Book 7r -t Ages 11+ r o e s Bo e p ok u S

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Measurement in Mathematics Series

© ReadyEdPubl i cat i ons Practical measuring activities the •f orr evi ew pur posesonfor l y•

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classroom.

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Written by Gerry Westenberg. Illustrated by Rod Jefferson. © Ready-Ed Publications - 2001 Published by Ready-Ed Publications, P.O. Box 276, Greenwood ,WA, 6024 Email: info@readyed.com.au Website: www.readyed.com.au COPYRIGHT NOTICE Permission is granted for the purchaser to photocopy sufficient copies for non-commercial educational purposes. However this permission is not transferable and applies only to the purchasing individual or institution.

ISBN 1 86397 184 X

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Contents

Introduction - Overview of Topics

4

Materials Required

5

Measurement: How Long? How Far?

6

Calculate the Distance: Air Routes of Australia

7

Measuring in Kilometres

8

Shapes: Perimeter of Polygons

9

Perimeter of Polygons

10

Circling Around

11

12

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Circles Again

r o e t s Bo r e p ok u S

What’s the Cost?

13

Everything Costs: Area and Cost

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Capacity

23

Cubic Measures

24

Cubic Metres

25

Measurement of Regions

14

Area of Rectangles

15

Area of Rectangles Again!

16

Triangles and Rectangles 1 Triangles and Rectangles 2 Hectares or Metres? The Choice is Yours!

17 18

19

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Volume

26

Measurement and Kilograms Suspension Timelines 1 Timelines 2

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Time and the Universe Time Zones Time Zones

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20 © R e a d y E d P u b l i c a t i o n s Volume and Displacement 21 Cubes 22l •f orr evi ew pur poseson y•

27

28

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31

32 33

Have You Got the Time?

34

What’s the Time?

35

Converting Time

36

Yearly Calendars 1

37

Yearly Calendars 2

38

39

Page 3

Intr oduction - Ov er vie w of T opics Introduction Over ervie view Topics This book is designed to be used in conjunction with your mathematics programme. The activities follow the curriculum appropriate to students working at this level. The book covers the following concepts:

Length R R R R R

Measure to the nearest millimetre, centimetre and metre. Complete calculations using kilometres. Find the perimeter of polygons. Find the diameter and circumference of circles. Relate the measurement of length to other measures.

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Area

Complete measure (informal) of various regions. Complete measure (informal) of triangular regions. Calculate the area of rectangles. Understand the relationship between the area of triangles and rectangles. Understand the relationship between hectares and square metres. Relate the measurement of area to other measures.

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R R R R R R

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Volume/Capacity

Measure in litres and millilitres. Measure volume by displacement. Make 3D shapes using cubes. Measure the volume of 3D models. Measure the capacity of containers. Cubic measures: Build a model using cubic metres. Understand the relationship between cubic metres and cubic centimetres. Develop the understanding of volume in cubic metres. R Relate the measurement of volume to other measures.

R R R R R R

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Mass R R R R

Measure mass in kilograms and grams. Undertake the suspension and projection of objects. Measure mass using suspension and projection. Relate the measurement of mass to other measures.

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Time R R R R R R R

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Complete activities and calculations based on calendars. Understand, use and construct timelines. Understand the seasons and planetary motion. Demonstrate knowledge of geographical position. Read time clocks. Measure time in minutes and seconds. Calculate the conversion of time units.

Page 4

Materials Required In addition to the usual classroom stationery items, the following materials are required for some of the activity pages: R tape measure or metre ruler R graduated containers R M.A.B. blocks R 1 cm cubes

r o e t s Bo r e p ok u S

R large elastic bands

R encyclopedias or other reference books R trundle wheel

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R scales

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Page 5

Measurement: How Long? How Far?

R Use a ruler to find the lengths of the following items. Choose three more items and measure their length.

r o e t s Bo r e p ok u S

the blackboard

cm

m

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mm

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Item: Find the distance

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mm

cm

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R Using a tape measure, metre ruler or a trundle wheel, find the distance of the following. Choose two more distances to measure and list them with their measurements.

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From your room to the canteen From your room to the office

Page 6

Calculate the Distance: Air Routes of Australia Darwin

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2852

Brisbane

1622

Perth 3279

752

Sydney

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1161

650 1260

706

Melbourne

610

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R Use the map to answer these.

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Hobart

1. See if you can travel around Australia, starting and finishing in Perth, visiting every capital city

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only once? What was the route you took? ..............................................................................

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.........................................................................

How far did you travel? ...........................

Is there a shorter route than yours? ...............................

If there is, how far is the shortest route? ............

2. Using the routes shown the shortest distance from Darwin to Adelaide is .............................. Design a shorter route. Mark it on the map. Use your ruler and the distances on the map to help you make an estimate. Complete the statement below: The new route is about ...................................... km shorter than the old route. 3. What is the distance of a return flight from Hobart to Sydney? ........................................... 4. A person wishes to travel from Sydney to Melbourne, then to Adelaide and Perth and then return to Sydney. Calculate the shortest distance possible for the traveller. It is ...................................... km. Ready-Ed Publications

Page 7

Measuring in Kilometres Home

School

Supermarket

Friend

Cousin

Home

0

3

2.4

1.3

6

School

3

0

0.64

3.8

9.55

Supermarket Friend

0.64

0

6.37

7.32

1.3

3.8

6.37

0

8.4

6

9.55

7.32

8.4

0

All distances given in kilometres (km).

R Using the above table, find the distance Jared would travel if he went:

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Cousin

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(Example: If Jared went from school, to his cousin’s house, then the supermarket and then home, he would have travelled 9.55 + 7.32 + 2.4 = 19.27 km.)

a) From home to his cousin’s house via school. ........................................................................ b) From home to school, then to his friend’s house, the supermarket and then home

© ReadyEdPubl i cat i ons From school to the supermarket and then home. ................................................................... •f orr evi ew pur posesonl y• From his cousin’s to the supermarket, then return to his cousin’s and finally home. again. ...................................................................................................................................

c) d)

............................................................................................................................................

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e) What would be the shortest distance to visit all the destinations, starting and finishing at home? Write down the route and the distance.

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............................................................................................................................................ ............................................................................................................................................

Home

9.55

6

3 3.8

0.64

8.4

1.3

2.4

6.37

Friend

Supermarket Page 8

Shapes: Perimeter of Polygons

R Match the number of sides to the shape. Number of sides 3

1. Find the perimeter of the following shapes: a) a regular hexagon, side length 10 cm.

Shape

..........................................................

octagon

9

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b) a regular octagon, side length 7 m.

triangle

7

..........................................................

decagon

10

c) a quadrilateral of side lengths 4 cm,

5 cm, 6 cm, 8 cm. ...............................

pentagon

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6 8

hexagon

d) a regular septagon of side length 8 km.

4

nonagon

..........................................................

5

septagon

e) a pentagon of side lengths 4 mm,

6 mm, 5 mm, 4 mm, 3 mm. .................

2. Find the perimeter in mm of each of these polygons.

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R List the shapes in order of perimeter length. Start with the object with the longest perimeter. ........................................................................................................................................ ........................................................................................................................................ Ready-Ed Publications

Page 9

Perimeter of Polygons

Measure the perimeter of all the numbered polygons in the diagram below. Show answers to the nearest millimetre.

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B

C

A

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G

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I

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K

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Circling Around

The diameter of a circle is shown by a line that passes through the centre point of the circle from one side to the other. The distance around the circle is called the circumference. The circumference of a circle can be found by multiplying the diameter by 3.14. In mathematics we call this number π (pronounced ‘pie’). Collect four circular objects and complete the chart below. Object

r o e t s Bo r e p ok u S Diameter (Find the centre)

2. 3. 4.

© ReadyEdPubl i cat i ons A round• tablef has a diameter ofi 80 the circumference. .................................... or r ev ecm. wCalculate pur p oseso nl y•

R Solve these problems using 3.14 as π. 1.

Circumference (Measured)

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1.

Circumference (Calculated)

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2. A gardener plans a circular herb garden, with a surrounding border. If the diameter of the herb garden is 4 m, how many metres will the border be? ...................................................

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............................................................................................................................................. ............................................................................................................................................. 3. The diameter of the wheel of a car is 75 cm. How far will the car travel in one complete

turn of the wheel? ......................................... .................................................................... .................................................................... .................................................................... .................................................................... Ready-Ed Publications

Page 11

Circles Again

The diameter of a circle can be found by dividing the circumference by π. So if the circumference of a plate is 45 cm, what is the diameter? Round your answer to two decimal places. D (diameter)

Circumference (C)

=

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π

=

45 3.14

=

14.33 cm

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Remember, π is not exactly 3.14, so the answer is not exact.

R Try these. Work out the answer to the nearest decimal point.

1. The circumference of a wheel is 250 cm. What is the diameter? ......................................... .............................................................................................................................................

2. A frisbee has a circumference of 34 cm. Will it fit into a square box with sides of 8 cm?

© ReadyEdPubl i cat i ons ............................................................................................................................................. •f orr evi ew pur posesonl y•

Why or why not? ..................................................................................................................

3. Find the diameter of these circles to the nearest tenth of a centimetre: b

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a

C = 2.8 cm

C = 6.6 cm

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C = 12 cm

a) .......................................... b) .......................................... c) ....................................... 4. Find the missing measurements to the nearest tenth of a centimetre: Object

Diameter

a Clockface

78.2 cm

b Frisbee

16 cm

c Hoop

50 cm

d Plate Page 12

Circumference

What’s the Cost?

R The cost of pine wood laminate is \$2.50 per metre.

1. I wish to put this laminate around the edge of a table top. The dimensions are 2.4 m x 1.2 m. How much will it cost me to edge the table? ........................................................................... 2. How much will it cost to edge the bench top below? ...............................................................

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60 cm

60 cm

R It costs Paul 86¢ to drive 12 km. Using the table below, calculate the costs of the following trips:

3. Sydney to Melbourne ...........................................................................................................

© ReadyEdPubl i cat i ons Albury to Ballarat .................................................................................................................. •f orr evi ew pur posesonl y• Adelaide to Sydney ..............................................................................................................

4. Adelaide to Melbourne ......................................................................................................... 5. 6.

Sydney

Melbourne

Canberra

Albury

Ballarat

0

1410

731

1111

1014

620

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Melbourne

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731

Canberra

1111

Albury

1014

Ballarat

620

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989

285

779

1110

989

0

736

306

111

285

736

0

337

847

779

306

337

0

417

1110

111

847

417

0

All distances given in kilometres (km)

Page 13

Measurement of Regions

R Fold a piece of paper in half and then into quarters as shown:

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Use this shape to measure the area of:

..............................................................

..............................................................

The door

..............................................................

A scrapbook

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..............................................................

Fold another piece of paper as follows:

© ReadyEdPubl i cat i ons Your maths book •f or.............................................................. r evi ew pur posesonl y• ..............................................................

The door

..............................................................

A scrapbook

..............................................................

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Use this shape to measure the area of:

R Choose five other items from your classroom to measure, using both pieces of paper:

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1. .....................

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2. .....................

3. .....................

4. ....................

5. ..........................

What was the area of your desk using the square paper? ............................................................ What was the area of your desk using the triangular paper? ......................................................... What was the area of your maths book using the square paper? .................................................. What was the area of your maths book using the triangular paper? .............................................. R Compare all the other areas. What relationship can you find between the number of squares needed to measure an object, and the number of triangles needed for the same object? ............................................................ ................................................................................................................................................... ................................................................................................................................................... Page 14

Area of Rectangles

1. Calculate the area of the following rectangles using Area = Length x Width. a)

b)

2m

5m

10 m ...................................

c)

...................................

6m

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24 cm

6 km

...................................

7 cm

...................................

6 km

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R Find the area of the shapes at the bottom of the page. Hint: Find a way to make each shape into a rectangle and then work out the area. An example is done for you below.

Method 1: Subtraction 6m

2m

3m

2m

5m

Area of large rectangle =lxw =6x5 = 30 m2

Area of small rectangle 2m © Read yEdPu i cat i ons = l xb wl =2x2 6m =p 4m •f orr evi ew pur osesonl y•

2m

4m

2

Total area = 30 - 4 = 26 m2

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2m

4m

3m

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Area of large rectangle =lxw =6x3 = 18 m2

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Area of small rectangle =lxw =2x4 = 8 m2

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2. Use one of the methods to find the area of these shapes: 15 m 3m

6 km

5m

5 km 4 km

2m

12 m

3 km

10 km

2 cm b) ..........................................

c) ...................................... Page 15

Area of Rectangles Again!

1. Find the area of the shaded regions:

a.

1234567890123456789 1234567890123456789 1234567890123456789 1234567890123456789 1234567890123456789 1234567890123456789 1234567890123456789 2 km 1234567890123456789 1234567890123456789 6 km 1234567890123456789 3 km 1234567890123456789 1234567890123456789 1234567890123456789 1234567890123456789 1234567890123456789 1234567890123456789 1234567890123456789

c.

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1234567890123456789012345678 10 cm 1234567890123456789012345678 1234567890123456789012345678 1234567890123456789012345678 1234567890123456789012345678 1234567890123456789012345678 1234567890123456789012345678 1234567890123456789012345678 1234567890123456789012345678 2 cm 1234567890123456789012345678 5 cm 1234567890123456789012345678 1234567890123456789012345678 1234567890123456789012345678 12345678901234567890123456788 cm 1234567890123456789012345678 3 cm 1234567890123456789012345678 1234567890123456789012345678 4 cm 1234567890123456789012345678 2 cm 1234567890123456789012345678 1234567890123456789012345678 3 cm 1234567890123456789012345678 1234567890123456789012345678 1234567890123456789012345678

d.

2 cm

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7 km

b.

1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 8 cm 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456 1234567890123456

123456789012345678901234 123456789012345678901234 1 123456789012345678901234 123456789012345678901234 123456789012345678901234 1234567890123456789012343 123456789012345678901234 123456789012345678901234 123456789012345678901234 123456789012345678901234 123456789012345678901234 4 123456789012345678901234 123456789012345678901234 7 123456789012345678901234 5 123456789012345678901234 123456789012345678901234 123456789012345678901234 123456789012345678901234 4 123456789012345678901234 123456789012345678901234 123456789012345678901234 123456789012345678901234 3 123456789012345678901234 1234567890123456789012343 123456789012345678901234 123456789012345678901234

b.

.............................................................................

c.

.............................................................................

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d.

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2. An old tablecloth, measuring 0.9 m x 1.3 m, was used by Sarah to make a poncho style cape. She needed to cut a 20 cm x 20 cm hole for her head. How much material was left for the poncho?

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a.

©R eadyEdPubl i cat i ons 6 cm 10 mm •f orr evi ew pur posesonl y• .............................................................................

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................................................................................... ................................................................................... ...................................................................................

3. Joe needs to cut four rectangles from one large sheet of wood measuring 2400 mm x 1800 mm. One rectangle is 140 mm x 900 mm. One is 800 mm x 180 mm, one is 540 mm x 300 mm and the other is 256 mm x 190 mm. How much wood was left after all this? ................................................................................................................................................... ................................................................................................................................................... Page 16

Triangles and Rectangles 1 4m

Area = L x W 3m

=4x3 = 12 m2

This has now been divided into two triangles, each one half of the rectangle.

BUT

R Use what you know about area of rectangles to find the area of triangles. 9m

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So

It can be made into two equal triangles.

The area of a right-angle triangle = ½ of the area of a rectangle. Area of

= ½ (L x W)

For example:

Area of

= ½ (L x W) = ½ (6 x 12) = ½ (72 cm2) = 36 cm2

6 cm

12 cm

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1 m Area = L x W =9x1 = 9 m2

Now tr y tthese: hese:Re try © adyEdPubl i cat i ons R Find the area of these triangles and shapes. a)

4 mm

27 m •f orr evi ew p r p oses onl y• b) u 9m 7 mm 6 km

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c)

................................................................... d)

3 km

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................................................................. e)

...................................................................

f)

................................................................. g)

5m

................................................................... h)

3 cm

9m 870 cm ................................................................. Ready-Ed Publications

2m

7m

6.4 mm 21.3 mm

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4 cm 8 cm ................................................................... Page 17

Triangles and Rectangles 2

You know that a rectangle divided into two can make two right-angled triangles.

Do you remember?

The area of a right-angled triangle is ........................................................................................... Does this work for any triangle?

1

3 cm

2 cm

Area of

1 = ½ (4 x 3) = ½ (12) =6

Area of

2 = ½ (2 x 3) = ½ (6) =3

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4 cm

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Total Area = 3 + 6 = 9 cm2

© ReadyEdPubl i cat i ons Area of whole ½ (l x h) •f o==r vi ew pur posesonl y• ½r (6e x 3) We can work this out using the height of the triangle.

= ½ (18) = 9 cm2

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a)

2 mm

b) 6m

3 mm

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................................................................. c)

9.4 km

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...................................................................

d)

2 km

4 km

5 km .................................................................

Page 18

...................................................................

Hectares or Metres? The Choice is Y ours! Yours!

A square 100 m x 100 m is called a hectare. 100 m

1 hectometre

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100 m

=

So 100 m x 100 m = 10 000 m

= 1 hectare

1 hectometre

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= 1 Hectare. 1. Find the area of a rectangular field 300 m x 500 m. Convert this to hectares. 2

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............................................................................................................................................

2. A field is to be ploughed. Its dimensions are 250 m x 175 m. Find the area in m2 and then in hectares. ............................................................................................................................................

3. Find the area of the following plots of land in m2 or in hectares. 250 m

b)

© Re adyEdPubl i cat i ons 68 m 674 m •f orr evi ew pur posesonl y •

.....................................................................

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c)

938 m

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..................................................................... d)

800 m

209 m

500 m

200 m

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250 m

..................................................................... e)

.....................................................................

1200 m 400 m 400 m

200 m 300 m

.....................................................................

Page 19

Ev erything Costs: Area and Cost Everything

1. It costs \$36 per square metre to carpet a house. Find the cost of having carpet fitted to the following rooms: 3.8 m a) b) 2.4 m 1.6 m

2.7 m

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.....................................................................

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..................................................................... ..................................................................... 5.9 m c) d) 2.3 m 3.2 m

.....................................................................

2. A farmer has a yield of 3.4 tonnes of wheat for every hectare. What is the yield in tonnes of the following fields? Round your answers to two decimal places. a)

b)

384 m

560 m

296l m © ReadyEdPub i cat i ons ..................................................................... •f orr evi ew pu..................................................................... r p osesonl y• 986 m 740 m

293 m

c)

d)

864 m

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3. It costs \$2.26 per m2 to tile a floor. Find the cost of tiling the following areas: a) 8m

b)

6.4 m

3.2 m

9m

..................................................................... c)

..................................................................... d)

4.2 m 2.1 m ..................................................................... Page 20

4.7 m 3.6 m ..................................................................... Ready-Ed Publications

Volume and Displacement Volume can be measured by the amount of water displaced (or removed). Do you know the story of Archimedes and his bath?

Volume can be measured in cubic centimetres (cm3) or cubic metres (m3).

r o e t s Bo r e p ok u S 500

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500

The diagram above shows that the object in the beaker displaced 100 ml. Therefore, the volume of the object must be 100 ml.

R Find 10 objects and calculate their volume by measuring the amount of water they displace from a marked container. Complete the table below.

© ReadyEdPubl i cat i ons Object Displacement •f orr evi e w pur posesVolume onl y•

Note: Make sure that the objects you choose cannot be harmed by water!

.........................................................................................................................................

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......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... ......................................................................................................................................... .........................................................................................................................................

Extr a Extra Find three more objects. Estimate their volume and check by displacement. Record your results on the back of the sheet. Ready-Ed Publications

Page 21

Cubes

a.

What is volume and surface area? I’m glad you asked. A simple explanation is that volume is the number of blocks used to make the shape, and the surface area is the number of sides that can actually be seen (including the bottom).

r o e t s Bo r e p ok u S For example, if you make this shape, it would have a volume of 3 cubes and a surface area of 14 squares.

d.

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c.

b.

1. Use the shapes to complete the table below. (Remember that the models are made with 1 cm cubes.)

Volume Surface Area © Rea dyEdPubl i c at i ons a. •f orr evi ew pur posesonl y•

Model

b.

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2. How many different models can you make:

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c.

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a. using 5 cubes? ..................................... b. using 9 cubes? .....................................

Model

Volume

Surface Area

Which shapes have the greatest volume and least surface area? ........................................... Page 22

Capacity

Capacity is the amount of substance that a container can hold. It is usually measured in: cubic centimetres cm3 or cubic metres m3 or cubic millimetres mm3 1. Find ten containers. Fill each of your containers with water and then use a graduated jug, like the one pictured, to measure the volume of water held in each container. The volume a container holds shows its capacity.

r o e t s Bo r e p ok u S Capacity

2. Enter your information on the chart below.

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Container

......................................................................................................................... ......................................................................................................................... ......................................................................................................................... .........................................................................................................................

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• ......................................................................................................................... ......................................................................................................................... .........................................................................................................................

.........................................................................................................................

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......................................................................................................................... .........................................................................................................................

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3. Now find four other containers and estimate each container’s capacity. Record your estimations below. Then check their actual capacity, using a graduated container. Record the capacity below.

Container

o c . che e r Estimated Capacity Actual Capacity o t r s super

........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................ ........................................................................................................................................

Page 23

Cubic Measures

Using M.A.B.s, we are going to explore the relationship between cubic metres and cubic centimetres.

10 high

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10 long

Diagram 1

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To show a cubic metre we will need to make a model. Make a model 10 cubes high, by 10 cubes long, by 10 cubes wide as in Diagram 1. This will give you an idea of how big a cubic metre actually is.

Diagram 2 © ReadyEdPub l i cat i ons Diagram 2• shows you av cubic metre liker with the s shaded part showing f o rwhat r e i e wlooks pu po es o nl yyour•model. Number of cubes = .....................................................

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Now, to find out the number of cubic centimetres in a cubic metre, we need to count the number of cubes in our model.

However, in each cube there are ten flats. To calculate the number of flats, multiply the number of cubes by 10.

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Number of flats = ........................................................

But, in each flat, there are 100 one cm cubes. To calculate the number of 1 cm3 in the model, multiply the number of flats by 100. Number of 1 cm3 =......................................................

So, there are .............................................................. cm3 in one cubic metre!

Now measure your room’s length and width. For the height of the room you can use 3 m. Calculate how many cubic metres there are in your room. ....................................................... How many cm3 is that? ...............................................

Page 24

Cubic Metres

1. A box has dimensions of 40 cm x 30 cm x 60 cm. a) What is the volume in cm3? b) Convert this to m3.

............................................................................. .............................................................................

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2. A shipping container is 17 m x 3.1 m x 3.5 m. Calculate its volume in m3.

............................................................................................................................................

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............................................................................................................................................

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3. A refrigerator has dimensions of 160 cm x 45 cm x 35 cm. How many cubic metres would it take up?

............................................................................................................................................ ............................................................................................................................................

4. Fill in the missing numbers:

Depth cm •f orWidth r evi ew pur po sesonl ym•

Length a

41 cm

360 cm

240 cm

b

4.2 m

1.3 m

0.8 m

d e f

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c

100 cm

75 cm

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2.4 m

60 cm 80 cm

3

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3

0.24

40 cm

96000

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1.3 m

4.5

84600

5. An Olympic pool has a length of 50 m, a width of 10 m and a depth of 6 m. What is the volume in m3? ............................................................................................................................... 6. An ice box has dimensions of 0.9 m x 0.35 m x 0.4 m. What is its volume? ........................................................................................................................................

Page 25

Volume One litre of water weighs one kilogram. One cubic metre of water weighs one tonne. One millilitre of water weighs one gram. One cubic millimetre of water weighs one gram. R Give the weight of water in these containers.

r o e t s Bo r e p ok u S b.

c.

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a.

a. ....................................... b. ......................................... c. .......................................... 8

d.

e.

f.

g.

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d. .............................

24 cm

e. .............................

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Sol ve tthese hese pr oblems! Solv problems!

15 mm

15

f. ...........................

2.4 m

1.6

g. ............................

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8 cm

0.6

1. An aquarium has dimensions of 1.2 m, 80 cm and 50 cm. What weight of water will it

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hold? ....................................................................................................................................

2. The local dam measures 31 km x 2 km x 74 m. How many tonnes of water could the dam hold? ................................................................................................................................... 3. 1 m3 of a liquid chemical costs \$4.38. How much would it cost to fill a container 3.4 m x 2.2 m x 1.4 m? ..................................................................................................................... 4. One litre of ice cream costs \$3.23. How much would it cost to buy 256 litres for an ice cream parlour? .................................................................................................................... 5. Ten ice cream cones can be made from 1 litre of ice cream. Each ice cream costs \$1.20. How many ice creams can I make from the 256 litres? How much money will I get from the sale of the ice creams? ....................................................................................................... Page 26

Measurement and Kilograms

R Using a set of scales, measure the weight of the following items.

Items

Grams

Kilograms

Pen Ruler Pencil case

Bag

Choose five more items to measure, list below and then weigh them.

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Maths book

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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1. Add up the weights of the items you recorded above and give your answer in grams and kg. ........................................................................................................................................

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2. Jane, Joe and Natasha are stuck in a mine shaft. Jane weighs 90 kg, Joe 96 kg and Natasha 83 kg.

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a. What is their combined weight? ........................................................................................ b. Can they all get into a bucket which can hold 296 kg, and get to the top together? (The bucket is quite large!) ..................................................................................................................

3. Fred buys 5 books, each weighing 2.3 kg, 2 pencil cases weighing 450 grams each, and a dictionary weighing 3.8 kg. What is the total weight of the items that Fred purchased? ........................................................................................................................................

Page 27

Suspension

Use 4 - 6 elastic bands, and select 10 items for suspending and weighing. Use items such as a book, a pencil case and so on. You will also need some scales. desk top

Attach each item to the elastic bands and using a tape measure, measure the distance the bands stretch. Next weigh the object and put your results into the table below.

Item

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Weight

in kg or grams travelled in cms

3. 4. 5. 6. 7.

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8. 9.

10.

Distance

tape measure

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2.

item

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1.

elastic bands

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Have you finished? Choose two more items, suspend each and see if you can estimate their weight. Check your answer by weighing!

2. Now put each item on the desk top and attach it to the elastic bands. Pull the item back 20 cm and let it go. Measure how far the object travels on the desk top. Pull back 20 cm.

Measure this distance.

Page 28

Timelines 1

means the years ‘before the birth of Christ’.

means anno Domini - ‘in the year of our Lord’. We use this for the years after the birth of Christ.

Place these dates on the timeline. Use a reference book to help you find five more dates.

1000 BC

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1. 490 BC The Battle of Marathon.

3. AD 1750 George Washington fights the English.

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2. 55 BC Caesar invades Britain.

4. AD 1000 Leif Erickson sailed for America. 5. AD 1 Birth of Christ.

© ReadyEdPub i cBC at i o sDavid. 6. l 1000 Time ofn King •f orr evi ew pur p7.oAD se sApollo on l y 1973 13 lands• on the moon.

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8. AD 1066 Battle of Hastings.

9. AD 1815 Battle of Waterloo.

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10. AD 1187 Battle of Hattin.

11. ................................................... 12. ................................................... 13. ................................................... 14. ................................................... 15. ...................................................

Page 29

Timelines 2

Year

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You might like to include the following:

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Make up a time line of your own with important dates and events that have occurred in your lifetime.

R a baby brother or sister is born; R your first tooth falls out; R you win a sporting event; R you move house; R you start preschool and so on.

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+

Time and the Universe

+

+

+

+

It takes one day for the earth to complete one revolution on its axis. It takes one year for the earth to make one revolution of the sun.

+ + +

1. All the planets in our solar system have different lengths for a day and a year. Use a reference book to help you complete the table. Planet Mercury

b)

Venus

c)

Earth

d)

Mars

e)

Jupiter

f)

Saturn

Length of Day

Length of Year

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a)

r o e t s Bo r e p ok u S Distance from Sun

© ReadyEdPubl i cat i ons • f orr evi ew pur posesonl y• Pluto

g)

Uranus

h)

Neptune

i)

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On Earth, the time of the seasons is different for the northern hemisphere and the southern hemisphere.

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So, when it is summer in Australia it is winter in the USA, and when it is autumn in Australia it is spring in the USA.

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2. By looking at the temperatures and the months, identify each place with its graph. Temp. 40oC a

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Perth

0 oC

.......

New York .......

d

F

M

A

M

J

J

A

S

O

N

Hobart

.......

Miami

.......

D Months Page 31

Time Zones 1

What time is it in London? in P ar is? in ... ? Par aris?

The world is divided into 24 time zones. Why? So that clocks will show the same time in each place for sunrise, noon and sunset.

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London

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The difference in time from one zone to another is one hour. If you go west, each 15o of longitude is one hour earlier. If you go east, each 15o of longitude is one hour later.

New York

Rome

Delhi

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Sydney

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1. If it is 4.00 pm in Perth, what time is it in:

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a) London? ....................... b) Sydney?............................ c) New York? ........................

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2. Jacob lives in Sydney. At 8 pm he calls his grandparents in London. What is the time in London? ..............................................

3. It is 2.30 am in Rome. What time is it in: a) Delhi? ..................................................

4. If I fly from Sydney to Perth and leave at breakfast time (7.00 am), what time will I arrive in Perth? (Hint: The flight takes 3 hours). ................................................................................

Extension Look in an encyclopedia or other reference books to find what happens to time at the International Date Line. Page 32

Teac he r

R These are the Australian time zones in non-daylight saving periods.

Time Zones 2 Western 6.00 pm

Eastern 8.00 pm Central 7.30 pm

r o e t s Bo r e p ok u S Western

Central

Breakfast

Arrive at school

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R In the table below write the times you would usually do each event in the column describing your time zone. Then say what time it would be in the other two time zones. Eastern

© ReadyEdPubl i cat i ons orr evi ew pur posesonl y• Dinner •f Lunch

Arrival home

Bedtime

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During summer, NSW, Victoria, and SA have “daylight saving”, while WA and Queensland do not. States with daylight saving turn their clocks back one hour, e.g. it appears that the sun rises at 7.00 am rather than at 6.00 am. This would now mean that the difference between time in Perth and Sydney is three hours rather than two hours. The time difference between Perth and Adelaide will now be two and a half hours, although the Sydney-Adelaide time difference would remain as before.

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Now complete the table as above, this time using summer (daylight saving) times. Western

Breakfast

Central

Eastern

Arrive at school Lunch Arrival home Dinner Bedtime Ready-Ed Publications

Page 33

Have You Got the Time?

Time Cloc ks Clock

1. Make the times shown on the clock faces:

3 7

6

5

11 12 1

4

2 3

7

5

4

10 9 8

3.35

10 9 8

10 9 8

11 12 1

2

3

7

6

5

11 12 1

4

10 9 8

10 9 8

3.20

2

10 9 8

6

5

11 12 1

4

2 3

7

6

4

10 9 8

3

7

6

5

11 12 1

2

10 9 8

3

7

6

5

11 12 1

4

2 3

7

6

5

11 12 1

4

12.40

2

10 9 8

10 9 8

7

6

5

4

10 9 8

9.52

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10 9 8

10 9 8

11 12 1

7

6

5

11 12 1

7

6

5

11 12 1

2 4

2

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6

Page 34

11.30

4

2

3

7

6

5

11 12 1

4

2

3

7

6

5

11 12 1

4

6.30

3

2

7

6

5

11 12 1

4

2 3

7

6

5

4

10.34

10 9 8

3

7

6

3 d) ...................

4

2

5

4

11 12 1

5

11 12 1

4

2 3

7

6

5

4

1.16

11 12 1

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3 a) ...................

3 g) ................... 7

5

11 12 1

2. Write down the time to the nearest minute. 10 9 8

2

8.40 © ReadyEd9.29 Publ i cat i on4.34 s •f orr evi ew pur posesonl y• 3

7

3

2.40

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10 9 8

6

2

11 12 1

r o e t s Bo r e p ok 8.32 6.45 u 7.20 S

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10 9 8

2

11 12 1

m . u

10 9 8

11 12 1

10 9 8

10 9 8

10 9 8

7

6

5

11 12 1

7

6

5

11 12 1

2

4

2

3 b) ...................

3 e) ...................

4

2 3

7

6

5

4

h) ...................

10 9 8

10 9 8

10 9 8

7

6

5

11 12 1

7

6

5

11 12 1

7

6

5

2

3

c) ......................

3

f) .......................

3

i) .......................

4

2

4

2 4

What’s the Time?

Time in hour es. hourss and minut minutes.

R How many minutes are there between the two times? 1. 2.45 pm and 2.55 pm.............................

2.

4.15 am and 4.55 pm ..........................

3. 9.45 am and 1.20 pm.............................

4.

6.55 am and 7.05 am ..........................

5. 3.10 am and 5.20 am.............................

6.

2.45 am and 5.40 am ..........................

7. 2.24 am and 3.24 am.............................

8.

12.00 am and 12.00 pm ......................

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9.

3.42 pm and 5.24 am? ...................................................................

10. 2.50 pm and 7.30 pm? ................................................................... 11. 12.00 pm and 1.15 am? ................................................................. R Write in the difference between these times in hours and minutes. 12.

15.

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R How many hours and minutes are there between:

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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........................................ 14.

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........................................

.........................................

17.

......................................... Page 35

Converting Time

R How many seconds in: 1.

3 mins, 24 secs? ..............................................

2.

5 mins, 17 secs? ..............................................

3.

2 mins, 49 secs? ..............................................

4.

8 mins, 28 secs? ..............................................

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How many minutes in:

R

2 hours, 27 mins? .............................................

6.

3 hours, 48 mins? .............................................

7.

9 hours, 6 mins? ...............................................

8.

22 hours, 15 mins? ...........................................

9.

10 hours, 45 mins? ...........................................

How many hours in:

R

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5.

© ReadyEdPubl i cat i ons 11. 7 days, 12 hours? ............................................. • f orr evi ew pur posesonl y• How many minutes in: 10. 4 days, 11 hours? .............................................

R

13. 5 weeks, 2 days? .............................................

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14. 37 weeks, 5 days, 10 hours? ............................

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12. 2 days, 12 hours? .............................................

15. How many minutes in one year? ..........................................................................................

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...........................................................................................................................................

16. How many seconds in 6 months (of 4 weeks each), 3 weeks and 5 days? ............................ ........................................................................................................................................... 17. Think of your own time word problem. Write it here. Can your neighbour or partner solve this problem? .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... Page 36

Yearly Calendars 1

R Use the calendar on the next page to answer these questions.

Normal Year

Leap Year

R On what day of the week is: Australia Day? Christmas Day?

January 7?

................................................................................. ................................................................................. .................................................................................

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Boxing Day?

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.................................................................................

February 29?

.................................................................................

March 30?

.................................................................................

October 12?

.................................................................................

R How many weeks and days in:

................................................................................. © ReadyE dPubl i cat i ons March? ................................................................................. •f orr evi ew................................................................................. pur posesonl y• February? July?

R How many Fridays in: .................................................................................

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November?

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June?

.................................................................................

R What is the date of:

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The third Wednesday in June?

.................................................................................

The second Tuesday in May?

.................................................................................

The first Monday in October?

.................................................................................

R How many days between July 10 and August 7?

.................................................................................

Page 37

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Normal Year (1997)

Yearly Calendars 2

Year (1996)

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• A “Leap”

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Answers Air Routes of Australia (Page 7) a) P - A - H - M - S - B - D - P, 10951, 2. 4765, direct is about 2565 - 2200 km shorter, 3. 2632 km, 4. 6753 km. Measuring in Kilometres (Page 8) a) 12.55 km, b) 15.57 km, c) 3.04 km, d) 20.64 km, e) home - friend - school - supermarket cousin - home, 19.06 km. Shapes: Perimeter of Polygons (Page 9) (Note: the printing process may distort shapes.) Perimeter of polygons: 1a) 60 cm, b) 56 m, c) 23 cm, d) 56 km, e) 22 mm. 2a) 105 mm, b) 40 mm, c) 95 mm, d) 120 mm, e) 180 mm, f) 134 mm, g) 213 mm. Order: b, c, a, e, g, d, f.

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Perimeter of Polygons (Page 10) (Note: the printing process may distort shapes.) a) 345 mm, b) 62 mm, c) 125 mm, d) 123 mm, e) 80 mm, f) 80 mm, g) 112 mm, h) 94 mm, i) 120 mm, j) 55 mm, k) 55 mm, l) 48 mm. Circling Around (Page 11) 1. 251.2 cm, 2. 12.56 m, 3. 235.5 cm.

Circles Again (Page 12) 1. 79.62 cm, 2. no, diameter = 10.83 cm, 3a) 3.8 cm, b) 0.9 cm, c) 2.1 cm, 4a) 24.9 cm, b) 50.2 cm, c) 157 cm d) 31.2 cm. What’s the Cost? (Page 13) 1. \$18.00, 2. \$22.00, 3. \$70.88, 4. \$52.39, 5. \$29.89, 6. \$101.05, 7. \$79.62.

© ReadyEdPubl i cat i ons Area of Rectangles (Page 15) •f orr evi ew pur posesonl y• 1a) 20 m , b) 30 m , c) 168 cm , d) 36 km , 2a) 81 m , b) 24 cm , c) 128 km . Measurement of Regions (Page 14) You use twice as many triangles as you do squares. 2

2

2

2

2

2

2

Area of Rectangles Again (Page 16) 1a) 36 km2, b) 40 cm2, c) 52 cm2, d) 83mm2, 2. 1.13 m2, 3. 3839360 mm2.

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Triangles and Rectangles 2 (Page 18) a) 3 mm2, b) 39 m2, c) 9.4 km2, d) 10 km2.

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Triangles and Rectangles 1 (Page 17) a) 14 mm2, b) 121.5 m2, c) 9 km2, d) 10.2 m2, e) 68.16 mm2, f) 24.5 m2, g) 3.915 m2, h) 44 cm2.

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Hectares or Metres (Page 19) 1. 15 hectares, 2. 43 750 m2 or 4.375 hectares, 3a) 1.7 hectares or 17 000 m2, b) 63.22 hectares, 63 2212 m2, c) 10 hectares or 10 000 m2, d) 24.2 hectares or 242 200 m2, e) 64 hectares or 640 000 m2. Everything Costs (Page 20) 1a) \$138.24, b) \$369.36, c) \$679.68, d) \$231.84, 2a) 140.90 tonnes, b) 38.65 tonnes, c) 9.26 tonnes, d) 289.65 tonnes, 3a) \$81.36, b) \$46.28, c) \$9.97, d) \$38.24. Cubic Measures (Page 24) 1000 cubes, 10 000 flats, 1000 000 1 cm cubes, 1000 000 cm3 = 1 m3. Cubic Metres (Page 25) 1. 72 000 cm3, 0.072 m3, 2. 184.45 m3, 3. 0.25 m3, 4a) 3542400 cm3, 3.54 m3, b) 4368000 cm3, 4.37 m3, c) 40 cm, 240000cm3, d) 30 cm, 0.096 m3, e) 1.875 m, 4500000 cm3, f) 0.027 m, 0.086 m3. 5. 3000m3 6 . .126m3 Ready-Ed Publications

Page 39

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Volume (Page 26) a. 500 g, b. 800 g, c. 300 g, d. 512 g, e. 5376 kg, 5.376 tonnes, f. 5400 g, g. 2.3 tonnes. 1. 0.48 tonnes or 480 kg, 2. 4 588 000 tonnes, 3. \$45.87, 4. \$826.88, 5. 2560 ice creams, \$3072.00. Measurement & Kilograms (Page 27) 2a. Combined weight is 226 kg, b. Yes they could, 3. 16.2 kg. Timelines (Page 29) 6, 1, 2, 5, 4, 8, 10, 3, 9, 7. Time and the Universe (Page 31) 1a. 58 000 000 km, 58.7 days, 88 days; b. 108 000 000 km, 243 days, 224.7 days; c. 150 000 000 km, 23 hours 56 min 4 seconds, 365.26 days; d. 228 000 000 km, 24 hours 37 min 22 seconds, 687 days; e. 778 000 000 km, 9 hours 50 min 28 seconds, 11.86 years; f. 1 400 000 000 km, 10 hours 13 min 58 seconds, 29.46 years; g. 30 000 000 000 km, 17 hours 14 min; 84.01 years. h. 4 500 000 000 km, 19 hours 12 min, 164.8 years; i. 6 000 000 000 km, 6 days 9 hours 36 min, 248.4 years. 2a.Perth, b. Miami, c. Hobart, d. New York. Time Zones (Page 32) 1a. 8am, b. 7.00pm, c. 3.00am, 2. 6am, 3a. 6.30am, b. 10.30am, 4. 8.00am. Extension: The day changes. Have You Got the Time? (Page 34) a. 1.55, b. 9.00, c. 12.10, d. 6.00, e. 11.40, f. 3.05, g. 9.42, h. 9.25, i. 10.20. What’s the Time? (Page 35) 1. 10 min, 2. 760 min, 3. 215 min, 4. 10 min, 5. 130 min, 6. 175 min, 7. 60 min, 8. 720 mins, 9. 13 hours 42 min, 10. 4 hours 40 min, 11. 13 hours 15 min, 12. 2 hours 6 min, 13. 4 hours 25 min, 14. 5 hours 15 min, 15. 3 hours 5 min, 16. 5 hours 20 min, 17. 2 hours 50 min. Converting Time (Page 36) 1. 204 sec, 2. 317 sec, 3. 169 sec, 4. 508 sec, 5. 147 min, 6. 228 min, 7. 546 min, 8. 1335 min, 9. 645 min, 10. 107 hours, 11. 180 hours, 12. 3600 min, 13. 53 280 min, 14. 380 760 min, 15. 524 160 min, 16. 16761600 sec. Yearly calendar (Page 37) Normal Leap Sunday Friday Thursday Wednesday Friday Thursday Tuesday Sunday -Thursday Sunday Saturday Sunday Saturday 4 weeks, 2 days 4 weeks, 2 days 4 weeks, 2 days 4 weeks, 2 days 3 weeks, 6 days 4 weeks, 4 4 4 5 18th 19th 13th 14th 6th 7th 28 28

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