
ent fi
gure
s.
• Le
arne
rs s
houl
d al
so b
e ab
le to
wor
k ou
t the
fact
or o
f enl
arge
men
t or r
educ
tion
of a
figu
re.
Tota
l tim
e fo
r tra
nsfo
rma-
tions
:
9 ho
urs
MATHEMATICS GRADES 7-9
148 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
3.2
Geo
met
ry o
f 3d
obj
ects
Cla
ssify
ing
3d o
bjec
ts
• R
evis
e pr
oper
ties
and
defin
ition
s of
the
5 P
lato
nic
solid
s in
term
s of
th
e sh
ape
and
num
ber o
f fac
es, t
he
num
ber o
f ver
tices
and
the
num
ber
of e
dges
• R
ecog
nize
and
des
crib
e th
e pr
oper
ties
of:
-sp
here
s
-cy
linde
rs
Bui
ldin
g 3d
mod
els
• U
se n
ets
to c
reat
e m
odel
s of
ge
omet
ric s
olid
s, in
clud
ing:
-cu
bes
-pr
ism
s
-py
ram
ids
-cy
linde
rs
Wha
t is
diffe
rent
to G
rade
8?
• P
rope
rties
of s
pher
es a
nd c
ylin
ders
• N
ets
of c
ylin
ders
Plat
onic
sol
ids
• P
rope
rties
of P
lato
nic
solid
s sh
ould
be
revi
sed
• P
lato
nic
solid
s ar
e a
spec
ial g
roup
of p
olyh
edra
that
hav
e fa
ces
that
are
co
ngru
ent r
egul
ar p
olyg
ons.
• Th
ere
are
only
5 P
lato
nic
solid
s:
-te
trahe
dron
-he
xahe
dron
(cub
e)
-oc
tahe
dron
-do
deca
hedr
on
-ic
osah
edro
ns
• Th
e na
me
of e
ach
Pla
toni
c so
lid is
der
ived
from
its
num
ber o
f fac
es.
• P
lato
nic
solid
s pr
ovid
e an
inte
rest
ing
cont
ext i
n w
hich
to in
vest
igat
e th
e re
latio
nshi
p be
twee
n th
e nu
mbe
r of f
aces
, ver
tices
and
edg
es. B
y lis
ting
thes
e pr
oper
ties
for a
ll th
e P
lato
nic
solid
s le
arne
rs c
an in
vest
igat
e th
e pa
ttern
that
em
erge
s, to
com
e up
with
the
gene
ral r
ule:
V
– E
+ F
= 2,
whe
re V
= n
umbe
r of v
ertic
es; E
= n
umbe
r of e
dges
; F =
num
ber o
f fa
ces
usi
ng a
nd c
onst
ruct
ing
nets
• U
sing
and
con
stru
ctin
g ne
ts a
re u
sefu
l con
text
s fo
r exp
lorin
g or
con
solid
atin
g pr
oper
ties
of p
olyh
edra
.
• Le
arne
rs s
houl
d re
cogn
ize
the
nets
of d
iffer
ent s
olid
s.
• Le
arne
rs s
houl
d m
ake
sket
ches
of t
he n
ets
usin
g th
eir k
now
ledg
e of
the
the
shap
e an
d nu
mbe
r of f
aces
of t
he s
olid
s, b
efor
e dr
awin
g an
d cu
tting
out
the
nets
to
bui
ld m
odel
s.
• S
ince
lear
ners
hav
e m
ore
know
ledg
e ab
out t
he s
ize
of th
e in
tern
al a
ngle
s of
po
lygo
ns, a
nd c
an m
easu
re a
ngle
s, th
eir c
onst
ruct
ions
of n
ets
shou
ld b
e m
ore
accu
rate
.
• Le
arne
rs h
ave
to w
ork
out t
he re
lativ
e po
sitio
n of
face
s of
the
nets
in o
rder
to
build
the
3D m
odel
.
Tota
l tim
e fo
r ge
omet
ry o
f 3D
obj
ects
:
9 ho
urs
MATHEMATICS GRADES 7-9
149CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
dat
a ha
ndlin
g5.
1 C
olle
ct,
orga
nize
and
su
mm
ariz
e da
ta
Col
lect
dat
a
• P
ose
ques
tions
rela
ting
to s
ocia
l, ec
onom
ic, a
nd e
nviro
nmen
tal i
ssue
s
• S
elec
t and
just
ify a
ppro
pria
te s
ourc
es
for t
he c
olle
ctio
n of
dat
a
• D
istin
guis
h be
twee
n sa
mpl
es a
nd
popu
latio
ns, a
nd s
ugge
st a
ppro
pria
te
sam
ples
for i
nves
tigat
ion
• S
elec
t and
just
ify a
ppro
pria
te
met
hods
for c
olle
ctin
g da
ta
org
aniz
e an
d su
mm
ariz
e da
ta
• O
rgan
ize
num
eric
al d
ata
in d
iffer
ent
way
s in
ord
er to
sum
mar
ize
by
dete
rmin
ing:
-m
easu
res
of c
entra
l ten
denc
y
-m
easu
res
of
disp
ersi
on
incl
udin
g ex
trem
es a
nd o
utlie
rs
• O
rgan
ize
data
acc
ordi
ng to
mor
e th
an o
ne c
riter
ia
Wha
t is
diffe
rent
to G
rade
8?
• O
rgan
izin
g da
ta a
ccor
ding
to m
ore
than
one
crit
eria
• O
utlie
rs
• S
catte
r plo
ts
dat
a se
ts a
nd c
onte
xts
Lear
ners
sho
uld
be e
xpos
ed to
a v
arie
ty o
f con
text
s th
at d
eal w
ith s
ocia
l and
en
viro
nmen
tal i
ssue
s, a
nd s
houl
d w
ork
with
giv
en d
ata
sets
, rep
rese
nted
in
a va
riety
of w
ays,
that
incl
ude
big
num
ber r
ange
s, p
erce
ntag
es a
nd d
ecim
al
fract
ions
. Lea
rner
s sh
ould
then
pra
ctis
e or
gani
zing
and
sum
mar
izin
g th
is d
ata,
an
alys
ing
and
inte
rpre
ting
the
data
, and
writ
ing
a re
port
abou
t the
dat
a.
Com
plet
e a
data
cyc
le
Lear
ners
sho
uld
com
plet
e at
leas
t one
dat
a cy
cle
for t
he y
ear,
star
ting
with
pos
ing
thei
r ow
n qu
estio
ns, s
elec
ting
the
sour
ces
and
met
hod
for c
olle
ctin
g, re
cord
ing,
or
gani
zing
, rep
rese
ntin
g, th
en a
naly
sing
, sum
mar
izin
g, in
terp
retin
g an
d re
porti
ng
on th
e da
ta. C
halle
nge
lear
ners
to th
ink
abou
t wha
t kin
ds o
f que
stio
ns a
nd d
ata
need
to b
e co
llect
ed to
be
repr
esen
ted
on a
his
togr
am, a
pie
cha
rt, a
bar
gra
ph, a
lin
e gr
aph
or a
sca
tter p
lot.
Tota
l tim
e fo
r co
llect
ing
and
orga
nizi
ng
data
:
4 ho
urs
MATHEMATICS GRADES 7-9
150 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
5.2
rep
rese
nt
data
rep
rese
nt d
ata
• D
raw
a v
arie
ty o
f gra
phs
by h
and/
tech
nolo
gy to
dis
play
and
inte
rpre
t da
ta in
clud
ing:
-ba
r gra
phs
and
doub
le b
ar g
raph
s
-hi
stog
ram
s w
ith
give
n an
d ow
n in
terv
als
-pi
e ch
arts
-br
oken
-line
gra
phs
-sc
atte
r plo
ts
rep
rese
ntin
g da
ta
• P
ie c
harts
to re
pres
ent d
ata
do n
ot h
ave
to b
e ac
cura
tely
dra
wn
with
a c
ompa
ss
and
prot
ract
or, e
tc. L
earn
ers
can
use
any
roun
d ob
ject
to d
raw
a c
ircle
, the
n di
vide
the
circ
le in
to h
alve
s an
d qu
arte
rs a
nd e
ight
hs if
nee
ded,
as
a gu
ide
to
estim
ate
the
prop
ortio
ns o
f the
circ
le th
at n
eed
to b
e sh
own
to re
pres
ent t
he
data
. Wha
t is
impo
rtant
is th
at th
e va
lues
or p
erce
ntag
es a
ssoc
iate
d w
ith th
e da
ta, a
re s
how
n pr
opor
tiona
lly o
n th
e pi
e ch
art.
• D
raw
ing,
read
ing
and
inte
rpre
ting
pie
char
ts is
a u
sefu
l con
text
to re
-vis
it eq
uiva
lenc
e be
twee
n fra
ctio
ns a
nd p
erce
ntag
es, e
.g. 2
5% o
f the
dat
a is
re
pres
ente
d by
a 1 4 s
ecto
r of t
he c
ircle
.
• It
is a
lso
a co
ntex
t in
whi
ch le
arne
rs c
an fi
nd p
erce
ntag
es o
f who
le n
umbe
rs e
.g.
if 25
% o
f 300
lear
ners
like
rugb
y, h
ow m
any
(act
ual n
umbe
r) le
arne
rs li
ke ru
gby?
• H
isto
gram
s ar
e us
ed to
repr
esen
t gro
uped
dat
a sh
own
in in
terv
als
on th
e ho
rizon
tal a
xis
of th
e gr
aph.
Poi
nt o
ut th
e di
ffere
nces
bet
wee
n hi
stog
ram
s an
d ba
r gra
phs,
in p
artic
ular
bar
gra
phs
that
repr
esen
t dis
cret
e da
ta (e
.g. f
avou
rite
spor
ts) c
ompa
red
to h
isto
gram
s th
at s
how
cat
egor
ies
in c
onse
cutiv
e, n
on-
over
lapp
ing
inte
rval
, (e.
g. te
st s
core
s ou
t of 1
00 s
how
n in
inte
rval
s of
10)
. The
ba
rs o
n ba
r gra
phs
do n
ot h
ave
to to
uch
each
oth
er, w
hile
in a
his
togr
am th
ey
have
to to
uch
sinc
e th
ey s
how
con
secu
tive
inte
rval
s.
• B
roke
n-lin
e gr
aphs
refe
r to
data
gra
phs
that
repr
esen
t dat
a po
ints
join
ed b
y a
line
and
are
not t
he s
ame
as s
traig
ht li
ne g
raph
s th
at a
re d
raw
n us
ing
the
equa
tion
of th
e lin
e.
• B
roke
n-lin
e gr
aphs
are
use
d to
repr
esen
t dat
a th
at c
hang
es c
ontin
uous
ly o
ver
time,
e.g
. ave
rage
dai
ly te
mpe
ratu
re fo
r a m
onth
. Eac
h da
y’s
tem
pera
ture
is
repr
esen
ted
by a
poi
nt o
n th
e gr
aph,
and
onc
e th
e w
hole
mon
th h
as b
een
plot
ted,
the
poin
ts a
re jo
ined
to s
how
a b
roke
- lin
e gr
aph.
• B
roke
n-lin
e gr
aphs
are
use
ful t
o re
ad ‘t
rend
s’ a
nd p
atte
rns
in th
e da
ta, f
or
pred
ictiv
e pu
rpos
es e
.g. W
ill th
e te
mpe
ratu
res
go u
p or
dow
n in
the
next
mon
th?
• A
scat
ter p
lot i
s us
ed to
repr
esen
t dat
a th
at in
volv
es tw
o di
ffere
nt c
riter
ia a
nd
the
grap
h is
use
d to
look
at t
he re
latio
nshi
p be
twee
n th
e tw
o cr
iteria
. e.g
. How
do
es th
e pe
rform
ance
of l
earn
ers
in m
athe
mat
ics
com
pare
to th
eir p
erfo
rman
ce
in E
nglis
h? E
ach
poin
t on
the
grap
h re
pres
ents
the
resu
lts o
f one
lear
ner i
n M
athe
mat
ics
and
Eng
lish.
Afte
r all
the
resu
lts h
ave
been
plo
tted,
you
can
co
mpa
re th
e re
latio
nshi
p be
twee
n pe
rform
ance
in E
nglis
h an
d m
athe
mat
ics
for
all t
he le
arne
rs i.
e. if
they
sco
re h
igh
in M
athe
mat
ics,
do
they
als
o sc
ore
high
in
Eng
lish?
or,
if th
ey s
core
hig
h in
mat
hem
atic
s do
they
sco
re lo
w in
Eng
lish,
or
is th
ere
no re
latio
nshi
p be
twee
n w
hat t
hey
scor
e on
mat
hem
atic
s to
wha
t the
y sc
ore
in E
nglis
h?
• Th
e sc
atte
r plo
t allo
ws
one
to s
ee tr
ends
and
mak
e pr
edic
tions
, as
wel
l as
iden
tify
outli
ers
in th
e da
ta.
Tota
l tim
e fo
r re
pres
entin
g da
ta:
3 ho
urs
MATHEMATICS GRADES 7-9
151CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
5.2
rep
rese
nt
data
rep
rese
nt d
ata
• D
raw
a v
arie
ty o
f gra
phs
by h
and/
tech
nolo
gy to
dis
play
and
inte
rpre
t da
ta in
clud
ing:
-ba
r gra
phs
and
doub
le b
ar g
raph
s
-hi
stog
ram
s w
ith
give
n an
d ow
n in
terv
als
-pi
e ch
arts
-br
oken
-line
gra
phs
-sc
atte
r plo
ts
rep
rese
ntin
g da
ta
• P
ie c
harts
to re
pres
ent d
ata
do n
ot h
ave
to b
e ac
cura
tely
dra
wn
with
a c
ompa
ss
and
prot
ract
or, e
tc. L
earn
ers
can
use
any
roun
d ob
ject
to d
raw
a c
ircle
, the
n di
vide
the
circ
le in
to h
alve
s an
d qu
arte
rs a
nd e
ight
hs if
nee
ded,
as
a gu
ide
to
estim
ate
the
prop
ortio
ns o
f the
circ
le th
at n
eed
to b
e sh
own
to re
pres
ent t
he
data
. Wha
t is
impo
rtant
is th
at th
e va
lues
or p
erce
ntag
es a
ssoc
iate
d w
ith th
e da
ta, a
re s
how
n pr
opor
tiona
lly o
n th
e pi
e ch
art.
• D
raw
ing,
read
ing
and
inte
rpre
ting
pie
char
ts is
a u
sefu
l con
text
to re
-vis
it eq
uiva
lenc
e be
twee
n fra
ctio
ns a
nd p
erce
ntag
es, e
.g. 2
5% o
f the
dat
a is
re
pres
ente
d by
a 1 4 s
ecto
r of t
he c
ircle
.
• It
is a
lso
a co
ntex
t in
whi
ch le
arne
rs c
an fi
nd p
erce
ntag
es o
f who
le n
umbe
rs e
.g.
if 25
% o
f 300
lear
ners
like
rugb
y, h
ow m
any
(act
ual n
umbe
r) le
arne
rs li
ke ru
gby?
• H
isto
gram
s ar
e us
ed to
repr
esen
t gro
uped
dat
a sh
own
in in
terv
als
on th
e ho
rizon
tal a
xis
of th
e gr
aph.
Poi
nt o
ut th
e di
ffere
nces
bet
wee
n hi
stog
ram
s an
d ba
r gra
phs,
in p
artic
ular
bar
gra
phs
that
repr
esen
t dis
cret
e da
ta (e
.g. f
avou
rite
spor
ts) c
ompa
red
to h
isto
gram
s th
at s
how
cat
egor
ies
in c
onse
cutiv
e, n
on-
over
lapp
ing
inte
rval
, (e.
g. te
st s
core
s ou
t of 1
00 s
how
n in
inte
rval
s of
10)
. The
ba
rs o
n ba
r gra
phs
do n
ot h
ave
to to
uch
each
oth
er, w
hile
in a
his
togr
am th
ey
have
to to
uch
sinc
e th
ey s
how
con
secu
tive
inte
rval
s.
• B
roke
n-lin
e gr
aphs
refe
r to
data
gra
phs
that
repr
esen
t dat
a po
ints
join
ed b
y a
line
and
are
not t
he s
ame
as s
traig
ht li
ne g
raph
s th
at a
re d
raw
n us
ing
the
equa
tion
of th
e lin
e.
• B
roke
n-lin
e gr
aphs
are
use
d to
repr
esen
t dat
a th
at c
hang
es c
ontin
uous
ly o
ver
time,
e.g
. ave
rage
dai
ly te
mpe
ratu
re fo
r a m
onth
. Eac
h da
y’s
tem
pera
ture
is
repr
esen
ted
by a
poi
nt o
n th
e gr
aph,
and
onc
e th
e w
hole
mon
th h
as b
een
plot
ted,
the
poin
ts a
re jo
ined
to s
how
a b
roke
- lin
e gr
aph.
• B
roke
n-lin
e gr
aphs
are
use
ful t
o re
ad ‘t
rend
s’ a
nd p
atte
rns
in th
e da
ta, f
or
pred
ictiv
e pu
rpos
es e
.g. W
ill th
e te
mpe
ratu
res
go u
p or
dow
n in
the
next
mon
th?
• A
scat
ter p
lot i
s us
ed to
repr
esen
t dat
a th
at in
volv
es tw
o di
ffere
nt c
riter
ia a
nd
the
grap
h is
use
d to
look
at t
he re
latio
nshi
p be
twee
n th
e tw
o cr
iteria
. e.g
. How
do
es th
e pe
rform
ance
of l
earn
ers
in m
athe
mat
ics
com
pare
to th
eir p
erfo
rman
ce
in E
nglis
h? E
ach
poin
t on
the
grap
h re
pres
ents
the
resu
lts o
f one
lear
ner i
n M
athe
mat
ics
and
Eng
lish.
Afte
r all
the
resu
lts h
ave
been
plo
tted,
you
can
co
mpa
re th
e re
latio
nshi
p be
twee
n pe
rform
ance
in E
nglis
h an
d m
athe
mat
ics
for
all t
he le
arne
rs i.
e. if
they
sco
re h
igh
in M
athe
mat
ics,
do
they
als
o sc
ore
high
in
Eng
lish?
or,
if th
ey s
core
hig
h in
mat
hem
atic
s do
they
sco
re lo
w in
Eng
lish,
or
is th
ere
no re
latio
nshi
p be
twee
n w
hat t
hey
scor
e on
mat
hem
atic
s to
wha
t the
y sc
ore
in E
nglis
h?
• Th
e sc
atte
r plo
t allo
ws
one
to s
ee tr
ends
and
mak
e pr
edic
tions
, as
wel
l as
iden
tify
outli
ers
in th
e da
ta.
Tota
l tim
e fo
r re
pres
entin
g da
ta:
3 ho
urs
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
5.3
inte
rpre
t, an
alys
e an
d re
port
dat
a
inte
rpre
t dat
a
• C
ritic
ally
read
and
inte
rpre
t dat
a re
pres
ente
d in
a v
arie
ty o
f way
s.
• C
ritic
ally
com
pare
two
sets
of d
ata
rela
ted
to th
e sa
me
issu
e
ana
lyse
dat
a
• C
ritic
ally
ana
lyse
dat
a by
ans
wer
ing
ques
tions
rela
ted
to:
-D
ata
colle
ctio
n m
etho
ds
-S
umm
ary
stat
istic
s of
dat
a
-S
ourc
es o
f err
or a
nd b
ias
in th
e da
ta
rep
ort d
ata
• S
umm
ariz
e da
ta in
sho
rt pa
ragr
aphs
th
at in
clud
e
-dr
awin
g co
nclu
sion
s ab
out t
he d
ata
-m
akin
g pr
edic
tions
bas
ed o
n th
e da
ta
-m
akin
g co
mpa
rison
s be
twee
n tw
o se
ts o
f dat
a
-id
entif
ying
sou
rces
of e
rror
and
bi
as in
the
data
-ch
oosi
ng a
ppro
pria
te s
umm
ary
stat
istic
s fo
r the
dat
a (m
ean,
m
edia
n, m
ode,
rang
e)
-th
e ro
le o
f ext
rem
es a
nd o
utlie
rs in
th
e da
ta
dev
elop
ing
criti
cal a
naly
sis
skill
s
• Le
arne
rs s
houl
d co
mpa
re th
e sa
me
data
repr
esen
ted
in d
iffer
ent w
ays
e.g.
in a
pi
e ch
art o
r a b
ar g
raph
or a
tabl
e, a
nd d
iscu
ss w
hat i
nfor
mat
ion
is s
how
n an
d w
hat i
s hi
dden
; the
y sh
ould
eva
luat
e w
hich
form
of r
epre
sent
atio
n w
orks
bes
t for
th
e gi
ven
data
.
• Le
arne
rs s
houl
d co
mpa
re g
raph
s on
the
sam
e to
pic
but w
here
dat
a ha
s be
en
colle
cted
from
diff
eren
t gro
ups
of p
eopl
e, a
t diff
eren
t tim
es, i
n di
ffere
nt p
lace
s or
in d
iffer
ent w
ays.
Her
e le
arne
rs s
houl
d di
scus
s di
ffere
nces
bet
wee
n th
e da
ta
with
an
awar
enes
s of
bia
s re
late
d to
the
impa
ct o
f dat
a so
urce
s an
d m
etho
ds o
f da
ta c
olle
ctio
n on
the
inte
rpre
tatio
n of
the
data
.
• Le
arne
rs s
houl
d co
mpa
re d
iffer
ent w
ays
of s
umm
ariz
ing
the
sam
e da
ta s
ets,
de
velo
ping
an
awar
enes
s of
how
dat
a re
porti
ng c
an b
e m
anip
ulat
ed; t
hey
shou
ld e
valu
ate
whi
ch s
umm
ary
stat
istic
s be
st re
pres
ent t
he d
ata.
• Le
arne
rs s
houl
d co
mpa
re g
raph
s of
the
sam
e da
ta, w
here
the
scal
es o
f th
e gr
aphs
are
diff
eren
t. H
ere
lear
ners
sho
uld
disc
uss
diffe
renc
es w
ith a
n aw
aren
ess
of h
ow re
pres
enta
tion
of d
ata
can
be m
anip
ulat
ed; t
hey
shou
ld
eval
uate
whi
ch fo
rm o
f rep
rese
ntat
ion
wor
ks b
est f
or th
e gi
ven
data
.
• Le
arne
rs s
houl
d co
mpa
re d
ata
on th
e sa
me
topi
c, w
here
one
set
of d
ata
has
extre
mes
or o
utlie
rs, a
nd d
iscu
ss d
iffer
ence
s w
ith a
n aw
aren
ess
of th
e ef
fect
of
the
extre
mes
or o
utlie
rs o
n th
e in
terp
reta
tion
of th
e da
ta. I
n pa
rticu
lar,
extre
mes
af
fect
the
rang
e an
d ou
tlier
s w
hich
are
iden
tified
on
scat
ter p
lots
.
• Le
arne
rs s
houl
d w
rite
repo
rts o
n th
e da
ta in
sho
rt pa
ragr
aphs
.
Tota
l tim
e fo
r an
alys
ing,
in
terp
retin
g,
sum
mar
izin
g an
d re
porti
ng
data
:
3,5
hour
s
MATHEMATICS GRADES 7-9
152 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
5.4
Prob
abili
tyPr
obab
ility
• C
onsi
der s
ituat
ions
with
equ
ally
pr
obab
le o
utco
mes
, and
:
-de
term
ine
prob
abili
ties
of
com
poun
d ev
ents
usi
ng tw
o-w
ay
tabl
es a
nd tr
ee d
iagr
ams
-de
term
ine
the
prob
abili
ties
of
outc
omes
of e
vent
s an
d pr
edic
t th
eir r
elat
ive
frequ
ency
in s
impl
e ex
perim
ents
-co
mpa
re re
lativ
e fre
quen
cy w
ith
prob
abili
ty a
nd e
xpla
in p
ossi
ble
diffe
renc
es
Prob
abili
ty e
xper
imen
tsIn
Gra
des
8 an
d 9
prob
abili
ty e
xper
imen
ts a
re le
ss im
porta
nt, a
nd le
arne
rs s
houl
d co
nsid
er p
roba
bilit
y fo
r hyp
othe
tical
eve
nts.
In G
rade
9, l
earn
ers
have
to c
onsi
der
outc
omes
of c
ompo
und
even
ts a
nd u
se tw
o-w
ay ta
bles
and
tree
dia
gram
s to
wor
k ou
t the
pro
babi
lity
of a
n ou
tcom
e.
Prob
abili
ty o
f com
poun
d ev
ents
For e
xam
ple,
wha
t is
the
prob
abili
ty o
f a w
oman
giv
ing
birth
to tw
o bo
ys a
fter e
ach
othe
r? A
two-
way
tabl
e ca
n be
use
d:
1st b
irth
2nd
birth
Boy
Girl
Boy
BB
BG
Girl
GB
GG
Two
boys
afte
r eac
h ot
her (
BB
) is
1 of
4 p
ossi
ble
outc
omes
, so
the
prob
abili
ty o
f tw
o bo
ys is
1 o
ut o
f 4, o
r 25%
.
How
doe
s th
is p
roba
bilit
y ch
ange
if y
ou a
sk w
hat i
s th
e pr
obab
ility
of g
ivin
g bi
rth to
th
ree
boys
afte
r eac
h ot
her?
A tr
ee d
iagr
am c
an th
en b
e us
ed:
Girl
[GG
G]
Girl
Boy
Girl
[BB
G]
Boy
[BBB
]
Girl
[BG
G]
Boy
[BGB
]
Girl
[GB
G]
Boy
[GBB
] Bo
y [G
GB]
Boy
Girl
Boy
Girl
2nd b
irth
3rd b
irth
1st b
irth
Tota
l tim
e fo
r pr
obab
ility
:
4,5
hour
s
MATHEMATICS GRADES 7-9
153CAPS
Co
nte
nt
ar
eato
PiC
sC
on
CeP
ts a
nd
sK
ills
som
e C
lar
iFiC
atio
n n
ote
s o
r t
eaC
Hin
G G
uid
elin
esd
ur
atio
n
(in h
ours
)
5.4
Prob
abili
tyto
tal o
utco
mes
8
Thre
e bo
ys a
fter e
ach
othe
r, [B
BB
], is
1 o
ut 8
of p
ossi
ble
outc
omes
, hen
ce th
e pr
obab
ility
of t
hree
boy
s af
ter e
ach
othe
r is
1 8 or 1
2,5%
.
rev
isio
n/a
sses
smen
t:A
t thi
s st
age
lear
ners
sho
uld
have
bee
n as
sess
ed o
n:
• tra
nsfo
rmat
ion
geom
etry
• ge
omet
ry o
f 3D
obj
ects
• co
llect
ing,
org
aniz
ing,
repr
esen
ting,
ana
lysi
ng, s
umm
ariz
ing,
inte
rpre
ting
and
repo
rting
dat
a
• pr
obab
ility
Tota
l tim
e fo
r rev
isio
n/as
sess
men
t fo
r the
term
12 h
ours
MATHEMATICS GRADES 7-9
154 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
SECTION 4: ASSESSMENT
4.1 introduCtion
Assessment is a continuous planned process of identifying, gathering and interpreting information regarding the per-formance of learners, using various forms of assessment. It involves four steps: generating and collecting evidence of achievement; evaluating this evidence; recording the findings and using this information to understand and thereby assist the learner’s development in order to improve the process of learning and teaching. Assessment should be both informal and formal. In both cases regular feedback should be provided to learners to enhance their learning experience. This will assist the learner to achieve the minimum performance level of 40% to 49% required in Math-ematics for promotion purposes.
4.2 tyPes oF assessment
The following types of assessment are very useful in mathematics; as a result teachers are encouraged to use them to serve the purpose associated with each.
Baseline assessment: mathematics teachers who might want to establish whether their learners meet the basic skills and knowledge levels required to learn a specific Mathematics topic will use baseline assessment. Knowing learners’ level of proficiency in a particular Mathematics topic enables the teacher to plan her/his Mathematics lesson appropriately and to pitch it at the appropriate level. Baseline assessment, as the name suggests, should therefore be administered prior to teaching a particular Mathematics topic. The results of the baseline assessment should not be used for promotion purposes.
diagnostic assessment: It is not intended for promotion purposes but to inform the teacher about the learner’s Mathematics problem areas that have the potential to hinder performance. Two broad areas form the basis of diag-nostic assessment: content-related challenges where learners find certain difficulties to comprehend, and psycho-social factors such as negative attitudes, Mathematics anxiety, poor study habits, poor problem-solving behaviour, etc. Appropriate interventions should be implemented to assist learners in overcoming these challenges early in their school careers.
Formative assessment: Formative assessment is used to aid the teaching and learning processes, hence assess-ment for learning. It is the most commonly used type of assessment because it can be used in different forms at any time during a Mathematics lesson, e.g. short class works during or at the end of each lesson, verbal questioning dur-ing the lesson. It is mainly informal and should not be used for promotion purposes. The fundamental distinguishing characteristic of formative assessment is constant feedback to learners, particularly with regard to learners’ learning processes. The information provided by formative assessment can also be used by teachers to inform their methods of teaching.
summative assessment: Contrary to the character of formative assessment, summative assessment is carried out after the completion of a Mathematics topic or a cluster of related topics. It is therefore referred to as assessment of learning since it is mainly focusing on the product of learning. The results of summative assessment are recorded and used for promotion purposes. The forms of assessment presented in Table 4.1 are examples of summative as-sessment.
MATHEMATICS GRADES 7-9
155CAPS
4.3 inFormal or daily assessment
Assessment for learning has the purpose of continuously collecting information on learner performance that can be used to improve their learning.
Informal assessment is a daily monitoring of learners’ progress. This is done through observations, discussions, prac-tical demonstrations, learner-teacher conferences, informal classroom interactions, etc. Informal assessment may be as simple as stopping during the lesson to observe learners or to discuss with learners how learning is progressing. Informal assessment should be used to provide feedback to learners and to inform planning for teaching, but need not be recorded. It should not be seen as separate from the learning activities taking place in the classroom.
Self-assessment and peer assessment actively allow learners to assess themselves. This is important as it allows learners to learn from, and reflect on their own performance. The results of the informal daily assessment tasks are not formally recorded unless the teacher wishes to do so. The results of daily assessment tasks are not taken into account for promotion purposes.
4.4 Formal assessment
Formal assessment comprises School-Based Assessment (SBA) and End of the Year Examination. Formal assessment tasks are marked and formally recorded by the teacher for promotion purposes. All Formal Assessment tasks are subject to moderation for the purpose of quality assurance and to ensure that appropriate standards are maintained. The SBA component may take various forms. However, tests, examinations, projects, assignments and investigations are recommended for Mathematics. The Senior Phase Mathematics minimum formal programme of assessment tasks are outlined in Table 4.1
table 4.1: minimum requirements for formal assessment: senior Phase mathematics
Forms of assessment
minimum requirements per term number of tasks per
yearWeighting
Term 1 Term 2 Term 3 Term 4
sBa
Test 1 1 1 3
40%
Examination 1 1
Assignment 1 1 1 3
Investigation 1 1 2
Project 1 1
total 2 3 3 2 10*
end of the year examination 1 60%
*To be completed before the End of the year Examination
tests and examinations are individualised assessment tasks and should be carefully designed to ensure that learners demonstrate their full potential in Mathematics content. The questions should be carefully spread to cater for different cognitive levels of learners. Tests and examinations are predominantly assessed using a memorandum.
the assignment, as is the case with tests and examinations, is mainly an individualised task. It can be a collection of past questions, but should focus on more demanding work as any resource material can be used, which is not the case in a task that is done in class under supervision.
MATHEMATICS GRADES 7-9
156 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Projects are used to assess a range of skills and competencies. Through projects, learners are able to demonstrate their understanding of different Mathematics concepts and apply them in real-life situations. Caution should, how-ever, be exercised not to give projects that are above learners’ cognitive levels. The assessment criteria should be clearly indicated on the project specification and should focus on the Mathematics involved and not on duplicated pictures and facts copied from reference material. Good projects contain the collection and display of real data, fol-lowed by deductions that can be substantiated.
Investigation promotes critical and creative thinking. It can be used to discover rules or concepts and may involve inductive reasoning, identifying or testing patterns or relationships, drawing conclusions, and establishing general trends. To avoid having to assess work which is copied without understanding, it is recommended that whilst initial investigation could be done at home, the final write-up should be done in class, under supervision, without access to any notes. Investigations are assessed with rubrics, which can be specific to the task, or generic, listing the number of marks awarded for each skill. These skills include:
• organizing and recording ideas and discoveries using, for example, diagrams and tables.
• communicating ideas with appropriate explanations
• calculations showing clear understanding of mathematical concepts and procedures.
• generalizing and drawing conclusions,
The forms of assessment used should be appropriate to the age and cognitive level of learners. The design of these tasks should cover the content of the subject and designed to achieve the broad aims of the subject. Appropriate instruments, such as rubrics and memoranda, should be used for marking. Formal assessments should cater for a range of cognitive levels and abilities of learners as shown in Table 4.2:
MATHEMATICS GRADES 7-9
157CAPS
table 4.2: Cognitive levels
desCriPtion and eXamPles oF CoGnitive levelsCognitive levels description of skills to be demonstrated examples
Knowledge(≈25%)
• Estimation and appropriate rounding of numbers
• Straight recall
• Identification and direct use of correct formula
• Use of mathematical facts
• Appropriate use of mathematical vocabulary
1. Estimate the answer and then calculate with a calculator:
62 816325 + 279 [Grade 7]
2. Use the formula A = πr2 to calculate the area of a circle if the diameter is equal to 10 cm. [Grade 8]
3. Write down the y-intercept of the function y = 2x + 1 [Grade 9]
routine procedures
(≈45%)
• Perform well-known procedures
• Simple applications and calculations which might involve many steps
• Derivation from given information may be involved
• Identification and use (after changing the subject) of correct formula
• Generally similar to those encountered in class
1. Determine the mean of 5 Grade 7 learners’ marks if they have respectively achieved 25; 40; 21; 85; 14 out of 50. [Grade 7]
2. Solve x in x – 6 = 9 [Grade 8]
3. R600 invested at r% per annum for a period of 3 years yields R150 interest. Calculate the value of r if SI = P.n.r
100 . [Grade 9]
Complex procedures
(≈20%)
• Problems involving complex calculations and/or higher order reasoning
• Investigate elementary axioms to generalize them into proofs for straight line geometry, congruence and similarity
• No obvious route to the solution
• Problems not necessarily based on real world contexts
• Making significant connections between different representations
• Require conceptual understanding
1. Mr Mnisi pays R75 for a book which he marks up to provide 20% profit. He then sells it for cash at 4% discount. Calculate the selling price. [Grade 7]
2. A car travelling at a constant speed travels 60 km in 18 minutes. How far, travelling at the same constant speed, will the car travel in 1 hour 12 minutes? [Grade 8]
3. Use investigation skills to prove that the angles on a straight line are supplementary. [Grade 9]
Problem solving(≈10%)
• Unseen, non-routine problems (which are not necessarily difficult)
• Higher order understanding and processes are often involved
• might require the ability to break the problem down into its constituent parts
1. The sum of three consecutive numbers is 87. Find the numbers. [Grade 7]
2. Mary travels a distance of km in 6 hours if she travels at an average speed of 20 km/h on her bicycle. What should be her average speed if she wants to cover the same distance in 5 hours? [Grade 8]
3. The combined age of a father and son is 84 years old. In 6 years time the father will be twice as old as the son was 3 years ago. How old are they now? [Grade 9]
4.5 reCordinG and rePortinG
Recording is a process in which the teacher documents the level of a learner’s performance in a specific assessment task. It indicates the learner’s progress towards the achievement of the knowledge as prescribed in the National Curriculum and Assessment Policy Statements. Records of learner performance should provide evidence of the learner’s conceptual progression within a grade and her/his readiness to be promoted to the next grade. Records of learner performance should also be used to verify the progress made by teachers and learners in the teaching and learning process.
MATHEMATICS GRADES 7-9
158 CURRICULUM AND ASSESSMENT POLICY STATEMENT (CAPS)
Reporting is a process of communicating learner performance to learners, parents, schools, and other stakeholders. Primary schooling is a critical period for the acquisition of foundational Mathematics skills and conceptual knowledge. Reporting of learner performance is therefore essential and should not be limited to the quarterly report card. Other methods of reporting should be explored, e.g. parents’ meetings, school visitation days, parent-teacher conferences, phone calls, letters. These extreme, but worthwhile modalities will ensure that any underperformance is communi-cated promptly and appropriate measures of intervention are implemented collaboratively by teachers and parents. Formal reporting is done on a 7-point rating scale (see Table 4.3)
table 4.3: scale of achievement for the national Curriculum statement Grades 7 - 9
ratinG Code desCriPtion oF ComPetenCe PerCentaGe
7 Outstanding achievement 80 – 100
6 meritorious achievement 70 – 79
5 Substantial achievement 60 – 69
4 Adequate achievement 50 – 59
3 moderate achievement 40 – 49
2 Elementary achievement 30 – 39
1 Not achieved 0 – 29
4.6 moderation oF assessment
Moderation refers to the process that ensures that the assessment tasks are fair, valid and reliable. Moderation should be carried out internally at school and/or externally at district, provincial and national levels. Given that the promotion of learners in the Senior Phase is largely dependent upon the SBA (which contributes 40%); the moderation process should be intensified to ensure that:
• learners are not disadvantaged by the invalid and unreliable assessment tasks,
• quality assessment is given and high but achievable standards are maintained.
4.7 General
This document should be read in conjunction with:
4.7.1 National policy pertaining to the programme and promotion requirements of the National Curriculum Statement Grades R-12; and
4.7.2 National Protocol for Assessment Grades R-12.