Solve two-step equations1wp2gx3v9tlj3j77py2y6x0f-wpengine.netdna-ssl.com/... · Solve two-step...
Transcript of Solve two-step equations1wp2gx3v9tlj3j77py2y6x0f-wpengine.netdna-ssl.com/... · Solve two-step...
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
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.
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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
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.
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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
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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.
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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 Esthercycles60milesover4days.
Onday1shecycles14miles.
Onday2shecycles32km.
Onday4shecyclestwiceasfarasshedoesonday3
Howfardoesshecycleonday4?
Giveunitswithyouranswer.
9 Useamapofyourlocalarea.
Findsomethingthatisapproximately:
a) 1mileawayfromyourschool
b) 1kmawayfromyourschool
c) 5milesawayfromyourschool
d) 5kmawayfromyourschool
Compareanswerswithapartner.
30
50