Student BookSERIES
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Length, Perimeter and Area
Teacher BookSERIES
F
Length, Perimeter and Area
Copyright ©
Series F – Length, Perimeter and Area
Contents
Topic 1 – Units of length (pp. 1–8)
• m, cm, mm ___________________________________________
• findandorderlength ___________________________________
• metrestokilometres ___________________________________
• spotthedistance–apply ________________________________
• wordproblems–solve__________________________________
Topic2–Travellingfar(pp.9–16)
• measuredistances _____________________________________
• mapsandscale _______________________________________
• speedanddistance ____________________________________
• flagit!–apply ________________________________________
• the city to school – create _______________________________
Topic3–Perimeter(pp.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 ©
Series F – Length, Perimeter and Area
Contents
Section1–Answers(pp.1–32)
• units of length ______________________________________ 1
• travellingfar ________________________________________ 9
• perimeter __________________________________________ 17
• area ______________________________________________ 25
Section2–Assessmentwithanswers(pp.33–42)
• units of length ______________________________________ 33
• travellingfar ________________________________________ 35
• perimeter __________________________________________ 37
• area ______________________________________________ 39
Section3–Objectives(p.43)
Series Authors:
Rachel Flenley
Nicola Herringer
Please note: Thesepageshavebeendesignedtoprintto‘shrinktoprintablearea’asthisisacommondefaultsettingonmanycomputers.Theremaybeminordiscrepancieswithmeasurementsasindividualprintersandphotocopiersprinttoslightlydifferentproportions.
SERIES TOPIC
1F 1Copyright © 3P Learning
Length, Perimeter and Area
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
Length, Perimeter and Area
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
3F 1Copyright © 3P Learning
Length, Perimeter and Area
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
F 14Copyright © 3P Learning
Length, Perimeter and Area
Mr Marlowe’s class went on an excursion to the circus. He asked his pupils 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 Whatwasthedifferencebetween thehighestandthelowestguess? _______________
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
5F 1Copyright © 3P Learning
Length, Perimeter and Area
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 DistancefromLondontoEdinburgh
d Amarathonrace
f Lengthoftheschoolplayground
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
F 16Copyright © 3P Learning
Length, Perimeter and Area
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
7F 1Copyright © 3P Learning
Length, Perimeter and Area
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
F 18Copyright © 3P Learning
Length, Perimeter and Area
a Ifthereare60brochuresinastackandeachofthemare8mmthick,howhigh isthestack?
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
Day 1TodaywelefthomeatPlymouthanddrovestraighttoBournemouth. km
Day 2WeleftBournemouthafterbreakfastthenwehadlunchinMaidstone. WestayedthenightinCambridge. km
Day 3WedrovetoNottinghamtofindoutaboutgettinganewpuppy! km
Day 4Wehadtoleaveearlythismorningasitturnsoutthepuppywewantis inChester.
km
Day 5Ournewpuppyisaboy!WenamedhimChester,afterthetownhecamefrom. WedecidedtotravelbacktoNottinghamtoshowChestertoourcousins. km
Day 6TodaywedroveallthewayfromNottinghamtoBath.Dadwantedto keepgoingtillwegothomebutmummadehimstop. km
Day 7Todaywedrovetherestofthewayhome. km
173 km
145 km
135 km
223 km
200 km
232 km
70 km
261 km
Chester
Nottingham
Stroud
Bath
Plymouth
Bournemouth
Maidstone
Cambridge
200
358
145
173
173
504
232
1 785
SERIES TOPIC
11FCopyright © 3P Learning
Length, Perimeter and Area 2
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
F12Copyright © 3P Learning
Length, Perimeter and Area2
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
13FCopyright © 3P Learning
Length, Perimeter and Area 2
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
F14Copyright © 3P Learning
Length, Perimeter and Area2
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 the 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
15FCopyright © 3P Learning
Length, Perimeter and Area 2
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
F16Copyright © 3P Learning
Length, Perimeter and Area2
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?Doyouneedto refineit?
•Howwillyourecordtherouteforyourcharity?Amap?Ascaleddrawing?Thisis abigtaskinitselfsoyoumaywanttodivideuptheroleswithinthegroup.
Answers will vary.
Answers will vary.
Answers will vary.
SERIES TOPIC
17FCopyright © 3P Learning
Length, Perimeter and Area 3
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 Arectanglewithtwo4cmsidesand two3cmsides.
P = cm
Teacher check.
18
12 14
16 12
3628
SERIES TOPIC
F18Copyright © 3P Learning
Length, Perimeter and Area3
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
*Not drawn to scale.
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
19FCopyright © 3P Learning
Length, Perimeter and Area 3
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
F20Copyright © 3P Learning
Length, Perimeter and Area
a b
c
3
Irregularshapesarenotsymmetrical.Thismeansweneedtomeasureeachside.
2
3
Why? __________________________________________________________________________________
_______________________________________________________________________________________
4m
3 m
6m
14m
9m
Playground A4m
4m
10 m
6m
6m
3 m
Playground B
Perimeter – calculate perimeter
P = cm
P = cm
6cm
3 cm
3 cm
1 cm
1 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 playgrounds would be the least expensive to fence?
1 cm
1 cm
2 cm
1 cm
3 cm
4cm
3 cm
5cm
24
20
20
Playground B
The perimeter of Playground B is smaller than the perimeter of Playground A.
Playground A = 36 m Playground B = 33 m
SERIES TOPIC
21FCopyright © 3P Learning
Length, Perimeter and Area 3
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 Shadethehexagonstoconstructashape withaperimeterof36m.
b Shadethehexagonstoconstructashape withaperimeterof60m.
2 m
2 m 2 m
2
a Drawarectanglewithaperimeterof12cm.
c Drawarectanglewithaperimeterof16cm.
b Drawarectanglewithaperimeterof20cm.
d Drawarectanglewithaperimeterof10cm.
Teacher check.
Teacher check.
SERIES TOPIC
F22Copyright © 3P Learning
Length, Perimeter and Area3
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
23FCopyright © 3P Learning
Length, Perimeter and Area 3
What to do
Perimeter problems solve
a Thelengthofarectangleisdoubleitswidth.Findtheperimeterifthewidth is 200 cm.
b Thelengthofarectangleis6timesitswidth.Findthelengthandwidthoftherectangleiftheperimeteris7metres.
c Charlieranaroundtheschool3times.Howfardidsherun?Writeyouranswer inkm.
d Jakewantstobuildafencearoundhisswimmingpooltocomplywithsafetyregulations.Ifthelengthofhispoolareais6metresandthewidthis4metres,howmuchwillitcost?Fencingcosts$55.50ametre.
100 m
280 m
200 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
F24Copyright © 3P Learning
Length, Perimeter and Area3
What to do
More perimeter problems solve
12 cm
a Theareaofeachsquareis9cm2.Whatistheperimeterofthisfigure?
b Thefigureismadeupof14squares.Eachsquarehasanareaof36cm2. Whatistheperimeter?
c Theareaofthisrectangleis336cm2.Ifallthesmallerrectanglesareexactlythesame,whatistheperimeterofonerectangle?
The side of each square must be 3 cm.
24 × 3 = 72
Total perimeter is 72 cm
If the area is 336 cm 2, the length of the large rectangle must be 28 cm.
The width of a small rectangle must be 4 cm, since 28– 12 = 16 and 16 ÷ 4 = 4
The side of each square must be 6 cm.
There are 34 sides.
34 × 6 = 204
Total perimeter is 204 cm.
SERIES TOPIC
25FCopyright © 3P Learning
Length, Perimeter and Area 4
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
F26Copyright © 3P Learning
Length, Perimeter and Area4
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
*Not drawn to scale.
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
27FCopyright © 3P Learning
Length, Perimeter and Area 4
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=20cm²
Triangle=20cm²÷2=10cm²4cm
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
*Not drawn to scale.
15 24
20
9
21 24 30
14 15
12 12
SERIES TOPIC
F28Copyright © 3P Learning
Length, Perimeter and Area4
Order these European countries 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
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
*Not drawn to scale.
UnitedKingdom
Ireland
France
Germany
Spain
Portugal Italy
Greece
Country Area
UnitedKingdom 242900km²
Ireland 70300km²
France 632800km²
Italy 310000km²
Greece 132000km²
Spain 506000km²
Portugal 92100km²
Germany 357000km²
1km²=1000000m²
1 _________________________
4 _________________________
7 _________________________
2 _________________________
5 _________________________
8 _________________________
3 _________________________
6 _________________________
3
6 4.5 6
2.5 1.44
Ireland
United Kingdom
Spain
Portugal
Italy
France
Greece
Germany
SERIES TOPIC
29FCopyright © 3P Learning
Length, Perimeter and Area 4
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
F30Copyright © 3P Learning
Length, Perimeter and Area4
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
31FCopyright © 3P Learning
Length, Perimeter and Area 4
What to do
Area puzzles solve
a Howmany1cm²tilesdoIneedtocoverthiswall?
Howmany4cm²tilesdoIneedtocoverthissamewall?
b Howmany2cm²tilesdoIneedto coverawallthatis6cmby6cm?
c Howmany5cm²tilesdoIneedtocoverawallthatis 15cmby5cm?
8 cm
4cm
Solvetheseareapuzzles:
32
8
18
15
SERIES TOPIC
F32Copyright © 3P Learning
Length, Perimeter and Area4
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
9cm
6cm
3 cm
3 cm
9cm
*Not drawn to scale.
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
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
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
Copyright © 3P Learning
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
Skills Not yet Kind of Got it
• 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
Convert into metres:
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
Copyright © 3P Learning
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
Skills Not yet Kind of Got it
• 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
Convert into metres:
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
Copyright © 3P Learning
Series F Topic 3 Assessment
Perimeter Name ____________________
Skills Not yet Kind of Got it
• 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
*Not drawn to scale.
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
Copyright © 3P Learning
Series F Topic 3 Assessment
Perimeter Name ____________________
Skills Not yet Kind of Got it
• 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
*Not drawn to scale.
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
Copyright © 3P Learning
Series F Topic 4 Assessment
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 Aswimmingpoolmeasuring25m×4m
d Aphonemeasuring4.5cm× 10 cm
Area= cm2
Area= cm2
Area= cm2
Area= cm2
Area= cm2
Area= cm2
1 cm
1 cm
40
Copyright © 3P Learning
Series F Topic 4 Assessment
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 ____________________
*Not drawn to scale.
1 cm
1 cm
Skills Not yet Kind of Got it
• Findstheareaofshapesusinggrids
• UsesformulaL×Wtofindareaofrectangles
• Findsareaoftriangles
• Makesappropriateunitchoicesformeasuring
• Recognisesshapescanhavesameperimetersbutdifferentareas
41
Copyright © 3P Learning
Series F Topic 4 Assessment
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 Aswimmingpoolmeasuring25m×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
Copyright © 3P Learning
Series F Topic 4 Assessment
a
Area= m2
b
Area= cm2
c
Area= m2
Skills Not yet Kind of Got it
• 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
*Not drawn to scale.
1 cm
1 cm
9 20 0.5
cm ²
ha
km ²
cm ²
Sample answers:
Answers will vary.
43
Copyright © 3P Learning
Series F – Length, Perimeter and Area
Series F Objectives
2006 Primary Framework Core Objectives
Topic 1Units of Length
Usingandapplyingmathematics• solveone-andtwo-stepproblemsinvolvingwholenumbersanddecimalsandall fouroperations,choosingandusingappropriatecalculationstrategies,includingcalculatoruse
Measuring• read,choose,useandrecordstandardmetricunitstoestimateandmeasurelength,weightandcapacitytoasuitabledegreeofaccuracy,e.g.thenearestcentimetre;convertlargertosmallerunitsusingdecimalstooneplace,e.g.change2.6kgto2600g
Topic 2Travelling far
Usingandapplyingmathematics• solveone-andtwo-stepproblemsinvolvingwholenumbersanddecimalsandall fouroperations,choosingandusingappropriatecalculationstrategies,includingcalculatoruse
Measuring• read,choose,useandrecordstandardmetricunitstoestimateandmeasurelength,weightandcapacitytoasuitabledegreeofaccuracy,e.g.thenearestcentimetre;convertlargertosmallerunitsusingdecimalstooneplace,e.g.change2.6kgto2600g
• interpretareadingthatliesbetweentwounnumbereddivisionsonascale• drawandmeasurelinestothenearestmillimetre;measureandcalculatetheperimeterofregularandirregularpolygons;usetheformulafortheareaofarectangletocalculateitsarea
Topic 3Perimeter
Usingandapplyingmathematics• solveone-andtwo-stepproblemsinvolvingwholenumbersanddecimalsandall fouroperations,choosingandusingappropriatecalculationstrategies,includingcalculatoruse
Measuring• read,choose,useandrecordstandardmetricunitstoestimateandmeasurelength,weightandcapacitytoasuitabledegreeofaccuracy,e.g.thenearestcentimetre;convertlargertosmallerunitsusingdecimalstooneplace,e.g.change2.6kgto2600g
• drawandmeasurelinestothenearestmillimetre;measureandcalculatetheperimeterofregularandirregularpolygons;usetheformulafortheareaofarectangletocalculateitsarea
Topic 4 Area
Usingandapplyingmathematics• solveone-andtwo-stepproblemsinvolvingwholenumbersanddecimalsandall fouroperations,choosingandusingappropriatecalculationstrategies,includingcalculatoruse
Measuring• read,choose,useandrecordstandardmetricunitstoestimateandmeasurelength,weightandcapacitytoasuitabledegreeofaccuracy,e.g.thenearestcentimetre;convertlargertosmallerunitsusingdecimalstooneplace,e.g.change2.6kgto2600g
• drawandmeasurelinestothenearestmillimetre;measureandcalculatetheperimeterofregularandirregularpolygons;usetheformulafortheareaofarectangletocalculateitsarea