Introducing the ratio symbol

1 Theratiosshowshadedpartstonon-shadedparts.

Matchtheratios,statementsandbarmodels.

2:3 fivetotwo

5:2 threetotwo

2:5 twotothree

3:2 twotofive

2

Whoiscorrect?

Explainyouranswer.

3 Danihassomecounters,cubesandmarbles.

Completethesentences.

Theratioofcounterstomarblesis :

Theratioofmarblestocubesis :

Theratioofcubestocountersis :

Theratioofcounterstocubesis :

Theratioofcounterstocubestomarblesis : :

4 Bretthasdrawnsometrianglesandsquares.

Theratiooftrianglestosquaresis1:3

a) Aretheremoretrianglesormoresquares?

Explainhowyouknow.

b) Bretthasdrawnmorethan10shapes.

DrawwhatBrettmighthavedrawn.

©WhiteRoseMaths2019

The ratio of purple to yellow is 5 : 4

It is 4 : 5

Mo Alex

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5 Herearesomerulersandsomepencils.

a) Whatistheratioofpencilstorulers? :

b) Herearesomemorerulersandpencils.

Whoiscorrect?

Explainyouranswer.

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6 Theratioofhorsestochickensinafieldis2:5

Herearethehorses.Drawthechickens.

7 Shadesquaressothattheratioofshadedtonon-shadedsquares

is1:4

a) b) c)

8 Aboxcontainsdark,whiteandmilkchocolates.

38

oftheboxaredarkchocolates.

12

oftheboxaremilkchocolates.

Therestarewhitechocolates.

Whatdoeseachratiorepresent?

a) 1:3

b) 4:1

c) 3:5

The ratio of pencils to rulers is the

same as in part a).

Ron is wrong because there are more pencils

and more rulers.

Ron

Dora

Calculating ratio

1 Evaisbakingcakesandcookies.

Forevery1cake,shewillbake2cookies.

a) IfEvabakes3cakes,howmanycookieswillshebake?

b) IfEvabakes10cookies,howmanycakeswillshebake?

2 Theratioofredtoyellowcountersis2:3

Thereare20countersintotal.

Howmanycountersofeachcolourarethere?

Youcancolourthecounterstohelpyou.

yellow red

3 Tomhas5greencubesforevery3yellowcubes.

Hehas16cubesintotal.

Drawadiagramtorepresentthis.

4 Estherisbuildingatowerofcubes.

Theratioofredtoyellowcubesis3:1

Thetowerhas6yellowcubes.Howmanyredcubesarethere?

5 Nijahplays21gamesofchess.

Forevery2gamesshewins,sheloses5games.

Howmanymoregamesdoesshelosethanwin?

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6 a) Huanismakingadrinkbymixing1partjuicewith5partswater.

Completethetabletoshowtheamountshewouldneedtouse.

Juice Water

1litre 5litres

2litres

4litres

100ml

200ml

300ml

30litres

750ml

b) Huanmakes1litre500mlofdrinkintotal.

Howmuchjuiceandwaterdoesheneedtouse?

juice water

©WhiteRoseMaths2019

7 AgroupofstudentsstudyFrenchorGermanintheratio3:7

a) Whichsubjecthasthemoststudents?

b) Drawadiagramtorepresentthis.

c) Thereare80studentsintotal.

HowmanymorestudentsstudyGermanthanFrench?

8 Describeasituationforeachbarmodel.

a) green

blue28

b)

green

blue

28

c) green

blue28

Compareanswerswithapartner.

Whatisthesameandwhatisdifferent?

Using scale factors

1 a)Hereisarectangle.

Drawanotherrectanglewhereeachsideistwiceasbig.

b) Hereisasquare.

Drawanothersquarewhereeachsideis4timesasbig.

2 a) Explainwhatitmeansforashapetobeenlargedbyascale

factorof2

b) Enlargetheshapesbyascalefactorof2

3 Completethesentence.

Ashapeinwhicheachsidehastripledinsizehasbeenenlargedby

ascalefactorof

©WhiteRoseMaths2019

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4 Hereisarectangle.

a) Measurethesidelengthsoftherectangleandlabelthemon

thediagram.

b) Enlargetherectanglebyascalefactorof3andlabelthe

sidelengths.

5 Thesidesoftherectangleareincreasedbyascalefactorof2

Whatistheperimeterofthenewshape?

cm

©WhiteRoseMaths2019

6 Theshapehasbeenenlargedbyascalefactorof112

Fillinthedimensionsofthenewshape.

7 TriangleAhasbeenenlargedbyascalefactorof5tomaketriangleB.

Findtheperimeterofeachtriangle.

perimeterofA= perimeterofB=

1cm

1cm

15cm

8cm

10cm

cm

cm

cm

14km

A

B75km

Ratio and proportion problems

1 Whitneybuys6cansoflemonadefor£3

a) Howmuchdo12canscost?

b) Howmuchdo3canscost?

c) Howmuchdo15canscost?

2 Theratioofredtogreengrapesinabowlis3:1

a) Explainwhatthismeans.

b) Thereare12moreredgrapesthangreengrapes.

Whatisthetotalnumberofgrapesinthebowl?

3 Amirismakingsomechocolatechipbiscuits.

Hehasthislistofingredientstomake6biscuits.

a) HowmuchofeachingredientdoesAmirneedtomake

2biscuits?

butter g plainflour g

sugar g chocolatechips g

b) HowmuchofeachingredientdoesAmirneedtomake

10biscuits?

butter g plainflour g

sugar g chocolatechips g

c) Amirhas240gofchocolatechips.

Whatisthemaximumnumberofbiscuitshecanmake?

©WhiteRoseMaths2019

£3

Chocolate chip biscuits (makes6)

120gbutter

72gsugar

180gplainflour

60gchocolatechips

A supporting video can be found at https://vimeo.com/432268751

4 Dexterhassome20pand50pcoinsinajar.

Foreverythree20pcoinshehasone50pcoin.

Thereare12coinsinthejarintotal.

Howmuchmoneyisinthejar?

5 Adrinkismadeusing3partsorangejuiceto2partslemonade.

Esthermakes1.2litresofthisdrink.

Howmuchorangejuicedoessheneed?

ml

6 Twoshopssellthesamecerealbutindifferent-sizedboxes.

Shop A

500gofcornflakes

£2.10

Shop B

750gofcornflakes

£3.30

Whichshopisbettervalueformoney? Shop

Explainwhy.

©WhiteRoseMaths2019

7 Doradrawstwosimilarrectangles.

Thelengthandwidthofbothrectanglesareevennumbers.

Whatisthelargestpossibleareaforthesmallrectangle?

cm2

8 Aishahastwoboxesofsweets.

• Inthefirstbox,theratioofredsweetstogreensweetsis3:1

• Inthesecondbox,forevery2orangesweetsthereare

3yellowsweets.

• Thereisthesamenumberofsweetsineachbox.

• Thereare12yellowsweetsinthesecondbox.

Howmanysweetsareinthefirstbox?

My larger rectangle is 4 times the size of the

smaller one.

The perimeter of the larger rectangle is 48 cm.