2014 CurriculumPRIMARY

MATHS

Year 6Book 1 of 2

Resources and

teacher ideas for every objective

of the 2014 Curriculum

PM Year 6 Book 1 of 2.indd 1 26/11/2014 15:43:24

Primary Maths Prim-Ed Publishing www.prim-ed.com iii

FOREWORD

CONTENTS

Primary Maths is a photocopiable, six-level, year–specific series designed to address the Primary Framework National Curriculum for Mathematics objectives of:

• number •ratioandproportion • algebra • measurement • geometry • statistics.

Each book in the Primary Maths series includes: • atleastoneactivitypageforeachobjectivewhichcanbephotocopiedordisplayedonaninteractive

whiteboard • comprehensiveteachersnotestoaccompanyeachactivity • additionalteachersnotesonactivitiesandgames • assessmentchecklists • additionalphotocopiableresources • interactivewhiteboardresourcesavailabletodownload.

The Year 6 books in the Primary Maths series are: Primary Maths – Number, Ratio, Proportion and Algebra Primary Maths – Measurement, Geometry and Statistics Primary Maths – The big interactive book of understanding shape/measuring

Teachers notes:

How to use this book ............................................. iv–vSetting up a maths classroom ................................. viActivities and games .................................................. viiAssessment checklists ........................................ viii-xiAdditional resources ........................................ xii–xvii

Pupil activities with accompanying teachers notes:

Number and place value ................................. 2–9Reading, writing, ordering and comparing numbers ................................................ 2–5Rounding .................................................................... 6–7Negative numbers ................................................... 8–9

Addition, subtraction, multiplication and division .................................................. 10–39

Long multiplication ............................................. 10–11Long and short division ..................................... 12–17Mental calculations ........................................... 18–19Factors and multiples ........................................ 20–25Prime numbers ..................................................... 26–27Order of operations ............................................ 28–29Multi-step problems .......................................... 30–37Estimation ............................................................. 38–39

Fractions (including decimals and percentages .................................................. 40–69

Simplifying fractions ......................................... 40–41

Comparing and ordering fractions ................ 42–43

Adding fractions ................................................. 44–45

Subtracting fractions ........................................ 46–47

Multiplying fractions ......................................... 48–49

Dividing fractions ............................................... 50–51

Fraction and decimal equivalents .................. 52–53

Place value in decimals .................................... 54–57

Multiplying decimals ......................................... 58–59

Dividing decimals ............................................... 60–61

Rounding decimals ............................................ 62–65

Equivalent fractions, decimals and percentages ................................................. 66–69

Ratio and proportion ................................... 70–85Quantity problem-solving ................................ 70–71

Percentage problem-solving ........................... 72–79

Scaling and similar shapes .............................. 80–81

Unequal sharing and grouping problems .... 82–85

Algebra ....................................................... 86–105Simple formulae ................................................. 86–89

Number sequences ............................................. 90–99

Missing number problems .......................... 100–101

Equations with two variables .................... 102–105

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The Primary Maths series provides teachers with a number of varied and challenging activities. At least one activity, often more, is provided for each objective of the Primary National Curriculum for Mathematics.

Suggestions for using the activities in this book:

Objective:• Decide which curriculum objective you wish to address and choose the appropriate activity page(s).

Oral work and mental calculation starter:• Choose which oral and mental activities you will use, from the list provided, to introduce the lesson or sharpen

pupils’ skills.• Someoftheactivitieshaveaccompanyinginteractivewhiteboardactivitiestohelpintroducethelessonandcapture

pupils’ attention.• These activities should occupy the first 5–10 minutes of the lesson.

Main teaching activity:• Decide how much teacher input you will provide for the main activity and whether pupils will be working

individually, in pairs or as a group.• Depending upon the abilities of the pupils in your class, decide whether any additional activities will be needed, from

the list provided, or whether these can be used during subsequent lessons.• This activity should occupy approximately 30 minutes.

Plenary:• Decide what opportunities will be provided during the plenary session. Will pupils be given the opportunity to share

and explain work, compare strategies used or summarise the key facts they have learnt?• Think about how you can use the plenary session to assess pupils’ progress and therefore inform your future

planning.• The plenary should occupy the final 10 minutes of the lesson.

Pupil activity pages:The pupil activities follow a common format:

How to use this book

Title explanation

After initial discussion, some activities can be completed individually, and others in small groups or as a whole class.

The ‘Challenge’ activity can be completed by early finishers or those pupils requiring extension of the task. Pupils may need to complete the activity on the back of the worksheet or investigate an activity further by using concrete materials or creating their own ideas linked to the objective.

The objective provides the teacher with the focus of the activity. It is written in the form of a general objective.

An icon denotes the curriculum strand for each activity.

Number Ratio and Proportion Algebra Measurement Geometry Statistics

TEACHERS NOTES

NNumber

MMeasurement

GGeometry

RPRatio and Proprotion

AAlgebra

SStatistics

Primary Maths Prim-Ed Publishing www.prim-ed.com v

Assessment

AssessmentchecklistshavebeenincludedfortheYear6‘Number’,‘RatioandProportion’and‘Algebra’objectives.Seepages vii–xi. These can be used to assess each pupil’s understanding of the key objectives covered.

• Teaching notes for the strands have been included on page vii. These comprise background information and suggested activities and games.

• Extra teacher resources have been included on pages xii–xvii. These can be enlarged if necessary and used in appropriate activities or as display posters.

• Interactivewhiteboardactivitieshavebeenprovidedtohelpteachtheobjectives.Thesecanbedownloadedfromwww.prim-ed.com.

The objective tells the teacher which strand and objective from the Primary National Curriculum for Mathematics is being covered.

Oral work and mental calculation activities are suggested, for introducing the lesson or sharpening/developing oral and mental skills. The activities should occupy the first 5-10 minutes of the lesson.

Some activities have interactive whiteboard activities available to download. If an interactive activity is provided it is listed here.

The title of the main teaching activity is given. The photocopiable activity is on the page facing the teachers notes. The main activity should occupy approximately 30 minutes.

Answers to all activities are provided.

Suggest ions for addit iona l activities are provided. They can be completed during the lesson, or in subsequent lessons. They can be used to aid differentiation.

Teachers pages

Ateacherspageaccompanieseachpupilworksheet.Itprovidesthefollowinginformation:

How to use this book

Use the key to write the appropriate code next to each task the pupil completes.

A summary of the tasks pupils will complete.

TEACHERS NOTES

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TEACHERS NOTES

Setting up a mathematics classroom

By having the following materials and visual representations around them, pupils can better engage in mathematical learning.

• Allowroomtomovesopupilscaninvestigatethingsaround the room. Organise desks and floor space appropriately.

• Displaya‘Numbers’chartthatincludesthousands,ten thousands, hundred thousands and millions.

• Displayanumberlineatalevelwherepupilscanuseit.Includenegativenumbersonthenumberline.

• Display numbers, number words and a visualrepresentation of numbers.

• Displayaplacevaluechartwhichincludesfractions(tenths, hundredths and thousandths).

• Displaya100square.

• Ensureyouhaveagoodrangeofmathsgamesanduse them regularly.

• Providecalculators.

• Display‘timestables’charts.

• Haveananalogueanddigitalclockintheclassroom(12-hour and 24-hour).

• Displaypicturesoflabelled2-Dand3-Dshapes.

• Provideathermometer.

• Provide construction materials such as cardboardboxes, cylinders, paper, scissors and so on.

• Ensure you have adequate concrete materials toteach each strand (refer to page vii).

• Allowpupilsopportunitiestoinvestigateoutsidetheclassroom in the school environment.

• Display a chart showing equivalent fractions,decimals and percentages.

• Displayormakevariousgraphssuchaspictograms,bar charts, block graphs, Venn diagrams, Carroll diagrams, line graphs and pie charts.

• Display a class birthday chart which includes themonths of the year.

• Displayanduseacalendar.

• Display a poster showing equivalent metric andimperial measures.

• Have computer software related to mathematicsavailable for use on the classroom computer(s) or in the computer room.

• Displayapostershowingdifferentangles.

• Providearangeofmeasuringequipmentforlength,mass and capacity.

• Displaytheeightcompassdirections:N,S,E,W,NE,NW,SE,SW.

• Ensure you have a good selection of interactivemaths resources for use on a whiteboard (refer to www.prim-ed.com).

Primary Maths Prim-Ed Publishing www.prim-ed.com vii

TEACHERS NOTES

Counting and understanding number/ Knowing and using number facts

– Activities and games• Play‘Bingo’toconsolidatebasicfactsormatchequivalent

fractions, decimals and percentages etc. Vary by calling out the answer in some games and the number sentence or problem in others. Blank bingo cards are on page xvii.

• Divide theclass into teamsandselectonepupil fromeach team to stand at the board ready to write. Call out a number (e.g. 1089) or basic fact (e.g. 25 – 6, 7 x 9, double 12). The first pupil to write the correct answer wins a point for his/her team.

• GivedirectionsforpupilstotakeoutamountsofBase10blocks to add or subtract given decimal numbers with an unlike number of decimal places. Impress on pupils that the blocks have the value they give them – longs can be ones, tens, hundreds, tenths or hundredths. It may help understanding to use a counter as a decimal point. Recording of results is not important, development of understanding of concepts is the focus.

• Usecalculatorstogeneratelargenumbers;forexample,show a number on the calculator that is between 847 639and857639;768274and768374;900000and900003;420762and420027;549387and594387;600000and500000;999999and888888;7269486and 7 296 488.

• Boardthesenumberpatterns,thenhavepupilscontinuethe patterns.

7, 13, 19, , , , , , , , , ,

106, 212, 318, , , , , , , , , 2, 5, 11, 23, , , , , , , , ,

Pupils make patterns of their own to share with classmates.

• Estimationisanessentialskillandshouldbeusedpriorto any calculation.

– Have pupils estimate how many people can stand in their classroom—treat this as a record attempt. Pupils describe how this may be checked without filling the room.

– Estimate, then calculate, how many months, days and hours they have been alive.

– Estimate, then calculate, how many letters are used in a whole newspaper, library book and or/class reading book. Describe how they worked out the answer.

Materials required

• placevalueblocks• interconnectingcubes• placevaluemats(seepagesxiiandxiii)• calculators• fractioncharts(seepagexvi)• abacus• tablescharts(seepagexv)• 100schart(seepagexiv)• numberlines• bingocards(seepagexvii)

viii www.prim-ed.com Prim-Ed Publishing Primary Maths

AAssessment

Pupils’ names Read

and

writ

e nu

mbe

rs u

p to

10

000

000.

Ord

er a

nd c

ompa

re n

umbe

rs u

p to

10

000

000

.

Dete

rmin

e th

e va

lue

of e

ach

digi

t in

num

bers

up

to

10 0

00 0

00.

Roun

d w

hole

num

bers

.

Use

nega

tive

num

bers

in c

onte

xt.

Calc

ulat

e in

terv

als

acro

ss z

ero.

Solv

e nu

mbe

r pr

oble

ms

invo

lvin

g or

derin

g an

d co

mpa

ring

num

bers

.

Solv

e nu

mbe

r pr

oble

ms

invo

lvin

g ro

undi

ng

who

le n

umbe

rs.

Solv

e nu

mbe

r pr

oble

ms

invo

lvin

g ne

gativ

e nu

mbe

rs.

KeyD = DemonstratedNFO = Needs further

opportunity

YEAR 6 NUMBER AND PLACE VALUE – ASSESSMENT CHECKLIST

Primary Maths Prim-Ed Publishing www.prim-ed.com ix

AAssessment

Pupils’ names Usin

g lo

ng m

ultip

licat

ion

for

4-di

git

x 2-

digi

t nu

mbe

rs.

Use

long

div

isio

n fo

r 4-

digi

t ÷

2-di

git

num

bers

.

Inte

rpre

t di

visi

on r

emai

nder

s as

num

bers

and

fr

actio

ns.

Roun

d di

visi

on r

emai

nder

s.

Use

shor

t di

visi

on f

or 4

-dig

it ÷

2-di

git

num

bers

.

Perf

orm

men

tal c

alcu

latio

ns w

ith m

ixed

op

erat

ions

.

Iden

tify

com

mon

fac

tors

.

Iden

tify

com

mon

mul

tiple

s.

Iden

tify

prim

e nu

mbe

rs.

Use

know

ledg

e of

ord

er o

f op

erat

ions

to

carr

y ou

t ca

lcul

atio

ns.

Solv

e ad

ditio

n m

ulti-

step

pro

blem

s.

Solv

e su

btra

ctio

n m

ulti-

step

pro

blem

s.

Solv

e pr

oble

ms

invo

lvin

g +,

–, x

and

÷.

Use

estim

atio

n to

che

ck a

nsw

ers

to

calc

ulat

ions

.

KeyD = DemonstratedNFO = Needs further

opportunity

YEAR 6 ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION – ASSESSMENT CHECKLIST

x www.prim-ed.com Prim-Ed Publishing Primary Maths

AAssessment

Pupils’ names Use

com

mon

fac

tors

to

sim

plify

fra

ctio

ns.

Use

com

mon

mul

tiple

s to

exp

ress

fr

actio

ns.

Com

pare

and

ord

er f

ract

ions

.

Add

frac

tions

with

diff

eren

t de

nom

inat

ions

and

mix

ed n

umbe

rs.

Subt

ract

fra

ctio

ns w

ith d

iffer

ent

deno

min

atio

ns a

nd m

ixed

num

bers

.

Mul

tiply

sim

ple

pairs

of

prop

er f

ract

ions

.

Divi

de p

rope

r fr

actio

ns b

y w

hole

nu

mbe

rs.

Asso

ciat

e a

frac

tion

with

div

isio

n.

Calc

ulat

e de

cim

al f

ract

ion

equi

vale

nts

for

a si

mpl

e fr

actio

n.

Iden

tify

the

valu

e of

eac

h di

git

in

num

bers

giv

en t

o th

ree

deci

mal

pla

ces.

Mul

tiply

and

div

ide

num

bers

by

10, 1

00

and

1000

.

Mul

tiply

dec

imal

s to

tw

o pl

aces

by

who

le

num

bers

.

Use

writ

ten

divi

sion

met

hods

for

de

cim

als

up t

o tw

o pl

aces

.

Roun

d an

swer

s to

a r

equi

red

degr

ee o

f di

fficu

lty.

Know

equ

ival

ence

s be

twee

n fr

actio

ns,

deci

mal

s an

d pe

rcen

tage

s.

KeyD = DemonstratedNFO = Needs further opportunity

YEAR 6 FRACTIONS (INCLUDING DECIMALS AND PERCENTAGES) – ASSESSMENT CHECKLIST

Primary Maths Prim-Ed Publishing www.prim-ed.com xi

AAssessment

Pupils’ names Solv

e m

issi

ng v

alue

s pr

oble

ms

usin

g m

ultip

licat

ion

and

divi

sion

fac

ts.

Solv

e pe

rcen

tage

pro

blem

s an

d us

e pe

rcen

tage

s fo

r co

mpa

rison

.

Solv

e pr

oble

ms

invo

lvin

g si

mila

r sh

apes

and

sc

ale.

Solv

e pr

oble

ms

invo

lvin

g un

equa

l sha

ring

and

grou

ping

.

Use

sim

ple

form

ulae

.

Gene

rate

and

des

crib

e lin

ear

num

ber

sequ

ence

s.

Expr

ess

mis

sing

num

ber

prob

lem

s al

gebr

aica

lly.

Find

pai

rs o

f nu

mbe

rs t

hat

satis

fy a

n eq

uatio

n w

ith t

wo

unkn

owns

.

Enum

erat

e po

ssib

ilitie

s of

com

bina

tions

of

two

varia

bles

.

KeyD = DemonstratedNFO = Needs further

opportunity

YEAR 6 RATIO, PROPORTION AND ALGEBRA – ASSESSMENT CHECKLIST

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Place value mat

Tens millions Millions Hundred

thousandsTen

thousands Thousands Hundreds Tens Ones

TEACHER RESOURCES

Primary Maths Prim-Ed Publishing www.prim-ed.com xiii

TEACHER RESOURCES

Place value mat

Ten thousands

(10 000)

Thousands

(1000)

Hundreds

(100)

Tens

(10)

Ones

(1)•

Tenths

(1/10)

Hundredths

(1/100)

Thousandths

(1/1000)

Ten thousands

(10 000)

Thousands

(1000)

Hundreds

(100)

Tens

(10)

Ones

(1)•

Tenths

(1/10)

Hundredths

(1/100)

Thousandths

(1/1000)

xiv www.prim-ed.com Prim-Ed Publishing Primary Maths

100 chart

1 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29

30 31 32 33 34 35 36 37 38 39

40 41 42 43 44 45 46 47 48 49

50 51 52 53 54 55 56 57 58 59

60 61 62 63 64 65 66 67 68 69

70 71 72 73 74 75 76 77 78 79

80 81 82 83 84 85 86 87 88 89

90 91 92 93 94 95 96 97 98 99

0–99 chart

TEACHER RESOURCES

Primary Maths Prim-Ed Publishing www.prim-ed.com xv

TEACHER RESOURCES

Basic multiplication facts

x 0 1 2 3 4 5 6 7 8 9 10

0 0 0 0 0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6 7 8 9 10

2 0 2 4 6 8 10 12 14 16 18 20

3 0 3 6 9 12 15 18 21 24 27 30

4 0 4 8 12 16 20 24 28 32 36 40

5 0 5 10 15 20 25 30 35 40 45 50

6 0 6 12 18 24 30 36 42 48 54 60

7 0 7 14 21 28 35 42 49 56 63 70

8 0 8 16 24 32 40 48 56 64 72 80

9 0 9 18 27 36 45 54 63 72 81 90

10 0 10 20 30 40 50 60 70 80 90 100

Basic multiplication facts

x 0 1 2 3 4 5 6 7 8 9 10

0 0 0 0 0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6 7 8 9 10

2 0 2 4 6 8 10 12 14 16 18 20

3 0 3 6 9 12 15 18 21 24 27 30

4 0 4 8 12 16 20 24 28 32 36 40

5 0 5 10 15 20 25 30 35 40 45 50

6 0 6 12 18 24 30 36 42 48 54 60

7 0 7 14 21 28 35 42 49 56 63 70

8 0 8 16 24 32 40 48 56 64 72 80

9 0 9 18 27 36 45 54 63 72 81 90

10 0 10 20 30 40 50 60 70 80 90 100

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TEACHER RESOURCES

Equivalent fractions, decimals and percentages

Fraction Decimal Percentage

1 100%

0.5 50%

0.33 33 13 %

0.66 66 23 %

0.25 25%

0.75 75%

0.2 20%

0.4 40%

0.6 60%

Fraction Decimal Percentage

0.8 80%

0.125 12 12 %

0.375 37 12 %

0.1 10%

0.3 30%

0.7 70%

0.9 90%

0.01 1%

0.99 99%

Fraction chart

whole 11

half

third

quarter

sixth

eighth

twelfth

13

13

12

14

14

14

16

16

16

16

16

18

18

18

18

18

18

18

112

112

112

112

112

112

112

112

112

112

112

11

12132314

43

51

52

53

54

18

83

101

103

107

109

1001

10099

Primary Maths Prim-Ed Publishing www.prim-ed.com xvii

TEACHER RESOURCES

Bingo cards (blank)

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TEACHER INFORMATIONA

Algebra

Oral work and mental calculation

• Asaclass,workouttheruleforandcompletelargefunction machines.

• Introducetheuseofsymbolsanddiscusstheirmeaning;forexample,Theareaofarectangleislxb (length x breadth), the perimeter of a triangle is 3l (length x 3).

• Verballyworkoutproblemssuchasthenumberofmonths in a year using the symbols m (months) and y (years).

• Workoutandrecordaformulatoshowthecostof3sweets (s) at 5p each.

Interactive whiteboard activity

Interactive whiteboard activity available to support this copymaster. Visit www.prim-ed.com.

Main teaching activity

Find the formula (page 87)

Additional activities suitable for developing the objective

• Workoutperimetersusingformulas;forexample,

The perimeter of a square is 4l. Each side of the square is 5 cm, so what is the perimeter?

The perimeter of a rectangle is 2 x (l + b). What is the perimeter if l = 6 cm and b = 4 cm?

Answers

1. (a) (b)

(c) (d)

2. (a) 150n (b)y÷5 (c) 3x + 4 (d) y - 12 = 20 (y = 32) (e) £x + £15 = £45 (x = £30)

3. (a) 5n x 1.75p (b) 4n + 7 (c) l x b

Challenge: Teacher check

Rule: 3n Rule: n ÷ 2

5 15 2 1

6 18 4 2

7 21 6 3

8 24 8 4

9 27 10 5

Rule: n ÷ 9 Rule: n x 10, +2

81 9 1 12

72 8 2 22

63 7 3 32

54 6 4 42

45 5 5 52

ALGEBRA

Objective

• Usesimpleformulae.

Objective

Primary Maths Prim-Ed Publishing www.prim-ed.com 87

5n = £1.75 4n + 7 = 155n x 35p

FIND THE FORMULA

Expressesrelationshipsasaformula,usinglettersasasymbol.

Write some problems of your own and see if a friend can work out the algebraic sentence to solve it.

1. Work out the rule which will help you complete each table.

(a) (b) (c) (d)

2. Read the scenario and the problem. Write an algebraic sentence to represent the problem. If there is enough information, solve the problem.

(a)

(b)

(c)

(d)

(e)

3. Match the problem to the formula.

(a) 5 chocolate bars cost (b) 4 times a number (c) Area of a rectangle. £1.75. plus 7 equals 15.

Rule:

5 15

18

7 21

24

9

Rule:

2 1

2

6 3

4

10

Rule:

81 9

8

63

6

45 5

Rule:

1 12

22

3

4 42

5

Scenario Problem Algebraic sentence

Trucks have n wheels. How many wheels would 150 trucks have?

Mike has y sweets.He shares the sweets among 5 friends. How many sweets does each friend get?

Mary has x pencils.Her friend has three times that amount plus 4 more. How many pencils has her friend?

Jane had y CDs.She gave 12 of them to Chris. She then had 20. How many CDs had she at first?

Alex has £x He won £15 in a competition. He now has £45. How much money had he at first?

CHALLENGE

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TEACHER INFORMATIONA

Algebra

Oral work and mental calculation

• Verballymakeupwordproblemstogivennumbersentences involving formulae and equations. Work out the answers.

• Explaindifferentcalculationsthatcanbeusedtosolve the same problem. Discuss which calculation methods are preferred and why.

• Answergivenwordproblems,usingformulaeandequations to represent the information.

Interactive whiteboard activity

Interactive whiteboard activity available to support this copymaster. Visit www.prim-ed.com.

Main teaching activity

Formulae and equations (page 89)

Additional activities suitable for developing the objective

• Writewordproblemstogivennumbersentencesinvolving formulae and equations. Work out the answers.

• Writetwodifferentmethodsthatcouldbeusedtosolve the same word problem correctly. Work out the answers.

• Answergivenwordproblems,usingformulaeandequations to represent the information.

Answers

1. (a) 5 (b) 9 (c) 7 (d) 4 (e) 15 (f) 7 (g) 6 (h) 20

2. (a) (b) (c) (d)

(e)

3. (a)2n (b)n+2 (c)n–4 (d)2n÷4(e) n (f) 3n (g) 1/2n(orn÷2)

(h) Answers will vary, but one simple answer would be: n + n + 3n + 1/2n, (or 51/2n)

Challenge: Teacher check

5 8 813 16

29

9 8 617 14

31

7 8 415 12

27

3 7 910 16

26

8 6 414 10

24

ALGEBRA

Objective

• Usesimpleformulae.

Objective

Primary Maths Prim-Ed Publishing www.prim-ed.com 89

5 8

29

7 4

27

3 9

26

8 4

24

9 6

31

5 n 8

n + 5 n + 8

29

5 8 8

13 16

29

FORMULAE AND EQUATIONS

Representsinformationorunknownnumbersusingformulaeorequations.

Check your answers to Question 3 by substituting numbers for each letter ‘n’. Tick ( ) them if they are correct and cross ( ) them if they are incorrect. Redo the incorrect answers in a different coloured pen/pencil.

1 . Solve these equations.

(a) n + 7 = 12 (b) 3n = 27 (c) 2n + 4 = 18 (d) 5n = 20

n = n = n = n =

(e) n – 8 = 7 (f) 2n – 2 =12 (g) 7n = 42 (h) n – 4 = 16

n = n = n = n =

2. In these diagrams, the number in each box is made by adding the two numbers above it. Complete the missing numbers. Question (a) is done as an example. Follow the arrows.

(a) (n + 5) + (n + 8) = 29 5 + 8 = 13 29 – 13 = 16 2n = 16, :.n = 8

(b) (c) (d) (e)

3. Write simple algebraic formulae for these word problems. (a) Kelly has n apples. Priya has twice as many apples as Kelly.

How many apples does Priya have?

(b) Kelly is given 2 more apples. How many apples does she have altogether?

(c) Kelly gives away 4 apples. How many apples does she have left?

(d) Priya shares her apples equally between herself and 3 other friends. How many apples do they get each?

(e) John bakes n biscuits. He bakes the same amount of jam tarts as biscuits. How many jam tarts does John bake?

(f) John bakes 3 times as many muffins as biscuits. How many muffins does John bake?

(g) John bakes only half as many cup cakes as biscuits. How many cup cakes does John bake?

(h) How many items does John bake altogether? Try and write your answer as simply as possible.

apples

apples

apples

apples

jam tarts

muffins

cup cakes

CHALLENGE