maths booklet-upper years

8/13/2019 Maths Booklet-Upper Years

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PrimaryEdition

ASpecialthankyoutoRockinghamLakesP.SinW.Awhodevelopedthisbooklet

UsingtheSMARTboardisagreattooltohelpme

countbackinonesfromthebiggest

number!

WhenIworkedout6+7Idecidedtotry

NearDoubling.Iknowthat6+6=12soI

addedon1fromthe7tomake13!

IcanuseSkipCountingtofind

outhowmuchmoneyIhave.10,

20,30,40


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2

UsingBasic Facts

21 2 > 22: 6 > 2525 7 > 31

RememberingBasicNumberFactshelpsustoworkwithnumbersquickerandwithease.Differentpeoplerememberdifferentnumber

facts.Howmanynumberfactscanyouremember?

91 31 > 211 71 51 > 211

39 29 > 21

2111 2111 >3111

41 81 > 21161 61 > 21136 36 > 61

3 3 > 53 y 3 > 5

6 y 5 > 314 4 > 7

41 26 > 26

86. 36 > 61

31 . 21 > 21

7 y 5 > 35 23 . 3 > 21


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3

Skip Counting

Countforwardsandbackwardsby2s3 5 7 9 21 23 25 27 29 31 33

Countforwardsandbackwardsby5s6 21 26 31 36 41 46 51 56 61 66 7176 81 86 91 96 :1 :6 211 216 221Countforwardsandbackwardsby10sstartingfrom

differentpoints21 31 41 51 61 71 81 91 :1 2119 29 39 49 59 69 79 89 99 :9 219Countforwardsandbackwardsby100s211 311 411 511 611 711 811 911

Letsskipcountby2s! 2468101214

1618

Wecanskipcountlotsofthingslikeourpencils,Lego, toys, counters


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4

Counting On

Countonbyonesfromthebiggestnumbertocalculateanadditionnumbersentence.

45 : > 5445 46 47 48 49 4: 51 52 53 54

9 68 > 7668 69 6: 71 72 73 74 75 76

78 24 > 978 79 7: 81 82 83 84 85 86 87 88 89 8: 91

9 8 > 269 : 21 22 23 24 25 26

Remembertolockthebiggestnumberinyourheadandthencarefullycountalongthenumberlineand

stopatthesecondnumber.26 7

26 27 28 29 2: 31 32

Keepthefirst

numberinyour

memory

Countalongthe

numberline6

spacesandthen

stop


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5

Counting BackCountbackbyonesfromthebiggestnumberto

calculateasubtractionnumbersentence.34 9 > 2634 33 32 31 2: 29 28 27 26

68 7 > 6268 67 66 65 64 63 62

79 23 > 6779 78 77 76 75 74 73 72 71 6: 69 68 67

232 23 > 2 :232 231 22: 229 228 227 226 225 224 223 222 221 21:Remembertolockthebiggestnumberinyourheadandthencarefullycountbackalongthenumberline

andstopatthesecondnumber.24 . 7

24 23 22 21 : 9 8

Keepthefirst

numberinyour

memory

Countbackalong

thenumberline6

spacesandthen

stop


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6

+ Addition +Grouping of Place Value

Separatenumbersintothousands,hundreds,tensandonesandthencalculatetheanswer

34 35 >31 4 31 5 >

51 8>58256 63 >

211 51 6 61 3>211 :1 8>2:8239 256 >

211 31 9 211 51 6>311 71 24>384Remembertoaddthehundreds,thetensandtheonestogether.Dontforgetanyofthenumbers!

PlaceValuecanbeusedasamentalmathsstrategybyitselfandwhenusingotherstrategieslikecountingon.


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7

- Subtraction -Grouping of Place Value

Separatenumbersintohundreds,tensandonesandthencalculatetheanswer.

56 43 > @ 5141> 21 21 4> 246. 3 > 451 6 413

:7 . 54 > @ :151> 61 61 4> 647. 4 > 4:1 7 514348 223 > @ 311211>211 211316> 23641. 21>31311418211213 8. 3> 6

2645 2432 > @21116114152111411312

2111. 2111 > 1611. 411 > 311 311 21 4> 32441. 31 > 215. 2 > 4


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8

Ten-Frames

+ Addition +Givesomefromonenumbertoanothertomake

easiernumberstoworkwith.9 8 jt 21 6 7 9 jt 21 5

Move5fromthe27tomake20.Thenadd20and22together.

Move2from7tothe8.Thiswillmake10. Move2fromthe6tothe8.Thiswillmaketen26 38 isthesameas 31 33 > 53


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9

DoublingWhenyoudoubleanumberyouaddittoitself.

Epvcmjoh 2 2 2 > 3 Epvcmjoh 3 3 3 > 5Epvcmjoh 4 4 4 > 7 Epvcmjoh 5 5 5 > 9Epvcmjoh 6 6 6 > 21 Epvcmjoh 7 7 7 > 23Epvcmjoh 8 8 8 > 25 Epvcmjoh 9 9 9 > 27Epvcmjoh : : : > 29 Epvcmjoh 21 21 21 > 31Epvcmjoh 22 22 22 > 33 Epvcmjoh 23 23 23 > 35

HalvingWhenyouhalveanumberyoubreakit

into2equalparts.Ibmg pg 3 > 2 Ibmg pg 5 > 3Ibmg pg 7 > 4 Ibmg pg 9 > 5Ibmg pg 21 > 6 Ibmg pg 23 > 7Ibmg pg 25 > 8 Ibmg pg 27 > 9Ibmg pg 29 > : Ibmg pg 31 > 21

Knowingthedoublesofnumbershelpsyoutohalvethemaswell.DoublingandHalvinghelpsusto

calculatemathsproblemsmorequicklybyusingdifferentmentalmathsstrategiesliketenframes

andbridging


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10

Use Counting On to Solve

SubtractionWecansolvesubtractionnumbersentencesbyCounting

Oninsteadofcountingback.SometimesCountingOnmakesiteasiertosolveasubtractionproblem.

28 . 25 > 4Jotufbe pg Dpvoujoh Cbdl

28 27 26 25 24 23 22 21 : 9 8 7 6 5 4ju jt fbtjfs boe rvjdlfs up Dpvou Po

Tubsu bu 25 boe tupq bu 2825 26 27 2836 . 27 > :

Jotufbe pg Dpvoujoh Cbdl36 35 34 33 32 31 2: 29 28 27 26 25 24 23 22 21 :Ju jt fbtjfs boe rvjdlfs up Dpvou Po

Tubsu bu 27 boe tupq bu 3627 28 29 2: 31 32 33 34 35 36

4: . 34 > 27Jotufbe pg Dpvoujoh Cbdl

4: 49 48 47 46 45 44 43 42 41 3: 39 38 37 36 35 3433 32 31 2: 29 28 27Ju jt fbtjfs boe rvjdlfs up Dpvou Po

Tubsu bu 34 boe tupq bu 4:34 35 36 37 38 39 3: 41 42 43 44 45 46 47 48 49 4:


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11

Number LinesWithNumberlines,wecanmakejumps

tosolve

number

problems.

1 2 3 4 5 6 78 9 : 21 22 23

51 52 5354 55 56 57 58 59 5: 61

WecanuseNumberLineswithothermathsstrategiessuch

as

tenframes)4*34 46 > jt uif tbnf bt 31, 49

Givethe3from23tothe35tomake38andthenimagineanumberlinebyaddingonthe20.

21 21

49 59 69)4*57 24 > jt uif tbnf bt 5: 21

Givethe3from13to46tomake49andthenimagineanumberlinebyaddingonthe10

21

5: 6:

237> 7Usingthenumberlinewecanstartat12andjumpback6numbers

togiveusananswerof6

619> 53Wecanalsojumpby

biggernumberstomakeitquickertofindthe

answer

6


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12

Number Combinations

NumberCombinations

work

together

to

make

mathsproblemseasier.Recognitionofnumbercombinationstotenmustbeautomatic

6 6 > 21 8 4 > 21 9 3 > 21 : 2 > 21 7 > 212: 2 > 31 24 8 > 31 23 9 > 31 22 : > 31 26 6>3136 36 > 61 46 26 > 61 56 6 > 61 31 41 > 61

BridgingWhenbridgingnumbersyouaddorsubtractfromthe

numbers

in

aproblem

to

make

it

easier

to

solve.

Bridgingtomultiplesof10helpstomakemaths

problemseasiertosolve.

45 39 >43 , )39 , 3* > 43 , 41 > 73

48 66>)4 , 48* , 63 > 51 , 63 > :3

Bridgeto30Take2from34andgive

it to 28

Bridgeto40Take3from55andgive

itto37


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13

x Multiplication x(Grouping)

Multiplyinginpartshelpsustoworkwithsmallernumbers.Ithelpsustousebasicnumberfacts

(timestables)andnumbercombinationstosolvemultiplicationproblems.

43 y 7 > 41y 7 > 291 boe 3 y 7 > 23 291 , 23 > 2:36 y 74 > 71y 6 > 411 boe 4 y 6 > 26 411 , 26 > 42634 y 29> 31 y 21> 311 boe 31y 9 > 271 311 , 271 > 471

4 y 21> 41 boe 4 y 9 > 35 41 , 35 > 65471 , 65 > 525Multiplyingmeanswecanalsohalveanddouble

numberstomakeiteasier.

35 y 7 ibmgpg 35 jt 23 23 y 7 > 83 83 , 83 > 255

29 y 8 ibmgpg 29 jt : : y 8 > 74 74 , 74 > 237

25 y 9 ibmg pg 25 jt 8 8 y 9 > 67 67 , 67 > 223

27 y 6 ibmgpg 27 jt 9 9 y 6 > 51 51 , 51 > 91


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14

Division (Sharing)

Immediaterecallofmultiplicationfacts(timestables)isessentialtosolvedivisionalgorithms.

23 4 > 5Weneedtofindouthowmanyitemsareineachgroupsowe

make3groupsandequallysharethe12items.

21 3 > 6Weneed2groupsand

Equallysharethe10items

29 7 > 4Weneed6groupsand

equallysharethe18items


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15

Number Families

Knowingtherelationshipbetweenadditionand

subtraction,division

and

multiplication,

helps

us

to

workwithnumberswhenwesolvenumberstories

andnumbersentences.

24 , 8 > 31 8 , 24 > 31 31 8 > 24 31 24 > 8

6 y 4 > 26 4 y 6 > 26 26 4 > 6 26 6 > 4

NumberFamilieshelpustosolvehiddennumberproblems39 . > 5 isthesameas39 5 >

67 > 232 isthesameas232 67 > 2: > 6 isthesameas2: 6 >

:y > 74 isthesameas74 : > 6 > 5 isthesameas5 y 6 >We

can

work

out

hidden

numbers

by

using

the

relationshipsbetweennumberoperations(+ x).


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16

65ismadeupofdifferentparts

Combination of NumbersNumbersaremadeupofpartstomakeawhole.Knowingthe

differentpartsofnumbershelpsustouseothermental

mathsstrategies

like

Place

Value,

Number

Families

and

Bridging.Itishelpfultoknowthecombinationsfornumbers

5,10,20,50and100.

2110ismadeupof

differentparts

: 2 > 21

4 8 > 213 >21

5 7 > 218 4 > 21

7 5 > 21 6 6 > 21

5 2 > 6

4 3 > 6 3 4 > 6

2 5 > 6


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17

Hidden Number StoriesReadthenumberstorycarefully.Highlighttheimportantmathswor

Writeoutthenumbersentenceusingthehighlightedwordstohelpy

Solvethehiddennumberbyaddingorsubtractingwiththenumbersyou

NumberStory NumberSentence MissMurrayhadsomefishinherfishtank.She

wentshoppingandbought7morefishandnowshehas18.HowmanyfishdidMissMurrayhaveto

beginwith?

8> 29

Miss

Lee

had

17pencils.

She

gavesomepencils

out

tothechildrenandnowsheonlyhas12left.How

manypencilsdidMissLeegiveouttothechildren?28. > 23

Samboughtsomelolliesfromshop.Shehad3bags

with4lolliesineachbag.HowmanylolliesdidSam

havealltogether?4y 5 >

MrsJones

had

12glitter

pens.

She

decided

to

share

thembetween3students.Howmanypensdideachstudentget? 23 4>

22

6

5

23


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18

Website

Go to

Lake Munmorah Public School websitewww.lakemunmor-p.schools.nsw.edu.au/

Click on KLAs

Click on Maths

Here you will find many interesting and fun activities for your children.

Games

If you need help working Maths into any of these games contact theschool and we will give you some ideas.

Snakes and Ladders

Cards

Trouble

Headache

Connect 4 Tick-tack toe

Battleship

Any dice game . You can always change the numbers on your diceor purchase ones with many numbers already on them.

First to 20 toss a dice and continue add the number you toss onyour next turn. (Make larger numbers for older children)


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GLOSSARYOther words for:

Addition plus Eg: 3 plus 2 equals 5

+ add on 3 add on 2 equals 5count on 3 count on 2 equals 5and 3 and 2 equals 5sum of The sum of 3 and 2 is 5

Subtraction take away Eg: 8 take away 5 equals 3

- minus 8 minus 5 equals 3subtract 8 subtract 5 equals 3less than 5 less than 8 is 3difference between The difference between

8 and 5 is 3

Multiplication lots of Eg: 3 lots of 5 equals 15

groups of

3 groups of 5 equals 15

times 3 times 5 equals 15multiplied by 3 multiplied by 5 is 15product of The product of 3 and 5

is 15

Division quotient of Eg:The quotient of 15 and 5

is 3divided by 15 divided by 5 is 3 is 5shared equally 15 shared equally

between 3 is 5how many groups of How many groups of 5 in

15 ? Answer 3


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NOTES

maths booklet-upper years

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