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2014 CurriculumPRIMARY

MATHS

Year 5Book 1 of 2

Resources and

teacher ideas for every objective

of the 2014 Curriculum

PM Year 5 Book 1 of 2.indd 1 26/11/2014 15:44:04

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

Foreword

Contents

Each book in the Primary Maths series includes:

• atleastoneactivitypageforeachobjectivewhichcan be photocopied or displayed on an interactive whiteboard

• comprehensiveteachersnotestoaccompanyeachactivity

• additionalteachersnotesonactivitiesandgames

• assessmentchecklists

• additionalphotocopiableresources

• interactivewhiteboardresourcesavailabletodownload.

The Year 5 books in the Primary Maths series are:

Primary Maths – Number

Primary Maths – Measurement, Geometry and Statistics

Teachers notes:How to use this book ....................................iv-vSetting up a maths classroom ............................... viActivities and games ........... viiAssessment checklists ...................... viii-xiiiAdditional resources ........................xiv-xix

Pupil activities with accompanying teachers notes:

Number and place value ................................2-27

Reading, writing, ordering and comparing numbers ............................2-11

Counting forwards and backwards ......................12-17

Negative numbers .......18-21

Rounding ........................22-25

Roman numerals ..........26-27

Addition and subtraction .................... 28-47

Formal written methods of addition ..........................28-29

Formal written methods of subtraction ...............30-33

Mental calculations ....34-41

Checking calculations using rounding .............42-43

Word problems .............44-47

Multiplication and division ...........................48-91

Multiples and

factors .............................48-53

Prime numbers .............54-55

Formal written methods of multiplication ..........56-61

Mental multiplication and division ...................62-67

Formal written methods of division ......................68-73

Multiplying and dividing by 10, 100 and 1000 ...74-79

Square and cube numbers .........................80-83

Word problems .............84-91

Fractions (including decimals and percentages)......... 92-131

Comparing and ordering fractions .........................92-93

Equivalent fractions ....94-95

Mixed numbers and improper fractions .......96-97

Adding and subtracting fractions .........................98-99

Multiplying fractions .................... 100-101

Decimals as fractions .....................102-107

Thousandths ..............108-111

Rounding decimals ..112-113

Reading, writing, ordering and comparing decimals .....................114-117

Decimal problems ... 118-123

Percentages ..............124-131

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

• number • measurement • geometry • statistics.

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

An icon denotes the curriculum strand for each activity.

Number

Measurement

Geometry

Statistics

Teachers notes

GGeometry

NNumber

MMeasurement

SStatistics

The Primary Maths series provides teachers with a number of varied and challenging activities. At least one activity, oftenmore,isprovidedforeachobjectiveofthePrimary 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.

• Someoftheactivitieshaveaccompanyinginteractivewhiteboardactivitiestohelpintroducethelessonandcapturepupils’ 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 40 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 15 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 theteacher with the focus of the activity. It is written in the form ofageneralobjective.

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

AssessmentAssessmentchecklistshavebeenincludedfortheYear5‘Number’objectives.Seepagesviii-xiii.Thesecanbeusedtoassess each pupil’s understanding of the key objectives covered.

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

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

• Interactivewhiteboardactivitieshavebeenprovidedtohelpteachtheobjectives.Thesecanbedownloadedfromwww.prim-ed.com.

Teachers notesHow to use this book

The objective tells the teacher which strand andobjective fromthePrimary 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 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 40 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 pagesAteacherspageaccompanieseachpupilworksheet.Itprovidesthefollowinginformation:

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

A summary of the tasks pupils will complete.

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

Teachers notesSetting 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’chart.

• Display a number line with positive and negativenumbers.

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

• Displayaplacevaluechart,fromhundredthousandthsto hundredths.

• Displayadditionandsubtractionfacts.

• Displaya100square.

• Ensureyouhaveagoodrangeofmathsgamesanduse them regularly.

• Providecalculators.

• Display‘timestables’charts.

• Haveananalogueanddigitalclockintheclassroom(12-hourand24-hour).

• Provideathermometer.

• Displaypicturesoflabelled2-Dand3-Dshapes.

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

• Provideprotractors,rulersandsetsquares.

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

• Allowpupilsopportunitiestoinvestigateoutsidetheclassroom in the school environment.

• Displayachartshowingsimpleequivalentfractions,decimals and percentages.

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

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

• Displayanduseacalendar.

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

• Displayapostershowingallcoinsandnotes.

• Providearangeofmeasuringequipmentforlength,mass and capacity.

• Displaytheeightcompassdirections.

• Displayapostershowingdifferentangles.

• Ensureyouhaveagoodselectionofinteractivemathsresources for use on a whiteboard (refer to www.prim-ed.comfordownloads).

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

Teachers notesActivities and games

• Play‘Bingo’toconsolidatebasicfactsetc.Varybycallingout the answer in some games and the number sentence or problem in others. Blank bingo cards are on page xix.

• Dividetheclassintoteamsandselectonepupilfromeach 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.

• GivedirectionsforpupilstotakeoutamountsofBase10 blocks 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.

Materials required

• placevalueblocks• interconnectingcubes• placevaluemats(seepagesxivandxv)• calculators• fractioncharts(seepagexviii)• abacus• tablescharts(seepagexvii)• 100schart(seepagexvi)• numberlines• bingocards(seepagexix)

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

AAssessment

Pupils’ names

Read

, writ

e, o

rder

and

com

pare

num

bers

to

at

leas

t 1

000

000.

Dete

rmin

e th

e va

lue

of e

ach

digi

t to

1

000

000.

Coun

t fo

rwar

ds in

ste

ps o

f po

wer

s of

10

for

any

num

ber

up t

o 1

000

000.

Coun

t ba

ckw

ards

in s

teps

of

pow

ers

of

10 f

or a

ny n

umbe

r up

to

1 00

0 00

0.

Inte

rpre

t ne

gativ

e nu

mbe

rs in

con

text

.

Coun

t fo

rwar

ds w

ith p

ositi

ve a

nd

nega

tive

who

le n

umbe

rs.

Coun

t ba

ckw

ards

with

pos

itive

and

ne

gativ

e w

hole

num

bers

.

Roun

d an

y nu

mbe

r up

to

1 00

0 00

0 to

th

e ne

ares

t 10

, 100

, 100

0, 1

0 00

0 an

d 10

0 00

0.

Solv

e nu

mbe

r pr

oble

ms

and

prac

tical

pr

oble

ms.

Read

Rom

an n

umer

als

to 1

000

(M).

Reco

gnis

e ye

ars

writ

ten

in R

oman

nu

mer

als.

KeyD = DemonstratedNFO = Needs further

opportunity

Year 5 Number and place value – assessment checklist

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

AAssessment

Pupils’ names

Add

who

le n

umbe

rs w

ith m

ore

than

fo

ur d

igits

usi

ng f

orm

al w

ritte

n m

etho

ds.

Subt

ract

who

le n

umbe

rs w

ith m

ore

than

fou

r di

gits

usi

ng f

orm

al w

ritte

n m

etho

ds.

Add

num

bers

men

tally

.

Subt

ract

num

bers

men

tally

.

Use

roun

ding

to

chec

k an

swer

s to

ca

lcul

atio

ns.

Solv

e ad

ditio

n m

ulti-

step

pro

blem

s in

co

ntex

t.

Solv

e su

btra

ctio

n m

ulti-

step

pro

blem

s in

con

text

.


opportunity

Year 5 Addition and subtraction – assessment checklist

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

AAssessment Year 5 Multiplication and division – assessment checklist 1

Pupils’ names

Iden

tify

mul

tiple

s.

Iden

tify

fact

ors.

Know

and

use

the

voc

abul

ary

of p

rime

num

bers

, prim

e fa

ctor

s an

d co

mpo

site

nu

mbe

rs.

Esta

blis

h w

heth

er a

num

ber

up t

o 10

0 is

prim

e.

Reca

ll pr

ime

num

bers

up

to 1

9.

Mul

tiply

num

bers

up

to f

our

digi

ts b

y a

one-

digi

t nu

mbe

r, us

ing

form

al w

ritte

n m

etho

ds.

Mul

tiply

num

bers

up

to f

our

digi

ts b

y a

two-

digi

t nu

mbe

r, us

ing

form

al w

ritte

n m

etho

ds.

Mul

tiply

num

bers

men

tally

, dra

win

g up

on k

now

n fa

cts.

Divi

de n

umbe

rs m

enta

lly, d

raw

ing

upon

kn

own

fact

s.

Divi

de n

umbe

rs u

p to

fou

r di

gits

by

a on

e-di

git

num

ber,

usin

g fo

rmal

writ

ten

met

hods

.


opportunity

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

AAssessmentYear 5 Multiplication and division – assessment checklist 2

Pupils’ names

Mul

tiply

who

le n

umbe

rs a

nd d

ecim

als

by 1

0, 1

00 a

nd 1

000.

Divi

de w

hole

num

bers

and

dec

imal

s by

10

, 100

and

100

0.

Reco

gnis

e an

d us

e sq

uare

num

bers

and

th

e no

tatio

n 2 .

Reco

gnis

e an

d us

e cu

be n

umbe

rs a

nd

the

nota

tion

3 .

Solv

e pr

oble

ms

invo

lvin

g m

ultip

licat

ion

usin

g fa

ctor

s, m

ultip

les,

squa

res

and

cube

s.

Solv

e pr

oble

ms

invo

lvin

g di

visi

on u

sing

fa

ctor

s, m

ultip

les,

squa

res

and

cube

s.

Solv

e pr

oble

ms

invo

lvin

g ad

ditio

n,

subt

ract

ion,

mul

tiplic

atio

n an

d di

visi

on,

and

a co

mbi

natio

n of

the

se.

Solv

e m

ultip

licat

ion

prob

lem

s in

volv

ing

scal

ing

by s

impl

e fr

actio

ns a

nd r

ates

.

Solv

e di

visi

on p

robl

ems

invo

lvin

g sc

alin

g si

mpl

e fr

actio

ns a

nd r

ates

.KeyD = DemonstratedNFO = Needs further

opportunity

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

AAssessment Year 5 Fractions (including decimals and percentages) – assessment checklist 1

Pupils’ names

Com

pare

and

ord

er f

ract

ions

who

se

deno

min

ator

s ar

e m

ultip

les

of t

he s

ame

num

ber.

Iden

tify,

nam

e an

d w

rite

equi

vale

nt

frac

tions

.

Reco

gnis

e m

ixed

num

bers

and

impr

oper

fr

actio

ns, a

nd c

onve

rt f

rom

one

to

the

othe

r.

Add

frac

tions

with

the

sam

e de

nom

inat

or, o

r m

ultip

les

of t

he s

ame

num

ber.

Subt

ract

fra

ctio

ns w

ith t

he s

ame

deno

min

ator

, or

mul

tiple

s of

the

sam

e nu

mbe

r.

Mul

tiply

pro

per

frac

tions

by

who

le

num

bers

.

Mul

tiply

mix

ed n

umbe

rs b

y w

hole

nu

mbe

rs.

Read

and

writ

e de

cim

al n

umbe

rs a

s fr

actio

ns.

Reco

gnis

e an

d us

e th

ousa

ndth

s an

d re

late

the

m t

o te

nths

, hun

dred

ths

and

deci

mal

equ

ival

ents

.


opportunity

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

AAssessmentYear 5 Fractions (including decimals and percentages) – assessment checklist 2

Pupils’ names

Roun

d de

cim

als

with

tw

o de

cim

al p

lace

s to

the

nea

rest

who

le n

umbe

r.

Roun

d de

cim

als

with

tw

o de

cim

al p

lace

s to

one

dec

imal

pla

ce.

Read

, writ

e, o

rder

and

com

pare

num

bers

w

ith u

p to

thr

ee d

ecim

al p

lace

s.

Solv

e pr

oble

ms

invo

lvin

g nu

mbe

r up

to

thre

e de

cim

al p

lace

s.

Reco

gnis

e th

e pe

r ce

nt s

ymbo

l (%

) an

d un

ders

tand

thi

s re

late

s to

‘num

ber

of

part

s pe

r hu

ndre

d’.

Writ

e pe

rcen

tage

s as

a f

ract

ion

with

de

nom

inat

or 1

00.

Writ

e pe

rcen

tage

s as

a d

ecim

al.

Solv

e pr

oble

ms

whi

ch r

equi

re

know

ledg

e of

per

cent

age,

dec

imal

and

fr

actio

n eq

uiva

lent

s.


opportunity

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

Place value mat

Hundred thousands

Ten thousands Thousands Hundreds Tens Ones

Teachers notes

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

Teachers notesPlace 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)

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

Teachers notes100 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

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

Teachers notesBasic 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

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

Teachers notesFraction chart

2

Equivalent fractions, decimals and percentages

Fraction Decimal Percentage1/4 0.25 25%

1/2 0.5 50%

3/4 0.75 75%

1/10 0.1 10%

2/10 0.2 20%

3/10 0.3 30%

4/10 0.4 40%

1/100 0.01 1%

99/100 0.99 99%

1/1 1 100%

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

Bingo cards (blank)

Teachers notes

TEACHER INFORMATION

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

MULTIPLICATION AND DIVISION

NNumber

Oral work and mental calculation• Estimateanswerstodivisionsumsusingrounding,

beforecompletingthem,asacheckingstrategy.

• Experimentwithdifferentpencilandpapermethods ofworkingoutdivisionproblems.Explainorallyhow methodswork.

• DemonstrateTU÷Usums,firstwithoutandthen withremainders.

• Explainthatwhencalculationsaresetoutin columns,tensshouldbeundertensandunitsunder units.

Main teaching activityShortdivisionwithremainders(page69)

Additional activities suitable for developing the objective• Estimateanswerstodivisionsumsusingrounding,


• Completea10x10multiplicationgrid.

• CompleteTU÷Usums,firstwithoutandthenwith remainders.

• SolvewordproblemsinvolvingTU÷U.

Answers 1. (a)12r2 (b)19r2 (c)12r1

(d)16r3 (e)12r3 (f)18r2

(g)19r2 (h)14r1

Challenge:

(a)11 (b)2

Objective• Dividenumbersupto4digitsbyaone-digitnumberusingtheformalwrittenmethodofshortdivisionand interpretremaindersappropriatelyforthecontext.

Primary Maths Prim-Ed Publishing www.prim-ed.com 69

NNumber

Objective

Work out the division problem on the back of this sheet. Sarah has 90 balloons. She shares them between 8 friends.

(a) Each friend gets balloons. (b) There are balloons left.

1. Useshortdivisiontosolvethesesums.

(f) 592 (g) 478 (h) 685

(a) 7 8 6

– (10x7)

– (2x7)

Answer= r

(c) 8 9 7

– (10x8)

– (2x8)

Answer= r

(b) 3 5 9

– (10x3)

– (9x3)

Answer= r

(d) 4 6 7

– (10x4)

– (6x4)

Answer= r

(e) 6 7 5

– (10x6)

– (2x6)

Answer= r

Example:89÷5

5 8 9

– 5 0 (10x5)

3 9

– 3 5 (7x5)

4

Answer= 17r4

SHORT DIVISION WITH REMAINDERS

• CompletesTU÷Udivisionsumswithremainders.

CHALLENGE

TEACHER INFORMATION



NNumber

Objective• Dividenumbersupto4digitsbyaone-digitnumberusingtheformalwrittenmethodofshortdivision.



• Experimentwithdifferentpencilandpapermethodsofworkingoutdivisionproblems.Explainorallyhowmethodswork.

• DemonstrateTU÷Usums,firstwithoutandthenwithremainders.ExtendtoHTU÷Usums.

• Explainthatwhencalculationsaresetoutincolumns,hundredsshouldbeunderhundreds,tensshouldbeundertensandunitsunderunits.

Interactive whiteboard activityInteractivewhiteboardactivityavailabletosupportthiscopymaster.Visitwww.prim-ed.com.

Main teaching activityDivision(page71)




• CompleteTU÷Usums,firstwithoutandthenwithremainders.ExtendtoHTU÷Usums.

• SolvewordproblemsinvolvingHTU÷U.

Answers 1. (a)23 (b)13 (c)16 (d)12 (e)43

(f)32 (g)6 (h)18 (i)13 (j)34

(k)26 (l)13 (m)14 (n)14 (o)23

(p)18 (q)17 (r)15 (s)14 (t)17

(u)29 (v)14 (w)16 (x)18 (y)12

2. (a)204 (b)230 (c)261 (d)130 (e)174

(f)121 (g)115 (h)131 (i)131 (j)171

(k)204 (l)131 (m)142 (n)81 (o)141

(p)91 (q)141 (r)131 (s)45 (t)31

(u)41 (v)226 (w)246 (x)48 (y)254

3. Teachercheck

Challenge: 174bananas


NNumber

Objective

348 bananas were shared evenly between two boxes. How many bananas went into each box?

Use multiples of the divisor to complete these division sums.

1. Solvethesetwo-digitdivisionproblemsusingmultiplesofthedivisor.

(a)369 (b) 565 (c) 464 (d) 784 (e) 286

(f) 396 (g) 954 (h)472 (i) 678 (j) 268

(k)378 (l) 791 (m)456 (n)342 (o) 492

(p)236 (q) 468 (r) 575 (s) 684 (t) 585

(u)387 (v) 798 (w)696 (x) 590 (y) 896

2. Dividethesethree-digitnumbers.Remembertousemultiplesofthedivisor.

(a)4816 (b) 3690 (c) 3783 (d) 5650 (e) 2348

(f) 8968 (g) 7805 (h)7917 (i) 6786 (j) 5855

(k)4816 (l) 7917 (m)3426 (n)5405 (o) 4564

(p)4364 (q) 5705 (r) 6786 (s) 6270 (t) 5155

(u)5205 (v) 4904 (w)3738 (x) 5240 (y) 3762

3. CheckyouranswerstoQuestions1and2withacalculator.Tickthosethatarecorrectandcrossthosethatareincorrect.Redothosethatarewrong.

Example: 1 4 4 5 6 – 4 0 (10 x 4) 1 6 10 + 4 = 14, so 56 ÷ 4 = 14 – 1 6 (4 x 4) 0

DIVISION

• Dividestwo–andthree-digitnumbersbyaone-digitnumber.

CHALLENGE

TEACHER INFORMATION



NNumber

Objective• Dividenumbersupto4digitsbyaone-digitnumberusingtheformalwrittenmethodofshortdivisionand

interpretremaindersappropriatelyforthecontext.



• Experimentwithdifferentpencilandpapermethodsofworkingoutdivisionproblems.Explainorallyhowmethodswork.

• DemonstrateTU÷Usums,firstwithoutandthenwithremainders.ExtendtoHTU÷Usums.

• Explainthatwhencalculationsaresetoutincolumns,hundredsshouldbeunderhundreds,tensshouldbeundertensandunitsunderunits.

Main teaching activityDivisionwithremainders(page73)




• CompleteTU÷Usums,firstwithoutandthenwithremainders.ExtendtoHTU÷U.

• SolvewordproblemsinvolvingHTU÷U.

Answers 1. (a)6r3 (b)16r1 (c)9r2

(d)4r2 (e)5r3 (f)9r2

(g)6r2 (h)6r3 (i)7r3

(j)16r4

2. (a)12r1 (b)9r1 (c)4r3

(d)17r1 (e)5r2 (f)12r1

(g)9r1 (h)8r5 (i)8r2

(j)17r3 (k)14r2 (l)33r1

(m)23r1 (n)16r1 (o)29r1

(p)10r4 (q)25r2 (r)13r5

(s)24r1 (t)10r4 (u)29r1

(v)19r3 (w)13r1 (x)10r6

3. (a)161r1 (b)219r1 (c)161r1

(d)121r2 (e)191r3 (f)112r1

(g)241r3 (h)121r1 (i)195r2

(j)356r1 (k)126r3 (l)133r3

(m)142r2 (n)146r1 (o)185r3

(p)271r2 (q)152r5 (r)127r4

(s)468r1 (t)129r3

Challenge: 157r1


NNumber

Objective

Mrs Smith had 472 blocks, which she divided into three containers.

How many blocks were in each container? r

A remainder is the number that is left over after the problem is complete.Remainder is represented by ‘r’.

1. Solvethesedivisionproblemswithremainders.

(a)27÷4= r (b) 33÷2= r

(c)47÷5= r (d) 26÷6= r

(e)38÷7= r (f) 29÷3= r

(g)50÷8= r (h) 57÷9= r

(i) 73÷10= r (j) 84÷5= r

2. Dividethesetwo-digitnumberswithremainders.Remembertousemultiplesofthedivisor.

(a) 337 (b) 546 (c) 627

(d) 235 (e) 947 (f) 785

(g) 328 (h)869 (i) 974

(j) 588 (k) 686 (l) 267 (m)493 (n)697

(o)388 (p) 994 (q) 377 (r) 796 (s) 497

(t) 774 (u)259 (v) 479 (w)679 (x) 886

3. Dividethesethree-digitnumberswithremainders.Remembertousemultiplesofthedivisor.

(a)2323 (b) 3658 (c) 4645 (d) 7849 (e) 5958

(f) 7785 (g) 4967 (h)8969 (i) 3587 (j) 2713

(k)4507 (l) 7934 (m)3428 (n)6877 (o) 4743

(p)3815 (q) 6917 (r) 5639 (s) 2937 (t) 6777

Example: 1 4 r 1 4 5 7 – 4 0 (10 x 4) 1 7 – 1 6 (4 x 4) 1

DIVISION WITH REMAINDERS

• Dividestwo–andthree-digitnumbersbyaone-digitnumbertosolveproblemswithremainders.

CHALLENGE

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