The mathematics overview and learning objectives...
Transcript of The mathematics overview and learning objectives...
3The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
The
Fram
ewor
k fo
r sec
onda
ry m
athe
mat
ics:
ove
rvie
w a
nd le
arni
ng o
bjec
tive
s
Ove
rvie
w o
f str
ands
Stra
nds
Sub
-str
ands
Stra
nds
Sub
-str
ands
1 M
athe
mat
ical
pro
cess
es a
nd a
pplic
atio
ns3
Alg
ebra
1.1
Repr
esen
ting
3.1
Equa
tions
, for
mul
ae, e
xpre
ssio
ns a
nd id
entit
ies
1.2
Ana
lysi
ng –
use
mat
hem
atic
al re
ason
ing
3.2
Sequ
ence
s, fu
nctio
ns a
nd g
raph
s
1.3
Ana
lysi
ng –
use
app
ropr
iate
mat
hem
atic
al p
roce
dure
s4
Geo
met
ry a
nd m
easu
res
1.4
Inte
rpre
ting
and
eval
uatin
g4.
1 G
eom
etric
al re
ason
ing
1.5
Com
mun
icat
ing
and
refle
ctin
g4.
2 Tr
ansf
orm
atio
ns a
nd c
oord
inat
es
2 N
umbe
r4.
3 Co
nstr
uctio
n an
d lo
ci
2.1
Plac
e va
lue,
ord
erin
g an
d ro
undi
ng4.
4 M
easu
res
and
men
sura
tion
2.2
Inte
gers
, pow
ers
and
root
s5
Sta
tist
ics
2.3
Frac
tions
, dec
imal
s, p
erce
ntag
es, r
atio
and
pro
port
ion
5.1
Spec
ifyin
g a
prob
lem
, pla
nnin
g an
d co
llect
ing
data
2.4
Num
ber o
pera
tions
5.2
Proc
essi
ng a
nd re
pres
entin
g da
ta
2.5
Men
tal c
alcu
latio
n m
etho
ds5.
3 In
terp
retin
g an
d di
scus
sing
resu
lts
2.6
Writ
ten
calc
ulat
ion
met
hods
5.4
Prob
abili
ty
2.7
Calc
ulat
or m
etho
ds
2.8
Chec
king
resu
lts
5The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
Lear
ning
obj
ecti
ves
1 M
athe
mat
ical
pro
cess
es a
nd a
pplic
atio
nsSo
lve
prob
lem
s, e
xplo
re a
nd in
vest
igat
e in
a ra
nge
of c
onte
xts
Incr
ease
the
chal
leng
e an
d bu
ild p
rogr
essi
on a
cros
s th
e ke
y st
age,
and
for g
roup
s of
pup
ils b
y:
•in
crea
sing
the
com
plex
ity
of th
e ap
plic
atio
n, e
.g. n
on-r
outin
e, m
ulti-
step
pro
blem
s, e
xten
ded
enqu
iries
•re
duci
ng th
e fa
mili
arit
y of
the
cont
ext,
e.g.
new
con
text
s in
mat
hem
atic
s, c
onte
xts
draw
n fr
om o
ther
subj
ects
, oth
er a
spec
ts o
f pup
ils’ l
ives
•in
crea
sing
the
tech
nica
l dem
and
of th
e m
athe
mat
ics
requ
ired,
e.g
. mor
e ad
vanc
ed c
once
pts,
mor
e di
ffic
ult p
roce
dure
s
•in
crea
sing
the
degr
ee o
f ind
epen
denc
e an
d au
tono
my
in p
robl
em-s
olvi
ng a
nd in
vest
igat
ion
1.1
Repr
esen
ting
Year
7Ye
ar 8
Year
9
Year
10
Year
11
Exte
nsio
n
iden
tify
the
nece
ssar
y in
form
atio
n to
un
ders
tand
or s
impl
ify
a co
ntex
t or p
robl
em;
repr
esen
t pro
blem
s,
mak
ing
corr
ect u
se
of s
ymbo
ls, w
ords
, di
agra
ms,
tabl
es a
nd
grap
hs; u
se a
ppro
pria
te
proc
edur
es a
nd to
ols,
in
clud
ing
ICT
iden
tify
the
mat
hem
atic
al fe
atur
es
of a
con
text
or
prob
lem
; try
out
and
co
mpa
re m
athe
mat
ical
re
pres
enta
tions
; sel
ect
appr
opria
te p
roce
dure
s an
d to
ols,
incl
udin
g IC
T
brea
k do
wn
subs
tant
ial
task
s to
mak
e th
em
mor
e m
anag
eabl
e;
repr
esen
t pro
blem
s an
d sy
nthe
sise
in
form
atio
n in
al
gebr
aic,
geo
met
rical
or
gra
phic
al fo
rm;
mov
e fr
om o
ne fo
rm
to a
noth
er to
gai
n a
diff
eren
t per
spec
tive
on th
e pr
oble
m
com
pare
and
eva
luat
e re
pres
enta
tions
; ex
plai
n th
e fe
atur
es
sele
cted
and
just
ify
the
choi
ce o
f re
pres
enta
tion
in
rela
tion
to th
e co
ntex
t
choo
se a
nd c
ombi
ne
repr
esen
tatio
ns fr
om a
ra
nge
of p
ersp
ectiv
es;
intr
oduc
e an
d us
e a
rang
e of
mat
hem
atic
al
tech
niqu
es, t
he m
ost
effic
ient
for a
naly
sis
and
mos
t eff
ectiv
e fo
r co
mm
unic
atio
n
syst
emat
ical
ly m
odel
co
ntex
ts o
r pro
blem
s th
roug
h pr
ecis
e an
d co
nsis
tent
use
of
sym
bols
and
re
pres
enta
tions
, and
su
stai
n th
is th
roug
hout
th
e w
ork
6 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
1.2
Ana
lysi
ng –
use
mat
hem
atic
al re
ason
ing
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
clas
sify
and
vis
ualis
e pr
oper
ties
and
patt
erns
; gen
eral
ise
in s
impl
e ca
ses
by
wor
king
logi
cally
; dra
w
sim
ple
conc
lusi
ons
and
expl
ain
reas
onin
g;
unde
rsta
nd th
e si
gnifi
canc
e of
a
coun
ter-
exam
ple;
ta
ke a
ccou
nt o
f fe
edba
ck a
nd le
arn
from
mis
take
s
visu
alis
e an
d m
anip
ulat
e dy
nam
ic
imag
es; c
onje
ctur
e an
d ge
nera
lise;
mov
e be
twee
n th
e ge
nera
l an
d th
e pa
rtic
ular
to
test
the
logi
c of
an
argu
men
t; id
entif
y ex
cept
iona
l cas
es o
r co
unte
r-ex
ampl
es;
mak
e co
nnec
tions
with
re
late
d co
ntex
ts
use
conn
ectio
ns w
ith
rela
ted
cont
exts
to
impr
ove
the
anal
ysis
of
a si
tuat
ion
or p
robl
em;
pose
que
stio
ns a
nd
mak
e co
nvin
cing
ar
gum
ents
to ju
stify
ge
nera
lisat
ions
or
solu
tions
; rec
ogni
se th
e im
pact
of c
onst
rain
ts o
r as
sum
ptio
ns
iden
tify
a ra
nge
of s
trat
egie
s an
d ap
prec
iate
that
mor
e th
an o
ne a
ppro
ach
may
be
nece
ssar
y;
expl
ore
the
effe
cts
of v
aryi
ng v
alue
s an
d lo
ok fo
r inv
aria
nce
and
cova
rianc
e in
mod
els
and
repr
esen
tatio
ns;
exam
ine
and
refin
e ar
gum
ents
, con
clus
ions
an
d ge
nera
lisat
ions
; pr
oduc
e si
mpl
e pr
oofs
mak
e pr
ogre
ss b
y ex
plor
ing
mat
hem
atic
al
task
s, de
velo
ping
an
d fo
llow
ing
alte
rnat
ive
appr
oach
es;
exam
ine
and
exte
nd
gene
ralis
atio
ns; s
uppo
rt
assu
mpt
ions
by
clea
r ar
gum
ent a
nd fo
llow
th
roug
h a
sust
aine
d ch
ain
of re
ason
ing,
in
clud
ing
proo
f
pres
ent r
igor
ous
and
sust
aine
d ar
gum
ents
; re
ason
indu
ctiv
ely,
de
duce
and
pro
ve;
expl
ain
and
just
ify
assu
mpt
ions
and
co
nstr
aint
s
1.3
Ana
lysi
ng –
use
app
ropr
iate
mat
hem
atic
al p
roce
dure
sW
ithin
the
appr
opria
te ra
nge
and
cont
ent:
mak
e ac
cura
te m
athe
mat
ical
dia
gram
s, g
raph
s an
d co
nstr
uctio
ns o
n pa
per a
nd o
n sc
reen
; cal
cula
te a
ccur
atel
y, s
elec
ting
men
tal m
etho
ds o
r cal
cula
ting
devi
ces
as a
ppro
pria
te; m
anip
ulat
e nu
mbe
rs, a
lgeb
raic
exp
ress
ions
and
equ
atio
ns, a
nd a
pply
rout
ine
algo
rithm
s; us
e ac
cura
te n
otat
ion,
incl
udin
g co
rrec
t sy
ntax
whe
n us
ing
ICT;
reco
rd m
etho
ds, s
olut
ions
and
con
clus
ions
; est
imat
e, a
ppro
xim
ate
and
chec
k w
orki
ng
7The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
1.4
Inte
rpre
ting
and
eva
luat
ing
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
inte
rpre
t inf
orm
atio
n fr
om a
mat
hem
atic
al
repr
esen
tatio
n or
co
ntex
t; re
late
find
ings
to
the
orig
inal
con
text
; ch
eck
the
accu
racy
of
the
solu
tion;
exp
lain
an
d ju
stify
met
hods
an
d co
nclu
sion
s; co
mpa
re a
nd e
valu
ate
appr
oach
es
use
logi
cal a
rgum
ent
to in
terp
ret t
he
mat
hem
atic
s in
a
give
n co
ntex
t or t
o es
tabl
ish
the
trut
h of
a s
tate
men
t; gi
ve
accu
rate
sol
utio
ns
appr
opria
te to
the
cont
ext o
r pro
blem
; ev
alua
te th
e ef
ficie
ncy
of a
ltern
ativ
e st
rate
gies
an
d ap
proa
ches
just
ify th
e m
athe
mat
ical
feat
ures
dr
awn
from
a c
onte
xt
and
the
choi
ce o
f ap
proa
ch; g
ener
ate
fulle
r sol
utio
ns b
y pr
esen
ting
a co
ncis
e,
reas
oned
arg
umen
t us
ing
sym
bols
, di
agra
ms,
gra
phs
and
rela
ted
expl
anat
ions
mak
e se
nse
of, a
nd
judg
e th
e va
lue
of, o
wn
findi
ngs
and
thos
e pr
esen
ted
by o
ther
s; ju
dge
the
stre
ngth
of
empi
rical
evi
denc
e an
d di
stin
guis
h be
twee
n ev
iden
ce a
nd p
roof
; ju
stify
gen
eral
isat
ions
, ar
gum
ents
or s
olut
ions
show
insi
ght i
nto
the
mat
hem
atic
al
conn
ectio
ns in
the
cont
ext o
r pro
blem
; cr
itica
lly e
xam
ine
stra
tegi
es a
dopt
ed
and
argu
men
ts
pres
ente
d; c
onsi
der
the
assu
mpt
ions
in th
e m
odel
and
reco
gnis
e lim
itatio
ns in
the
accu
racy
of r
esul
ts
and
conc
lusi
ons
just
ify a
nd e
xpla
in
solu
tions
to p
robl
ems
invo
lvin
g an
unf
amili
ar
cont
ext o
r a n
umbe
r of
feat
ures
or
varia
bles
; com
men
t co
nstr
uctiv
ely
on
reas
onin
g, lo
gic,
pr
oces
s, re
sults
and
co
nclu
sion
s
1.5
Com
mun
icat
ing
and
refl
ecti
ng
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
com
mun
icat
e ow
n fin
ding
s ef
fect
ivel
y,
oral
ly a
nd in
writ
ing,
an
d di
scus
s an
d co
mpa
re a
ppro
ache
s an
d re
sults
with
oth
ers;
reco
gnis
e eq
uiva
lent
ap
proa
ches
refin
e ow
n fin
ding
s an
d ap
proa
ches
on
the
basi
s of
dis
cuss
ions
w
ith o
ther
s; re
cogn
ise
effic
ienc
y in
an
appr
oach
; rel
ate
the
curr
ent p
robl
em a
nd
stru
ctur
e to
pre
viou
s si
tuat
ions
revi
ew a
nd re
fine
own
findi
ngs
and
appr
oach
es o
n th
e ba
sis
of d
iscu
ssio
ns
with
oth
ers;
look
for
and
refle
ct o
n ot
her
appr
oach
es a
nd b
uild
on
pre
viou
s ex
perie
nce
of s
imila
r situ
atio
ns
and
outc
omes
use
a ra
nge
of fo
rms
to c
omm
unic
ate
findi
ngs
effe
ctiv
ely
to
diff
eren
t aud
ienc
es;
revi
ew fi
ndin
gs a
nd
look
for e
quiv
alen
ce to
di
ffer
ent p
robl
ems
with
si
mila
r str
uctu
re
rout
inel
y re
view
and
re
fine
findi
ngs
and
appr
oach
es; i
dent
ify
how
oth
er c
onte
xts
wer
e di
ffer
ent f
rom
, or
sim
ilar t
o, th
e cu
rren
t si
tuat
ion
and
expl
ain
how
and
why
the
sam
e or
diff
eren
t str
ateg
ies
wer
e us
ed
use
mat
hem
atic
al
lang
uage
and
sy
mbo
ls e
ffec
tivel
y in
pr
esen
ting
conv
inci
ng
conc
lusi
ons
or fi
ndin
gs;
criti
cally
refle
ct o
n ow
n lin
es o
f enq
uiry
w
hen
expl
orin
g; s
earc
h fo
r and
app
reci
ate
mor
e el
egan
t for
ms
of c
omm
unic
atin
g ap
proa
ches
and
so
lutio
ns; c
onsi
der t
he
effic
ienc
y of
alte
rnat
ive
lines
of e
nqui
ry o
r pr
oced
ures
9The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
2 N
umbe
r
2.1
Plac
e va
lue,
ord
erin
g an
d ro
undi
ng
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
unde
rsta
nd a
nd u
se
deci
mal
not
atio
n an
d pl
ace
valu
e; m
ultip
ly
and
divi
de in
tege
rs
and
deci
mal
s by
10,
10
0, 1
000,
and
exp
lain
th
e ef
fect
read
and
writ
e po
sitiv
e in
tege
r pow
ers
of 1
0;
mul
tiply
and
div
ide
inte
gers
and
dec
imal
s by
0.1
and
0.0
1
exte
nd k
now
ledg
e of
inte
ger p
ower
s of
10;
reco
gnis
e th
e eq
uiva
lenc
e of
0.1
, 1 10
and
10–1
; mul
tiply
and
di
vide
by
any
inte
ger
pow
er o
f 10
conv
ert b
etw
een
ordi
nary
and
st
anda
rd in
dex
form
re
pres
enta
tions
, usi
ng
sign
ifica
nt fi
gure
s as
ap
prop
riate
; jus
tify
the
repr
esen
tatio
n us
ed
and
choi
ce o
f acc
urac
y in
rela
tion
to th
e pr
oble
m a
nd a
udie
nce
for t
he s
olut
ion
enga
ge in
m
athe
mat
ical
task
s w
here
usi
ng n
umbe
rs
in s
tand
ard
form
is
ess
entia
l to
the
calc
ulat
ions
invo
lved
; cr
itica
lly e
xam
ine
the
effe
ct o
f num
eric
al
repr
esen
tatio
ns
on th
e ac
cura
cy o
f th
e so
lutio
n, e
.g.
unde
rsta
nd h
ow e
rror
s ca
n be
com
poun
ded
in
cal
cula
tions
com
mun
icat
e th
e so
lutio
n to
a p
robl
em,
expl
aini
ng th
e lim
itatio
ns o
f acc
urac
y,
usin
g up
per a
nd
low
er b
ound
s
com
pare
and
ord
er
deci
mal
s in
diff
eren
t co
ntex
ts; k
now
that
w
hen
com
parin
g m
easu
rem
ents
the
units
mus
t be
the
sam
e
orde
r dec
imal
s
roun
d po
sitiv
e w
hole
nu
mbe
rs to
the
near
est
10, 1
00 o
r 100
0, a
nd
deci
mal
s to
the
near
est
who
le n
umbe
r or o
ne
deci
mal
pla
ce
roun
d po
sitiv
e nu
mbe
rs
to a
ny g
iven
pow
er
of 1
0; ro
und
deci
mal
s to
the
near
est w
hole
nu
mbe
r or t
o on
e or
tw
o de
cim
al p
lace
s
use
roun
ding
to m
ake
estim
ates
and
to g
ive
solu
tions
to p
robl
ems
to a
n ap
prop
riate
de
gree
of a
ccur
acy
10 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
2.2
Inte
gers
, pow
ers
and
root
s
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
unde
rsta
nd n
egat
ive
num
bers
as
posi
tions
on
a n
umbe
r lin
e;
orde
r, ad
d an
d su
btra
ct
inte
gers
in c
onte
xt
add,
subt
ract
, mul
tiply
an
d di
vide
inte
gers
exam
ine
and
exte
nd
the
inde
x la
ws
to
esta
blis
h th
e m
eani
ng
of n
egat
ive,
frac
tiona
l an
d ze
ro p
ower
s,
incl
udin
g us
e of
su
rd n
otat
ion
exam
ine
and
exte
nd
the
inde
x la
ws
to
esta
blis
h th
e m
eani
ng
of in
vers
e op
erat
ions
in
rela
tion
to in
dice
s, i.
e.
the
inve
rse
oper
atio
n of
rais
ing
a po
sitiv
e nu
mbe
r to
pow
er n
is
rais
ing
the
resu
lt of
this
op
erat
ion
to p
ower
1 n
solv
e a
prob
lem
us
ing
ratio
nal a
nd
irrat
iona
l num
bers
, in
clud
ing
surd
s
reco
gnis
e an
d us
e m
ultip
les,
fact
ors,
prim
es (l
ess t
han
100)
, co
mm
on fa
ctor
s, hi
ghes
t com
mon
fa
ctor
s and
low
est
com
mon
mul
tiple
s in
sim
ple
case
s; us
e si
mpl
e te
sts o
f div
isibi
lity
use
mul
tiple
s, fa
ctor
s,
com
mon
fact
ors,
hi
ghes
t com
mon
fa
ctor
s, lo
wes
t co
mm
on m
ultip
les
and
prim
es; f
ind
the
prim
e fa
ctor
dec
ompo
sitio
n of
a n
umbe
r, e.
g.
8000
= 2
6 × 5
3
use
the
prim
e fa
ctor
de
com
posi
tion
of
a nu
mbe
r
reco
gnis
e th
e fir
st fe
w
tria
ngul
ar n
umbe
rs;
reco
gnis
e th
e sq
uare
s of
num
bers
to a
t le
ast 1
2 ×
12 a
nd th
e co
rres
pond
ing
root
s
use
squa
res,
pos
itive
an
d ne
gativ
e sq
uare
ro
ots,
cub
es a
nd
cube
root
s, a
nd in
dex
nota
tion
for s
mal
l po
sitiv
e in
tege
r pow
ers
use
ICT
to e
stim
ate
squa
re ro
ots
and
cu
be ro
ots
use
inde
x no
tatio
n fo
r in
tege
r pow
ers;
know
an
d us
e th
e in
dex
law
s fo
r mul
tiplic
atio
n an
d di
visi
on o
f pos
itive
in
tege
r pow
ers
11The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
2.3
Frac
tion
s, d
ecim
als,
per
cent
ages
, rat
io a
nd p
ropo
rtio
n
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
expr
ess
a sm
alle
r who
le
num
ber a
s a
frac
tion
of
a la
rger
one
; sim
plify
fr
actio
ns b
y ca
ncel
ling
all c
omm
on fa
ctor
s an
d id
entif
y eq
uiva
lent
fr
actio
ns; c
onve
rt
term
inat
ing
deci
mal
s to
frac
tions
, e.g
. 0.
23 =
23 10
0; u
se
diag
ram
s to
com
pare
tw
o or
mor
e si
mpl
e fr
actio
ns
reco
gnis
e th
at a
re
curr
ing
deci
mal
is a
fr
actio
n; u
se d
ivis
ion
to
conv
ert a
frac
tion
to a
de
cim
al; o
rder
frac
tions
by
writ
ing
them
with
a
com
mon
den
omin
ator
or
by
conv
ertin
g th
em
to d
ecim
als
unde
rsta
nd th
e eq
uiva
lenc
e of
sim
ple
alge
brai
c fr
actio
ns;
know
that
a re
curr
ing
deci
mal
is a
n ex
act
frac
tion
expl
ain
the
patt
erns
fo
und
in re
curr
ing
deci
mal
s; ju
stify
w
hy d
ecim
als
recu
r or
term
inat
e by
co
nsid
erin
g fa
ctor
s of
th
e de
nom
inat
or
expl
ore
the
hist
oric
al
and
cultu
ral r
oots
of
the
num
ber s
yste
m
and
use
alge
bra
to
just
ify a
nd p
rove
som
e of
its
feat
ures
, e.g
. tha
t al
l rec
urrin
g de
cim
als
can
be e
xpre
ssed
as
a
frac
tion
show
insi
ght i
nto
the
infin
ite d
ensi
ty o
f the
nu
mbe
r lin
e; m
ake
sens
e of
the
proo
f tha
t √2
is ir
ratio
nal
add
and
subt
ract
si
mpl
e fr
actio
ns a
nd
thos
e w
ith c
omm
on
deno
min
ator
s; ca
lcul
ate
sim
ple
frac
tions
of q
uant
ities
an
d m
easu
rem
ents
(w
hole
-num
ber
answ
ers)
; mul
tiply
a
frac
tion
by a
n in
tege
r
add
and
subt
ract
fr
actio
ns b
y w
ritin
g th
em w
ith a
com
mon
de
nom
inat
or; c
alcu
late
fr
actio
ns o
f qua
ntiti
es
(frac
tion
answ
ers)
; m
ultip
ly a
nd d
ivid
e an
in
tege
r by
a fr
actio
n
use
effic
ient
met
hods
to
add,
subt
ract
, mul
tiply
an
d di
vide
frac
tions
, in
terp
retin
g di
visi
on a
s a
mul
tiplic
ativ
e in
vers
e;
canc
el c
omm
on fa
ctor
s be
fore
mul
tiply
ing
or
div
idin
g
unde
rsta
nd a
nd a
pply
ef
ficie
nt m
etho
ds to
ad
d, su
btra
ct, m
ultip
ly
and
divi
de fr
actio
ns,
inte
rpre
ting
reci
proc
als
as m
ultip
licat
ive
inve
rses
12 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
2.3
Frac
tion
s, d
ecim
als,
per
cent
ages
, rat
io a
nd p
ropo
rtio
n (c
onti
nued
)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
unde
rsta
nd p
erce
ntag
e as
the
‘num
ber o
f par
ts
per 1
00’; c
alcu
late
si
mpl
e pe
rcen
tage
s an
d us
e pe
rcen
tage
s to
com
pare
sim
ple
prop
ortio
ns
inte
rpre
t per
cent
age
as th
e op
erat
or ‘s
o m
any
hund
redt
hs
of’ a
nd e
xpre
ss o
ne
give
n nu
mbe
r as
a pe
rcen
tage
of a
noth
er;
calc
ulat
e pe
rcen
tage
s an
d fin
d th
e ou
tcom
e of
a g
iven
per
cent
age
incr
ease
or d
ecre
ase
reco
gnis
e w
hen
frac
tions
or
perc
enta
ges
are
need
ed to
com
pare
pr
opor
tions
; sol
ve
prob
lem
s in
volv
ing
perc
enta
ge c
hang
es
reco
gnis
e th
e eq
uiva
lenc
e of
pe
rcen
tage
s, fr
actio
ns
and
deci
mal
s
use
the
equi
vale
nce
of fr
actio
ns, d
ecim
als
and
perc
enta
ges
to
com
pare
pro
port
ions
unde
rsta
nd th
e re
latio
nshi
p be
twee
n ra
tio a
nd p
ropo
rtio
n;
use
dire
ct p
ropo
rtio
n in
sim
ple
cont
exts
; use
ra
tio n
otat
ion,
sim
plify
ra
tios
and
divi
de a
qu
antit
y in
to tw
o pa
rts
in a
giv
en ra
tio;
solv
e si
mpl
e pr
oble
ms
invo
lvin
g ra
tio a
nd
prop
ortio
n us
ing
info
rmal
str
ateg
ies
appl
y un
ders
tand
ing
of th
e re
latio
nshi
p be
twee
n ra
tio a
nd
prop
ortio
n; s
impl
ify
ratio
s, in
clud
ing
thos
e ex
pres
sed
in d
iffer
ent
units
, rec
ogni
sing
link
s w
ith fr
actio
n no
tatio
n;
divi
de a
qua
ntity
into
tw
o or
mor
e pa
rts
in
a gi
ven
ratio
; use
the
unita
ry m
etho
d to
so
lve
sim
ple
prob
lem
s in
volv
ing
ratio
and
di
rect
pro
port
ion
use
prop
ortio
nal
reas
onin
g to
sol
ve
prob
lem
s, c
hoos
ing
the
corr
ect n
umbe
rs
to ta
ke a
s 10
0%, o
r as
a w
hole
; com
pare
two
ratio
s; in
terp
ret a
nd
use
ratio
in a
rang
e
of c
onte
xts
iden
tify
whe
n a
prob
lem
in n
umbe
r, al
gebr
a, g
eom
etry
or
sta
tistic
s in
volv
es
prop
ortio
nalit
y; u
se
mul
tiplic
ativ
e m
etho
ds
fluen
tly in
the
solu
tion,
in
clud
ing
inve
rse
calc
ulat
ions
, e.g
. w
ith p
erce
ntag
es
mod
el re
al c
onte
xts
whe
re q
uant
ities
var
y in
dire
ct p
ropo
rtio
n,
incl
udin
g re
peat
ed
prop
ortio
nal c
hang
e,
e.g.
gro
wth
/dec
ay; u
se
alge
brai
c m
etho
ds
whe
re a
ppro
pria
te a
nd
cons
ider
lim
itatio
ns o
f th
e m
odel
(as i
n 2.
4)
unde
rsta
nd a
nd u
se
dire
ct a
nd in
vers
e pr
opor
tion;
sol
ve
prob
lem
s in
volv
ing
inve
rse
prop
ortio
n (in
clud
ing
y ?
1/x
2 )
(as i
n 2.
4)
13The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
2.4
Num
ber o
pera
tion
s
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
unde
rsta
nd a
nd u
se th
e ru
les
of a
rithm
etic
and
in
vers
e op
erat
ions
in
the
cont
ext o
f pos
itive
in
tege
rs a
nd d
ecim
als
unde
rsta
nd a
nd u
se th
e ru
les
of a
rithm
etic
and
in
vers
e op
erat
ions
in
the
cont
ext o
f int
eger
s an
d fr
actio
ns
unde
rsta
nd th
e ef
fect
s of
mul
tiply
ing
and
divi
ding
by
num
bers
be
twee
n 0
and
1;
cons
olid
ate
use
of th
e ru
les
of a
rithm
etic
and
in
vers
e op
erat
ions
reco
gnis
e an
d us
e re
cipr
ocal
s as
a
mul
tiplic
ativ
e in
vers
e in
con
text
s su
ch a
s en
larg
emen
t; ex
plor
e th
e be
havi
our o
f the
re
cipr
ocal
func
tion
(y
= 1
/x) f
or la
rge
and
smal
l val
ues
of x
mod
el re
al c
onte
xts
whe
re q
uant
ities
var
y in
dire
ct p
ropo
rtio
n,
incl
udin
g re
peat
ed
prop
ortio
nal c
hang
e,
e.g.
gro
wth
/dec
ay; u
se
alge
brai
c m
etho
ds
whe
re a
ppro
pria
te a
nd
cons
ider
lim
itatio
ns o
f th
e m
odel
(as i
n 2.
3)
unde
rsta
nd a
nd u
se
dire
ct a
nd in
vers
e pr
opor
tion;
sol
ve
prob
lem
s in
volv
ing
inve
rse
prop
ortio
n (in
clud
ing
y ?
1/x
2 )
(as i
n 2.
3)
use
the
orde
r of
oper
atio
ns, i
nclu
ding
br
acke
ts
use
the
orde
r of
oper
atio
ns, i
nclu
ding
br
acke
ts, w
ith m
ore
com
plex
cal
cula
tions
unde
rsta
nd th
e or
der
of p
rece
denc
e of
op
erat
ions
, inc
ludi
ng
pow
ers
14 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
2.5
Men
tal c
alcu
lati
on m
etho
ds
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
reca
ll nu
mbe
r fa
cts,
incl
udin
g po
sitiv
e in
tege
r co
mpl
emen
ts to
100
an
d m
ultip
licat
ion
fact
s to
10
× 10
, and
qui
ckly
de
rive
asso
ciat
ed
divi
sion
fact
s
reca
ll eq
uiva
lent
fr
actio
ns, d
ecim
als
and
perc
enta
ges;
use
know
n fa
cts
to
deriv
e un
know
n fa
cts,
in
clud
ing
prod
ucts
in
volv
ing
num
bers
su
ch a
s 0.
7 an
d 6,
and
0.
03 a
nd 8
sele
ct m
enta
l or
writ
ten
stra
tegi
es
and
calc
ulat
ing
devi
ces
appr
opria
te
to th
e st
age
of th
e pr
oble
m; c
alcu
late
ac
cura
tely
with
re
cipr
ocal
s, p
ower
s,
trig
onom
etric
al
func
tions
and
num
bers
in
sta
ndar
d fo
rm
(as i
n 2.
6 an
d 2.
7)
sele
ct a
nd ju
stify
an
app
ropr
iate
and
ef
ficie
nt c
ombi
natio
n of
met
hods
of
calc
ulat
ion,
i.e.
m
enta
l, w
ritte
n, IC
T or
cal
cula
tor t
o so
lve
prob
lem
s
(as i
n 2.
6)
appr
ecia
te w
hen
resu
lts
of c
alcu
latio
ns c
an b
e m
ore
eleg
antly
and
ex
actly
com
mun
icat
ed
usin
g su
rds
and
π, ra
tiona
lisin
g a
deno
min
ator
whe
re
appr
opria
te, e
.g.
a tr
igon
omet
rical
so
lutio
n
(as i
n 2.
6)
stre
ngth
en a
nd e
xten
d m
enta
l met
hods
of
calc
ulat
ion
to in
clud
e de
cim
als,
frac
tions
an
d pe
rcen
tage
s,
acco
mpa
nied
whe
re
appr
opria
te b
y su
itabl
e jo
ttin
gs; s
olve
sim
ple
prob
lem
s m
enta
lly
stre
ngth
en a
nd e
xten
d m
enta
l met
hods
of
calc
ulat
ion,
wor
king
w
ith d
ecim
als,
fr
actio
ns, p
erce
ntag
es,
squa
res
and
squa
re
root
s, c
ubes
and
cub
e ro
ots;
solv
e pr
oble
ms
men
tally
use
know
n fa
cts
to
deriv
e un
know
n fa
cts;
exte
nd m
enta
l m
etho
ds o
f cal
cula
tion,
w
orki
ng w
ith d
ecim
als,
fr
actio
ns, p
erce
ntag
es,
fact
ors,
pow
ers
and
root
s; so
lve
prob
lem
s m
enta
lly
mak
e an
d ju
stify
es
timat
es a
nd
appr
oxim
atio
ns o
f ca
lcul
atio
ns
mak
e an
d ju
stify
es
timat
es a
nd
appr
oxim
atio
ns o
f ca
lcul
atio
ns
mak
e an
d ju
stify
es
timat
es a
nd
appr
oxim
atio
ns o
f ca
lcul
atio
ns
exam
ine
and
refin
e es
timat
es a
nd
appr
oxim
atio
ns o
f ca
lcul
atio
ns in
volv
ing
roun
ding
15The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
2.6
Wri
tten
cal
cula
tion
met
hods
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
use
effic
ient
writ
ten
met
hods
to a
dd
and
subt
ract
who
le
num
bers
and
dec
imal
s w
ith u
p to
two
plac
es
use
effic
ient
writ
ten
met
hods
to a
dd a
nd
subt
ract
inte
gers
and
de
cim
als
of a
ny s
ize,
in
clud
ing
num
bers
w
ith d
iffer
ing
num
bers
of
dec
imal
pla
ces
sele
ct m
enta
l or
writ
ten
stra
tegi
es
and
calc
ulat
ing
devi
ces
appr
opria
te
to th
e st
age
of th
e pr
oble
m; c
alcu
late
ac
cura
tely
with
re
cipr
ocal
s, p
ower
s,
trig
onom
etric
al
func
tions
and
num
bers
in
sta
ndar
d fo
rm
(as i
n 2.
5 an
d 2.
7)
sele
ct a
nd ju
stify
an
app
ropr
iate
and
ef
ficie
nt c
ombi
natio
n of
met
hods
of
calc
ulat
ion,
i.e.
m
enta
l, w
ritte
n, IC
T or
cal
cula
tor t
o so
lve
prob
lem
s
(as i
n 2.
5)
appr
ecia
te w
hen
resu
lts
of c
alcu
latio
ns c
an b
e m
ore
eleg
antly
and
ex
actly
com
mun
icat
ed
usin
g su
rds
and
π, ra
tiona
lisin
g a
deno
min
ator
whe
re
appr
opria
te, e
.g.
a tr
igon
omet
rical
so
lutio
n
(as i
n 2.
5)
mul
tiply
and
div
ide
thre
e-di
git b
y tw
o-di
git w
hole
num
bers
; ex
tend
to m
ultip
lyin
g an
d di
vidi
ng d
ecim
als
with
one
or t
wo
plac
es
by s
ingl
e-di
git w
hole
nu
mbe
rs
use
effic
ient
writ
ten
met
hods
for
mul
tiplic
atio
n an
d di
visi
on o
f int
eger
s an
d de
cim
als,
incl
udin
g by
de
cim
als
such
as
0.6
or
0.06
; und
erst
and
whe
re
to p
ositi
on th
e de
cim
al
poin
t by
cons
ider
ing
equi
vale
nt c
alcu
latio
ns
use
effic
ient
writ
ten
met
hods
to a
dd a
nd
subt
ract
inte
gers
and
de
cim
als
of a
ny s
ize;
m
ultip
ly b
y de
cim
als;
divi
de b
y de
cim
als
by tr
ansf
orm
ing
to
divi
sion
by
an in
tege
r
16 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
2.7
Calc
ulat
or m
etho
ds
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
carr
y ou
t cal
cula
tions
w
ith m
ore
than
one
st
ep u
sing
bra
cket
s an
d th
e m
emor
y; u
se th
e sq
uare
root
and
sig
n ch
ange
key
s
carr
y ou
t mor
e di
ffic
ult
calc
ulat
ions
eff
ectiv
ely
and
effic
ient
ly u
sing
th
e fu
nctio
n ke
ys fo
r si
gn c
hang
e, p
ower
s,
root
s an
d fr
actio
ns;
use
brac
kets
and
th
e m
emor
y
use
a ca
lcul
ator
ef
ficie
ntly
and
ap
prop
riate
ly to
pe
rfor
m c
ompl
ex
calc
ulat
ions
with
nu
mbe
rs o
f any
siz
e,
know
ing
not t
o ro
und
durin
g in
term
edia
te
step
s of
a c
alcu
latio
n;
use
the
cons
tant
, π
and
sign
cha
nge
keys
; us
e th
e fu
nctio
n ke
ys
for p
ower
s, ro
ots
and
frac
tions
; use
bra
cket
s an
d th
e m
emor
y
sele
ct m
enta
l or
writ
ten
stra
tegi
es
and
calc
ulat
ing
devi
ces
appr
opria
te
to th
e st
age
of th
e pr
oble
m; c
alcu
late
ac
cura
tely
with
re
cipr
ocal
s, p
ower
s,
trig
onom
etric
al
func
tions
and
num
bers
in
sta
ndar
d fo
rm
(as i
n 2.
5 an
d 2.
6)
criti
cally
exa
min
e al
tern
ativ
e m
etho
ds,
com
pare
str
ateg
ies
for:
•ca
lcul
atin
g (in
clud
ing
calc
ulat
ing
devi
ces)
•ch
ecki
ng
reco
gnis
e th
e lim
itatio
ns o
f som
e ap
proa
ches
(as i
n 2.
8)
refle
ct o
n a
solu
tion
to
a pr
oble
m c
omm
entin
g co
nstr
uctiv
ely
on th
e ch
oice
of c
alcu
latin
g st
rate
gies
(as i
n 2.
8)
ente
r num
bers
and
in
terp
ret t
he d
ispl
ay
in d
iffer
ent c
onte
xts
(dec
imal
s, p
erce
ntag
es,
mon
ey, m
etric
m
easu
res)
ente
r num
bers
and
in
terp
ret t
he d
ispl
ay
in d
iffer
ent c
onte
xts
(ext
end
to n
egat
ive
num
bers
, fra
ctio
ns,
time)
17The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
2.8
Chec
king
resu
lts
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
chec
k re
sults
by
cons
ider
ing
whe
ther
th
ey a
re o
f the
righ
t or
der o
f mag
nitu
de
and
by w
orki
ng
prob
lem
s ba
ckw
ards
sele
ct fr
om a
rang
e of
che
ckin
g m
etho
ds,
incl
udin
g es
timat
ing
in c
onte
xt a
nd u
sing
in
vers
e op
erat
ions
chec
k re
sults
usi
ng
appr
opria
te m
etho
dsid
entif
y a
rang
e of
ch
ecki
ng s
trat
egie
s an
d ap
prec
iate
that
mor
e th
an o
ne w
ay m
ay
be n
eces
sary
in th
e co
ntex
t of t
he p
robl
em
criti
cally
exa
min
e al
tern
ativ
e m
etho
ds,
com
pare
str
ateg
ies
for:
•ca
lcul
atin
g (in
clud
ing
calc
ulat
ing
devi
ces)
•ch
ecki
ng
reco
gnis
e th
e lim
itatio
ns o
f som
e ap
proa
ches
(as i
n 2.
7)
refle
ct o
n a
solu
tion
to
a pr
oble
m c
omm
entin
g co
nstr
uctiv
ely
on th
e ch
oice
of c
heck
ing
stra
tegi
es
(as i
n 2.
7)
19The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
3 A
lgeb
ra
3.1
Equa
tion
s, fo
rmul
ae, e
xpre
ssio
ns a
nd id
enti
ties
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
use
lett
er s
ymbo
ls to
re
pres
ent u
nkno
wn
num
bers
or v
aria
bles
; kn
ow th
e m
eani
ngs
of th
e w
ords
term
, ex
pres
sion
and
equa
tion
reco
gnis
e th
at le
tter
sy
mbo
ls p
lay
diff
eren
t ro
les
in e
quat
ions
, fo
rmul
ae a
nd fu
nctio
ns;
know
the
mea
ning
s of
the
wor
ds fo
rmul
a an
d fu
nctio
n
dist
ingu
ish
the
diff
eren
t rol
es p
laye
d by
lett
er s
ymbo
ls in
eq
uatio
ns, i
dent
ities
, fo
rmul
ae a
nd fu
nctio
ns
pres
ent c
onvi
ncin
g al
gebr
aic
argu
men
ts to
ju
stify
gen
eral
isat
ions
or
sol
utio
ns; r
elat
e ar
gum
ents
to th
e st
ruct
ure
of th
e co
ntex
t or
pro
blem
; pro
duce
si
mpl
e pr
oofs
exam
ine
and
refin
e al
gebr
aic
argu
men
ts
pres
ente
d to
exp
lain
ge
omet
rical
and
nu
mer
ical
pro
pert
ies;
choo
se a
nd c
ombi
ne
repr
esen
tatio
ns to
pr
esen
t a c
onvi
ncin
g pr
oof
use
sym
bols
and
re
pres
enta
tions
co
nsis
tent
ly to
pre
sent
a
form
al p
roof
, e.g
. de
rivin
g th
e fo
rmul
a fo
r sol
ving
qua
drat
ic
equa
tions
unde
rsta
nd th
at
alge
brai
c op
erat
ions
fo
llow
the
rule
s of
ar
ithm
etic
unde
rsta
nd th
at
alge
brai
c op
erat
ions
, in
clud
ing
the
use
of
brac
kets
, fol
low
the
rule
s of
arit
hmet
ic; u
se
inde
x no
tatio
n fo
r sm
all
posi
tive
inte
ger p
ower
s
use
inde
x no
tatio
n fo
r in
tege
r pow
ers
and
sim
ple
inst
ance
s of
th
e in
dex
law
s
use
alge
brai
c re
pres
enta
tion
to
synt
hesi
se k
now
n ru
les
of a
rithm
etic
, inc
ludi
ng
the
com
mut
ativ
e an
d di
strib
utiv
e la
ws;
just
ify
thes
e ge
nera
lisat
ions
, e.
g. u
sing
spa
tial
repr
esen
tatio
ns; u
se
alge
brai
c ar
gum
ent t
o ge
nera
lise
the
inde
x la
ws
for m
ultip
licat
ion
and
divi
sion
to in
clud
e ze
ro, n
egat
ive
and
frac
tiona
l pow
ers
appr
ecia
te th
e ge
nera
lity
of th
e fo
rms
a +
b =
c an
d ab
= c
, w
here
eac
h te
rm c
an
itsel
f be
an e
xpre
ssio
n;
use
this
insi
ght i
nto
stru
ctur
e to
dev
elop
flu
ency
in tr
ansf
orm
ing
mor
e co
mpl
ex
equa
tions
20 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
21The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
3.1
Equa
tion
s, fo
rmul
ae, e
xpre
ssio
ns a
nd id
enti
ties
(con
tinu
ed)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
sim
plify
line
ar a
lgeb
raic
ex
pres
sion
s by
co
llect
ing
like
term
s; m
ultip
ly a
sin
gle
term
ov
er a
bra
cket
(int
eger
co
effic
ient
s)
sim
plify
or t
rans
form
lin
ear e
xpre
ssio
ns b
y co
llect
ing
like
term
s; m
ultip
ly a
sin
gle
term
ov
er a
bra
cket
sim
plify
or t
rans
form
al
gebr
aic
expr
essi
ons
by ta
king
out
sin
gle-
term
com
mon
fact
ors;
add
sim
ple
alge
brai
c fr
actio
ns
deve
lop
fluen
cy in
tr
ansf
orm
ing
linea
r ex
pres
sion
s; ex
pand
th
e pr
oduc
t of t
wo
linea
r exp
ress
ions
of
the
form
x ±
n
and
fact
oris
e si
mpl
e qu
adra
tic e
xpre
ssio
ns;
esta
blis
h id
entit
ies s
uch
as th
e di
ffer
ence
of
two
squa
res;
com
pare
an
d ev
alua
te d
iffer
ent
repr
esen
tatio
ns o
f the
sa
me
cont
ext;
iden
tify
equi
vale
nt e
xpre
ssio
ns
and
conf
irm b
y tr
ansf
orm
atio
n
expa
nd a
nd fa
ctor
ise
quad
ratic
exp
ress
ions
; si
mpl
ify o
r tra
nsfo
rm
alge
brai
c fr
actio
ns,
e.g.
by
fact
oris
ing
and
canc
ellin
g co
mm
on
fact
ors;
com
pare
and
ev
alua
te d
iffer
ent
repr
esen
tatio
ns o
f the
sa
me
cont
ext;
iden
tify
equi
vale
nt e
xpre
ssio
ns
and
conf
irm th
is b
y tr
ansf
orm
atio
n
20 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
21The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
3.1
Equa
tion
s, fo
rmul
ae, e
xpre
ssio
ns a
nd id
enti
ties
(con
tinu
ed)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
cons
truc
t and
so
lve
sim
ple
linea
r eq
uatio
ns w
ith in
tege
r co
effic
ient
s (u
nkno
wn
on o
ne s
ide
only
) usi
ng
an a
ppro
pria
te m
etho
d (e
.g. i
nver
se o
pera
tions
)
cons
truc
t and
sol
ve
linea
r equ
atio
ns w
ith
inte
ger c
oeff
icie
nts
(unk
now
n on
eith
er o
r bo
th s
ides
, with
out a
nd
with
bra
cket
s) u
sing
ap
prop
riate
met
hods
(e
.g. i
nver
se o
pera
tions
, tr
ansf
orm
ing
both
si
des
in s
ame
way
)
cons
truc
t and
sol
ve
linea
r equ
atio
ns w
ith
inte
ger c
oeff
icie
nts
(with
and
with
out
brac
kets
, neg
ativ
e si
gns
anyw
here
in th
e eq
uatio
n, p
ositi
ve o
r ne
gativ
e so
lutio
n)
cons
truc
t lin
ear
equa
tions
and
sim
ple
linea
r ine
qual
ities
(one
va
riabl
e) to
repr
esen
t re
al-li
fe s
ituat
ions
or
mat
hem
atic
al
prob
lem
s; so
lve
linea
r equ
atio
ns
and
ineq
ualit
ies,
re
pres
entin
g th
e so
lutio
n in
the
cont
ext
of th
e pr
oble
m
cons
truc
t sim
ple
quad
ratic
equ
atio
ns
to re
pres
ent r
eal-
life
situ
atio
ns o
r m
athe
mat
ical
pro
blem
s an
d so
lve
them
us
ing
fact
oris
atio
n,
grap
hica
l or t
rial a
nd
impr
ovem
ent m
etho
ds;
just
ify th
e nu
mbe
r of
sol
utio
ns u
sing
al
gebr
aic
or g
raph
ical
ar
gum
ents
and
sel
ect
appr
opria
te s
olut
ions
, in
terp
retin
g th
eir
accu
racy
repr
esen
t rea
l-lif
e si
tuat
ions
or
mat
hem
atic
al p
robl
ems
invo
lvin
g:
•m
ore
com
plex
qu
adra
tic
equa
tions
, ch
oosi
ng a
n ap
prop
riate
m
etho
d of
so
lutio
n in
clud
ing
com
plet
ing
the
squa
re a
nd u
se o
f th
e fo
rmul
a
•di
rect
or i
nver
se
prop
ortio
n,
incl
udin
g y
? x
2 , y ?
1/x
2
rela
te a
lgeb
raic
so
lutio
ns to
gra
phic
al
repr
esen
tatio
n of
the
func
tions
use
grap
hs a
nd s
et
up e
quat
ions
to s
olve
si
mpl
e pr
oble
ms
invo
lvin
g di
rect
pr
opor
tion
use
alge
brai
c m
etho
ds
to s
olve
pro
blem
s in
volv
ing
dire
ct
prop
ortio
n; re
late
al
gebr
aic
solu
tions
to
gra
phs
of th
e eq
uatio
ns; u
se IC
T
as a
ppro
pria
te
22 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
3.1
Equa
tion
s, fo
rmul
ae, e
xpre
ssio
ns a
nd id
enti
ties
(con
tinu
ed)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
use
syst
emat
ic tr
ial a
nd
impr
ovem
ent m
etho
ds
and
ICT
tool
s to
find
ap
prox
imat
e so
lutio
ns
to e
quat
ions
such
as
x2 +
x =
20
(See
obj
ectiv
e ab
ove
fo
r pro
gres
sion)
(See
obj
ectiv
e ab
ove
fo
r pro
gres
sion)
(See
obj
ectiv
e ab
ove
fo
r pro
gres
sion)
expl
ore
way
s of
cons
truc
ting
mod
els
of re
al-li
fe si
tuat
ions
by
dra
win
g gr
aphs
an
d co
nstr
uctin
g al
gebr
aic
equa
tions
and
in
equa
litie
s
cons
truc
t a p
air o
f si
mul
tane
ous
linea
r eq
uatio
ns to
repr
esen
t re
al-li
fe si
tuat
ions
or
mat
hem
atic
al
prob
lem
s; ex
amin
e an
d co
mpa
re
alge
brai
c m
etho
ds o
f so
lutio
n; u
se g
raph
ical
re
pres
enta
tion
to
expl
ain
why
the
inte
rsec
tion
of tw
o lin
es g
ives
the
com
mon
so
lutio
n an
d w
hy s
ome
case
s ha
ve n
o co
mm
on
solu
tion
and
othe
rs
have
an
infin
ite n
umbe
r
sele
ct a
nd ju
stify
op
timum
met
hods
fo
r sol
ving
a p
air
of s
imul
tane
ous
linea
r equ
atio
ns in
a
varie
ty o
f con
text
s; co
nstr
uct s
ever
al
linea
r ine
qual
ities
in
one
and
two
varia
bles
to re
pres
ent
real
-life
situ
atio
ns
or m
athe
mat
ical
pr
oble
ms;
solv
e th
e in
equa
litie
s gr
aphi
cally
, ide
ntify
ing
and
inte
rpre
ting
the
solu
tion
set i
n th
e co
ntex
t of t
he p
robl
em
solv
e m
ore
com
plex
pa
irs o
f sim
ulta
neou
s eq
uatio
ns g
ener
ated
fr
om re
al-li
fe c
onte
xts
or g
eom
etric
al
inve
stig
atio
ns,
incl
udin
g pa
irs w
here
on
e is
line
ar a
nd th
e ot
her i
s qu
adra
tic o
r of
the
form
x2 +
y2 =
r2
23The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
3.1
Equa
tion
s, fo
rmul
ae, e
xpre
ssio
ns a
nd id
enti
ties
(con
tinu
ed)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
use
sim
ple
form
ulae
fr
om m
athe
mat
ics
and
othe
r sub
ject
s; su
bstit
ute
posi
tive
inte
gers
into
line
ar
expr
essi
ons
and
form
ulae
and
, in
sim
ple
case
s, d
eriv
e a
form
ula
use
form
ulae
from
m
athe
mat
ics
and
othe
r su
bjec
ts; s
ubst
itute
in
tege
rs in
to s
impl
e fo
rmul
ae, i
nclu
ding
ex
ampl
es th
at le
ad
to a
n eq
uatio
n to
so
lve;
subs
titut
e po
sitiv
e in
tege
rs in
to
expr
essi
ons
invo
lvin
g sm
all p
ower
s, e
.g.
3x2 +
4 o
r 2x3 ; d
eriv
e si
mpl
e fo
rmul
ae
use
form
ulae
from
m
athe
mat
ics
and
othe
r sub
ject
s; su
bstit
ute
num
bers
in
to e
xpre
ssio
ns a
nd
form
ulae
; der
ive
a fo
rmul
a an
d, in
sim
ple
case
s, c
hang
e its
su
bjec
t
deriv
e fo
rmul
ae, e
.g.
in th
e co
ntex
t of
men
sura
tion;
inte
rpre
t a
rang
e of
form
ulae
dr
awn
from
real
-life
co
ntex
ts a
nd o
ther
su
bjec
ts, r
elat
ing
the
varia
bles
to th
e co
ntex
t and
des
crib
ing
thei
r beh
avio
ur;
solv
e pr
oble
ms
by
man
ipul
atin
g fo
rmul
ae
deriv
e an
d us
e fo
rmul
ae th
at in
volv
e m
ore
varia
bles
or
mor
e co
mpl
ex
alge
brai
c ex
pres
sion
s; m
anip
ulat
e fo
rmul
ae
in o
rder
to re
ach
a so
lutio
n, s
how
insi
ght
into
the
mat
hem
atic
al
conn
ectio
ns, e
.g. u
sing
th
e co
ntex
t and
the
form
ulae
to e
xpla
in th
e pr
opor
tiona
l eff
ect o
f va
ryin
g va
lues
24 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
3.2
Sequ
ence
s, fu
ncti
ons
and
grap
hs
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
desc
ribe
inte
ger
sequ
ence
s; ge
nera
te
term
s of
a s
impl
e se
quen
ce, g
iven
a
rule
(e.g
. fin
ding
a
term
from
the
prev
ious
te
rm, f
indi
ng a
term
gi
ven
its p
ositi
on in
th
e se
quen
ce)
gene
rate
term
s of
a
linea
r seq
uenc
e us
ing
term
-to-
term
an
d po
sitio
n-to
-ter
m
rule
s, o
n pa
per a
nd
usin
g a
spre
adsh
eet o
r gr
aphi
cs c
alcu
lato
r
gene
rate
term
s of
a
sequ
ence
usi
ng te
rm-
to-t
erm
and
pos
ition
-to
-ter
m ru
les,
on
pape
r an
d us
ing
ICT
deve
lop,
com
pare
and
ev
alua
te a
lgeb
raic
and
sp
atia
l rep
rese
ntat
ions
of
situ
atio
ns th
at
gene
rate
seq
uenc
es;
inte
rpre
t, de
duce
and
ju
stify
gen
eral
isat
ions
fo
r the
nth
term
of
linea
r and
qua
drat
ic
sequ
ence
s, in
clud
ing
the
prop
ertie
s of
sq
uare
and
tria
ngul
ar
num
bers
gene
rate
seq
uenc
es
from
pat
tern
s or
pr
actic
al c
onte
xts
and
desc
ribe
the
gene
ral
term
in s
impl
e ca
ses
use
linea
r exp
ress
ions
to
des
crib
e th
e nt
h te
rm
of a
sim
ple
arith
met
ic
sequ
ence
, jus
tifyi
ng
its fo
rm b
y re
ferr
ing
to
the
activ
ity o
r pra
ctic
al
cont
ext f
rom
whi
ch it
w
as g
ener
ated
gene
rate
seq
uenc
es
from
pra
ctic
al c
onte
xts
and
writ
e an
d ju
stify
an
expr
essi
on to
des
crib
e th
e nt
h te
rm o
f an
arith
met
ic s
eque
nce
25The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
3.2
Sequ
ence
s, fu
ncti
ons
and
grap
hs (c
onti
nued
)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
expr
ess
sim
ple
func
tions
in w
ords
, th
en u
sing
sym
bols
; re
pres
ent t
hem
in
map
ping
s
expr
ess
sim
ple
func
tions
alg
ebra
ical
ly
and
repr
esen
t the
m
in m
appi
ngs
or o
n a
spre
adsh
eet
find
the
inve
rse
of a
lin
ear f
unct
ion
com
pare
gra
phic
al,
alge
brai
c an
d ge
omet
rical
re
pres
enta
tions
, in
clud
ing
map
ping
di
agra
ms,
to e
xpla
in
the
effe
ct o
f:
•ro
tatin
g th
e lin
e
y =
mx
+ c
thro
ugh
90° a
bout
any
po
int
•re
flect
ing
the
line
y
= m
x +
c in
the
line
y =
x
deriv
e pr
oper
ties
of
perp
endi
cula
r lin
es a
nd
of th
e in
vers
e fu
nctio
n
gene
rate
coo
rdin
ate
pairs
that
sat
isfy
a
sim
ple
linea
r rul
e; p
lot
the
grap
hs o
f sim
ple
linea
r fun
ctio
ns, w
here
y
is g
iven
exp
licitl
y in
term
s of
x, o
n pa
per a
nd u
sing
ICT;
re
cogn
ise
stra
ight
-line
gr
aphs
par
alle
l to
the
x-
axis
or
y-ax
is
gene
rate
poi
nts
in a
ll fo
ur q
uadr
ants
and
plo
t th
e gr
aphs
of l
inea
r fu
nctio
ns, w
here
y is
gi
ven
expl
icitl
y in
term
s of
x, o
n pa
per a
nd
usin
g IC
T; re
cogn
ise
that
equ
atio
ns o
f th
e fo
rm y
= m
x +
c co
rres
pond
to s
trai
ght-
line
grap
hs
gene
rate
poi
nts a
nd
plot
gra
phs o
f lin
ear
func
tions
, whe
re y
is
give
n im
plic
itly
in te
rms
of x
(e.g
. ay
+ bx
= 0
, y
+ bx
+ c
= 0
), on
pap
er
and
usin
g IC
T; fi
nd th
e gr
adie
nt o
f lin
es g
iven
by
equ
atio
ns o
f the
fo
rm y
= m
x +
c, gi
ven
valu
es fo
r m a
nd c
expl
ore
grap
hs o
f fu
nctio
ns o
f the
form
y
= xn (n
an
inte
ger)
and
reco
gnis
e th
eir
char
acte
ristic
sha
pes;
vary
the
valu
es o
f a, b
an
d c
in fu
nctio
ns su
ch
as y
= a
x2 + c
, y
= ax
3 + c
, y
= (x
+ b
)2 usi
ng a
gr
aph
plot
ter t
o ex
plai
n ho
w th
is tr
ansf
orm
s
the
grap
h
expl
ore
conn
ectio
ns
betw
een
the
form
of
the
equa
tion
and
the
resu
lting
gra
phs
of
quad
ratic
and
cub
ic
func
tions
such
as:
•y
= (x
+ 2
)(x –
5)
•y
= (x
– 2
)(x2 +
7x +
12)
•y
= x2 –
2x
+ 1
•y
= x3 +
3
incl
ude
feat
ures
suc
h
as ro
ots
of th
e eq
uatio
n,
inte
rcep
ts a
nd tu
rnin
g po
ints
expl
ore
grap
hs o
f ex
pone
ntia
l and
tr
igon
omet
rical
fu
nctio
ns a
nd re
cogn
ise
thei
r cha
ract
eris
tic
shap
es; a
pply
to th
e gr
aph
y =
f(x) t
he
tran
sfor
mat
ions
y
= f(
x) +
a, y
= a
f(x),
y =
f(x +
a),
y =
f(ax)
for
linea
r, qu
adra
tic, s
ine
and
cosi
ne fu
nctio
ns;
use
a gr
aph
plot
ter t
o ex
plai
n th
e ef
fect
of
tran
sfor
mat
ions
on
the
grap
h an
d ge
nera
lise
to
oth
er fu
nctio
ns
26 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
3.2
Sequ
ence
s, fu
ncti
ons
and
grap
hs (c
onti
nued
)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
plot
and
inte
rpre
t the
gr
aphs
of s
impl
e lin
ear
func
tions
aris
ing
from
re
al-li
fe s
ituat
ions
, e.g
. co
nver
sion
gra
phs
cons
truc
t lin
ear
func
tions
aris
ing
from
re
al-li
fe p
robl
ems
and
plot
thei
r co
rres
pond
ing
grap
hs;
disc
uss
and
inte
rpre
t gr
aphs
aris
ing
from
re
al s
ituat
ions
, e.g
. di
stan
ce–t
ime
grap
hs
cons
truc
t fun
ctio
ns
aris
ing
from
real
-life
pr
oble
ms
and
plot
thei
r co
rres
pond
ing
grap
hs;
inte
rpre
t gra
phs
aris
ing
from
real
situ
atio
ns, e
.g.
time
serie
s gr
aphs
sket
ch a
nd in
terp
ret
grap
hs th
at m
odel
real
-lif
e si
tuat
ions
, inc
ludi
ng
thos
e ge
nera
ted
from
oth
er su
bjec
ts
such
as
scie
nce;
us
e m
athe
mat
ical
ar
gum
ent t
o ju
stify
fe
atur
es o
f the
ir sh
apes
appl
y kn
owle
dge
of
mat
hem
atic
al fu
nctio
ns
to p
robl
ems
invo
lvin
g:
•op
timis
atio
n,
usin
g nu
mer
ical
, al
gebr
aic
and
grap
hica
l, te
chni
ques
, in
clud
ing
max
ima
and
min
ima
•us
ing
ICT
to fi
t a
curv
e to
dat
a fr
om a
real
con
text
su
ch a
s a
scie
nce
expe
rimen
t
•re
peat
ed
prop
ortio
nal
chan
ge, e
.g.
com
poun
d in
tere
st
set u
p a
mat
hem
atic
al
mod
el o
f a re
al-li
fe
cont
ext o
r pro
blem
, id
entif
ying
the
varia
bles
and
thei
r fu
nctio
nal r
elat
ions
hip;
us
e gr
aphs
and
sk
etch
es to
exp
lain
th
e be
havi
our o
f the
va
riabl
es a
nd to
exp
lain
or
just
ify th
e ef
fect
of
assu
mpt
ions
in
the
mod
el
use
ICT
to e
xplo
re th
e gr
aphi
cal r
epre
sent
atio
n of
alg
ebra
ic e
quat
ions
an
d to
inte
rpre
t how
pr
oper
ties o
f the
gra
ph
are
rela
ted
to fe
atur
es
of th
e eq
uatio
n,
e.g.
par
alle
l and
pe
rpen
dicu
lar l
ines
27The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
3.2
Sequ
ence
s, fu
ncti
ons
and
grap
hs (c
onti
nued
)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
inte
rpre
t the
mea
ning
of
var
ious
poi
nts a
nd
sect
ions
of s
trai
ght-
line
grap
hs, i
nclu
ding
in
terc
epts
and
in
ters
ectio
ns, e
.g. s
olvi
ng
simul
tane
ous l
inea
r eq
uatio
ns
29The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
4 G
eom
etry
and
mea
sure
s
4.1
Geo
met
rica
l rea
soni
ng
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
use
corr
ectly
the
voca
bula
ry, n
otat
ion
and
labe
lling
co
nven
tions
for l
ines
, an
gles
and
sha
pes
dist
ingu
ish
betw
een
conv
entio
ns,
defin
ition
s an
d de
rived
pr
oper
ties
exam
ine
and
refin
e ar
gum
ents
in
solu
tions
to
geom
etric
al p
robl
ems,
dist
ingu
ishin
g be
twee
n pr
actic
al d
emon
stra
tion
and
proo
f; pr
oduc
e si
mpl
e pr
oofs
exam
ine
and
crea
te
chai
ns o
f ded
uctiv
e re
ason
ing
in s
olut
ions
to
mor
e co
mpl
ex
geom
etric
al p
robl
ems
pres
ent r
igor
ous
and
sust
aine
d ar
gum
ents
in
the
solu
tion
of
geom
etric
al p
robl
ems;
cons
truc
t for
mal
ge
omet
rical
pro
ofs
iden
tify
para
llel a
nd
perp
endi
cula
r lin
es;
know
the
sum
of a
ngle
s at
a p
oint
, on
a st
raig
ht
line
and
in a
tria
ngle
; re
cogn
ise
vert
ical
ly
oppo
site
ang
les
iden
tify
alte
rnat
e an
gles
and
co
rres
pond
ing
angl
es;
unde
rsta
nd a
pro
of
that
:
•th
e an
gle
sum
of a
tr
iang
le is
180
° and
of
a q
uadr
ilate
ral
is 3
60°
•th
e ex
terio
r ang
le
of a
tria
ngle
is
equa
l to
the
sum
of
the
two
inte
rior
oppo
site
ang
les
expl
ain
how
to fi
nd,
calc
ulat
e an
d us
e:
•th
e su
ms
of th
e in
terio
r and
ex
terio
r ang
les
of q
uadr
ilate
rals
, pe
ntag
ons
and
hexa
gons
•th
e in
terio
r and
ex
terio
r ang
les
of
regu
lar p
olyg
ons
use
dyna
mic
imag
es to
de
mon
stra
te in
varia
nt
rela
tions
hips
bet
wee
n ra
dii,
chor
ds a
nd
tang
ents
in c
ircle
s; de
velo
p ar
gum
ents
to
exp
lain
and
just
ify
sim
ple
circ
le p
rope
rtie
s an
d th
eore
ms
exam
ine
and
crea
te
proo
fs o
f the
circ
le
theo
rem
s; us
e ci
rcle
th
eore
ms
to s
olve
pr
oble
ms
exam
ine
the
poin
ts
and
lines
use
d to
cre
ate
stan
dard
con
stru
ctio
ns
and
use
the
cond
ition
s of
con
grue
nce
to
pres
ent a
pro
of th
at th
e st
anda
rd c
onst
ruct
ions
ar
e ex
act
know
the
defin
ition
of
a ci
rcle
and
the
nam
es
of it
s pa
rts;
expl
ain
why
insc
ribed
regu
lar
poly
gons
can
be
cons
truc
ted
by e
qual
di
visi
ons
of a
circ
le
30 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
4.1
Geo
met
rica
l rea
soni
ng (c
onti
nued
)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
iden
tify
and
use
angl
e,
side
and
sym
met
ry
prop
ertie
s of
tria
ngle
s an
d qu
adril
ater
als;
expl
ore
geom
etric
al
prob
lem
s in
volv
ing
thes
e pr
oper
ties,
ex
plai
ning
reas
onin
g or
ally
, usi
ng s
tep-
by-s
tep
dedu
ctio
n su
ppor
ted
by d
iagr
ams
solv
e ge
omet
rical
pr
oble
ms
usin
g si
de
and
angl
e pr
oper
ties
of e
quila
tera
l, is
osce
les
and
right
-an
gled
tria
ngle
s an
d sp
ecia
l qua
drila
tera
ls,
expl
aini
ng re
ason
ing
with
dia
gram
s an
d te
xt;
clas
sify
qua
drila
tera
ls
by th
eir g
eom
etric
al
prop
ertie
s
solv
e pr
oble
ms
usin
g pr
oper
ties
of
angl
es, o
f par
alle
l and
in
ters
ectin
g lin
es a
nd
of tr
iang
les
and
othe
r po
lygo
ns, j
ustif
ying
in
fere
nces
and
ex
plai
ning
reas
onin
g w
ith d
iagr
ams
and
text
solv
e ge
omet
rical
pr
oble
ms
usin
g pr
oper
ties
of li
nes,
an
gles
, pol
ygon
s an
d ci
rcle
s; ju
stify
ar
gum
ents
and
so
lutio
ns u
sing
de
duct
ive
reas
onin
g
form
alis
e ex
istin
g kn
owle
dge
of li
nes,
angl
es a
nd p
olyg
ons b
y:
•us
ing
the
cong
ruen
ce
cond
ition
s (SS
S, S
AS,
RH
S, A
SA) t
o de
duce
fa
mili
ar p
rope
rtie
s of
tria
ngle
s and
qu
adril
ater
als,
e.g.
an
isos
cele
s tria
ngle
ha
s tw
o eq
ual
angl
es
•ex
plai
ning
w
hy st
anda
rd
cons
truc
tions
wor
k,
e.g.
obs
ervi
ng th
at
lines
join
ing
poin
ts
whe
re c
ompa
ss a
rcs
mee
t are
side
s of a
rh
ombu
s
(see
obj
ectiv
e ab
ove
for p
rogr
essio
n)
know
that
if tw
o 2-
D
shap
es a
re c
ongr
uent
, co
rres
pond
ing
side
s an
d an
gles
are
equ
al
unde
rsta
nd
cong
ruen
ce a
nd
expl
ore
sim
ilarit
y
draw
infe
renc
es a
bout
pr
oper
ties
of s
imila
r 2-
D s
hape
s an
d us
e pr
opor
tiona
l rea
soni
ng
to s
olve
geo
met
rical
an
d tr
igon
omet
rical
pr
oble
ms
inve
stig
ate
Pyth
agor
as’
theo
rem
, usin
g a
varie
ty
of m
edia
, thr
ough
its
hist
oric
and
cultu
ral
root
s, in
clud
ing
‘pic
ture
’ pr
oofs
visu
alis
e an
d m
anip
ulat
e dy
nam
ic im
ages
and
us
e sc
ale
draw
ing
to
inve
stig
ate
area
s of
squa
res o
n si
des o
f rig
ht-a
ngle
d an
d no
n rig
ht-a
ngle
d tr
iang
les,
rela
ting
findi
ngs t
o Py
thag
oras
’ the
orem
; us
e Py
thag
oras
’ the
orem
to
solv
e pr
oble
ms i
n 2-
D
and
sim
ple
3-D
cas
es
enga
ge w
ith a
nd
expl
ain
the
stag
es o
f a
varie
ty o
f pro
ofs
of
Pyth
agor
as’ t
heor
em;
use
Pyth
agor
as’
theo
rem
to s
olve
mor
e co
mpl
ex 3
-D p
robl
ems
pres
ent a
nd ju
stify
a
form
al p
roof
of
Pyth
agor
as’ t
heor
em
31The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
4.1
Geo
met
rica
l rea
soni
ng (c
onti
nued
)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
use
2-D
repr
esen
tatio
ns
to v
isua
lise
3-D
sha
pes
and
dedu
ce s
ome
of
thei
r pro
pert
ies
visu
alis
e 3-
D s
hape
s fr
om th
eir n
ets;
use
geom
etric
al p
rope
rtie
s of
cub
oids
and
sha
pes
mad
e fr
om c
uboi
ds;
use
sim
ple
plan
s an
d el
evat
ions
visu
alis
e an
d us
e 2-
D
repr
esen
tatio
ns o
f 3-D
ob
ject
s; an
alys
e 3-
D
shap
es th
roug
h 2-
D
proj
ectio
ns, i
nclu
ding
pl
ans
and
elev
atio
ns
visu
alis
e an
d de
scrib
e pr
oper
ties
of p
oint
s,
lines
and
pla
nes
in 3
-D
spac
e, in
clud
ing
cros
s se
ctio
ns c
reat
ed b
y sl
icin
g a
3-D
sha
pe
visu
alis
e an
d m
anip
ulat
e im
ages
to
est
ablis
h tr
igon
omet
rical
re
latio
nshi
ps b
y:
•ge
nera
ting
tria
ngle
s us
ing
a ro
tatin
g un
it ra
dius
(c
ircle
, cen
tre
the
orig
in)
•id
entif
ying
the
prop
ertie
s of
si
mila
r tria
ngle
s fo
rmed
by
enla
rgem
ents
of
the
circ
le
use
trig
onom
etric
al
rela
tions
hips
to s
olve
si
mpl
e pr
oble
ms
in 2
-D,
incl
udin
g be
arin
gs
deriv
e th
e fo
rmul
a ½
ab s
inC
for t
he
area
of a
tria
ngle
; us
e tr
igon
omet
rical
re
latio
nshi
ps to
so
lve
mor
e co
mpl
ex
2-D
pro
blem
s an
d pr
oble
ms
in 3
-D, s
uch
as th
e an
gle
betw
een
a lin
e an
d a
plan
e
draw
, ske
tch
and
com
pare
the
grap
hs
of tr
igon
omet
rical
fu
nctio
ns a
nd
tran
sfor
mat
ions
of
thes
e gr
aphs
; pro
ve th
e si
ne a
nd c
osin
e ru
les
and
use
them
to s
olve
2-
D a
nd 3
-D p
robl
ems
in a
rang
e of
con
text
s
32 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
4.2
Tran
sfor
mat
ions
and
coo
rdin
ates
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
unde
rsta
nd a
nd u
se th
e la
ngua
ge a
nd n
otat
ion
asso
ciat
ed w
ith
refle
ctio
ns, t
rans
latio
ns
and
rota
tions
use
prec
ise
lang
uage
an
d no
tatio
n to
des
crib
e an
d ge
nera
lise
the
resu
lts o
f com
bini
ng
tran
sfor
mat
ions
of 2
-D
shap
es o
n pa
per a
nd
usin
g IC
T, in
clud
ing:
•ro
tatio
ns a
bout
an
y po
int
•re
flect
ions
in a
ny
line
•tr
ansl
atio
ns u
sing
ve
ctor
not
atio
n
•a
tran
sfor
mat
ion
and
its in
vers
e
gene
rate
and
ana
lyse
pa
tter
ns, e
.g. I
slam
ic
desi
gns
expl
ain
and
dem
onst
rate
gr
aphi
cally
the
effe
cts
of c
ombi
ning
tr
ansl
atio
ns, u
sing
ve
ctor
not
atio
n,
incl
udin
g:
•th
e ru
le fo
r ad
ditio
n of
vec
tors
•sc
alar
m
ultip
licat
ion
of a
ve
ctor
(rep
eate
d ad
ditio
n)
expl
ain
and
dem
onst
rate
gr
aphi
cally
the
effe
cts
of c
ombi
ning
tr
ansl
atio
ns, u
sing
ve
ctor
not
atio
n,
incl
udin
g:
•th
e di
ffer
ence
of
two
vect
ors
•th
e re
sulta
nt o
f tw
o ve
ctor
s
•th
e co
mm
utat
ive
and
asso
ciat
ive
prop
ertie
s of
ve
ctor
add
ition
solv
e si
mpl
e ge
omet
rical
pro
blem
s in
2-D
usi
ng v
ecto
rs
reco
gnis
e an
d vi
sual
ise
the
sym
met
ries
of a
2-D
sh
ape
iden
tify
all t
he
sym
met
ries
of 2
-D
shap
es
iden
tify
refle
ctio
n sy
mm
etry
in 3
-D
shap
es
tran
sfor
m 2
-D s
hape
s by
: •re
flect
ing
in g
iven
m
irror
line
s
•ro
tatin
g ab
out a
gi
ven
poin
t
•tr
ansl
atin
g
tran
sfor
m 2
-D s
hape
s by
rota
tion,
refle
ctio
n an
d tr
ansl
atio
n, o
n pa
per a
nd u
sing
ICT
reco
gnis
e th
at
tran
slat
ions
, rot
atio
ns
and
refle
ctio
ns
pres
erve
leng
th a
nd
angl
e, a
nd m
ap o
bjec
ts
on to
con
grue
nt
imag
es
expl
ore
thes
e tr
ansf
orm
atio
ns a
nd
sym
met
ries
usin
g IC
T
try
out m
athe
mat
ical
re
pres
enta
tions
of
sim
ple
com
bina
tions
of
thes
e tr
ansf
orm
atio
ns
expl
ore
and
com
pare
m
athe
mat
ical
re
pres
enta
tions
of
com
bina
tions
of
tran
slat
ions
, rot
atio
ns
and
refle
ctio
ns o
f 2-D
sh
apes
, on
pape
r and
us
ing
ICT
devi
se in
stru
ctio
ns fo
r a
com
pute
r to
gene
rate
an
d tr
ansf
orm
sha
pes
33The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
4.2
Tran
sfor
mat
ions
and
coo
rdin
ates
(con
tinu
ed)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
unde
rsta
nd a
nd u
se th
e la
ngua
ge a
nd n
otat
ion
asso
ciat
ed w
ith
enla
rgem
ent;
enla
rge
2-D
sha
pes,
giv
en a
ce
ntre
of e
nlar
gem
ent
and
a po
sitiv
e in
tege
r sc
ale
fact
or; e
xplo
re
enla
rgem
ent u
sing
ICT
enla
rge
2-D
sha
pes,
gi
ven
a ce
ntre
of
enla
rgem
ent a
nd a
po
sitiv
e in
tege
r sca
le
fact
or, o
n pa
per a
nd
usin
g IC
T; id
entif
y th
e sc
ale
fact
or o
f an
enl
arge
men
t as
the
ratio
of t
he
leng
ths
of a
ny tw
o co
rres
pond
ing
line
segm
ents
; rec
ogni
se
that
enl
arge
men
ts
pres
erve
ang
le b
ut n
ot
leng
th, a
nd u
nder
stan
d th
e im
plic
atio
ns o
f en
larg
emen
t for
pe
rimet
er
enla
rge
2-D
sha
pes
usin
g po
sitiv
e,
frac
tiona
l and
neg
ativ
e sc
ale
fact
ors,
on
pape
r and
usi
ng
ICT;
use
reci
proc
als
as a
mul
tiplic
ativ
e in
vers
e in
the
cont
ext
of e
nlar
gem
ent;
reco
gnis
e th
e si
mila
rity
of re
sulti
ng s
hape
s an
d ex
plai
n th
e ef
fect
of
enl
arge
men
t on
perim
eter
enla
rge
3-D
sha
pes;
iden
tify
and
expl
ain
the
effe
cts
of e
nlar
gem
ent
on a
reas
and
vol
umes
of
sim
ilar s
hape
s an
d so
lids;
rela
te th
is
unde
rsta
ndin
g to
pr
actic
al c
onte
xts,
e.g
. in
bio
logy
m
ake
scal
e dr
awin
gsus
e an
d in
terp
ret m
aps
and
scal
e dr
awin
gs
in th
e co
ntex
t of
mat
hem
atic
s an
d ot
her
subj
ects
appl
y th
e pr
oper
ties
of s
imila
r tria
ngle
s an
d Py
thag
oras
’ the
orem
to
sol
ving
pro
blem
s pr
esen
ted
on a
2-D
co
ordi
nate
grid
; us
e a
3-D
coo
rdin
ate
grid
to re
pres
ent
sim
ple
shap
es
use
conv
entio
ns
and
nota
tion
for
2-D
coo
rdin
ates
in
all f
our q
uadr
ants
; fin
d co
ordi
nate
s of
po
ints
det
erm
ined
by
geo
met
rical
in
form
atio
n
find
the
mid
poin
t of
the
line
segm
ent A
B,
give
n th
e co
ordi
nate
s of
poi
nts
A a
nd B
use
the
coor
dina
te
grid
to s
olve
pro
blem
s in
volv
ing
tran
slat
ions
, ro
tatio
ns, r
efle
ctio
ns
and
enla
rgem
ents
34 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
4.3
Cons
truc
tion
and
loci
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
use
a ru
ler a
nd
prot
ract
or to
:
•m
easu
re a
nd d
raw
lin
es to
the
near
est
mill
imet
re a
nd
angl
es, i
nclu
ding
re
flex
angl
es, t
o th
e ne
ares
t deg
ree
•co
nstr
uct a
tr
iang
le, g
iven
tw
o si
des
and
the
incl
uded
ang
le
(SA
S) o
r tw
o an
gles
an
d th
e in
clud
ed
side
(ASA
)
use
stra
ight
edg
e an
d co
mpa
sses
to c
onst
ruct
:
•th
e m
idpo
int a
nd
perp
endi
cula
r bi
sect
or o
f a li
ne
segm
ent
•th
e bi
sect
or o
f an
ang
le
•th
e pe
rpen
dicu
lar
from
a p
oint
to
a lin
e
•th
e pe
rpen
dicu
lar
from
a p
oint
on
a
line
•a
tria
ngle
, giv
en
thre
e si
des
(SSS
)
use
stra
ight
edg
e an
d co
mpa
sses
to c
onst
ruct
tr
iang
les,
giv
en ri
ght
angl
e, h
ypot
enus
e an
d si
de (R
HS)
use
prop
ertie
s of
2-
D a
nd 3
-D s
hape
s to
mak
e ac
cura
te
cons
truc
tions
on
pape
r an
d us
ing
ICT;
incl
udin
g co
nstr
uctin
g tr
iang
les
from
com
bina
tions
of
sid
e an
d an
gle
fact
s, re
view
ing
and
gene
ralis
ing
findi
ngs
to id
entif
y w
hich
of
thes
e co
nditi
ons
defin
e un
ique
con
stru
ctio
ns
use
ICT
to e
xplo
re
cons
truc
tions
use
ICT
to e
xplo
re
thes
e co
nstr
uctio
nsus
e IC
T to
exp
lore
co
nstr
uctio
ns o
f tr
iang
les
and
othe
r 2-
D s
hape
s
use
rule
r and
pro
trac
tor
to c
onst
ruct
sim
ple
nets
of 3
-D s
hape
s,
e.g.
cub
oid,
regu
lar
tetr
ahed
ron,
squ
are-
base
d py
ram
id,
tria
ngul
ar p
rism
find
sim
ple
loci
, bot
h by
reas
onin
g an
d by
us
ing
ICT,
to p
rodu
ce
shap
es a
nd p
aths
, e.g
. an
equ
ilate
ral t
riang
le
find
the
locu
s of
a p
oint
th
at m
oves
acc
ordi
ng
to a
sim
ple
rule
, bot
h by
reas
onin
g an
d by
us
ing
ICT
visu
alis
e an
d de
scrib
e th
e lo
cus
of a
poi
nt
that
mov
es a
ccor
ding
to
a m
ore
com
plex
ru
le; e
xpla
in th
e pa
th u
sing
acc
urat
e ge
omet
rical
voc
abul
ary
and
nota
tion
and
use
a va
riety
of m
edia
, in
clud
ing
dyna
mic
ge
omet
ry s
oftw
are,
sk
etch
es a
nd g
raph
s
crea
te a
cha
in o
f re
ason
ing
to d
educ
e th
e eq
uatio
n of
a
circ
le b
y ap
plyi
ng
Pyth
agor
as’ t
heor
em to
th
e lo
cus
of a
poi
nt
35The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
4.4
Mea
sure
s an
d m
ensu
rati
on
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
choo
se a
nd u
se u
nits
of
mea
sure
men
t to
mea
sure
, est
imat
e,
calc
ulat
e an
d so
lve
prob
lem
s in
eve
ryda
y co
ntex
ts; c
onve
rt o
ne
met
ric u
nit t
o an
othe
r, e.
g. g
ram
s to
kilo
gram
s; re
ad a
nd in
terp
ret s
cale
s on
a ra
nge
of m
easu
ring
inst
rum
ents
choo
se a
nd u
se u
nits
of
mea
sure
men
t to
mea
sure
, est
imat
e,
calc
ulat
e an
d so
lve
prob
lem
s in
a ra
nge
of
cont
exts
; kno
w ro
ugh
met
ric e
quiv
alen
ts o
f im
peria
l mea
sure
s in
co
mm
on u
se, s
uch
as
mile
s, p
ound
s (lb
) an
d pi
nts
solv
e pr
oble
ms
invo
lvin
g m
easu
rem
ents
in a
va
riety
of c
onte
xts;
conv
ert b
etw
een
area
m
easu
res
(e.g
. mm
2 to
cm2 , c
m2 to
m2 , a
nd v
ice
vers
a) a
nd b
etw
een
volu
me
mea
sure
s (e
.g.
mm
3 to c
m3 , c
m3 to
m3 ,
and
vice
ver
sa)
inte
rpre
t and
use
co
mpo
und
mea
sure
s,
incl
udin
g fr
om o
ther
su
bjec
ts a
nd re
al li
fe;
solv
e pr
oble
ms
invo
lvin
g ra
tes;
conv
ert b
etw
een
com
poun
d m
easu
res,
ch
oosi
ng u
nits
mos
t su
ited
to th
e so
lutio
n
mak
e co
nnec
tions
be
twee
n th
e co
ntin
uity
of
the
num
ber l
ine
and
cont
inuo
us m
easu
res;
criti
cally
exa
min
e th
e m
easu
rem
ents
use
d in
a
prob
lem
and
thei
r eff
ect
on th
e ac
cura
cy o
f the
so
lutio
n, e
.g. u
nder
stan
d ho
w e
rror
s ca
n be
co
mpo
unde
d
com
mun
icat
e th
e so
lutio
n to
a p
robl
em
invo
lvin
g m
easu
rem
ent,
expl
aini
ng th
e lim
itatio
ns o
f ac
cura
cy u
sing
up
per a
nd
low
er b
ound
s
dist
ingu
ish
betw
een
and
estim
ate
the
size
of a
cute
, ob
tuse
and
refle
x an
gles
use
bear
ings
to s
peci
fy
dire
ctio
n
Inte
rpre
t and
exp
lore
co
mbi
ning
mea
sure
s in
to ra
tes o
f cha
nge
in
ever
yday
cont
exts
(e.g
. km
pe
r hou
r, pe
nce
per m
etre
); us
e co
mpo
und
mea
sure
s to
com
pare
in re
al-li
fe
cont
exts
(e.g
. tra
vel g
raph
s an
d va
lue
for m
oney
), us
ing
ICT
as a
ppro
pria
te.
36 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
4.4
Mea
sure
s an
d m
ensu
rati
on (c
onti
nued
)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
know
and
use
the
form
ula
for t
he a
rea
of
a re
ctan
gle;
cal
cula
te
the
perim
eter
and
are
a of
sha
pes
mad
e fr
om
rect
angl
es
deriv
e an
d us
e fo
rmul
ae
for t
he a
rea
of a
tr
iang
le, p
aral
lelo
gram
an
d tr
apez
ium
; ca
lcul
ate
area
s of
com
poun
d sh
apes
know
and
use
the
form
ulae
for t
he
circ
umfe
renc
e an
d ar
ea
of a
circ
le
pres
ent a
con
cise
re
ason
ed a
rgum
ent t
o de
rive
form
ulae
for:
•le
ngth
s of
circ
ular
ar
cs
•ar
eas
of s
ecto
rs o
f a
circ
le
•su
rfac
e ar
ea o
f a
cylin
der
•vo
lum
e of
a
cylin
der
solv
e pr
oble
ms
invo
lvin
g th
e us
e of
th
ese
form
ulae
pres
ent a
con
cise
re
ason
ed a
rgum
ent
whe
n de
rivin
g fo
rmul
ae fo
r the
su
rfac
e ar
eas
of
pyra
mid
s an
d co
nes;
expl
ore
conn
ectio
ns
betw
een:
•fo
rmul
ae fo
r th
e vo
lum
e of
a
pyra
mid
and
the
rela
ted
cubo
id
•fo
rmul
ae fo
r th
e su
rfac
e ar
ea
and
volu
me
of a
sp
here
and
the
circ
umsc
ribed
and
in
scrib
ed c
ubes
solv
e pr
oble
ms
invo
lvin
g th
e us
e of
th
ese
form
ulae
solv
e pr
oble
ms
invo
lvin
g m
ore
com
plex
shap
es
and
solid
s, in
clud
ing
segm
ents
of c
ircle
s and
fr
ustu
ms o
f con
es
calc
ulat
e th
e su
rfac
e ar
ea o
f cub
es a
nd
cubo
ids
know
and
use
the
form
ula
for t
he v
olum
e of
a c
uboi
d; c
alcu
late
vo
lum
es a
nd su
rfac
e ar
eas
of c
uboi
ds a
nd
shap
es m
ade
from
cu
boid
s
calc
ulat
e th
e su
rfac
e ar
ea a
nd v
olum
e of
rig
ht p
rism
s
37The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
5 St
atis
tics
5.1S
peci
fyin
g a
prob
lem
, pla
nnin
g an
d co
llect
ing
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
sugg
est p
ossi
ble
answ
ers,
giv
en a
qu
estio
n th
at c
an b
e ad
dres
sed
by s
tatis
tical
m
etho
ds
disc
uss
a pr
oble
m th
at
can
be a
ddre
ssed
by
stat
istic
al m
etho
ds
and
iden
tify
rela
ted
ques
tions
to e
xplo
re
sugg
est a
pro
blem
to
expl
ore
usin
g st
atis
tical
m
etho
ds, f
ram
e qu
estio
ns a
nd ra
ise
conj
ectu
res
inde
pend
ently
dev
ise
a su
itabl
e pl
an fo
r a m
ore
com
plex
sta
tistic
al
proj
ect,
sele
ctin
g su
itabl
e hy
poth
eses
to
addr
ess
the
prob
lem
eval
uate
pos
sibl
e di
ffic
ultie
s w
ith
plan
ned
appr
oach
es;
adju
st th
e pr
ojec
t pl
an a
ccor
ding
ly,
incl
udin
g re
cons
ider
ing
hypo
thes
es
deci
de w
hich
dat
a w
ould
be
rele
vant
to a
n en
quiry
and
pos
sibl
e so
urce
s
deci
de w
hich
dat
a to
col
lect
to a
nsw
er
a qu
estio
n an
d th
e de
gree
of a
ccur
acy
need
ed; i
dent
ify
poss
ible
sou
rces
; co
nsid
er a
ppro
pria
te
sam
ple
size
disc
uss
how
diff
eren
t se
ts o
f dat
a re
late
to
the
prob
lem
; ide
ntify
po
ssib
le p
rimar
y or
se
cond
ary
sour
ces;
dete
rmin
e th
e sa
mpl
e si
ze a
nd m
ost
appr
opria
te d
egre
e of
ac
cura
cy
just
ify th
e sa
mpl
ing
met
hod
sele
cted
, id
entif
y po
ssib
le
sour
ces
of b
ias
and
plan
how
to m
inim
ise
it
iden
tify
prac
tical
pr
oble
ms
such
as
non-
resp
onse
or
mis
sing
dat
a an
d re
fine
appr
oach
es to
min
imis
e th
eir i
mpa
ct o
n th
e va
lidity
of t
he re
sults
38 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
5.1S
peci
fyin
g a
prob
lem
, pla
nnin
g an
d co
llect
ing
(con
tinu
ed)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
plan
how
to c
olle
ct a
nd
orga
nise
sm
all s
ets
of
data
from
surv
eys
and
expe
rimen
ts:
•de
sign
dat
a co
llect
ion
shee
ts
or q
uest
ionn
aire
s to
use
in a
sim
ple
surv
ey
•co
nstr
uct
freq
uenc
y ta
bles
fo
r gat
herin
g di
scre
te d
ata,
gr
oupe
d w
here
ap
prop
riate
in
equ
al c
lass
in
terv
als
plan
how
to c
olle
ct
the
data
; con
stru
ct
freq
uenc
y ta
bles
with
eq
ual c
lass
inte
rval
s fo
r ga
ther
ing
cont
inuo
us
data
and
two-
way
ta
bles
for r
ecor
ding
di
scre
te d
ata
desi
gn a
surv
ey o
r ex
perim
ent t
o ca
ptur
e th
e ne
cess
ary
data
fr
om o
ne o
r mor
e so
urce
s; de
sign
, tria
l an
d if
nece
ssar
y re
fine
data
col
lect
ion
shee
ts;
cons
truc
t tab
les
for
gath
erin
g la
rge
disc
rete
an
d co
ntin
uous
set
s of
raw
dat
a, c
hoos
ing
suita
ble
clas
s in
terv
als;
desi
gn a
nd u
se tw
o-w
ay ta
bles
deci
de o
n th
e be
st
met
hods
for t
estin
g th
e hy
poth
eses
; se
lect
, jus
tify
and
use
the
data
-gat
herin
g te
chni
que
mos
t ap
prop
riate
to th
e co
ntex
t, de
cidi
ng
betw
een
a ra
nge
of s
ourc
es:
prim
ary
(obs
erva
tion,
con
trol
led
expe
rimen
t, da
ta
logg
ing)
and
sec
onda
ry
(spr
eads
heet
dat
a,
prin
ted
tabl
es, l
ists
)
sele
ct, j
ustif
y an
d us
e th
e da
ta-g
athe
ring
tech
niqu
e ap
prop
riate
to
com
plex
and
un
fam
iliar
pro
blem
s,
iden
tifyi
ng p
oten
tial
barr
iers
and
lim
itatio
ns;
iden
tify
wha
t ext
ra
info
rmat
ion
may
be
requ
ired
to p
ursu
e a
furt
her l
ine
of e
nqui
ry
sele
ct a
nd c
ritic
ally
ev
alua
te a
sam
plin
g sc
hem
e an
d a
met
hod
to in
vest
igat
e a
popu
latio
n, in
clud
ing
rand
om a
nd s
trat
ified
sa
mpl
ing;
exp
lain
the
effe
ct o
n re
liabi
lity
an
d va
lidity
colle
ct s
mal
l set
s of
da
ta fr
om su
rvey
s an
d ex
perim
ents
, as
plan
ned
colle
ct d
ata
usin
g a
suita
ble
met
hod
(e.g
. ob
serv
atio
n, c
ontr
olle
d ex
perim
ent,
data
lo
ggin
g us
ing
ICT)
gath
er d
ata
from
sp
ecifi
ed s
econ
dary
so
urce
s, in
clud
ing
prin
ted
tabl
es a
nd li
sts,
an
d IC
T-ba
sed
sour
ces,
in
clud
ing
the
inte
rnet
39The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
5.2
Proc
essi
ng a
nd re
pres
enti
ng d
ata
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
calc
ulat
e st
atis
tics
for
smal
l set
s of
dis
cret
e da
ta:
•fin
d th
e m
ode,
m
edia
n an
d ra
nge,
an
d th
e m
odal
cl
ass
for g
roup
ed
data
•ca
lcul
ate
the
mea
n, in
clud
ing
from
a s
impl
e fr
eque
ncy
tabl
e,
usin
g a
calc
ulat
or
for a
larg
er n
umbe
r of
item
s
calc
ulat
e st
atis
tics
for s
ets
of d
iscr
ete
and
cont
inuo
us
data
, inc
ludi
ng w
ith
a ca
lcul
ator
and
sp
read
shee
t; re
cogn
ise
whe
n it
is a
ppro
pria
te
to u
se th
e ra
nge,
mea
n,
med
ian
and
mod
e an
d,
for g
roup
ed d
ata,
the
mod
al c
lass
calc
ulat
e st
atis
tics
and
sele
ct th
ose
mos
t ap
prop
riate
to th
e pr
oble
m o
r whi
ch
addr
ess
the
ques
tions
po
sed
use
an a
ppro
pria
te
rang
e of
sta
tistic
al
met
hods
to e
xplo
re
and
sum
mar
ise
larg
e da
ta s
ets,
just
ifyin
g th
e ch
oice
s m
ade;
in
clud
e gr
oupi
ng
data
, est
imat
ing
and
findi
ng th
e m
ean,
m
edia
n, q
uart
iles
and
inte
rqua
rtile
rang
e
proc
ess
data
dra
wn
from
pro
blem
s in
volv
ing
seas
onal
ity
and
tren
ds in
a ti
me
serie
s; ch
oose
and
co
mbi
ne s
tatis
tical
m
etho
ds to
ana
lyse
th
e pr
oble
m, i
nclu
ding
m
ovin
g av
erag
es
40 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
5.2
Proc
essi
ng a
nd re
pres
enti
ng d
ata
(con
tinu
ed)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
cons
truc
t, on
pap
er
and
usin
g IC
T, g
raph
s an
d di
agra
ms
to
repr
esen
t dat
a,
incl
udin
g:
•ba
r-lin
e gr
aphs
•fr
eque
ncy
diag
ram
s fo
r gr
oupe
d di
scre
te
data
•si
mpl
e pi
e ch
arts
cons
truc
t gra
phic
al
repr
esen
tatio
ns, o
n pa
per a
nd u
sing
ICT,
an
d id
entif
y w
hich
ar
e m
ost u
sefu
l in
the
cont
ext o
f the
pro
blem
, in
clud
ing:
•pi
e ch
arts
for
cate
goric
al d
ata
•ba
r cha
rts
and
freq
uenc
y di
agra
ms
for
disc
rete
and
co
ntin
uous
dat
a
•si
mpl
e lin
e gr
aphs
fo
r tim
e se
ries
•si
mpl
e sc
atte
r gr
aphs
•st
em-a
nd-le
af
diag
ram
s
sele
ct, c
onst
ruct
an
d m
odify
, on
pape
r and
usi
ng IC
T,
suita
ble
grap
hica
l re
pres
enta
tions
to
prog
ress
an
enqu
iry
and
iden
tify
key
feat
ures
pre
sent
in th
e da
ta. I
nclu
de:
•lin
e gr
aphs
for
time
serie
s
•sc
atte
r gra
phs
to
deve
lop
furt
her
unde
rsta
ndin
g of
co
rrel
atio
n
cons
truc
t on
pape
r an
d us
ing
ICT
suita
ble
grap
hica
l re
pres
enta
tions
, in
clud
ing:
•hi
stog
ram
s fo
r gro
uped
co
ntin
uous
dat
a w
ith e
qual
cla
ss
inte
rval
s
•cu
mul
ativ
e fr
eque
ncy
tabl
es
and
diag
ram
s
•bo
x pl
ots
•sc
atte
r gra
phs
and
lines
of b
est f
it
(by
eye)
just
ify th
eir s
uita
bilit
y w
ith re
fere
nce
to th
e co
ntex
t of t
he p
robl
em
and
the
audi
ence
choo
se a
nd c
ombi
ne
suita
ble
grap
hica
l re
pres
enta
tions
to
prog
ress
an
unfa
mili
ar
or n
on-r
outin
e en
quiry
, in
clud
ing
hist
ogra
ms
with
equ
al o
r une
qual
cl
ass
inte
rval
s
use
prec
ise
and
cons
iste
nt g
raph
ical
re
pres
enta
tion
to
prog
ress
an
unfa
mili
ar
and
non-
rout
ine
enqu
iry
wor
k th
roug
h th
e en
tire
hand
ling
data
cyc
le to
ex
plor
e re
latio
nshi
ps
with
in b
i-var
iate
dat
a,
incl
udin
g ap
plic
atio
ns
to g
loba
l citi
zens
hip,
e.g
. ho
w fa
ir is
our s
ocie
ty?
41The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
5.3
Inte
rpre
ting
and
dis
cuss
ing
resu
lts
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
inte
rpre
t dia
gram
s an
d gr
aphs
(inc
ludi
ng p
ie
char
ts) a
nd d
raw
sim
ple
conc
lusi
ons
base
d on
th
e sh
ape
of g
raph
s an
d si
mpl
e st
atis
tics
for
a si
ngle
dis
trib
utio
n
inte
rpre
t tab
les,
gr
aphs
and
dia
gram
s fo
r dis
cret
e an
d co
ntin
uous
dat
a,
rela
ting
sum
mar
y st
atis
tics
and
findi
ngs
to th
e qu
estio
ns b
eing
ex
plor
ed
inte
rpre
t gra
phs
and
diag
ram
s an
d m
ake
infe
renc
es to
supp
ort
or c
ast d
oubt
on
initi
al
conj
ectu
res;
have
a
basi
c un
ders
tand
ing
of
corr
elat
ion
find
patt
erns
and
ex
cept
ions
and
exp
lain
an
omal
ies;
incl
udin
g in
terp
reta
tion
of
soci
al s
tatis
tics
and
eval
uatio
n of
the
stre
ngth
of a
ssoc
iatio
n w
ithin
bi-v
aria
te d
ata
(cor
rela
tion,
line
s of
be
st fi
t)
inte
rpre
t and
com
pare
di
strib
utio
ns, i
nclu
ding
cu
mul
ativ
e fr
eque
ncy
diag
ram
s; m
ake
and
disc
uss
infe
renc
es,
usin
g th
e sh
ape
of
the
dist
ribut
ions
and
m
easu
res
of a
vera
ge
and
spre
ad, i
nclu
ding
m
edia
n an
d qu
artil
es
expl
ain
and
just
ify
assu
mpt
ions
and
co
nstr
aint
s; in
clud
e in
terp
reta
tion
and
com
paris
on o
f hi
stog
ram
s w
ith
uneq
ual c
lass
inte
rval
sco
mpa
re tw
o si
mpl
e di
strib
utio
ns u
sing
the
rang
e an
d on
e of
the
mod
e, m
edia
n or
mea
n
com
pare
two
dist
ribut
ions
usi
ng th
e ra
nge
and
one
or m
ore
of th
e m
ode,
med
ian
and
mea
n
com
pare
two
or
mor
e di
strib
utio
ns
and
mak
e in
fere
nces
, us
ing
the
shap
e of
th
e di
strib
utio
ns a
nd
appr
opria
te s
tatis
tics
writ
e a
shor
t rep
ort o
f a
stat
istic
al e
nqui
ry,
incl
udin
g ap
prop
riate
di
agra
ms,
gra
phs
and
char
ts, u
sing
ICT
as
appr
opria
te; j
ustif
y th
e ch
oice
of p
rese
ntat
ion
writ
e ab
out a
nd
disc
uss
the
resu
lts o
f a
stat
istic
al e
nqui
ry u
sing
IC
T as
app
ropr
iate
; ju
stify
the
met
hods
us
ed
revi
ew in
terp
reta
tions
an
d re
sults
of a
st
atis
tical
enq
uiry
on
the
basi
s of
dis
cuss
ions
; co
mm
unic
ate
thes
e in
terp
reta
tions
and
re
sults
usi
ng s
elec
ted
tabl
es, g
raph
s an
d di
agra
ms
eval
uate
the
resu
lts
of a
sta
tistic
al
enqu
iry; r
evie
w a
nd
just
ify o
r ref
ine
the
choi
ce o
f sta
tistic
al
repr
esen
tatio
ns a
nd
rela
te su
mm
aris
ed d
ata
to th
e qu
estio
ns b
eing
ex
plor
ed
criti
cally
exa
min
e st
rate
gies
ado
pted
an
d ar
gum
ents
pr
esen
ted,
rela
ting
them
to th
e or
igin
al
hypo
thes
es; r
ecog
nise
th
e lim
itatio
ns o
f any
as
sum
ptio
ns a
nd th
e ef
fect
s th
at v
aryi
ng
assu
mpt
ions
cou
ld
have
on
conc
lusi
ons
draw
n fr
om d
ata
anal
ysis
use
stat
istic
al
anal
ysis
eff
ectiv
ely
in
pres
entin
g co
nvin
cing
co
nclu
sion
s; cr
itica
lly
refle
ct o
n ow
n lin
es
of e
nqui
ry; s
earc
h fo
r and
app
reci
ate
mor
e el
egan
t for
ms
of c
omm
unic
atin
g co
nclu
sion
s
42 The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
01061-2009DOM-EN © Crown copyright 2009
5.4
Prob
abili
ty
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
use
voca
bula
ry a
nd
idea
s of
pro
babi
lity,
dr
awin
g on
exp
erie
nce
inte
rpre
t the
resu
lts
of a
n ex
perim
ent
usin
g th
e la
ngua
ge o
f pr
obab
ility
; app
reci
ate
that
rand
om p
roce
sses
ar
e un
pred
icta
ble
inte
rpre
t res
ults
in
volv
ing
unce
rtai
nty
and
pred
ictio
nid
entif
y w
hen
the
even
ts in
a p
robl
em
are
mut
ually
exc
lusi
ve
or in
depe
nden
t; us
e an
d in
terp
ret t
ree
diag
ram
s to
repr
esen
t ou
tcom
es o
f com
bine
d ev
ents
and
to in
form
th
e ca
lcul
atio
n of
th
eir p
roba
bilit
ies;
deci
de w
hen
to a
dd
and
whe
n to
mul
tiply
pr
obab
ilitie
s
inte
rpre
t the
eff
ect
on p
roba
bilit
y of
co
ntex
ts in
volv
ing
sele
ctio
n w
ith a
nd
with
out r
epla
cem
ent;
choo
se a
nd c
ombi
ne
repr
esen
tatio
ns
to c
omm
unic
ate
prob
abili
ties
as p
art o
f a
solu
tion
to a
pro
blem
reco
gnis
e w
hen
and
how
to w
ork
with
pr
obab
ilitie
s as
soci
ated
w
ith in
depe
nden
t an
d m
utua
lly
excl
usiv
e ev
ents
whe
n in
terp
retin
g da
ta
unde
rsta
nd a
nd u
se
the
prob
abili
ty s
cale
fr
om 0
to 1
; fin
d an
d ju
stify
pro
babi
litie
s ba
sed
on e
qual
ly li
kely
ou
tcom
es in
sim
ple
cont
exts
; ide
ntify
all
the
poss
ible
mut
ually
ex
clus
ive
outc
omes
of a
si
ngle
eve
nt
know
that
if th
e pr
obab
ility
of a
n ev
ent
occu
rrin
g is
p th
en th
e pr
obab
ility
of i
t not
oc
curr
ing
is 1
− p
; use
di
agra
ms
and
tabl
es to
re
cord
in a
sys
tem
atic
w
ay a
ll po
ssib
le
mut
ually
exc
lusi
ve
outc
omes
for s
ingl
e ev
ents
and
for t
wo
succ
essi
ve e
vent
s
iden
tify
all t
he m
utua
lly
excl
usiv
e ou
tcom
es
of a
n ex
perim
ent;
know
that
the
sum
of
pro
babi
litie
s of
all
mut
ually
exc
lusi
ve
outc
omes
is 1
and
us
e th
is w
hen
solv
ing
prob
lem
s
43The National Strategies | Secondary Secondary mathematics subject leader development materials: Spring 2010
© Crown copyright 2009 01061-2009DOM-EN
5.4
Prob
abili
ty (c
onti
nued
)
Year
7Ye
ar 8
Year
9Ye
ar 1
0Ye
ar 1
1Ex
tens
ion
estim
ate
prob
abili
ties
by c
olle
ctin
g da
ta fr
om
a si
mpl
e ex
perim
ent
and
reco
rdin
g it
in
a fr
eque
ncy
tabl
e;
com
pare
exp
erim
enta
l an
d th
eore
tical
pr
obab
ilitie
s in
sim
ple
cont
exts
com
pare
est
imat
ed
expe
rimen
tal
prob
abili
ties
with
theo
retic
al
prob
abili
ties,
re
cogn
isin
g th
at:
•if
an e
xper
imen
t is
repe
ated
the
outc
ome
may
, and
us
ually
will
, be
diff
eren
t
•in
crea
sing
the
num
ber o
f tim
es
an e
xper
imen
t is
repe
ated
gen
eral
ly
lead
s to
bet
ter
estim
ates
of
prob
abili
ty
com
pare
exp
erim
enta
l an
d th
eore
tical
pr
obab
ilitie
s in
a ra
nge
of c
onte
xts;
appr
ecia
te
the
diff
eren
ce
betw
een
mat
hem
atic
al
expl
anat
ion
and
expe
rimen
tal e
vide
nce
use
rela
tive
freq
uenc
y as
an
estim
ate
of
prob
abili
ty, i
nclu
ding
si
mul
atio
n us
ing
ICT
to g
ener
ate
larg
er
sam
ples
; dis
cuss
its
relia
bilit
y ba
sed
on s
ampl
e si
ze a
nd
use
to in
terp
ret a
nd
com
pare
out
com
es o
f ex
perim
ents
expl
ore
a re
leva
nt a
nd
purp
osef
ul p
robl
em
invo
lvin
g un
cert
aint
y;
estim
ate
risk
by
mod
ellin
g re
al e
vent
s th
roug
h si
mul
atio
n;
just
ify d
ecis
ions
bas
ed
on e
xper
imen
tal
prob
abili
ty a
nd
com
men
t on
the
effe
ct o
f ass
umpt
ions
an
d sa
mpl
e si
ze
on th
e re
liabi
lity
of
conc
lusi
ons