Length, Perimeter and Area - 3P...

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Teacher Book - Series F

Length, Perimeter and Area

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Length, Perimeter and Area - Series F

Contents

Section 1 — Answers (p. 1–32)

units of length•

travelling far•

perimeter•

area•

Section 2 — Assessment with answers (p. 33–42)

units of length•

travelling far•

perimeter•

area•

Section 3 — Outcomes (p. 43–44)

1

9

17

25

33

35

37

39

1FSERIES TOPIC

Length, Perimeter and AreaCopyright © 3P Learning Ltd

Units of length—m, cm, mm

These units of measurement are used regularly in everyday life.

10 mm = 1 cm

100 cm = 1 m

1 000 m = 1 km

Estimate then measure these lengths. Which unit will you use?2

Object Estimate Measure

Height of a desk

Shoulder to the fingertips

Width of the door

Hand span

Pencil sharpener

Width of a fingernail

A4 paper length

Complete the measure of each item below by adding either mm, cm or m next to the number:1

a b

e

c

fd

20

13

14

2

4

28

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

1

cm

cm

Answers will vary.

mm

m

m

mm

KS78

2FSERIES TOPIC


Units of length—m, cm, mm

Convert these lengths to centimetres:

Convert these lengths to metres:

Convert these lengths to metres:

4

5

3

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

Convert these lengths to millimetres:

a

d

300 cm = m b

e

c

fm900 cm =

500 cm = m

m2 000 cm =

250 cm = m

m4 550 cm =

a

c

1 000 mm = m b

dm4 500 mm =

5 000 mm m

m500 mm =

6

a

d

5 cm =

7 cm =

mm

mm

b

e

3 cm =

11 cm =

mm mm

mm mm

c

f

9 cm =

15 cm =

a

d

50 mm = cm b

e

c

fcm15 mm =

20 mm = cm

cm156 mm =

223 mm = cm

cm495 mm =

1

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

50

70

3

1

4.5

5

0.5

9

5

20

2.5

45.5

1.5

25

15.6

22.3

49.5

30

110

90

150

This conversion box can help you convert units of length.

To convert from cm to mm, divide by 10.

To convert from cm to mm, multiply by 10.

mcm mm

× 100

÷ 100

× 10

÷ 10

× 1 000

÷ 1 000

BU13

3FSERIES TOPIC


Units of length - find and order length

Look carefully at how each rectangle is divided and find the missing length.1

1

1 m

30 cm cm

a

3 m

150 cmcm

b

200 cm

60 cmcm

c

100 cm

30 cm 20 cmm

d

Convert all the lengths to the same unit.

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

70

150

140

0.5

MU90

4FSERIES TOPIC


Units of length - find and order length

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

1.95 m

16 m

145 cm

2 mm

11 m

457 cm

1

2

3

4

5

6

Shortest

Tallest

Name Height of the clown on stilts

Peter 3 m 30 cm 330 cm 3.3 m

Sara 4 m 15 cm 415 cm 4.15 m

Omar 3 m 64 cm 364 cm 3.64 m

Julia 3 m 97 cm 397 cm 3.97 m

Heba 4 m 9cm 409 cm 4.09 m

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

a Who had the closest guess?

b How far off was this person?

c What was the difference between the highest and the lowest guess?

d Write your height and find the two people in your class who are closest to your height.

1

ladybird

fridge

door

giraffe

tree

flagpole

Omar

6 cm

85 cm

Answers will vary.

WY59

5FSERIES TOPIC


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 height of your house

e distance from Earth to the Moon

b distance from Melbourne to Sydney

d a marathon race

f distance around the school oval

a

a

a

a

d

d

d

d

2 000 m =

3 km =

1 500 m =

0.5 km =

km

m

km

b

b

b

b

e

e

e

e

5 000 m =

7 km =

3 645 m =

3.7 km =

km

m

km

m

km km

c

c

c

c

f

f

f

f

8 000 m =

4 km =

1 747 m =

8.2 km =

2 km or 2 220 m

300 km or 2 500 m

0.58 km or 600 m

0.85 km or 800 m

3.2 km or 3 100 m

1 900 m or 2.9 km

0.75 km or 0.79 km

1.58 km or 1 600 m

560 m or 0.565 km

855 m or 0.875 km

5.5 km or 5 600 m

7.25 km or 7 200 m

m m m

3

4

5

Which units of measurement do we already know about?

1 km = 1 000 m

1 m = 0.001 km

100 m = 0.1 km

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

1

2

m

m

km

km

km

m

1.5

3 000

500

7 000

3 700

4 000

8 200

5

3.645

8

1.747

FJ74

6FSERIES TOPIC


Units of length - metres to kilometres

Fill in the boxes to answer these word problems:7

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

0 km

0 km

1 km

10 km

+ + =kmkm

I have to convert here!

100 metres

100 m

1 000 metres600 metres

0 km 1 km

200 metres400 metres 800 metres

mkm

a Abdul walked 0.4 of a kilometre, Sara walked 20 metres and Kaitlyn walked half a kilometre. Write their names in the boxes below to show how far each of them walked.

b In a 10 km fun run event, Omar stopped after 6 ½ km, Peter stopped after 8 000 m and Heidi stopped 10 metres before the end.

Write their names in the boxes below to show how far each of them ran.

c Leng walked 250 metres to the bus stop, and then rode the bus for 3 km to the beach. When she arrived at the beach she went for a 4 km jog by the sea.

How many metres did she travel altogether?

1

200 m

400 m 600 m 800 m 1 000 m

Abdul

Kaitlyn

Peter

Omar Heidi

Sara

0.25 3 4 7 250

OZ36

7FSERIES TOPIC


This is an estimating game for two players.

The first player chooses two spots.•

The second player estimates the distance between the spots in mm. Measure from each spot’s edge.•

The second player draws a line between the spots and then measures the distance with their ruler. • They score 100 points for the right answer, 40 points for an estimate within 10 mm, and 20 points for an estimate within 20 mm.

The second player picks two spots for the first player.•

The player with the most points after 10 rounds wins!•

1 2

3

4

6

9

7

5

8

10

12

15

13

14

11

1DW58

Spot the distance apply

8FSERIES TOPIC


If there are 60 brochures in a stack and each of them are 8 mm thick, how high is the stack?1

A plank of wood is 5 metres long. If 150 cm is sawn off how much is left?2

How many 20 mm pieces of gold wire can be cut from 1 metre?3

If a finger nail grows 2 mm a week, how many cm would it grow in one year?4

One day I bought 3 sherbet sticks. Their lengths were 0.75 m, 50 cm and 75 cm. What was the total length? If sherbet sticks cost $2 a metre, how much did I spend?

5

1

solve

60 × 8 mm = 480 mm OR 48 cm

5 m = 500 cm

1 m = 1000 mm

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

.75 m + .5 m + .75 m = 2 m of sherbet stick

2 × $2 = $4

1000 mm ÷ 20 mm = 50 pieces

500 cm – 150 cm = 350 cm

DJ70

Word problems

9FSERIES TOPIC


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

a

c

3.6 km m

m9.3 km

e 5.6 km m

b

c

2.8 km m

m8.2 km

e 0.2 km m

c

c

0.6 km m

m7.1 km

e 0.1 km m

a

c

2 km 123 m km

km2 km 245 m

e

g

8 km 145 m km

km835 m

a

b

c

d

b

f

d

h

4 km 235 m

8 km 23 m

km

km

km

km

5 km 235 m

593 m

e

Sunset Cove to Sandy Beach

Melody Point to Shark Cliff

Reckless Rocks to Laguna Beach

Melody Point to Sandy Beach

via Shark Cliff

km

km

km

km

Laguna Beach to Shark Cliff

via Melody Pointkm

Shark Cliff

Sandy BeachSunset Cove

Reckless Rocks

Laguna Beach

Melody Point

2

1 245 m1 572 m

980 m390 m

415 m712 m

2.123

2.245

8.145

.835

3 600

9 300

5 600

2 800

8 200

200

600

7 100

100

4.235

5.235

8.023

.593

0.98

1.572

0.712

1.962

2.817

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

VI53

10FSERIES TOPIC


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.

4

5

Road maps sometimes have the distance between towns written on the road that connects them. This information helps you plan your journey.

Scarborough

Lexia

96 km

285 km142 km520 km

340 km

218 km336 km

Brighton

MullalooHastings

Doubleview Woodvale Embleton

2

Day 1 Today we left home at Doubleview and drove straight to Hastings.

Day 2 We left Hastings after breakfast then we had lunch in Mullaloo. We stayed the night in Brighton.

Day 3 We drove to Embleton to find out about getting a new puppy!

Day 4 We had to leave early this morning as it turns out the puppy we want is in Lexia.

Day 5 Our new puppy is a girl! We named her Lexie, after the town she came from. We decided to travel up to Scarborough to show Lexie to our cousins.

Day 6 Today we drove all the way from Scarborough to Woodvale. Dad wanted to keep going till we got home but Mum made him stop.

Day 6 Today we drove the rest of the way home.

km

km

km

km

km

km

km

420 km

km

340

662

336

621

96

935

420

3 410

GC61

11FSERIES TOPIC


What is the shortest distance by road from:

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

1

2

Travelling far - maps and scale

a home to school?

b home to park?

c the fire station to the shop?

d the school to the farm?

e home to the shop?

f Draw your own route on the map.

Which landmarks do you go past?

What is the total distance of your route?

a the fire station to the park?

b the park to home?

c home to the shop?

m

km

m

km

m

km

m

m

1 cm

schoolhome

fire station park

shop farm

2

Scale is used to show long distances on a map. This makes it easier for us to translate distance on a map to distance in the real world.

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

1 cm = 100 m

SCALE:

400

800

700

1 000

800

3

8

8

Teacher check

Teacher check

OQ29

12FSERIES TOPIC


Travelling far - maps and scale

Use the scale of 1 cm = 2 m to find the length of each line in metres (measure to the closest cm).

Complete this table using scale 1 cm = 3 cm:

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

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

3

4

5

6

m

m

m

a

b

c

Scale length in cm

2 5 15 4 6 9 10 8 12 7

True length in cm

6 15 45 12 18 27 30 24 36 21

Scale length in cm

5 10 15 7 12 9 11 2 8 6

True length in m

30 60 90 42 72 54 66 12 48 36

a What is the distance from Stop 1 to Stop 2?

b What is the distance from Stop 4 to Stop 5?

c What is the distance from Stop 2 to Stop 5?

d What is the total distance of this train route?

km

km

km

km

Stop 1Stop 2

Stop 3Stop 4

16 cm

4 cm 4 cm

8 cm

20 cmStop 5 Stop 6

2

22

10

14

40

20

40

130

VG99

13FSERIES TOPIC


Speed can be measured in kilometres per hour.

60 km per hour means that it takes one hour to travel 60 km and is written 60 km/h.

Travelling far - speed and distance

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

If a car travelled 300 km in 5 hours, work out how far it travelled in 2 hours and in 3 hours:

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

1

2

3

4

a b

c d

e f

76 km in an hour = 82 km in an hour =

100 km in 2 hours = 130 km in 2 hours =

180 km in 3 hours = 240 km in 4 hours =

km/h

0 km

0 km

0 km

300 km

560 km

2 hours

half an hour

3 hours

4 hours

hours

km

5 hours

8 hours

950 km

10 hours

2

km/h

km/h

km/h

km/h

km/h

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

1 hr = _______

1 hr = _______

1 hr = _______

76

50

60

82

65

60

120 km

35 km

475

5

280 km

60 km

70 km

95 km

180 km

UC47

14FSERIES TOPIC


Travelling far - speed and distance

If a snail travels 6 mm in 10 minutes, how far will it travel in one hour?5

If a car was travelling 60 km/h, how far would it have travelled after 10 minutes?6

Harriet walks at a speed of about 4 km/h. How long would it take for her to walk 20 km?7

If a truck was travelling 80 km/h, long would it take for a truck to travel 560 km?8

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?

9You need to convert the total minutes into hours.

2

36 mm

10 km

5 hours

7 hours

240 minutes OR 4 hours

SI22

15FSERIES TOPIC


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

On your marks, get set, go! You are about to participate in a race to collect as many flags as possible in less than 400 km.

Getting Ready

Use the space below to show your route and calculate the distance you cover between towns.

Start at Point A.1.

Work out how you will get to Point B collecting as many flags as you can at 2. various towns along the way. Use a calculator to help you add the distances.

You need to decide on your route. You may not exceed 400 km. 3.

What to do next

What to do

2

Flag it! apply

Answers will vary.

ZT79

16FSERIES TOPIC


Your group has been hired by your favourite charity to organise a 1 km fun run at your school.

You will plan and measure out the course and then get another group to test out your run.

The run needs to be exactly one kilometre in length. You’ll need markers at each 100 m point.

School rules must be followed. You may need to place signs indicating speeds for inside journeys.

The charity organisers will need detailed plans of your route and have asked your teacher to be their auditor. He or she may check on any or all of your calculations.

Once you think you are ready, submit your plans to your teacher. Stage your event.

Ask your teacher and the other groups for their feedback.

Work with your team to plan the route. Where do you predict 1 km will take • you? (You have to stay within the school grounds at all times.)

How will you measure the distances? What tools will you need? •

If you add obstacles such as climbing over equipment, remember to factor in • the distances involved in going up and down!

Once you have your route planned, test it out. Is it possible? Do you need to • refine it?

How will you record the route for your charity? A map? A scaled drawing? This • is a big task in itself so you may want to divide up the roles within the group.

What to do next

What to do

2

Getting Ready

Answers will vary.

PH87

The City to School create

17FSERIES TOPIC


Perimeter is the length around the outside of a shape.

The perimeter of the square is 8 centimetres. The perimeter of the rectangle is 10 centimetres.

Draw the following shapes and work out their perimeters:

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

7 cm

2 cm 1 cm

5 cm

7 cm

1 cm

a

6 cm

8 cm

d

b

9 cm

9 cm

e

c

a square with 3 cm sides. a rectangle with two 4 cm sides and two 3 cm sides.

a rectangle that is twice as long as it is wide.

a b

c

Perimeter - perimeter of shapes

3

cmP = cmP = cmP =

cmP =

cmP =

Teacher check.

18 16 12

28

36

IH60

18FSERIES TOPIC


Perimeter - perimeter of shapes

Find the perimeter of these regular polygons:

The perimeter of some regular polygons is given in the table below.Fill in the length of the sides:

3

4

These regular polygons have sides of equal lengths.

Perimeter 24 cm 40 cm 48 cm 25 cm

Length of each side 4 cm 10 cm 6 cm 5 cm

6 cm 4 cm 3 cm

2 cm2 cm

3 cm 4 cm5 cm

1 cm 1 cm

P = 16 cm P = 10 cm P = 6 cm P = 4 cm

cb

e

a

d

* not to scale

3

cmP =

cmP =

cmP =

cmP =

cmP =

What is the fastest way to do this?

20

30 32

18 16

EX36

19FSERIES TOPIC


Perimeter - calculate perimeter

Circle the largest number.

3

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

40 cm

1.5 m

20 cm

2 m

45 cm

1.8 m

20 cm

3 m

8 m

9 m 1 m 3 m

1.5 m

7 m2 m

2 m

6 m

a

f

g

h

b

c

d

e

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

170 cm

440 cm

6.6 m

22 m

48 m

28 m

56 m

3.4 m

VG75

20FSERIES TOPIC


Perimeter - calculate perimeter

Measure the sides of these irregular shapes to the nearest cm with your ruler and then find the perimeter.

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

2

3

Irregular shapes are not symmetrical. This means we need to measure each side.

b

ca

4 m

3 m

6 m

14 m

9 m

4 m

4 m

10 m

6 m

6 m

3 m

3

cmP =

cmP =

cmP =

Why?

A B

Pool B

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

Pool A = 36 m Pool B = 33

24

20

22

AB94

21FSERIES TOPIC


Perimeter - construct shapes

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

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 × 2P = 26 × 2P = 52 m

1

a Draw a rectangle with a perimeter of 12 cm.

a Shade the hexagons to construct a shape with a perimeter of 36 m.

c Draw a rectangle with a perimeter of 16 cm.

b Draw a rectangle with a perimeter of 20 cm.

b Shade the hexagons to construct a shape with a perimeter of 60 m.

d Draw a rectangle with a perimeter of 10 cm.

2 m

2 m 2 m

2

3

Teacher check.

Teacher check

Teacher check.

GB52

22FSERIES 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

Perimeter - construct shapes

1 cm

3

4

FP14

23FSERIES TOPIC


The length of a rectangle is double its width. Find the perimeter if the width is 200 cm.1

The length of a rectangle is 6 times its width. Find the length and width of the rectangle if the perimeter is 7 metres.

2

Charlie ran around the school 3 times. How far did she run? Write your answer in km.3

Jake wants build a fence around his swimming pool to comply with safety regulations. If the length of his pool area is 6 metres and the width is 4 metres, how much will it cost? Fencing costs $55.50 a metre.

4

100 m

280 m200 m

40 m

300 m

3

Perimeter problems solve

1200 cm OR 12 m

length = 3 m

width = 50 cm

1160 m × 3 = 3.48 km

20 × $55.50 = $1 110

WY22

24FSERIES TOPIC


Pentominoes are shapes that consists of five unit squares joined together so that each square shares at least one whole side with another square.

They were invented by a very clever man named Solomon Wolf Golomb.

Cut out the shapes below and fit them together to form a rectangle. What is the perimeter?

What to do

Getting Ready

3

Pentomino puzzle solve

UL23

25FSERIES TOPIC


Area - introducing area

4

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

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

Did you need to see all the squares to work out the area?

1

2

3

area =

area =

cm²

cm²

a

area =

area =

cm²

cm²

b

area =

area =

cm²

cm²

c

Area is the amount of space a shape covers. It is a 2D measurement.

We measure area in square units. For small areas we use square centimetres.1 cm

1cm

a bc

3 × 2 rectangle shaded.

4

15 20

No.

18

2 4

KD18

26FSERIES TOPIC


Area - introducing area

4

area = cm²

a

area = cm²

d

area = 20 m²

5 m

2 m

3 m

a

area = cm²

c

area = cm²

f

area =

area = cm²

b

area = m²

e

area =

5 cm

6 cm 4 cm 1 cm

4 cm

2 cm

5 cm

8 m

2 cm

3 cm4 m

4 cm 4 cm

5 cm

3 cm 3 cm

Find the areas of these shapes:4

We can use this formula to find the area of rectangles:

In these shapes you know the area but not the length of all the sides. Label the missing sides:5

14 m² 24 m²

b

c4 m

7m 8 m

Area = length x widthArea = 3 x 5 = 15 cm²

24

10 32 6

16 4

EU23

27FSERIES TOPIC


Area - area of triangles

Each triangle is half of a rectangle.

To find the area of a triangle, find the area of the rectangle and then divide by two.

Rectangle = 4 cm × 5 cm = 20 cm²Triangle = 20 cm² ÷ 2 = 10 cm²4 cm

5 cm

Find the area of the shaded triangles inside the rectangles.

Find the area of the shaded triangles inside the rectangles.

1

2

area = cm²

a

area = cm²

a

area = cm²

d

area = cm²d

area = cm²

c

area = cm²

f

area = cm²

f

area = cm²

b

area = cm²

b

area = cm²

e

area = cm²e

area = cm²

c

2 cm

8 cm

8 cm

10 cm

10 cm

3 cm

7 cm

7 cm

4 cm

3 cm

3 cm6 cm

8 cm

6 cm 6 cm

6 cm

6 cm

5 cm

5 cm2 cm

2 cm6 cm4 cm

4 cm

4

e

15 24

20

9

21 24 30

14 15

12 12

FV52

28FSERIES TOPIC


Area - hectares and square kilometres

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

Order the states and territories from smallest to largest areas:

1

2

area = hectares

a

area = hectares

d

1 __________________________

4 __________________________

7 __________________________

2 __________________________

5 __________________________

8 __________________________

3 __________________________

6 __________________________

area = hectares

b

area = hectares

e

area = hectares

c

area = hectares

f

300 m

100 m

100 m

450 m

300 m

200 m

250 m

100 m

120 m

120 m

400 m

150 m

WESTERN AUSTRALIA

NORTHEN TERRITORY

QUEENSLAND

NEW SOUTH WALES

SOUTHAUSTRALIA

TASMANIA

1 km² = 1 000 000 m²

Queensland 1 727 200 km²

New South Wales 801 600 km²

Victoria 227 600 km²

ACT 2 400 km²

Western Australia 2 525 500 km²

South Australia 984 000 km²

Tasmania 67 800 km²

Northern Territory 1 346 200 km²

4

Hectares are used to measure large spaces such as a football field.

1 ha = 10 000 m² 1 km² = 1 000 000 m²

An even larger unit is a square kilometre km². One square kilometre is equal to 100 hectares.

We write hectares as ha. One hectare is equal to 10 000 m².

3

6 4.5 6

2.5

1.44

ACT

New South Wales

Queensland

Tasmania

South Australia

Western Australia

Victoria

Northern Territory

BK52

29FSERIES TOPIC


Area - area and perimeter

Find the perimeter and area of each shape.

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

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:

1

2

3

1 cm

1 cm

cma cmb cmc

4

Answers will vary.

Answers will vary.

a P = ____________

A = ____________

c P = ____________

A = ____________

d P = ____________

A = ____________

b P = ____________

A = ____________

1 cm

16 cm

9 or 10 cm

12 cm

20 cm

16 cm²

4.5 cm²

9 cm²

16 cm²

ZO95

30FSERIES TOPIC


Area - area and perimeter

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

4

Teacher check.

EA65

31FSERIES TOPIC


How many 1 cm² tiles do I need to cover this wall?

18 cm

4 cm

2 How many 4 cm² tiles do I need to cover this same wall?

How many 2 cm² tiles do I need to cover a wall that is 6 cm by 6 cm?

3

How many 5 cm² tiles do I need to cover a wall that is 15 cm by 5 cm?

4

4

Area puzzles solve

32

8

18

15

EA45

32FSERIES TOPIC


Draw a composite shape that has an area of 50 cm².2

4

Teacher check.

Can you find the areas of these rooms? Circle the room that would be cheapest to carpet.Put a cross in the room that would be most expensive.

1

area = cm²a

area = cm²d

area = cm²c

area = cm²f

area = cm²b

area = cm²e

4 cm

6 cm

4 cm

9 cm

15 cm

9 cm

6 cm

9 cm

8 cm

8 cm

7 cm

11 cm

12 cm

6 cm

8 cm

5 cm

5 cm

3 cm

3 cm

3 cm

3 cm

2 cm

3 cm

2 cm

3 cm

8 cm

1 cm

2 cm

6 cm

CQ84

50

50 84 101

18

63

Composite calculations apply

33

Copyright © 3P Learning Ltd

Write the measurement that the arrows are pointing to:

Order these lengths from shortest to longest:

220 mm, 200 cm, 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

Units of length Name:______________

= _______ cm = _______ cma 50 m b 8 m = _______ cmc 11.2 m = _______ cmd 1.2 m

= ______ mm

= ______ m

= ______ mm

= ______ m

a 45 cm

a 500 cm

b 7 cm

b 7 500 cm

= ______ mm

= ______ m

c 12 cm

c 329 cm

= ______ mm

= ______ m

d 110 cm

d 2 000 cm

Skills Not yet Kind of Got it

Measures and records length in different units•

Converts between cm, mm and m •

Orders lengths of different units•

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

Topic 1 Assessment

34


Write the measurement that the arrows are pointing to:

Order these lengths from shortest to longest:

220 mm, 200 cm, 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

Units of length Name:______________

= _______ cm = _______ cma 50 m b 8 m = _______ cmc 11.2 m = _______ cmd 1.2 m

= ______ mm

= ______ m

= ______ mm

= ______ m

a 45 cm

a 500 cm

b 7 cm

b 7 500 cm

= ______ mm

= ______ m

c 12 cm

c 329 cm

= ______ mm

= ______ m

d 110 cm

d 2 000 cm


Measures and records length in different units•

Converts between cm, mm and m •

Orders lengths of different units•

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

Topic 1 Assessment

3 cm

Answers will vary.

5 000 800 1 120 120

1 10012070450

5 75 3.29 20

12.4 cm

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

35


Convert into kilometres:1

Name:______________Travelling Far

= __________________ km

= __________________ m = __________________ m

= __________________ m = __________________ m

= __________________ km

= __________________ km = __________________ km

a 5 000 m b 80 m

c 112 m d 400 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

a 45 cm

b 7 km

c 14 km

d 7.8 km


Converts between metres and kilometres •

Solves simple speed and distance problems•

Interprets scales to calculate distances•

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

Topic 2 Assessment

A

BC

DE

1 cm = 10 km

SCALE:

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

A to B ________________________

C to E ________________________

B to D _________________________

If you travel at an average speed of 70 km/h how long would it take you to get from Point A to Point E? ______________________

36


Convert into kilometres:1

Name:______________Travelling Far

= __________________ km

= __________________ m = __________________ m

= __________________ m = __________________ m

= __________________ km

= __________________ km = __________________ km

a 5 000 m b 80 m

c 112 m d 400 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

a 45 cm

b 7 km

c 14 km

d 7.8 km


Converts between metres and kilometres •

Solves simple speed and distance problems•

Interprets scales to calculate distances•

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

Topic 2 Assessment

A

BC

DE

1 cm = 10 km

SCALE:

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

A to B ________________________

C to E ________________________

B to D _________________________

If you travel at an average speed of 70 km/h how long would it take you to get from Point A to Point E? ______________________

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

40 km

80 km

70 km

3 hours

37


1

Name:____________Perimeter

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

Complete this table. All shapes are regular.

2

3

Length of each side 2.5 cm 6 cm

Perimeter 16 cm 25 cm


Measures the perimeter of shapes•

Creates shapes with specified perimeters•

Uses understanding of perimeter to calculate side lengths•

Topic 3 Assessment

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

2m3m

6m

14m

5 m

1 m

9 m

2 m

4 m

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

38


1

Name:____________Perimeter

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

Complete this table. All shapes are regular.

2

3

Length of each side 4 cm 2.5 cm 5 cm 6 cm

Perimeter 16 cm 20 cm 25 cm 30 cm


Measures the perimeter of shapes•

Creates shapes with specified perimeters•

Uses understanding of perimeter to calculate side lengths•

Topic 3 Assessment

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

2m3m

6m

14m

5 m

1 m

9 m

2 m

4 m

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

2 cm

2 cm

60 m

32 m

2 cm 2 cm Answers will vary.

14 m

3 m

3 m 2 m

5 m

4 m

3 m

2 m

6 m

2 m 2 m

39


Name:____________Area

Create 2 different shapes with an area of 18 cm²2

Topic 4 Assessment

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

a area = b area = c area =

d area = e area = f area =

cm² cm² cm²

cm² cm² cm²

a

d

b

e f

c

1 cm

Find the area of : 3

a

c

a rectangle measuring 6 cm x 5 cm

a box measuring 12 cm x 9 cm

b

d

a pool measuring 25 m x 4 m

a phone measuring 4.5 cm x 10 cm

40


Name:____________Area

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

Topic 4 Assessment

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

a area = b area = c area =

d area = e area = f area =

cm² cm² cm²

cm² cm² cm²

a

d

b

e f

c

1 cm

Find the area of : 3

a

c

a rectangle measuring 6 cm x 5 cm

a box measuring 12 cm x 9 cm

b

d

a pool measuring 25 m x 4 m

a phone measuring 4.5 cm x 10 cm

4

5

30 cm²

Sample answers:

108 cm²

100 m²

45 cm²

4

7

6

5.5

41


Name:____________Area

Topic 4 Assessment

Find the area of these triangles:4

area = m²a area = m²carea = cm²b

1 m1 m

4 cm

10 cm3 m

6 m

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

a b

c d

this page Africa

a city park an ipod

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

1 cm


Finds the area of of shapes using grids•

Uses formula L x W to find area of rectangles•

Finds area of triangles •

Makes appropriate unit choices for measuring•

Recognises shapes can have same perimeters but different areas•

42


Name:____________Area

Topic 4 Assessment

Find the area of these triangles:4

area = m²a area = m²carea = cm²b

1 m1 m

4 cm

10 cm3 m

6 m

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

a b

c d

this page Africa

a city park an ipod

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

1 cm


Finds the area of of shapes using grids•

Uses formula L x W to find area of rectangles•

Finds area of triangles •

Makes appropriate unit choices for measuring•

Recognises shapes can have same perimeters but different areas•

9 20 0.5

cm²

ha

km²

cm²

Sample answers:

43


Length, Perimeter and Area - Series F

RegionTopic 1Units of length

Topic 2Travelling far

Topic 3Perimeter

Topic 4Area

NSW

MS3.1 - Select and use the appropriate unit and device to measure lengths, distances and

perimeters

MS3.2 - Select and use the appropriate unit and device to calculate area

measure and record

lengths or distances

use combinations of

cm, mm, m and km

convert between cm,

mm, m and km to

compare lengths

record lengths to 3

decimal places

select and use the

appropriate unit and

device

question and explain

why two students

may obtain different

measures (WM)

solve problems

involving different

measures of length

(WM)

recognise the need for

a unit longer than a

metre

use abbreviation km

measure using km and

½ km

convert between km

and m

solve simple problems

using speed (WM)

find the perimeter of

a large area

calculate and compare

perimeters of squares,

rectangles and

triangles

find the relationship

between the lengths

of sides and the

perimeter for squares,

rectangles, equilateral

and isosceles triangles

explain that

perimeters of

squares, triangles

and rectangles can

be found by finding

the sum of the side

lengths

recognise the need for

a unit larger than a m²

recognise and explain

the need for a more

convenient unit than a

km²- hectares

select the appropriate

unit to calculate area

find the relationship

between length and

breadth and area

apply measurement

to everyday situations

(WM)

VIC

VELS Measurement – Level 4

use metric units to estimate and measure length, perimeter, area

measure as accurately as needed for the purpose of the activity

convert between metric units of length

create new problems based on familiar problem structures (WM)

QLD

EL Y 5 - Length and area can be estimated, measured and ordered using standard and non-

standard units of measure.

standard units, including cm, m, cm², m² and a range of instruments are used to measure and

order attributes of objects including length and area

links exist between different ways of recording the same measurement

reasonable estimates can be made using strategies that suit the situation

44


RegionTopic 1Units of length

Topic 2Travelling far

Topic 3Perimeter

Topic 4Area

SA

3.4 - Select appropriate attributes and systems to measure for a variety of purposes

3.5 - Use a range of standard tools to measure relationships between distances to calculate size

choose and use metric

units or non-metric

standard units to

compare, measure

and analyse

measure for a variety

of purposes

choose appropriate

strategies and units

of comparison

in planning

measurement

choose the

appropriate tools,

technologies and

units to measure

for a particular level

of accuracy, and

discusses how the

tools used affect

the precision of

measurements

choose and use metric

units or non-metric

standard units to

compare, measure

and analyse

estimate distances in

terms of metric units

identify relationships

between distances

to develop and use

formulae in order to

estimate and calculate

the perimeter of

polygons

recognise

relationships between

measurable attributes

of figures and objects,

and communicate

these relationships

in both everyday

and mathematical

language

identify relationships

between distances

to develop and use

formulae in order to

estimate and calculate

the area of shapes

WA/NT

M 9a.4, M 9b.4

select appropriate attributes, distinguish perimeter from area and choose units of a sensible size

for the descriptions and comparisons to be made.

measure area by counting uniform units, including part-units where required

ACT

17.LC.1 - measurement attributes of length, area, mass, capacity, volume, angle and time

17.LC.2 - informal and standard units of measurement of these attributes, including metre,

centimetre, millimetre, square metre, square centimetre, kilogram, gram, litre, millilitre,

degrees, hours and minutes

17.LC.3 - the concept of conservation, including different ways of recording the same

measurement (e.g. in metres, centimetres or millimetres)

17.LC.4 - the concept of measurements as approximations, with the measurement context

influencing levels of precision required and ways of refining measurements (e.g. by changing

units or instruments)

NZMeasurement - Use linear scales and whole numbers of metric units for length, area,

volume and capacity, weight (mass), angle, temperature, and time.

Length, Perimeter and Area - 3P...

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