Understand percentages

1 Completethesentenceforeachdiagram.

a) Thereare partsoutofa

hundredshaded.

Thisis %.

b) Thereare partsoutofa

hundredshaded.

Thisis %.

c) Thereare partsoutofa

hundredshaded.

Thisis %.

2 Completethetable.

Hundredsquare Percentage

82%

3 Shade15%ofthehundredsquarered.

Shade32%ofthehundredsquareblue.

Whatpercentageofthehundredsquareisnotshaded? %

©WhiteRoseMaths2019

©WhiteRoseMaths2019

4 a) Is1%ofthisbarmodelshaded?

1%

Explainyourreasoning.

b) Whatpercentageofeachbarmodelisshaded?

%

%

5 Passengersareboardingaplane.

Theplanehas100seats.

a) 10%oftheseatsarealreadyfull.

Howmanypassengersarealreadyontheplane?

b) 15%oftheseatshavenotbeenbooked.

Howmanyseatshavebeenbooked?

c) Howmanypassengersstillneedtoboardtheplane?

6 Dexterhas£1tospend.

Hebuyssomestickers.

WhatpercentageofhismoneydidDexterspend?

%

7 AishaandBretthavebeensellingticketsfortheschoolplay.

Thereare100seatsavailable.

• OnMondaytheysold34%ofthetickets.

• OnTuesdaytheysold42tickets.

• BytheendofWednesday,95%oftheticketshadbeensold.

HowmanyticketsdidtheysellonWednesday?

OnWednesdaytheysold tickets.

8 Shade85%ofthisbarmodel.

Compareanswerswithapartner.

I got 35p change.

Goo

d Work

Excellent

W

ell Done

VERY G OO

D

GREAT

W

hat a Star

WELL

DONE

Percentages as fractions and decimals

1 Herearefourhundredsquares.

A C

B D

Completethetable.

Hundredsquare

Percentage Fraction Decimal

A52

100

B

C

D

2

Provethat0.2isequalto20%.

Youmayusethehundredsquaretohelpyou.

Whydoyouthinksomepeoplethinkthat0.2isequalto2%?

3 Completethefraction,decimalandpercentageequivalents.

a) 32%=100

=

35%=100

=

48%=100

=

b) 17100

= %=

9100

= %=

90100

= %=

©WhiteRoseMaths2019

c) 0.29= %=100

0.71= %=100

0.03= %=100

©WhiteRoseMaths2019

4 Write<,>or=tocompletethestatements.

a) 50%5

100 d)40

100 40%

b) 25%50100 e)

70100 7%

c) 14%41100 f) 82%

82100

5 Writethevaluesinorderfromsmallesttogreatest.

a) 33%301003%

13100

b) 299%911009%

910

c) 2.52510025025%of100

251000

6 Convertthefractionstohundredths.

Completethedecimalandpercentageequivalents.

a) 150300=

100= = %

b) 25500=

100= = %

c) 48300=

100= = %

d) 1850=

100= = %

e) 1325=

100= = %

7 Circleallthefractionsthataregreaterthanorequalto50%.

1050

45

50100

3080

150

70140

8 JackandDoragoshoppingwiththesameamountofmoney.

Jackspends13ofhismoney.

Doraspends30%ofhermoney.

a) Whospendsmoremoney?

Usefractionandpercentageequivalencetoexplain

youranswer.

b) JackandDoraeachstartedwith£300

Howmuchmoneydotheyeachhaveleft?

Jack Dora

Read and interpret line graphs

1 Thegraphshowstheheightofasunfloweronthe

firstdayofeachweekfor6weeks.

a) Whatistheheightofthesunfloweratthe

startofweek3?

b) Whatistheheightofthesunfloweratthe

startofweek2?

c) Evathinkstheheightofthesunfloweratthestartofweek4is

75cm.ExplainwhyEvaiswrong.

d) Byhowmuchdoesthesunflowergrowfromthe

startofweek3tothestartofweek6?

2 Thegraphshowsthepopulationofatownattheendofeach

decadefrom1950to2000

a) Whatwasthepopulationattheendof1980?

b) Whatwasthepopulationattheendof2000?

c) Canyouaccuratelytellthepopulationin1991?Why?

d) Whichdecadehadtheleastpopulationincrease?

e) Predictthepopulationattheendof2020

Compareanswerswithapartner.

©WhiteRoseMaths2019

00

10

20

30

40

50

60

70

80

90

1 2 3 4 5 6week

hei

gh

t (c

m)

1950

0

2,000

4,000

6,000

8,000

10,000

12,000

1960 1970 1980 1990 2000 2010 2020

year

po

pu

lati

on

©WhiteRoseMaths2019

3 ThisgraphshowstheaveragerainfallinLondonandManchesterto

thenearest5mm.

a) HowmanymillimetresofrainfallsinLondoninMay?

b) WhichmonthsarethedriestinManchester?

c) WhichisthewettestmonthinLondon?

d) InJanuary,howmuchmorerainfallistherein

ManchesterthanLondon?

e) Howmanymonthsdoesitrainmorethan50mmin

LondonandManchester?

f) HowmuchmorerainfallisthereinManchester

thanLondoninDecember?

4 EnergyismeasuredinkWh(kilowatthours).

Thisgraphshowstheamountofenergybeingusedatdifferent

timesoftheyearinonehousehold.

Describethreethingsthatyouknowfromlookingatthegraph.

Describethreethingsthatyoucouldfindoutfromthegraph.

0

20

40

60

80

100

10

30

50

70

90

months of the year

London

Manchester

rain

fall

(mm

)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

0

1,000

2,000

3,000

500

1,500

2,500

months of the year

am

ou

nt

of

ener

gy

use

d (

kWh

)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Use line graphs to solve problems

1 Thisgraphshowshowmanymilesanaeroplanehasleftto

traveleachhouronitsjourneyfromLondontoNewYork.

a) Howmanyhoursistheflight?

b) HowmanymilesisthejourneyfromLondon

toNewYork?

c) After4hours,howmanymoremilesare

lefttotravel?

d) Howlongdoesittaketoflythefinal1,000miles?

e) Howmanymilesdoestheplanetravelbetween

2hoursand4hoursintotheflight?

f) Estimatehowfartheplanehastravelledafter

3hoursand30minutes.

2 Thegraphshowstherainfallinthefirst8daysinOctober.

a) Howmanymillimetresofrainfellonthe

7thOctober?

b) It rained every day in the first 8 days in October.

Isthisstatementcorrect?

Explainyouranswer.

c) TherecordamountofrainfallforOctoberis2.5cm

Hasanewrecordbeenset?

Explainyouranswer.

©WhiteRoseMaths2019

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8

day

rain

fall

(mm

)

00

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

1 2 3 4 5 6

flight time (hours)

dis

tan

ce le

ft t

o t

rave

l (m

iles)

7

©WhiteRoseMaths2019

3 Thisgraphshowstheconversionbetweenmilesandkilometres.

a) Howmanykilometresaretherein50miles?

b) Howmanymilesaretherein130km?

c) Explaintoapartnerhowyouworkedouttheanswersto

parta)andb).

d) Evacycles60miles.

Dextercycles80km.

Whocyclesthefurthest?

Howmuchfurtherdoesthepersoncycle?

e) Ronwantstoconvert800kmintomiles.

Ronisincorrect.Explainwhy.

Completetheconversion.

Showyourworking.

800km= miles

f) Ahigh-speedtraincantravelupto400kminanhour.

Howmanymilescanittravelinanhour?

0miles

10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

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90

100

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160ki

lom

etre

s

I can’t do it because my graph doesn’t

go high enough.