white rose maths - alexandra.hounslow.sch.uk · solve two-step equations 1 here is a part-whole...
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White Rose MathsHome Learning Video Links
Year 6
Summer Term Week 8 (w/c 15th June)
Lesson 1
Solve 2-step equations https://vimeo.com/428002477
Lesson 2
Find pairs of values https://vimeo.com/428002579
Lesson 3
Convert metric measures https://vimeo.com/428002669
Lesson 4
Miles and kilometres https://vimeo.com/428002822
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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
40
20
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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
![Page 4: White Rose Maths - alexandra.hounslow.sch.uk · Solve two-step equations 1 Here is a part-whole model. a) Write an equation for the part-whole model. b) Solve the equation to work](https://reader033.vdocuments.net/reader033/viewer/2022052000/6012a52f5dc8df6149391ee0/html5/thumbnails/4.jpg)
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
40
20
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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
![Page 6: White Rose Maths - alexandra.hounslow.sch.uk · Solve two-step equations 1 Here is a part-whole model. a) Write an equation for the part-whole model. b) Solve the equation to work](https://reader033.vdocuments.net/reader033/viewer/2022052000/6012a52f5dc8df6149391ee0/html5/thumbnails/6.jpg)
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
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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
![Page 8: White Rose Maths - alexandra.hounslow.sch.uk · Solve two-step equations 1 Here is a part-whole model. a) Write an equation for the part-whole model. b) Solve the equation to work](https://reader033.vdocuments.net/reader033/viewer/2022052000/6012a52f5dc8df6149391ee0/html5/thumbnails/8.jpg)
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
a + 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
![Page 9: White Rose Maths - alexandra.hounslow.sch.uk · Solve two-step equations 1 Here is a part-whole model. a) Write an equation for the part-whole model. b) Solve the equation to work](https://reader033.vdocuments.net/reader033/viewer/2022052000/6012a52f5dc8df6149391ee0/html5/thumbnails/9.jpg)
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
![Page 10: White Rose Maths - alexandra.hounslow.sch.uk · Solve two-step equations 1 Here is a part-whole model. a) Write an equation for the part-whole model. b) Solve the equation to work](https://reader033.vdocuments.net/reader033/viewer/2022052000/6012a52f5dc8df6149391ee0/html5/thumbnails/10.jpg)
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
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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
![Page 12: White Rose Maths - alexandra.hounslow.sch.uk · Solve two-step equations 1 Here is a part-whole model. a) Write an equation for the part-whole model. b) Solve the equation to work](https://reader033.vdocuments.net/reader033/viewer/2022052000/6012a52f5dc8df6149391ee0/html5/thumbnails/12.jpg)
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
![Page 13: White Rose Maths - alexandra.hounslow.sch.uk · Solve two-step equations 1 Here is a part-whole model. a) Write an equation for the part-whole model. b) Solve the equation to work](https://reader033.vdocuments.net/reader033/viewer/2022052000/6012a52f5dc8df6149391ee0/html5/thumbnails/13.jpg)
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
![Page 14: White Rose Maths - alexandra.hounslow.sch.uk · Solve two-step equations 1 Here is a part-whole model. a) Write an equation for the part-whole model. b) Solve the equation to work](https://reader033.vdocuments.net/reader033/viewer/2022052000/6012a52f5dc8df6149391ee0/html5/thumbnails/14.jpg)
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.
![Page 15: White Rose Maths - alexandra.hounslow.sch.uk · Solve two-step equations 1 Here is a part-whole model. a) Write an equation for the part-whole model. b) Solve the equation to work](https://reader033.vdocuments.net/reader033/viewer/2022052000/6012a52f5dc8df6149391ee0/html5/thumbnails/15.jpg)
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
![Page 16: White Rose Maths - alexandra.hounslow.sch.uk · Solve two-step equations 1 Here is a part-whole model. a) Write an equation for the part-whole model. b) Solve the equation to work](https://reader033.vdocuments.net/reader033/viewer/2022052000/6012a52f5dc8df6149391ee0/html5/thumbnails/16.jpg)
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.
![Page 17: White Rose Maths - alexandra.hounslow.sch.uk · Solve two-step equations 1 Here is a part-whole model. a) Write an equation for the part-whole model. b) Solve the equation to work](https://reader033.vdocuments.net/reader033/viewer/2022052000/6012a52f5dc8df6149391ee0/html5/thumbnails/17.jpg)
6 Amarathonisapproximately26.2miles.
Howfaristhisinkilometres?
7 Themaximumspeedlimitonresidentialroadsin
theUKis30milesperhour.
InFrance,themaximumspeedlimitonresidential
roadsis50kilometresperhour.
a) Whichcountryhasthehigherspeedlimitfortheseroads?
___________________
b) Whatisthedifferencebetweenthespeed
limitsinmilesperhour?
©WhiteRoseMaths2019
8 Esthercycles60milesover4days.
Onday1shecycles14miles.
Onday2shecycles32km.
Onday4shecyclestwiceasfarasshedoesonday3
Howfardoesshecycleonday4?
Giveunitswithyouranswer.
9 Useamapofyourlocalarea.
Findsomethingthatisapproximately:
a) 1mileawayfromyourschool
b) 1kmawayfromyourschool
c) 5milesawayfromyourschool
d) 5kmawayfromyourschool
Compareanswerswithapartner.
30
50