Solve two-step equations

1 Hereisapart-wholemodel.

a) Writeanequationforthepart-wholemodel.

b) Solvetheequationtoworkoutthevalueof

=

2 Ifeachmultilinkcuberepresentsx,formandsolveanequationto

findthevaluex.

x=

3 Thereisthesamenumberofcountersundereachcup.

Thereare16countersintotal.

a) Useytorepresentthenumberofcountersundereachcup.

Writeanequationintermsofy.

b) Solvetheequationtofindthevalueofy.

y=

c) Howmanycountersareundereachcup?

4 Writeanalgebraicequationtorepresenteachbarmodel.

Findthevaluesofaandb.

a) 21

a a 9

b)46

3b 10

a= b=

©WhiteRoseMaths2019

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20

5 Solvetheequations.

a) 5x+1=31 d) 9=2y+8

x= y=

b) 3x–3=9 e) 10g–2=46

x= g=

c) 4p–11=3 f) 4+3y=28

p= y=

6 Danithinksofanumber.

Shedoublesitandadds3

Shegetstheanswer15

a) WriteanequationtorepresentDani’sproblem.

b) Solvetheequationtofindhernumber.

©WhiteRoseMaths2019

7 Alexisyyearsold.

HerfriendBrettis3yearsolder.

Thetotaloftheiragesis25

HowoldareAlexandBrett?

Alexis Brettis

8

a) Workoutthecostofonebananaandoneorange.

Onebananacosts Oneorangecosts

b) Comparemethodswithapartner.

£1.52 £1.20

Find pairs of values (2)

1 Class6aretryingtosolveanumberpuzzle.

+ + =10

a)

DoyouagreewithDexter?

Explainwhy.

b)

WhatisthevalueofthecircleinDora’snumberpuzzle?

=

c) Findotherpairsofvaluesthatthetriangleandcirclecouldequal.

Findthreepairs.

= = = =

= =

2 aandbarewholenumbers.

2a+b=14

Completethetabletoshowdifferentpossiblevaluesforaandb.

a 0 1 2 3 4 5 6 7

2a 0 2

b 14

2a + b 14 14 14 14

3 canddarebothintegerslessthan15butgreaterthanzero.

3c–d=2

Completethetabletoshowdifferentpossiblevaluesforcandd.

c 1 2 3 4 5

3c 3

d 1

3c – d 2 2 2

b) Explainwhytherearenootherpossiblevaluesforcandd.

©WhiteRoseMaths2019

The triangle could be 3 and the circle could be 4

Dexter

The triangle is worth 4

Dora

4 xandyarebothmultiplesof5lessthan100

If2x=y,circlethepossiblevaluesofxandy.

5 Hereisarectangle.

xandyarebothintegers.

Therectanglehasaperimeterof28cm.

a) Writeanequationtorepresenttheperimeteroftherectangle.

b) Listallthepossiblepairsofvaluesforxandy.

Compareanswerswithapartner.Howdoyouknowyouhave

foundallthepossiblevalues?

©WhiteRoseMaths2019

6 Aishaisbuyingsomestationeryforschool.

Shespendsexactly£1

Listthepossiblecombinationsofpencils

andpensthatAishacouldhavebought.

7 Ronhasfourdigitcards.

• Twoofthecardshavethesamevalue.

• Allofthecardsarelessthan10butgreaterthanzero.

• Allofthecardsareodd.

• Thesumofthefourcardsis24

Findtwopossiblesetsofcards.

Set 1

Set 2

8

2ab=48

a) Findapairofpossiblevaluesforaandb.

a= b=

b) Workwithapartnertofindasmanypairsofvaluesasyoucan.

y

x

pen15p

pencil

10p

x=20,y=20

x=20,y=10

x=10,y=20

y=90,x=45

x=35,y=70

Convert metric measures

1 Howmanycentimetrecubescanyoufitalongametrestick?

Whatdoesthistellyou?

2 Completethesentences.

a) Thereare gramsin1kilogram.

Thereare kilogramsinonetonne.

b) Thereare millilitresin1litre.

c) Thereare millimetresin1centimetre

Thereare centimetresin1metre.

Thereare metresin1kilometre.

3 Completethebarmodels.

a)

1km 1km 1km 1km

1,000m 1,000m

Thereare min4km.

b)

1kg 1kg 1kg 1kg 1kg 1kg12kg

1,000g 1,000g 1,000g

Thereare gin612kg.

4 Completetheconversions.

a) 2kg= g b) 1l= ml

5kg= g 5l= ml

10kg= g 11l= ml

12kg= g

5 Abagofdogfoodweighs2.5kg.

Writethisweightingrams.

©WhiteRoseMaths2019

6 Whatmeasurementsarethearrowspointingto?

Labelthemonthenumberline.

0 21

0 5 131mm

cm

7 Completetheconversions.

a) 10mm= cm mm=1.1cm

11mm= cm mm=10.1cm

mm=11cm

b) 2.1km= m 2.01km= m

2.001km= m 2.011km= m

8 Write>,<or=tocompletethestatements.

a) 100m 1km b) 5.1l 5,100ml

10m 10cm 607l 0.607ml

10.1mm 101cm 0.05l 5ml

©WhiteRoseMaths2019

9 DoraandAmiraretryingtoconvert1.05metresintomillimetres.

Whodoyouagreewith?___________________

Explainyourthinking.

10 Whatisthemassofoneoftheboxes?

Giveyouransweringrams.

11 Thereare1,000kginonetonne.

a) Howmanygramsarethereinonetonne?

b) Acarweighs1.3tonnes.

Writetheweightofthecaringrams.

You can multiply 1.05 by 100 to convert it into centimetres, then

multiply the product by 10 to convert it into millimetres.

Dora

You can just multiply 1.05 by 1,000!

Amir

2 kg1 kg

Miles and kilometres

1 Tickthestatementsthataretrue.

Usethebarmodeltohelpyou.

1mile 1mile 1mile 1mile 1mile

1km 1km 1km 1km 1km 1km 1km 1km

a) 5 miles is approximately equal to 8 kilometres.

b) 1 mile is longer than 1 kilometre.

c) 2 kilometres is longer than 1 mile.

d) 2 kilometres is longer than 2 miles.

2 Fillinthemissingnumbersonthenumberline.

0

200 5

164

miles

km

3 Completetheconversions.

a) 5miles≈ kilometres b) miles≈16kilometres

10miles≈ kilometres mile≈1.6kilometres

15miles≈ kilometres miles≈0.8kilometres

4 Completetheconversions.

a) miles≈160km d) 95miles≈ km

b) 45miles≈ km e) 7.5miles≈ km

c) ≈640km f) 2miles≈ km

5

HereisWhitney’sworkingout.

5 miles ≈ 8 km

10 miles ≈ 13 km+ 5+ 5

ExplainWhitney’smistake.

©WhiteRoseMaths2019

If 5 miles is approximately 8 kilometres, then 10 miles is approximately 13 kilometres.

6 Amarathonisapproximately26.2miles.

Howfaristhisinkilometres?

7 Themaximumspeedlimitonresidentialroadsin

theUKis30milesperhour.

InFrance,themaximumspeedlimitonresidential

roadsis50kilometresperhour.

a) Whichcountryhasthehigherspeedlimitfortheseroads?

___________________

b) Whatisthedifferencebetweenthespeed

limitsinmilesperhour?

©WhiteRoseMaths2019

8 Esthercycles70milesover4days.

Onday1shecycles14miles.

Onday2shecycles32km.

Onday4shecyclestwiceasfarasshedoesonday3

Howfardoesshecycleonday4?

Giveunitswithyouranswer.

9 Useamapofyourlocalarea.

Findsomethingthatisapproximately:

a) 1mileawayfromyourschool

b) 1kmawayfromyourschool

c) 5milesawayfromyourschool

d) 5kmawayfromyourschool

Compareanswerswithapartner.

30

50

Family Challenge

Friday 19th June