length, perimeter and area - · pdf file• travelling far_____ 9 • perimeter ......

Student BookSERIES

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Length, Perimeter and Area

Teacher BookSERIES

F


Copyright ©

Series F – Length, Perimeter and Area

Contents

Topic 1 – Units of length (p. 1 - 8)• m, cm, mm ___________________________________________

• findandorderlength ___________________________________

• metrestokilometres ___________________________________

• spotthedistance–apply ________________________________

• wordproblems–solve__________________________________

Topic2–Travellingfar(p.9-16)• measuredistances _____________________________________

• mapsandscale _______________________________________

• speedanddistance ____________________________________

• flagit!–apply ________________________________________

• the city to school – create _______________________________

Topic3–Perimeter(p.17-24)• perimeterofshapes____________________________________

• calculateperimeter ____________________________________

• constructshapes ______________________________________

• perimeterproblems–solve ______________________________

• moreperimeterproblems–solve _________________________

Topic4–Area(p.25-32)• introducingarea _______________________________________

• areaoftriangles _______________________________________

• hectaresandsquarekilometres __________________________

• areaandperimeter ____________________________________

• areapuzzles–solve ____________________________________

• compositecalculations–apply ___________________________

Date completed

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Series Authors:

Rachel Flenley

Nicola Herringer

Please note: Thesepageshavebeendesignedtoprintto‘shrinktoprintablearea’asthisisacommondefaultsettingonmanycomputers.Theremaybeminordiscrepancieswithmeasurementsasindividualprintersandphotocopiersprinttoslightlydifferentproportions.

Copyright ©


Contents

Section1–Answers(p.1-32)• units of length ______________________________________ 1

• travellingfar ________________________________________ 9

• perimeter __________________________________________ 17

• area ______________________________________________ 25

Section2–Assessmentwithanswers(p.33-42)• units of length ______________________________________ 33

• travellingfar ________________________________________ 35

• perimeter __________________________________________ 37

• area ______________________________________________ 39

Section3–Outcomes(p.43-44)

Series Authors:

Rachel Flenley

Nicola Herringer

Please note: Thesepageshavebeendesignedtoprintto‘shrinktoprintablearea’asthisisacommondefaultsettingonmanycomputers.Theremaybeminordiscrepancieswithmeasurementsasindividualprintersandphotocopiersprinttoslightlydifferentproportions.

SERIES TOPIC

1F 1Copyright © 3P Learning


Estimate and then measure these lengths. Which unit will you use?

Object Estimate Measure

a Heightofadesk

b Shouldertothefingertips

c Widthofthedoor

d Handspan

e Pencilsharpener

f Widthofafingernail

g A4paperlength

a

20

d

13

b

14

e

2

c

4

f

28

Complete the measure of each item below by adding either mm, cm or m next to the number:

Theseunitsofmeasurementareused regularlyineverydaylife.

10 mm = 1 cm 100 cm = 1 m 1000m =1km

Units of length – m, cm, mm

2

1

It makes sense to say 3 metres instead of 300 centimetres.

cm

cm

mm

m

m

mm

Answers will vary.

SERIES TOPIC

F 12Copyright © 3P Learning


0 cm 51 6 102 7 113 8 12 14 154 9 13

Convert these lengths to metres:

Convert these lengths to metres:

Convert these lengths to centimetres:

Convert these lengths to millimetres:

Thisconversionboxcanhelpyou convertunitsoflength.

4

5

3

6

m mmcm

× 100

÷ 100

× 10

÷ 10

× 1 000

÷ 1 000

Units of length – m, cm, mm

To convert from mm to cm, divide by 10.

To convert from cm to mm, multiply by 10.

To convert from mm to m, divide by 1 000.

a 5cm = mm

d 7cm = mm

b 3 cm = mm

e 11 cm = mm

c 9cm = mm

f 15cm= mm

a 50mm = cm

d 15mm = cm

b 20 mm = cm

e 156mm = cm

c 223 mm = cm

f 495mm = cm

a 300 cm = m

d 900cm = m

b 500cm = m

e 2 000 cm = m

c 250cm = m

f 4550cm= m

a 1 000 mm = m

c 4500mm= m

b 5000mm= m

d 500mm = m

50

5

3

1

70

1.5

9

4.5

30

2

5

5

110

15.6

20

0.5

90

22.3

2.5

150

49.5

45.5

SERIES TOPIC



Look carefully at how each shape is divided and find the missing length:

a

b

c

d

Units of length – find and order length

1

Don’t forget to check your answers match the units.

1 m

30 cm cm

3 m

150cm cm

200 cm

60cm cm

100 cm

30 cm 20 cmm

Convert all the lengths to the same unit.

70

150

140

0.5

SERIES TOPIC



Mr Marlowe’s class went on an excursion to the circus. He asked his students to guess the height of a clown on stilts. Fill in the missing heights:

Here is a list of some objects and their heights. Put them in order from shortest to tallest:2

3

door

flagpole

fridge

ladybird

tree

giraffe

1.95m

16m

145cm

2 mm

11 m

457cm

1 ______________________

2 ______________________

3 ______________________

4 ______________________

5 ______________________

6 ______________________

Shortest

Tallest

Name Height of the Clown on Stilts

Peter 3 m 30 cm 3.3 m

Sara 415cm 4.15m

Omar 3m64cm 3.64m

Julia 397cm 3.97m

Heba 4m9cm 409cm

It turned out that the clown was 3 m and 58 cm tall.

a Whohadtheclosestguess? _______________

b Howfaroffwasthisperson? _______________

c Whatwasthedifferencebetweenthehighestandthelowestguess? _______________

d Writeyourheightandfindthetwopeopleinyourclasswhoareclosesttoyourheight.

Units of length – find and order length

ladybird

fridge

door

giraffe

tree

flagpole

330 cm

4 m 15 cm

364 cm

3 m 97 cm

4.09 m

Omar

6 cm

85 cm

Answers will vary.

SERIES TOPIC



a

d

b

e

c

f

a

d

b

e

c

f

Whichunitsofmeasurementdowealreadyknowabout?

1km =1000m

1m =0.001km

100m =0.1km

Units of length – metres to kilometres

Write these lengths in kilometres:

Write these lengths in metres:

Which is shorter? Circle the shorter distance:

Which is longer? Circle the longer distance:

2

Would you use metres or kilometres to measure the following lengths?1

a Driveway

c Heightofyourhouse

e DistancefromEarthtotheMoon

b DistancefromMelbournetoSydney

d Amarathonrace

f Distancearoundtheschooloval

2kmor2220m

300kmor2500m

0.58kmor600m

0.85kmor800m

3.2kmor3100m

1900mor2.9km

0.75kmor0.79km

1.58kmor1600m

560mor0.565km

855mor0.875km

5.5kmor5600m

7.25kmor7200m

3

4

5

To convert from km to m, multiply by 1 000. To convert from m to km, divide by 1 000.

a 2 000 m = km

d 1500m = km

b 5000m = km

e 3645m = km

c 8 000 m = km

f 1747m = km

a 3km = m

d 0.5km= m

b 7km = m

e 3.7km= m

c 4km = m

f 8.2km= m

2

1.5

3 000

500

7 000

3 700

4 000

8 200

5

3.645

8

1.747

m

m

km

km

km

m

SERIES TOPIC



Fill in the boxes to answer these word problems:

a Abdulwalked0.4ofakilometre,Sarawalked20metresandKaitlynwalkedhalfakilometre.Writetheirnamesintheboxesbelowtoshowhowfareachofthemwalked.

b Ina10kmfunrunevent,Omarstoppedafter612 km,Peterstoppedafter8000mandHeidistopped

10mbeforetheend.Writetheirnamesintheboxesbelowtoshowhowfareachofthemran.

c Lengwalked250mtothebusstop,andthenrodethebusfor3kmtothebeach.Whenshearrivedatthebeachshewentfora4kmjogbythesea.

How many metresdidshetravelaltogether?

km + km + km = m

7

Mark these lengths in metres on the line below. The first one has been done for you.6

0km 1km

0km 10km

100 m

1000metres600metres

0km 1km

200metres400metres 800metres100metres

Units of length – metres to kilometres

I have to convert here!

200 m

400 m 600 m 800 m 1 000 m

Abdul

Kaitlyn

Peter

Omar Heidi

Sara

0.25 43 7 250

SERIES TOPIC



What to do

Spot the distance apply

Thisisanestimatinggamefortwoplayers.

•Thefirstplayerchoosestwospots.

•Thesecondplayerestimatesthedistancebetweenthespotsinmm.Measurefromeachspot’sedge.

•Thesecondplayerdrawsalinebetweenthespotsandthenmeasuresthedistancewiththeirruler.Theyscore100pointsfortherightanswer,40pointsforanestimatewithin10mm,and20pointsforanestimatewithin20mm.

•Thesecondplayerpickstwospotsforthefirstplayer.

•Theplayerwiththemostpointsafter10roundswins!

1 2

3

4

6

9

7

5

8

10

12

15

13

14

11

SERIES TOPIC



a Ifthereare60brochuresinastackandeachofthemare8mmthick,howhighisthestack?

b Aplankofwoodis5mlong.If150cmissawnoff,howmuchisleft?

c Howmany20mmpiecesofgoldwirecanbecutfrom1m?

d Ifafingernailgrows2mmaweek,howmanycmwoulditgrowin1year?

e OnedayIbought3sherbetsticks.Theirlengthswere0.75m,50cmand75cm.Whatwasthetotallength?Ifsherbetstickscost$2ametre,howmuchdidIspend?

What to do

Word problems solve

60 × 8 mm = 480 mm or 48 cm

5 m = 500 cm

500 cm – 150 cm = 350 cm

52 weeks in a year × 2 = 104 mm or 10.4 cm

0.75 m + 0.5 m + 0.75 m = 2 m of sherbet stick

2 × $2 = $4

1 m = 1 000 mm

1 000 mm ÷ 20 mm = 50 pieces

SERIES TOPIC

9FCopyright © 3P Learning

Length, Perimeter and Area 2

a SunsetCovetoSandyBeach km

b MelodyPointtoSharkCliff km

c RecklessRockstoLagunaBeach km

d MelodyPointtoSandyBeachviaSharkCliff km

e LagunaBeachtoSharkCliffviaMelodyPoint km

Travelling far – measure distances

Write these distances in decimal notation:

Write these distances in metres:

Look carefully at Mermaid Island and work out how long these walking trails are. Record all answers in kilometres.

1

2

3

Shark Cliff

Sandy BeachSunset Cove

Reckless Rocks

Laguna Beach

Melody Point1245m

1572m

980m390m

415m712m

To convert from m to km, divide by 1 000.

a 2km123m = km

c 2km245m = km

e 8km145m = km

g 835m = km

b 4km235m = km

d 5km235m = km

f 8km23m = km

h 593m = km

a 3.6km = m

d 9.3km = m

g 5.6km = m

b 2.8km = m

e 8.2km = m

h 0.2km = m

c 0.6km = m

f 7.1km = m

i 0.1km = km

2.123

2.245

8.145

0.835

4.235

5.235

8.023

0.593

3 600

9 300

5 600

2 800

8 200

200

600

7 100

100

0.98

1.572

0.712

1.962

2.817

SERIES TOPIC

F10Copyright © 3P Learning

Length, Perimeter and Area2

Roadmapssometimeshavethedistancebetweentownswrittenontheroadthatconnectsthem.Thisinformationhelpsyouplanyourjourney.

Travelling far – measure distances

Here is a page from Hannah’s journal where she has noted the places she went to during a road trip with her family. Add the distances that they travelled each day.

What is the total distance that Hannah and her family travelled? Show all of your working below. km

4

5

Scarborough

Lexia96 km

285 km142 km520 km

340 km

218 km336 km

Brighton

MullalooHastings

Doubleview Woodvale Embleton

Day 1TodaywelefthomeatDoubleviewanddrovestraighttoHastings. km

Day 2WeleftHastingsafterbreakfastthenwehadlunchinMullaloo.WestayedthenightinBrighton. km

Day 3WedrovetoEmbletontofindoutaboutgettinganewpuppy! km

Day 4WehadtoleaveearlythismorningasitturnsoutthepuppywewantisinLexia. km

Day 5Ournewpuppyisagirl!WenamedherLexie,afterthetownshecamefrom.WedecidedtotraveluptoScarboroughtoshowLexietoourcousins. km

Day 6TodaywedroveallthewayfromScarboroughtoWoodvale.Dadwantedtokeepgoingtillwegothomebutmummadehimstop. km

Day 7Todaywedrovetherestofthewayhome. km

420 km

340

662

336

621

96

935

420

3 410

SERIES TOPIC



Now, suppose the scale is 1 cm = 1 km. What is the shortest distance by road from:

a thefirestationtothepark? km

b theparktohome? km

c hometotheshop? km

Scaleisusedtoshowlongdistancesonamap.Thismakesiteasierforustotranslatedistanceonamaptodistanceintherealworld.

Travelling far – maps and scale

What is the shortest distance by road from:

a hometoschool? m

b hometothepark? m

c thefirestationtotheshop? m

d theschooltothefarm? m

e hometotheshop? m

f Drawyourownrouteonthemap.Whichlandmarksdoyougopast? _______________________________________________________

Whatisthetotaldistanceofyourroute?

1

2

Use this map to answer the questions below. Look carefully at the scale.

1 cm

schoolhome

fire station

park

shop

farm

1 cm = 100 m

SCALE:

400

800

700

1 000

800

Teacher check

Teacher check

3

8

8

SERIES TOPIC



Complete this table using a scale of 1 cm = 6 m:

Use this map* of a train route to answer the questions using this scale 4 cm = 10 km:

Complete this table using a scale of 1 cm = 3 cm:

Use the scale of 1 cm = 2 m to draw these lines in the boxes:3

4

5

6

Scale length in cm 2 5 15 4 6 9 10 8 12 7

True length in cm

Scale length in cm 5 10 15 7 12 9 11 2 8 6

True length in m

a WhatisthedistancefromStop1toStop2? km

b WhatisthedistancefromStop4toStop5? km

c WhatisthedistancefromStop2toStop5? km

d Whatisthetotaldistanceofthistrainroute? km

Stop 1Stop 2

Stop 3Stop 4

16 cm

4 cm 4 cm

8 cm

20 cmStop 5 Stop 6

Travelling far – maps and scale

*Not drawn to scale.

a 22 m

b 16m

c 9m

40

20

40

130

6 15 45 12 18 27 30 24 36 21

30 60 90 42 72 54 66 12 48 36

SERIES TOPIC



If a car travelled 950 km in 10 hours, show how long it took to travel half way:

If a car travelled 560 km in 8 hours, work out how far it travelled in half an hour and in 4 hours:

If a car travelled 300 km in 6 hours, work out how far it travelled in 2 hours and in 3 hours:

Look at these distances and the time it took. Work out the speeds. Express your answer as km/h:

Travelling far – speed and distance

Speedcanbemeasuredinkilometresperhour.60kmperhourmeansthatittakes1hourtotravel60kmandiswrittenas60km/h.

1

2

3

4

0km

0km

560km

0km 300km

2hours

halfanhour

3hours

4hours

hours 10hours

1hr=__________

1hr=__________

1hr=__________

To work these out, you need to first calculate what can be covered in 1 hour and then multiply and divide as needed.

a 76kminanhour = km/h

c 100kmin2hours = km/h

e 180kmin3hours = km/h

b 82kminanhour = km/h

d 130kmin2hours = km/h

f 240kmin4hours = km/h

8hours

6hours

950kmkm

76

50

60

82

65

60

100 km 50 km150 km

35 km 280 km 70 km

95 km

475

5

SERIES TOPIC



Travelling far – speed and distance

If a snail travels 6 mm in 10 minutes, how far will it travel in 1 hour?

If a car was travelling 60 km/h, how far would it have travelled after 10 minutes?

Harriet walks at a speed of about 4 km/h. How long would it take for her to walk 20 km?

If a truck was travelling 80 km/h, how long would it take for a truck to travel 560 km?

Rahed is training for a 40 km marathon. He runs at an average speed of 6 minutes a km. What time can he expect to finish the marathon in?

5

6

7

8

9

You need to convert the total minutes into hours.

36 mm

10 km

5 hours

7 hours

240 minutes or 4 hours

SERIES TOPIC



Usethespacebelowtoshowyourrouteandcalculatethedistanceyoucoverbetweentowns.

What to do next

What to do

Getting ready

Flag it! apply

90

85

25

60

115

40

40

40

40

50

140

35

50

20

20

30

Olinda Echoville

Stoling

York

Chelsea

Milltown

Bontern

A

BRainbow Point Flagstuff

Trenton

Simonstown

Onyourmarks,getset,go!Youareabouttoparticipateinaracetocollectasmanyflagsaspossibleinlessthan400km.

1 StartatPointA.

2 WorkouthowyouwillgettoPointBcollectingasmanyflagsasyoucanatvarioustownsalongtheway.Useacalculatortohelpyouaddthedistances.

3 Youneedtodecideonyourroute.Youmaynotexceed400km.

Answers will vary.

SERIES TOPIC



What to do next Onceyouthinkyouareready,submityourplanstoyourteacher.Stageyourevent.

Askyourteacherandtheothergroupsfortheirfeedback.

What to do

Getting ready

The City to School create

Yourgrouphasbeenhiredbyyourfavouritecharity toorganisea1kmfunrunatyourschool.

Youwillplanandmeasureoutthecourseandthen getanothergrouptotestoutyourrun.

Therunneedstobeexactly1kilometreinlength. You’llneedmarkersateach100mpoint.

Schoolrulesmustbefollowed.Youmayneedtoplacesignsindicatingspeedsforinsidejourneys.

Thecharityorganiserswillneeddetailedplansofyourrouteandhaveaskedyourteachertobetheirauditor.Heorshemaycheckonanyorallofyourcalculations.

•Workwithyourteamtoplantheroute.Wheredoyoupredict1kmwilltakeyou?(Youhavetostaywithintheschoolgroundsatalltimes.)

•Howwillyoumeasurethedistances?Whattoolswillyouneed?

•Ifyouaddobstaclessuchasclimbingoverequipment,remembertofactorinthedistancesinvolvedingoingupanddown!

•Onceyouhaveyourrouteplanned,testitout.Isitpossible?Doyouneedtorefineit?

•Howwillyourecordtherouteforyourcharity?Amap?Ascaleddrawing?Thisisabigtaskinitselfsoyoumaywanttodivideuptheroleswithinthegroup.

Answers will vary.

Answers will vary.

Answers will vary.

SERIES TOPIC



d

P = cm

e

P = cm

a

P = cm

b

P = cm

c

P = cm

Draw the following shapes and work out their perimeters:

c Arectanglethatistwiceaslongasitiswide.

P =

Perimeteristhelengtharoundtheoutsideofashape.

Perimeter – perimeter of shapes

Theperimeterofthesquareis8cm. Theperimeteroftherectangleis10cm.

These shapes are not to scale, so you can’t use your ruler to work out the perimeter. Can you find the perimeter of these shapes?

1

2

2 cm

2 cm

2 cm 2 cm

3 cm

3 cm

2 cm 2 cm

7cm

2 cm1 cm

5cm

7cm

1 cm

6cm

8 cm

9cm

9cm

a Asquarewith3cmsides.

P = cm

b Arectanglewithtwo4cmsidesandtwo3cmsides.

P = cm

Teacher check.

18

12 14

16 12

3628

SERIES TOPIC



a

d

b

e

c

6cm 4cm

4cm3 cm5cm

Find the perimeter of these regular polygons*:

The perimeters of some regular polygons are given in the table below. Fill in the length of the sides:

Theseregularpolygons*havesidesofequallengths.

Perimeter – perimeter of shapes

3

4

Perimeter 24cm 40cm 48cm 25cm

Length of each side


2 cmP = 16 cm

2 cmP = 10 cm

1 cmP = 6 cm

1 cmP = 4 cm

What is the fastest way to do this?

P = cm

P = cm

P = cm

P = cm

P = cm20

30 32

18 16

4 cm 10 cm 6 cm 5 cm

SERIES TOPIC



a

b

c

e

g

d

f

h

Perimeter – calculate perimeter

Find the perimeter of these shapes. Choose a unit of measurement to express your answer.1

20 cm

2 m

40cm

45cm

1.5m

1.8 m

7m2 m

6m

These shapes are all symmetrical. How does that help me?

P =

P =

P =

1.5m

20 cm

P =

3 m

8 m

P =

9m 1 m 3 m

2 m

P =

P =

P =

170 cm

440 cm

6.6 m

22 m

48 m

28 m

56 m

3.4 m

SERIES TOPIC



a b

c

3

Irregularshapesarenotsymmetrical.Thismeansweneedtomeasureeachside.

2

3

Why? __________________________________________________________________________________

_______________________________________________________________________________________

4m

3 m

6m

14m

9m

Pool A4m

4m

10 m

6m

6m

3 m

Pool B

Perimeter – calculate perimeter

P = cm

P = cm

6cm

3 cm

3 cm

1 cm1 cm

1 cm

1 cm

2 cm

2 cm

4cm

Find the perimeters of these irregular shapes:

P = cm

1 cm

3 cm

4cm

2 cm

2 cm

3 cm

3 cm

2 cm

Which of these designs for backyard pools would be the least expensive to fence?

1 cm1 cm

2 cm

1 cm

3 cm

4cm

3 cm

5cm

24

20

20

Pool B

The perimeter of Pool B is smaller than the perimeter of Pool A.

Pool A = 36 m Pool B = 33 m

SERIES TOPIC



Look carefully at this hexagonal grid. If the side of each hexagon is 2 m, what is the perimeter of the shaded area?

P = Number of sides × 2

P = 26 × 2

P = 52 m

Perimeter – construct shapes

Use this 1 cm dot paper to draw some shapes with different perimeters.1

a Shadethehexagonstoconstructashapewithaperimeterof36m.

b Shadethehexagonstoconstructashapewithaperimeterof60m.

2 m

2 m 2 m

2

a Drawarectanglewithaperimeterof12cm.

c Drawarectanglewithaperimeterof16cm.

b Drawarectanglewithaperimeterof20cm.

d Drawarectanglewithaperimeterof10cm.

Teacher check.

Teacher check.

SERIES TOPIC



On the left is a staircase shape. Use the 1 cm dot paper to redraw the shape so that the perimeter is twice as big:

Now draw another version with the perimeter three times as big:

3

1 cm

4

Perimeter – construct shapes

SERIES TOPIC



What to do

Perimeter problems solve

a Thelengthofarectangleisdoubleitswidth.Findtheperimeterifthewidthis 200 cm.

b Thelengthofarectangleis6timesitswidth.Findthelengthandwidthoftherectangleiftheperimeteris7metres.

c Charlieranaroundtheschool3times.Howfardidsherun?Writeyouranswerinkm.

d Jakewantstobuildafencearoundhisswimmingpooltocomplywithsafetyregulations.Ifthelengthofhispoolareais6metresandthewidthis4metres,howmuchwillitcost?Fencingcosts$55.50ametre.

100 m

280 m200 m

40m

300 m

1 200 cm or 12 m

Length = 3 m

Width = 50 cm

1 160 m × 3 = 3.48 km

20 × $55.50 = $1 110

SERIES TOPIC



What to do

More perimeter problems solve

a Theareaofeachsquareis9cm2.Whatistheperimeterofthisfigure?

b Thefigureismadeupof14squares.Eachsquarehasanareaof36cm2. Whatistheperimeter?

c Theareaofthisrectangleis288cm2.Ifallthesmallerrectanglesareexactlythesame,whatistheperimeterofonerectangle?

12 cm

The side of each square must be 3 cm.

24 × 3 = 72

Total perimeter is 72 cm

If the area is 288cm 2, the length of the large rectangle must be 24 cm.

The width of a small rectangle must be 3 cm, since 24– 12 = 12 and 12 ÷ 4 = 3

The side of each square must be 6 cm.

There are 34 sides.

34 × 6 = 204

Total perimeter is 204 cm.

SERIES TOPIC



a

Area= cm2

b

Area= cm2

c

Area= cm2

What is the area of each rectangle? Each square in the grid has an area of 1 cm². Some of the squares have been marked in for you.

d Didyouneedtoseeallthesquarestoworkoutthearea?__________

What is the area of each shaded shape? Each square in the grid has an area of 1 cm².

Shade the grid to show a rectangle with the area of 6 cm².

Area – introducing area

1

2

3

Areaistheamountofspaceashapecovers.Itisa2Dmeasurement.Wemeasureareainsquareunits.Forsmallareasweusesquarecentimetres. 1 cm

1 cm

a

Area= cm2

b

Area= cm2

c

Area= cm2

4

15 20 18

2 4

Answers will vary.

3 × 2 rectangle shaded.Sample answer.

No

SERIES TOPIC



In each shape*, you are given the area but one side is not labelled. Label the missing side:

Find the areas of these shapes*:

Wecanusethisformulatofindtheareaofrectangles:

Area=length×width

Area=3×5=15cm2

a b c

d e f

a b c

6cm

4cm

2 cm

5cm

2 cm

3 cm

8 m

4m

4cm

4cm

1 cm

4cm

5cm

5cm

3 cm 3 cm

4

5

Area – introducing area


Area= cm2

Area= cm2

Area= cm2

Area= cm2

Area= m2

Area= cm2

Area=20m2

4m

Area=14m2

7mArea=24m2

8 m

24

10 32 6

16 4

5 m

2 m

3 m

SERIES TOPIC



Find the area of the shaded triangles*:

d

Area= cm2

e

Area= cm2

f

Area= cm2

a

Area= cm2

b

Area= cm2

c

Area= cm2

a

Area= cm2

b

Area= cm2

c

Area= cm2

d

Area= cm2

e

Area= cm2

f

Area= cm2

Find the area of the shaded triangles inside the rectangles*:

Area – area of triangles

Eachtriangleishalfofarectangle.Tofindtheareaofatriangle,findtheareaoftherectangleandthendividebytwo.

Rectangle=4cm×5cm=20cm²Triangle=20cm²÷2=10cm²

4cm

5cm

1

2

8 cm

3 cm

7cm

4cm

10 cm

3 cm

3 cm

6cm

8 cm

6cm

10 cm

6cm7cm

6cm

8 cm

5cm

2 cm

2 cm

5cm

6cm

2 cm

4cm

6cm

4cm


15 24

20

9

21 24 30

14 15

12 12

SERIES TOPIC



Order the states and territories from smallest to largest areas:

Find the area of each large area*. Write your answer in hectares.

Hectaresareusedtomeasurelargespacessuchasafootballfield.Wewritehectaresasha.Onehectareisequalto10000m².Anevenlargerunitisasquarekilometrekm².Onesquarekilometreisequalto100hectares.

1ha=10000m² 1km²=1000000m²

Area – hectares and square kilometres

1

2

1 _________________________

4 _________________________

7 _________________________

2 _________________________

5 _________________________

8 _________________________

3 _________________________

6 _________________________

a

Area= hectares

b

Area= hectares

c

Area= hectares

300 m

100 m250m

100 m

120 m

120 m

d

Area= hectares

e

Area= hectares

f

Area= hectares

100 m

450m

200 m

300 m400m

150m

States and Territories Area

Queensland 1727200km²

New South Wales 801600km²

Victoria 227600km²

ACT 2400km²

WesternAustralia 2525500km²

SouthAustralia 984000km²

Tasmania 67800km²

NorthernTerritory 1346200km²

1km²=1000000m²

WESTERNAUSTRALIA

NORTHERNTERRITORY

QUEENSLAND

NEWSOUTHWALES

SOUTH AUSTRALIA

TASMANIA


3

6 4.5 6

2.5 1.44

ACT

New South Wales

Queensland

Tasmania

South Australia

Western Australia

Victoria

Northern Territory

SERIES TOPIC



Use the 1 cm grid below to draw three shapes with areas of 10 cm² but with different perimeters. Record the perimeter of each shape:

Use the grid below to draw two shapes with a perimeter of 12 cm but with different areas:

Area – area and perimeter

Find the perimeter and area of each shape:1

2

3

a b

c d

P = __________

A=__________

P = __________

A=__________

P = __________

A=__________P = __________

A=__________

a P = cm b P = cm c P = cm

1 cm

1 cm

1 cm

1 cm

Answers will vary.

Answers will vary.

16 cm

14 cm

12 cm

20 cm

16 cm²

12 cm²

9 cm²

16 cm²

SERIES TOPIC



Draw 3 different rectangles that have a perimeter of 24 cm and record the area in the table. The first row in the table is a hint of where to start.

Draw as many different rectangles as you can with the area of 36 cm². Label the length of each side:

4

5

Length Width Area

10 2

Area – area and perimeter

Teacher check.

Teacher check.

SERIES TOPIC



What to do

Area puzzles solve

a Howmany1cm²tilesdoIneedtocoverthiswall?

Howmany4cm²tilesdoIneedtocoverthissamewall?

b Howmany2cm²tilesdoIneedtocoverawallthatis6cmby6cm?

c Howmany5cm²tilesdoIneedtocoverawallthatis15cmby5cm?

8 cm

4cm

Solvetheseareapuzzles:

32

8

18

15

SERIES TOPIC



d

Area= cm2

e

Area= cm2

f

Area= cm2

a

Area= cm2

b

Area= cm2

c

Area= cm2

What to do next

Drawacompositeshapethathasanareaof50cm².

What to do

Composite calculations apply

Canyoufindtheareasoftheserooms*?Circletheroomthatwouldbecheapest tocarpet.

Putacrossintheroomthatwouldbemostexpensive.

4cm

9cm

12 cm

6cm

8 cm

8 cm

5cm

5cm

3 cm

2 cm

8 cm

1 cm2 cm

6cm6cm

9cm6cm

3 cm

3 cm

9cm


15cm8 cm

7cm

3 cm

11 cm

4cm3 cm

2 cm3 cm

Teacher check.

50

50 84 101

18 63

33Series F Topic 1 Assessment

Copyright © 3P Learning

Skills Not yet Kind of Got it

• Measuresandrecordslengthindifferentunits

• Convertsbetweencm,mmandm

• Orderslengthsofdifferentunits

Units of length Name ____________________

Write the measurement that the arrows are pointing to:

Order these lengths from shortest to longest:

220mm,200cm,1m,2.35m,532cm,2.35cm

Rule a line that is greater than 5 cm but less than 6 cm:

Convert into centimetres:

Convert into millimetres:

Convert into metres:

1

6

2

3

4

5

0 cm 51 6 102 7 113 8 12 14 154 9 13

a 50m=________cm b 8 m = ________ cm c 11.2 m = ______ cm d 1.2 m = _______ cm

a 45cm=______mm b 7cm=_______mm c 12 cm = ______ mm d 110 cm = _____ mm

a 500cm=_______m b 7500cm=_____m c 329cm=_______m d 2 000 cm = _____ m

34 Series F Topic 1 Assessment



• Measuresandrecordslengthindifferentunits

• Convertsbetweencm,mmandm

• Orderslengthsofdifferentunits

Units of length Name ____________________

Write the measurement that the arrows are pointing to:

Order these lengths from shortest to longest:

220mm,200cm,1m,2.35m,532cm,2.35cm

Rule a line that is greater than 5 cm but less than 6 cm:

Convert into centimetres:

Convert into millimetres:


1

6

2

3

4

5

0 cm 51 6 102 7 113 8 12 14 154 9 13

a 50m=________cm b 8 m = ________ cm c 11.2 m = ______ cm d 1.2 m = _______ cm

a 45cm=______mm b 7cm=_______mm c 12 cm = ______ mm d 110 cm = _____ mm

a 500cm=_______m b 7500cm=_____m c 329cm=_______m d 2 000 cm = _____ m

3 cm

Answers will vary.

5 000 800 1 120 120

12.4 cm

1 10012070450

5 75 3.29 20

2.35 cm, 220 mm, 1 m, 200 cm, 2.35 m, 532 cm

35


Series F Topic 2 Assessment

Round each line to the nearest cm and use the scale to calculate the following distances:

a EtoB ______________

b DtoE ______________

c CtoB ______________

d Ifyoutravelatanaveragespeedof70km/h,howlongwouldittakeyoutogetfromPointAto PointE(viapointsB,CandD)?Circlethebestanswer:

6hours2hours3hours


• Convertsbetweenmetresandkilometres

• Solvessimplespeedanddistanceproblems

• Interpretsscalestocalculatedistances

Travelling far Name ____________________

Convert into kilometres:1

a 5000m=__________km

c 112m =__________km

b 80m =__________km

d 400m =__________km

a 45cm =__________m

c 7km =__________m

b 14km =__________m

d 7.8km=__________m


Mali rode her bike 700 metres to the shops. She then rode the same distance back again. How many kilometres did she ride her bike for in total?

2

3

4 Jack walks roughly 5 km/h. He walks from school to the corner shop (1 200 m), from the shop to his friend’s place (3 433 m), and then home (146 m). Assuming he stops at the shops and his mate’s place only briefly, can he do this trip in less than an hour? Show your working out.

5

A

BC

D E

1cm=10km

SCALE:2 cm

2 cm

3 cm

3 cm

6cm

4cm

36



Round each line to the nearest cm and use the scale to calculate the following distances:

a EtoB ______________

b DtoE ______________

c CtoB ______________

d Ifyoutravelatanaveragespeedof70km/h,howlongwouldittakeyoutogetfromPointAto PointE(viapointsB,CandD)?Circlethebestanswer:

6hours2hours3hours


• Convertsbetweenmetresandkilometres

• Solvessimplespeedanddistanceproblems

• Interpretsscalestocalculatedistances

Travelling far Name ____________________

Convert into kilometres:1

a 5000m=__________km

c 112m =__________km

b 80m =__________km

d 400m =__________km

a 45cm =__________m

c 7km =__________m

b 14km =__________m

d 7.8km=__________m


Mali rode her bike 700 metres to the shops. She then rode the same distance back again. How many kilometres did she ride her bike for in total?

2

3

4 Jack walks roughly 5 km/h. He walks from school to the corner shop (1 200 m), from the shop to his friend’s place (3 433 m), and then home (146 m). Assuming he stops at the shops and his mate’s place only briefly, can he do this trip in less than an hour? Show your working out.

5

A

BC

D E

1cm=10km

SCALE:2 cm

2 cm

3 cm

3 cm

6cm

4cm

5

0.45

0.112

7 000

0.7 km + 0.7 km = 1.4 km

1.2 km + 3.433 km + 0.146 km = 4.779 km, which is less than 5 km, so YES Jack can do it in less than an hour.

0.08

14 000

0.4

7 800

50 km

90 km

30 km

37



Perimeter Name ____________________


• Measurestheperimeterofshapes

• Createsshapeswithspecifiedperimeters

• Usesunderstandingofperimetertocalculatesidelengths

1 Draw a square with a perimeter of 8 cm. Label the length of each side.

Draw a rectangle with a perimeter of 12 cm. Label the length of each side.

Complete this table. All shapes are regular.3

Length of each side 2.5cm 6cm

Perimeter 16cm 25cm


a

P =

b

P =

2 Fill in the missing side lengths and find the perimeters of these symmetrical shapes*:

5m

1 m

9m

2 m

4m

2 m

3 m

6m

14m

38



Perimeter Name ____________________


• Measurestheperimeterofshapes

• Createsshapeswithspecifiedperimeters

• Usesunderstandingofperimetertocalculatesidelengths

1 Draw a square with a perimeter of 8 cm. Label the length of each side.

Draw a rectangle with a perimeter of 12 cm. Label the length of each side.

Complete this table. All shapes are regular.3


a

P =

b

P =

2 Fill in the missing side lengths and find the perimeters of these symmetrical shapes*:

5m

1 m

9m

2 m

4m

2 m

3 m

6m

14m

Length of each side 2.5cm 6cm

Perimeter 16cm 25cm

60 m 32 m

2 cm

2 cm

2 cm 2 cmAnswers will vary.

14 m

3 m

3 m3 m 2 m

5 m4 m2 m6 m

4 cm 5 cm

20 cm 36 cm

39



Find the area of:

Area Name ____________________

Create 2 different shapes with an area of 18 cm²:2

What is the area of each shaded shape? Each square has an area of 1 cm².1

a

d

b

e f

c

3

a Arectanglemeasuring6cm×5cm

c Aboxmeasuring12cm×9cm

b Apoolmeasuring25m×4m

d Aphonemeasuring4.5cm× 10 cm

Area= cm2

Area= cm2

Area= cm2

Area= cm2

Area= cm2

Area= cm2

1 cm

1 cm

40



a

Area= m2

b

Area= cm2

c

Area= m2

Find the area of these triangles*:4

1 m

1 m

4cm

10 cm

3 m

6m

Would you choose cm², m², ha or km² to measure the area of the following?5

a This page

c Acitypark

b Africa

d AniPod

Create 2 shapes each with a perimeter of 10 cm but with different areas:6

Area Name ____________________


1 cm

1 cm


• Findstheareaofshapesusinggrids

• UsesformulaL×Wtofindareaofrectangles

• Findsareaoftriangles

• Makesappropriateunitchoicesformeasuring

• Recognisesshapescanhavesameperimetersbutdifferentareas

41



Find the area of:

Area Name ____________________

Create 2 different shapes with an area of 18 cm²:2

What is the area of each shaded shape? Each square has an area of 1 cm².1

a

d

b

e f

c

1 cm

1 cm

3

a Arectanglemeasuring6cm×5cm

c Aboxmeasuring12cm×9cm

b Apoolmeasuring25m×4m

d Aphonemeasuring4.5cm× 10 cm

Area= cm2

Area= cm2

Area= cm2

Area= cm2

Area= cm2

Area= cm2

Sample answers:

4

5

4

7

6

5.5

30 cm ²

108 cm ²

100 m ²

45 cm ²

Answers will vary.

42



a

Area= m2

b

Area= cm2

c

Area= m2


• Findstheareaofshapesusinggrids

• UsesformulaL×Wtofindareaofrectangles

• Findsareaoftriangles

• Makesappropriateunitchoicesformeasuring

• Recognisesshapescanhavesameperimetersbutdifferentareas

1 m

1 m

4cm

10 cm

3 m

6m

Would you choose cm², m², ha or km² to measure the area of the following?5

a This page

c Acitypark

b Africa

d AniPod

Create 2 shapes each with a perimeter of 10 cm but with different areas:6

Area Name ____________________

Find the area of these triangles*:4


1 cm

1 cm

9 20 0.5

cm ²

ha

km ²

cm ²

Sample answers:

Answers will vary.

43Series F Outcomes



RegionTopic 1 Units of length

Topic 2 Travelling far

Topic 3 Perimeter

Topic 4 Area

NSW

MS3.1–Selectandusetheappropriateunitanddevicetomeasurelengths,distancesandperimetersMS3.2–Selectandusetheappropriateunitanddevicetocalculatearea

•measureandrecordlengthsordistances

•usecombinationsofcm,mm,mandkm

•convertbetweencm,mm,mandkmtocomparelengths

•recordlengthsto 3decimalplaces

•selectandusetheappropriateunitanddevice

•questionandexplainwhytwostudentsmayobtaindifferentmeasures(WM)

•solveproblemsinvolvingdifferentmeasuresoflength(WM)

•recognisetheneedforaunitlongerthanametre

•useabbreviationkm•measureusingkmand12 km•convertbetweenkmandm

•solvesimpleproblemsusingspeed(WM)

•findtheperimeterofalargearea

•calculateandcompareperimetersofsquares,rectanglesandtriangles

•findtherelationshipbetweenthelengthsofsidesandtheperimeterforsquares,rectangles,equilateralandisoscelestriangles

•explainthatperimetersofsquares,trianglesandrectanglescanbefoundbyfindingthe sum of the sidelengths

•recognisetheneedforaunitlargerthanam²

•recogniseandexplaintheneedforamoreconvenientunitthanakm² –hectares

•selecttheappropriateunittocalculatearea

•findtherelationshipbetweenlengthandbreadthandarea

•applymeasurementtoeverydaysituations(WM)

VIC

VELS Measurement – Level 4

•usemetricunitstoestimateandmeasurelength,perimeter,area•measureasaccuratelyasneededforthepurposeoftheactivity•convertbetweenmetricunitsoflength•createnewproblemsbasedonfamiliarproblemstructures(WM)

QLD

EL Y 5 – Lengthandareacanbeestimated,measuredandorderedusingstandardandnon-standardunitsofmeasure

•standardunits,includingcm,m,cm²,m²andarangeofinstrumentsareusedtomeasureandorderattributesofobjectsincludinglengthandarea

•linksexistbetweendifferentwaysofrecordingthesamemeasurement•reasonableestimatescanbemadeusingstrategiesthatsuitthesituation

44 Series F Outcomes


RegionTopic 1 Units of length

Topic 2 Travelling far

Topic 3 Perimeter

Topic 4 Area

SA

3.4–Selectappropriateattributesandsystemstomeasureforavarietyofpurposes3.5–Usearangeofstandardtoolstomeasurerelationshipsbetweendistancestocalculatesize

•chooseandusemetricunitsornon-metricstandardunitstocompare,measureandanalyse

•measureforavarietyofpurposes

•chooseappropriatestrategiesandunitsofcomparisonin planning measurement

•choose the appropriatetools,technologiesandunitstomeasureforaparticularlevelofaccuracy,anddiscusseshowthetoolsusedaffecttheprecisionofmeasurements

•chooseandusemetricunitsornon-metricstandardunitstocompare,measureandanalyse

•estimatedistancesintermsofmetricunits

•identifyrelationshipsbetweendistancestodevelopanduseformulaeinordertoestimateandcalculatetheperimeter of polygons

•recogniserelationshipsbetweenmeasurableattributesoffiguresandobjects,andcommunicate theserelationshipsinbotheverydayandmathematicallanguage

•identifyrelationshipsbetweendistancestodevelopanduseformulaeinordertoestimateandcalculatethearea of shapes

WA/NT

M 9a.4, M 9b.4

•selectappropriateattributes,distinguishperimeterfromareaandchooseunitsofasensiblesizeforthedescriptionsandcomparisonstobemade

•measureareabycountinguniformunits,includingpart-unitswhererequired

ACT

17.LC.1measurementattributesoflength,area,mass,capacity,volume,angleandtime17.LC.2informalandstandardunitsofmeasurementoftheseattributes,includingmetre,

centimetre,millimetre,squaremetre,squarecentimetre,kilogram,gram,litre,millilitre,degrees,hoursandminutes

17.LC.3theconceptofconservation,includingdifferentwaysofrecordingthesamemeasurement(e.g.inmetres,centimetresormillimetres)

17.LC.4theconceptofmeasurementsasapproximations,withthemeasurementcontextinfluencinglevelsofprecisionrequiredandwaysofrefiningmeasurements(e.g.bychangingunitsorinstruments)


length, perimeter and area - · pdf file• travelling far_____ 9 • perimeter ......

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