Post on 29-May-2018
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
.
KeyD = DemonstratedNFO = Needs further
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
.
KeyD = DemonstratedNFO = Needs further
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
.
KeyD = DemonstratedNFO = Needs further
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.
KeyD = DemonstratedNFO = Needs further
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,
beforecompletingthem,asacheckingstrategy.
• 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
70 www.prim-ed.com Prim-Ed Publishing Primary Maths
MULTIPLICATION AND DIVISION
NNumber
Objective• Dividenumbersupto4digitsbyaone-digitnumberusingtheformalwrittenmethodofshortdivision.
Oral work and mental calculation• Estimateanswerstodivisionsumsusingrounding,
beforecompletingthem,asacheckingstrategy.
• Experimentwithdifferentpencilandpapermethodsofworkingoutdivisionproblems.Explainorallyhowmethodswork.
• DemonstrateTU÷Usums,firstwithoutandthenwithremainders.ExtendtoHTU÷Usums.
• Explainthatwhencalculationsaresetoutincolumns,hundredsshouldbeunderhundreds,tensshouldbeundertensandunitsunderunits.
Interactive whiteboard activityInteractivewhiteboardactivityavailabletosupportthiscopymaster.Visitwww.prim-ed.com.
Main teaching activityDivision(page71)
Additional activities suitable for developing the objective• Estimateanswerstodivisionsumsusingrounding,
beforecompletingthem,asacheckingstrategy.
• Completea10x10multiplicationgrid.
• 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
Primary Maths Prim-Ed Publishing www.prim-ed.com 71
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
72 www.prim-ed.com Prim-Ed Publishing Primary Maths
MULTIPLICATION AND DIVISION
NNumber
Objective• Dividenumbersupto4digitsbyaone-digitnumberusingtheformalwrittenmethodofshortdivisionand
interpretremaindersappropriatelyforthecontext.
Oral work and mental calculation• Estimateanswerstodivisionsumsusingrounding,
beforecompletingthem,asacheckingstrategy.
• Experimentwithdifferentpencilandpapermethodsofworkingoutdivisionproblems.Explainorallyhowmethodswork.
• DemonstrateTU÷Usums,firstwithoutandthenwithremainders.ExtendtoHTU÷Usums.
• Explainthatwhencalculationsaresetoutincolumns,hundredsshouldbeunderhundreds,tensshouldbeundertensandunitsunderunits.
Main teaching activityDivisionwithremainders(page73)
Additional activities suitable for developing the objective• Estimateanswerstodivisionsumsusingrounding,
beforecompletingthem,asacheckingstrategy.
• Completea10x10multiplicationgrid.
• 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
Primary Maths Prim-Ed Publishing www.prim-ed.com 73
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