Chapter11-Volume, Mass and Time

Measurement

Volume, mass and time

11

Measuring things is an important part of our lives: How long till my birthday? How heavy is my school bag? How much water is needed to fill the swimming pool? If you worked in a kitchen, you would be measuring all the time: How much flour is needed for a cake? What amount of water is needed to cook spaghetti? For how long do we roast a chicken? In this chapter, we look at how to measure volume, capacity, mass and time.

estimate, measure and convert volumes (cubic millimetres, cubic centimetres and cubic metres)

find the volume of a rectangular prism estimate, measure and convert capacities (millilitres, litres and kilolitres) know and use the relationships 1 cm3 = 1 mL, and 1 m3 = 1 kL estimate, measure and convert masses (milligrams, grams, kilograms and

tonnes) draw and interpret timelines using a scale round times to the nearest minute or hour add and subtract times and calculate time differences use time zones to calculate time differences between major cities interpret and use timetables.

volume The amount of space occupied by an object. cubic metre The volume of a cube with side length 1 metre. capacity The amount of fluid (liquid or gas) contained by an object. tonne A measuring unit of mass for heavy objects. time zone A region of the world in which all places experience the same

time of day. Eastern Standard Time The time zone for the eastern states of Australia.

Is there a difference between volume and mass? Do they mean the same thing? Can you explain what they are in your own words? Are big things always heavy? Can a big thing be light, or a small thing be heavy?

In this chapter you will:

Wordbank

Think!

VOLUME, MASS AND TIME 353 CHAPTER 11CHAPTER 11

354

NEW CENTURY MATHS 7

1 Each cube in these drawings represents one cubic centimetre (1 cm3). Find the volume of each gure.

2 Write the time shown on each of these clocks.

3 Write the times shown on these watches using 12-hour time (am or pm).

a b c d

e f g h

i j k l

12

2

3

4567

8

9

1011 1 12

2

3

4567

8

9

1011 112

2

3

4567

8

9

1011 1

12

2

3

4567

8

9

1011 1 12

2

3

4567

8

9

1011 112

2

3

4567

8

9

1011 1

a b c

d e f

13:20 20:17

a b c

04:15

Start up

Worksheet 11-01

Brainstarters 11

Worksheet 11-02

TV times

Skillsheet 11-01

Units of time

Skillsheet 11-02

Telling the time

Skillsheet 11-03

24-hour time

VOLUME, MASS AND TIME

355

CHAPTER 11

Volume

4 Write these as 24-hour times:a 4:00pm b 1:00am c 3:30amd 5:15am e 6:38pm f 12:30pmg 8:46am h 9:30pm i 10:17pm

5 Write these 24-hour times as 12-hour times:a 1800 hours b 0400 hours c 2200 hoursd 0530 hours e 1330 hours f 1915 hoursg 1930 hours h 2005 hours i 2145 hoursj 0630 hours k 1015 hours l 1140 hours

6 Test your general knowledge by answering these questions. a What is the meaning of BC and AD? b How many years in a century?c How many months in a year? d How many hours in a day?e How many minutes in an hour? f How many days in a year?g How many days in a month? h How many weeks in a year?i What is a leap year? Why are leap years necessary?

7 A leap year occurs when the year can be evenly divided by 4, except for years ending in 00 that are not exactly divisible by 400. The year 2000 was a leap year because it is divisible by 400. The year 2100 is not a leap year because it is not divisible by 400.a Make a list of all the leap years are there between 1891 and 1925.b How many leap years are there between 1991 and 2121?

8 Calculate:a 5 100 b 26 1000 c 1800 10d 7000 1000 e 350 100 f 2.4 100g 6.01 10 h 4.05 100 i 13.71 1000

Skillsheet 8-01

Multiplying by 10, 100, 1000

The volume of a solid is the amount of space occupied by the solid.

Applying strategies: Comparing volumes1 Bring to school as many different containers as you can nd. As a group, arrange

them in order, from smallest volume (occupying the least space) to largest volume (occupying the most space).

2 Write how the order was decided.3 Check your estimates by lling the containers with either water or sand and

comparing results.4 Discuss your results with your teacher.

Working mathematically

356 NEW CENTURY MATHS 7

How to measure volumeOften informal (everyday) units are used to refer to volume. For example:

cup a cup of our a cup of milk

Standard units of volumeAs with all measurements, we need agreed units for measuring volume. These are based on the cube. A cubic centimetre is the amount of space that a cube with each side measuring 1 cm would occupy. The volume of the cube is one cubic centimetre, or 1 cm3.A cubic millimetre is the amount of space that a cube with each side measuring 1 mm would occupy. The volume of the red cube is one cubic millimetre, or 1 mm3. There are 1000 cubic millimetres in one cubic centimetre.A cubic metre is the amount of space that a cube with each side 1 m would occupy, that is 1 m3. It is about the size of a box containing a large TV set. A shower recess is about 2.5 m3. There are 1 000 000 cubic centimetres in one cubic metre. The greatly reduced diagram below illustrates this.

1 Write an example of the items that could be measured by each of these units.a cup(s) b box(es) c handful d pinche bucket(s) f packet g capsule(s) h can(s)i teaspoon j wheelbarrow k carton l capful

Exercise 11-01

1 cm

1 cm

1 cubic millimetre

1 cm

1 cubic centimetre

100 cm (or 1 m)

100 cm

1 m3 = 100 cm 100 cm 100 cm= 1 000 000 cm3

100 cm

(or 1 m)

(or 1 m)

VOLUME, MASS AND TIME 357 CHAPTER 11

The diagram below will help you convert units.

1 cm3 = 10 mm 10 mm 10 mm= 1000 mm3

1 cm1 cm

1 cm

1 cm3

10 mm

1000 mm3

10 mm

10 mm

Unit Abbreviation Conversioncubic millimetre mm3 cubic centimetre cm3 1 cm3 = 1000 mm3 cubic metre m3 1 m3 = 1 000 000 cm3

m3 cm3 mm3

1 000 000 1000

1 000 000 1000

Example 1

1 Convert 12 000 mm3 into cm3.Solutionmm3 cm3 (1000) 12 000 mm3 = (12 000 1000) cm3

= 12 cm3

2 Convert 48 m3 into cm3.Solutionm3 cm3 ( 1 000 000) 48 m3 = (48 1 000 000) cm3

= 48 000 000 cm3

1 Copy and complete:a 3 cm3 = mm3 b 5 m3 = cm3 c 2.6 cm3 = mm3 d 4000 mm3 = cm3 e 7.2 m3 = cm3 f 66 000 mm3 = cm3 g 1 m3 = mm3 h 2300 cm3 = m3 i 126 000 000 cm3 = m3 j 3450 mm3 = cm3 k 25 m3 = mm3 l 78 000 mm3 = m3 m 63 000 cm3 = m3 n 1.4 mm3 = cm3

Exercise 11-02Example 1


Volume of a rectangular prism

2 Use any types of cubes to complete these constructions.a Build as many different solids as you can with a volume of 3 cubes (that is using

3 cubes). Sketch each one.b Build as many different solids as you can with a volume of 4 cubes (that is using

4 cubes). Sketch each one.c Build as many different solids as you can with a volume of 5 cubes. Sketch each one.

3 Match the correct volume (A to G) with each of the items (a to g) listed.a a bottle of liquid paper A 200 m3 b a box of tissues B 3890 m3 c a glass of water C 1250 cm3 d a bottle of lemonade D 5000 cm3 e a class room E 20 000 mm3 f a school hall F 250 cm3 g a cereal package G 2200 cm3

4 Use this link to discover how Computer Algebra Software can be used to help you convert units of volume.

CAS 11-01

Volume conversions

Applying strategies: Build a cubic metreAs a group activity, construct your own cubic metre. Write a short report on how you did it.


Example 2

This rectangular prism is made from 1 cm cubes. What is its volume?

SolutionThe cube has three layers. Each layer contains 16 cubes (count them).

Volume of the cube = (16 3) cm3 = 48 cm3

16 cubes in one layer

3 layers

Worksheet 11-03Volume


Finding the ruleIn Exercise 11-03, the number of cubes in each layer equals the length multiplied by the breadth (width) of the base of the prism (shaded darkest orange). This product is the area of the base. The number of layers is the height. This gives a rule for nding the volume of a rectangular prism:

Volume of a rectangular prism = area of base height= length breadth height

V = l b h

1 The shapes below are made of 1 cm cubes. Copy and complete the following table.

Shape Number of cubes in one layer Number of layers Volume (cm3)a

bc

de

f

a b

c

d

e f



The volume of a rectangular prism is:V = length breadth height V = l b h

Example 3

Find the volume of the rectangular prism on the right.Solution

V = area of base height = l b h = 18 12 8= 1728

The volume is 1728 cm3.

8 cm

18 cm12 cmbase

1 Find the volume of each of these rectangular prisms.

2 The table on the next page gives the dimensions of different rectangular prisms. Copy and complete it. (This exercise can also be done using a spreadsheet. Use this link to produce and complete the table.)

9 cm

5 cm5 cm 17 cm

21 cm

3 cm

4 cm

36 cm

3 cm

180 cm

3 cm

3 cm

15 cm15 cm

4 cma b c

d e

f

g

h

9 cm

17 cm

15 cm

2.4 m

1.8 m

33.5 m

1.2 m

3 m

11 m

Exercise 11-04

Spreadsheet 11-01

Volume of rectangular

prisms

Example 3


3 Find the volume of each of these shapes. (Hint: You will need to nd the volume of two rectangular prisms each time.)

Prism Length Width Height Volume

a 50 cm 50 cm 50 cm

b 5 cm 10 cm 18 cmc 4 m 2.5 m 1.4 m

d 24 mm 16 mm 11 mme 10 cm 10 cm 2000 cm3

f 5 mm 2 mm 100 mm3 g 1.5 m 3 m 27 m3

h 22 cm 5 cm 880 cm3

i 70 mm 10 mm 70 000 mm3 j 1.8 m 10 m 9 m3

3 cm2 cm

4 cm

7 cm 2 cm

1 cm

3 m

3 m 2 m 10 m

8 m

6 m

50 mm

45 mm

14 mm10 mm

20 m

m

50 cm

20 cm

1 cm25 cm

30 cm 12 cm

10 cm

28 cm

10 cm10 cm

24 cm

8 m8 m

8 m

45 m

16 m

32 m

8 mm

3 mm4 mm5 mm

a b

c d

g

e

f

3 mm

2 mm

SkillBuilder 20-01

The cube


The volumes of rectangular prismsUsing a spreadsheet, you can nd the volume of a rectangular prism given its dimensions.Step 1: Set up the spreadsheet as shown. It will calculate the volume in cell D4.

Step 2: Choose a value for the length to put in cell A4, a value for the breadth to put in B4 and a value for the height to put in C4. The volume automatically appears in D4.

Step 3: Change the cells A4, B4 and C4 to the dimensions of another rectangular prism. The volume will change.

Use your spreadsheet to answer Questions 1 and 3 in Exercise 11-04.

A B C D1 Volume of a rectangular prism23 Length Breadth Height Volume4 =A4*B4*C4

Using technology

Spreadsheet

Applying strategies and communicating: What is your volume?Imagine that you are made up of rectangular prisms.

1 With the help of a partner, make measurements of your body. Use them to nd dimensions (to the nearest centimetre) for each of the prism body parts.

2 Sketch each body part prism and label its dimensions.3 Use the prisms to nd your volume, in cm3.4 Write a report of what you did, showing all diagrams and calculations. Explain

how you found the dimensions (length, breadth and height) for the prisms. Do you believe you found a good approximation of your volume? Why?

neck

head

torso

arms

legs

feet



Capacity and liquid measureWhat is the capacity of the water tank?Capacity is the amount of uid (liquid or gas) in a container.The standard units of capacity are the litre (L) and the millilitre (mL). The same units are used to describe the volume of any liquid.A teaspoon holds about 5 mL.A tall standard carton of milk holds 1 L.

The diagram below will help you convert capacity units.

It is also useful to know the relationship between volume and capacity.

Applying strategies and reasoning: Packing sugar cubesSugar cubes are sold in boxes of 100. Each sugar cube is 1 cm by 1 cm by 1 cm. You need to design the cheapest cardboard box to hold the cubes (that is, using the smallest amount of cardboard). One example is:

However, this design does not use the smallest amount of cardboard.Draw your design for the box and explain how you decided that it was the cheapest design.

10 cm

5 cm

2 cm


Unit Abbreviation Conversionmillilitre mL litre L 1 L = 1000 mLkilolitre kL 1 kL = 1000 L

1 mL

1000 1000

1000 1000

1 L1 kL

1 cm3 contains 1 mL1 m3 contains 1000 L = 1 kL


This means that a cubic centimetre can hold 1 mL of liquid, while a cubic metre can hold 1000 L of liquid.

1 m3 = 1 kL

1 mL

1 cm3= 1000 L

1 000 000 =

Water, water, everywhereTo help you better understand the size of a litre and a kilolitre, here are some examples of water use in and around the home: Washing your hands/face uses 5 L Brushing your teeth (tap running) uses 5 L Brushing your teeth (tap not running) uses 1 L Cooking and making coffee/tea uses 8 L per day Flushing the toilet uses 9 L to 13 L Flushing the toilet (half ush) uses 4.5 L to 6 L Household tap uses 18 L per minute Washing the dishes (hand) uses 18 L Washing the dishes (dishwasher) uses 25 L per cycle Bath uses 85 L to 150 L Shower (8 minutes) uses 80 L to 120 L Washing machine (front loading) uses 120 L per cycle Washing machine (top loading) uses 180 L per cycle Washing the car (with hose) uses 100 L to 300 L Garden sprinkler uses 1 kL to 1.5 kL per hour Garden hose uses 1.8 kL per hour Swimming pool (backyard) uses 20 kL to 55 kL Bradbury swimming pool (Olympic 50 m) uses 1870 kLOn average, a four-person Sydney house (with garden) uses 936 litres of water per day. Half of it is used by outside taps or is ushed in a toilet.

Just for the record

How much water does your household use each day? Find out by asking your parents to show you the water bill.


1 Find the capacity of:a a variety of milk containers b four different-sized soft drink bottlesc a standard soft drink can d a standard cupe the petrol tanks of a variety of cars f your local swimming poolg a petrol tanker h a small fruit juice pack

2 Copy and complete:a 7000 mL = L b 2 L = mLc 3 L = mL d 10 000 mL = L

e 2500 mL = L f 1.5 L = mLg 4000 mL = L h 8.5 L = mLi 6.2 L = mL j 1750 mL = Lk 5 kL = L l 9000 L = kLm 25 000 kL = L n 520 mL = Lo 2.3 mL = L p 6 mL = kL

3 Use this link to discover how Computer Algebra Software can be used to convert unitsof capacity.

4 Match the correct capacity (A to J) with the items (a to j) listed:a car petrol tank A 200 mLb liquid paper B 23 kLc bath tub C 5 mLd bucket of water D 70 Le can of drink E 1250 mLf glass of water F 1875 kLg Olympic swimming pool G 20 mLh bottle of lemonade H 7 Li teaspoon I 375 mLj water storage tank J 180 L

5 A jug holds 2 L of water. How many 250 mL glasses could be lled from it?6 James is inviting 30 friends to a party. He calculates that each person will drink 1800 mL

of soft drink.a How many litres of soft drink must he buy?b James intends to buy large 2 L bottles of drink, how many bottles must he buy?

7 A bottle of medicine holds 100 mL. Tara was told to take 5 mL twice a day. For how many days can Tara take the medicine before it runs out?

8 A tap leaks 10 mL of water every 50 seconds. How much water will be lost in:a 1 second? b 1 minute?c 3 hours? d 1 day?

9 Your skin releases moisture as a way of controlling body temperature. On average 200 mL is released per hour. If all this moisture was captured, how long would it take to ll a 1.25 L soft drink bottle?

12---

Exercise 11-05

CAS 11-02

Capacity and volume


10 A lunch box is made in the shape of a rectangular prism. Its dimensions are 20 cm, 15 cm and 9 cm.a Find the volume of the lunch box, in cm3.b How many mL of water would t in the lunch box?

11 Jemma, the gardener, needs to purchase soil for her backyard. The dimensions of the yard are 15.2 m by 10.5 m. Find the volume of soil needed to cover the yard to a depth of 20 cm. (Note: The soil depth is in centimetres, not metres.)

12 Ginas swimming pool is in the shape of a rectangular prism, 8 m long, 4 m wide and 1.5 m deep.a Find the volume of the swimming pool.b How many litres of water would be needed to ll the pool? (Hint: 1 m3 holds 1 kL.)

13 A sh tank in the shape of a rectangular prism is 60 cm long, 40 cm high and 30 cm wide.a Find the volume of the tank.b How many litres of water will it hold?

14 Use the words volume and capacity in sentences to clearly show their mathematical meaning. Then use them in sentences to show a different meaning for each one.

Applying strategies and reasoning: Volume by displacementArchimedes, an ancient Greek mathematician and inventor, discovered that the volume of an object fully immersed in a uid equals the volume of the displaced uid. (Displaced means moved from its position.)1 Fill a measuring jug with 500 mL of water.2 Choose at least ve objects that can be safely immersed in the jug of water.3 Copy and complete the following table for each object.

Remember: 1 mL takes up the same space as 1 cm3.4 By placing a 1 cm cube in a medicine cup with water, show that a cubic centimetre

displaces 1 mL of water.5 By placing a cube with edges measuring 10 cm in a large measuring container,

show that 1 L of water is displaced by the cube.

Name of object

Original water level

Water level after putting object in

Difference in water level

Volume of object in cm3

500 mL500 mL500 mL500 mL500 mL



Minutes and secondsIn Chapter 2, you learned that there are 360 in a revolution because the ancient Babylonians used a base 60 number system and believed that a year lasted 360 days. (How many days is a year actually?) The Babylonians, who lived where Iraq is today in 2000 BC, invented the units for measuring angles and time. That is why there are 60 minutes in an hour and 60 seconds in a minute.The word minute has another meaning. When pronounced my-newt, it means tiny, but this meaning is also related to the minute as a unit of time. A minute is a tiny fraction of an hour, and comes from the Latin pars minuta prima, meaning the first division (or part) of an hour.The word second also means coming after first, and this meaning is also related to the second as a unit of time. Find out how.

Just for the record

Reading linear scalesUnderstanding and reading the scale on a measuring instrument, on a number line or on the axis of a graph is an important mathematical skill.1 Examine these examples.

a Complete the missing values on the scale below.

First, choose two values on the scale, say 100 and 120. Count the number of intervals (spaces) between the two values. There are four

intervals between 100 and 120. To nd the size of each interval, divide the difference between the two values by

the number of intervals:Difference = 120 100 = 20 km

Number of intervals = 4Size of an interval = 20 4

= 5 km Use the calculated size of an interval to complete the missing values:

b Complete the values on this scale.

Choose 50 and 60 on the scale. Number of intervals (between 50 and 60) = 5 Difference (between 50 and 60) = 60 50 = 10 years Size of an interval = 10 5 = 2 years.

100 160120 140 km

100 160120 140 km105 110 115 125 130 135 145 150 155

50 8060 70 years

50 8060 70 years52 54 56 58 62 64 66 68 72 74 76 78 82 84

Skillbank 11 SkillTest 11-01Reading scales


MassYou are asked to pick up: a cubic metre of feathers a cubic metre of cement

You can lift the feathers but not the cement! The volume is the same but the mass is different. Even though they each take up the same amount of space, one is much heavier. Mass is the amount of matter in an object. The standard unit of mass is one kilogram (kg). Other units used are the milligram (mg), the gram (g) and the tonne (t).A drawing pin has a mass of about 1 g.An egg has a mass of about 60 g.A litre of water has a mass of exactly 1 kg.A medium-sized car has a mass of about 1.5 t.

2 Now copy and complete the following scales:a

b

c

d

e

f

g

h

i

j

36 56 C40 44 48 52 60 64

200 mL240 280 320 360

500 g520 540 560 580

128 cm144 160

30 L45 75 90 10560

160 280200 240 min

200 kg300 400 500 600 700

12:00 6:00am 12:00 time ofmidnight

6:00pm 12:00midnight

6:00amnoon day

120 seconds180 240 300 360 420

100 mL300 400 500 600 700200


The diagram below will help you convert units.

Unit Abbreviation Conversionmilligram mg gram g 1 g = 1000 mgkilogram kg 1 kg = 1000 gtonne t 1 t = 1000 kg

t kg g

1000 1000

1000 1000

mg

1000

1000

Reecting: Mass of household objectsEach member of the group must nd the mass of eight household objects. Taking it in turns, each person names the object and the rest of the group guesses its mass. Use a table like this:

Check each guess against the actual mass and work out the difference between them.Did you get better at estimating by the end of the exercise? Why?

Object My estimate Actual mass Difference


Note: You will need a variety of weighing scales.1 Measure the mass of:

a this textbook b your lunchboxc your schoolbag d a shoee a pencil case f yourselfg a jumper h a bricki a ball (state what kind) j an apple

Exercise 11-06


2 Copy and complete:a 3000 g = kg b 2 t = kgc 4 kg = g d 9000 kg = te 7.5 t = kg f 10 000 mg = gg 2500 g = kg h 1.5 kg = gi 3800 kg = t j 3 g = mg

3 Use this link to discover how Computer Algebra Software can be used to convert unitsof mass.

4 Copy and complete, using a , or = sign to make each statement true:a 700 g 0.6 kg b 0.8 g 95 mgc 3500 kg 3.5 t d 1.7 kg 1700 ge 0.007 t 7 kg f 640 mg 0.7 gg 4000 mg 0.04 kg h 0.03 kg 3 g

5 Match the masses given (A to J) with the items (a to j) listed:a an egg A 400 gb an elephant B 16 gc a house brick C 25 kgd a medium-sized car D 80 kge an adult E 6 tf a can of soft drink F 500 gg a 50c piece G 10 kgh a 7-year-old child H 50 gi a tub of margarine I 3 kgj a large watermelon J 1 t

6 Measure the mass of 1 L of water. Write a report on how you did it.7 Find out the difference between gross mass and net mass.8 Find out the difference between mass and weight.

CAS 11-03Mass

conversions

Applying strategies: Investigating mass1 Investigate the sport of weight-lifting.2 a Obtain a schedule of postal charges from the post ofce. Imagine that you have

ve pen-friends in different parts of the world (you choose the countries) and want to send a Christmas present to each one. Choose the presents. Work out the mass of each present when wrapped to send by post, and calculate the cost of sending each one by airmail and by sea.

b Work out how much you will save by posting the presents early and sending them by sea.

3 Library researcha Choose 10 animals and estimate their masses. Check your answers at the library.b Find 10 record achievements that have something to do with mass, for example

heaviest man, lightest baby, etc.



TimelinesTimelines are the simplest types of calendars. They record events in the order in which they happen.A timeline for a puppys rst 32 weeks could look like this:

You need to work out the scale used on the timeline before you can get information from it. On this timeline there are eight major divisions between 0 and 32, so each interval represents 4 weeks.Now you can see that, at 24 weeks, the puppy chased its rst cat. It left its mother at about 6 weeks and at 20 weeks it started digging up the garden.

Worksheet11-04

History of the calendar

Weeks

opened eyes

leftmother

made a mess on

the carpet

learnt to play fetch

ate a slipper

dug up new plants

chased rst cat

ate cake from table

0 328 16 24

1 a Copy this timeline.

b How many years does each interval on the timeline represent? (This is called the scale of the timeline.)

c Write the following dates on the timeline in the correct boxes.AD 1 The birth of Christ753 BC The founding of the city of RomeAbout 1600 BC Introduction of the current Chinese year system3111 BC Start of the Mayan Long Count544 BC Date recorded as the birth of BuddhaAD 1792 Declaration of the 1st French RepublicAD 622 Traditional date for the ight of Muhammad

3000 BC 2000 BC 1000 BC 1000 AD

Exercise 11-07


2

This timeline shows some events from the rst 200 years of white settlement in Australia.a What is the scale of this timeline?b Match the letters on the timeline with these facts:

1851 Gold was discovered at Warrandyte, Victoria1932 Sydney Harbour Bridge was opened1974 Darwin was devastated by Cyclone Tracy1956 Melbourne hosted the Olympic Games1813 The explorers Blaxland, Wentworth and Lawson crossed the Blue Mountains1788 The First Fleet arrived in Jackson Cove1982 Brisbane hosted the Commonwealth Games1901 The Federation of the Australian States to form the Commonwealth of

Australia

3 The table below shows the names of Australias Governors-General and the year they each took ofce, from 1960 to 2001.

a Copy the timeline below and complete it by writing in the letters to indicate when each Governor-General took ofce. (Two have been done for you.)

b What is the scale of this timeline?c Which Governor-General was in ofce for the longest period of time?d Which Governor-General was in ofce for the shortest time?

Name Year

A Viscount Dunrossil 1960

B Lord Casey 1965

C Sir Zelman Cowen 1977D Viscount De LIsle 1961

E Right Reverend Dr Peter Hollingworh 2001

F Sir William Deane 1996

G Sir Paul Hasluck 1969H Sir John Kerr 1974

I William Hayden 1989

J Sir Ninian Stephen 1982

1770 1870 1970

G A

E D H

C F B

1960 1972 2008

A C

1984 1996


4 Draw a timeline to show these events for the period between 1945 and 2010:1969 People rst walked on the moon1945 World War II ended1989 Wayne Gardner won his rst Australian 500 cc Motorcycle Grand Prix19 The year you were born1985 The Aboriginal people were granted land rights to Uluru (Ayers Rock)1964 The Beatles toured Australia1983 Australia II won the Americas Cup1956 The rst television transmission in Australia occurred1954 Englishman Roger Bannister was the rst to run the mile in less than 4 minutes2000 Olympic Games were held in Sydney20 (Enter your own important event.)

5 Draw a timeline to display these famous Australian inventions and discoveries:1890 The Australian cattle dog was registered as the only purebred cattle dog in the

world1904 Kiwi Shoe Polish went on the market1906 The surf-lifesaving reel for use at Bondi Beach was invented1919 The preferential system of voting was rst used for

the House of Representatives1922 Vegemite was developed by Dr Cyril Callister1930 The worlds rst mechanised letter-sorter was

installed in the Sydney GPO, built by A. B. Corbett1945 The Hills rotary clothes line was invented by Lance

Hill1952 The Victa rotary lawnmower was developed by

Mervyn Victor Richardson1979 Race-cam was rst used by Channel Seven at the

Bathurst 1000 car races1983 The Bionic ear cochlear implant came on the market1988 Plastic banknotes, developed by the CSIRO, were

rst released6 a Work with a partner or in a small group to write a list of important events that have

occurred in your lifetime. Try to make a personal list.b Draw a timeline to show these events.

Communicating: Timeline displayWork by yourself or with a partner to develop a poster or display showing a timeline for one of the following: major disasters of the world historical events of another country achievements in science achievements in sport wars of the last 150 years women in history Prime Ministers of Australia the history of computers your school principals a topic approved by your teacher.



Converting units of timeExample 4

1 Round each of these amounts of time to the nearest hour:a 7.83 hours b 12 hours 19 minutes c 2 hours 43 minutes 30 secondsSolutiona 7.83 h 8 h

When rounding hours and minutes to the nearest hour, we use 30 minutes as the halfway mark because there are 60 minutes in an hour. For less than 30 minutes, round down and leave the number of hours unchanged. For 30 or more minutes, round up and add 1 to the number of hours.b 12 h 19 min 12 h (because 19 min 30 min)c 2 h 43 min 30 s 3 h (because 43 min 30 min)

2 Round each of these amounts of time to the nearest minute:a 11.4 minutes b 25 minutes 37 seconds c 3 hours 6 minutes 30 secondsSolutiona 11.4 min 11 min

When rounding minutes and seconds to the nearest minute, we use 30 seconds as the halfway mark because there are 60 seconds in a minute.b 25 min 37 s 26 min (because 37 s 30 s)c 3 h 6 min 30 s 3 h 7 min (because we round 30 s up)

1 Convert 7 minutes into seconds.Solution

1 minute = 60 secondsso: 7 minutes = 7 60 seconds

= 420 seconds2 Convert 91 days into weeks.

Solution7 days = 1 week

so: 91 days = 91 7 weeks= 13 weeks

Convert 275 minutes into hours and minutes.SolutionThere are 60 minutes in 1 hour.

275 60 = 4 remainder 35275 minutes = 4 h 35 min

Example 5

Example 6


Most scientic calculators have a degrees-minutes-seconds key, or , that is useful for calculations involving minutes and seconds (base 60). This key can be used to convert decimal answers for time to hours-and-minutes or minutes-and-seconds. Calculating the answer to Example 6 in this way:

275 minutes = 275 60 h= 4.583 333 3 h

Press to get 4 35 0 on the calculator display, which means 4 h 35 min.

DMS

1 State which unit of time (hours, minutes, or days) would be used to measure each of these events:a a day-night cricket matchb snapping your ngers ve times, as fast as possiblec running once around the school ovald building a housee ying from Sydney to Broken Hillf watching a video from beginning to endg the life span of a grasshopper

2 Write these times correct to the nearest hour:a 4 h 14 min b 11.5 h c 6 h 27 mind 7 h 48 min 19 s e 3.42 h f 2 h 30 min

3 Write these times correct to the nearest minute:a 17 min 51 s b 8.8 min c 4 min 7 sd 4 h 20 min 19 s e 12.31 min f 1 h 28 min 40 s

4 Convert:a 6 hours to minutes b 15 minutes to secondsc 9 weeks to days d 2.5 years to weekse 3 days to hours f 2 years to daysg 2 weeks to hours h 4.25 hours to minutesi 8.5 days to hours j 10 minutes to secondsk 7.2 centuries to years l 3 fortnights to days

5 Convert:a 480 seconds to minutes b 70 days to weeksc 96 hours to days d 200 minutes to hours and minutese 468 weeks to years f 560 seconds to minutes and secondsg 60 hours to days h 126 days to weeksi 330 seconds to minutes and seconds j 24 weeks to fortnightsk 135 minutes to hours and minutes l 470 years to centuriesm 405 minutes to hours and minutes n 167 minutes to hours and minutes

6 Find the number of seconds in:a 1 hour b 1 day c 1 year

7 Are you over a million seconds old? Find your age in seconds to answer this question.

12---

Exercise 11-08

Example 4

Example 6

Example 5


Time calculationsExample 7

What is the time 7 hours 40 minutes after 11:52pm?Solution7 hours after 11:52pm is 6:52am.40 minutes after 6:52am is 7:32am.

What is the difference in time between 8:35am and 3:10pm?SolutionFrom 8:35am to 9:00am = 25 minutesFrom 9:00am to 3:00pm = 6 hoursFrom 3:00pm to 3:10pm = 10 minutesTotal time difference = 25 min + 6 h + 10 min

= 6 h 35 minor:

Converting to 24-hour time rst, then using the calculators or key:8:35am = 0835, 3:10pm = 1510

15 10 8 35 gives the display 6350 which means 6 h 35 min.

Find 7 h 5 min 3 h 24 min.Solution

7 h 5 min 3 h 24 min = 6 h 65 min 3 h 24 min= (6 3) h + (65 24) min= 3 h 41 min

or:

Using the calculators or key:

7 5 3 24 gives the display 3410 which means 3 h 41 min.

Example 8

DMS

=

Example 9

DMS

=

Worksheet 11-05Time

calculations

1 What time will it be:a 5 hours after 3:00pm? b 8 hours after 11:00am?c 28 minutes after 7:15pm? d 3 hours 32 minutes after 9:45am?e 3 hours 19 minutes after 10:49pm? f 4 hours after 9:32am?g 9 hours after 5:14pm? h 45 minutes after 3:30pm?i 2 hours after 4:02am? j 12 hours 40 minutes after 2:45am?14---



World standard times

2 You may have discovered that it would be helpful to be able to count in time intervals. Use this link to go to an activity which enables you to practise counting time differences.

3 A marathon began at 10:20am. Here are some of the competitors and the times they ran:Mike 3:11 (3 h 11 min) Joe 2:23Anna 2:54 Pathena 3:01Ken 2:59 Gail 3:42

Write the runners in their order of nishing and the time each crossed the nishing line.4 What is the difference in time between:

a 7:15pm and 8:20pm? b 10:16am and 12:06pm?c 4:09am and 9:53am? d 11:15pm and 3:08am?e 7:27am and 1:12pm? f 9:36pm and 9:14am?g 7:45pm and 10:10pm? h 2:24am and 3:07am?i 4:15pm and 6:02pm? j 10:25am and 2:33pm?k 8:40am and 4:19pm? l 6:45am and 8:10pm?

5 Find:a 2 h 15 min + 4 h 32 min b 3 h 25 min + 8 h 27 minc 7 h 12 min + 5 h 18 min d 1 h 42 min + 6 h 27 mine 9 h 37 min + 2 h 52 min f 4 h 49 min + 7 h 18 min

6 Find:a 6 h 42 min 3 h 13 min b 12 h 37 min 5 h 6 minc 15 h 57 min 9 h 48 min d 6 h 2 min 4 h 17 mine 8 h 18 min 3 h 27 min f 5 h 31 min 3 h 48 min

Spreadsheet 11-02

Counting with time

Example 8

Example 9

World time zonesThe world is divided into 24 main time zones. Time is the same throughout each zone. The centre of each time zone is a meridian of longitude (an imaginary line running from the North Pole to the South Pole). The meridians are 15 apart. The system used to divide the world was first suggested by Sir Sanford Fleming (18271915), a Canadian civil engineer and scientist. In 1884, scientists from 27 nations met in Washington and devised the time system we now use.Fleming was also responsible for a telegraph communication system. The first cable laid was between Canada and Australia in 1902.Which major country uses only one time zone despite stretching across four time zones?

Just for the record Worksheet11-06World time

zones


The map below shows how times around the world are related. The Earth has been divided into standard time zones. Places within a time zone share the same time. All time is measured in relation to the time at Greenwich (in London), either ahead or behind Greenwich Mean Time (GMT). Australias time is ahead of Greenwich Mean Time since Australia is east of Greenwich. Americas time is behind Greenwich Mean Time since America is west of Greenwich.

180W 090W 30W 20E60W150W 120W 60E 90E 120E 150E 180E

International Date Line

International Date Line Greenw

ich Meridian

N

Rio deJaneiro

Honolulu

San FranciscoNew York

GreenwichGeneva

Moscow

BeijingHong

PerthSydney

Equator

Kong

West of Greenwich East of Greenwich

12:00 12:006:00am 10:00am 2:00pm8:00am2:00am 4:00am 4:00pm 6:00pm 8:00pm 10:00pm 12:00

Greenw

ich Meridian

80

60

40

20

0

20

40

60

midnight noon midnight

Helsinki

AthensOttawa

(behind GMT) (ahead of GMT)

1 State whether each of these cities is ahead of or behind Greenwich Mean Time:a Sydney b Auckland c Rio de Janeiro d Perthe Beijing f Honolulu g Moscow h Athensi Hong Kong j Helsinki k New York l Ottawa

2 From the given map, nd the time in each of these cities when it is noon in Greenwich:a Sydney b Perth c New York d Beijinge San Francisco f Honolulu g Moscow h Geneva

3 What is the time difference between:a Sydney and Perth? b Sydney and Beijing?c Sydney and Honolulu? d Sydney and Moscow?e Sydney and New York? f Perth and Beijing?g San Francisco and New York? h Honolulu and Moscow?i Geneva and Perth? j San Francisco and Geneva?

Exercise 11-10


Australian standard timesThis map shows the time zones for Australia.

Note: During daylight saving periods, add 1 hour.

4 If it is 2:00pm in Sydney, what is the time in:a Greenwich? b Perth? c New York? d Beijing?e San Francisco? f Honolulu? g Moscow? h Geneva?

5 A cricket match being played in India is telecast live at 7:00pm Sydney time. What is the local time of the cricket match if Sydneys time is 4 hours ahead of Indias?

6 Simone, in Newcastle, wants to use the Internet to chat with her cousin Zac in Vancouver, Canada. The time in Vancouver is 18 hours behind the time in Newcastle. At what time should Simone log on to the Internet to catch Zac when it is 3:00pm in Vancouver?

7 A plane leaves New Zealand at midday and takes 3 hours to y to Brisbane. What is the local time in Brisbane when the plane lands, if Brisbane is 2 hours behind New Zealand?

8 Find out what happens if you cross the International Date Line (IDL). Why isnt the IDL straight?

12---

Applying strategies and reasoning: Round tripPlan a trip around the world with at least three stopovers. Obtain some airline timetables so you can give details of departures and arrivals. Work out how much time is actually spent ying. Does it matter if you head east or west when you start? What effect does the International Date Line have on your trip?


NorthernTerritory

QueenslandWesternAustralia

SouthAustralia

New South Wales

Victoria

Tasmania

Australian Western Standard Time

(AWST)

Australian Eastern Standard Time

(AEST)

-2 hours - hour12 Zero

Australian Central Standard Time

(ACST)


Timetables

1 State whether each location is ahead of, behind or has the same time as Adelaide:a Sydney b Melbourne c Darwind Perth e Mt Isa (Qld) f Geraldton (WA)g Cobar (NSW) h Ceduna (SA) i Cairns (Qld)

2 What is the time difference between:a Sydney and Adelaide? b Melbourne and Perth? c Adelaide and Melbourne?d Hobart and Darwin? e Canberra and Perth? f Brisbane and Canberra?

3 If it is 11:00pm in Sydney, what time is it in:a Melbourne? b Adelaide? c Perth?d Darwin? e Hobart? f Canberra?

4 If it is 11:30pm in Adelaide, what time is it in:a Melbourne? b Sydney? c Perth?d Darwin? e Hobart? f Brisbane?

5 a Find out when daylight saving begins and ends.b Why do we have daylight saving?c How does daylight saving affect the different time zones?

Exercise 11-11

Worksheet 11-07

Tide chart

1 Airline timetableDaniel and his volleyball team need to y from Sydney to Brisbane for a championship tournament. Daniel logged on to the Internet site for Thomson Airways and found the following ight schedule for 12 October.

a How long does the ight take from Sydney to Brisbane?b The team would like to arrive at Sydney airport at 10:45am. How long will they need

to wait for the next available ight?c The team needs to be at the hotel in Brisbane by 12:30pm. If it takes 30 minutes to

drive from the airport to the hotel, what is the latest ight the team can catch from Sydney?

d What is the ight number of the ight that takes longer to reach Brisbane than the others? Give one reason why it might take longer.

Flight number Sydney departure time Brisbane arrival time

TH503TH511TH038TH114TH514TH051

090509351005104011051135

103011001130121012301300

Exercise 11-12


2 Bus Service Timetable

a How long does the trip from Sydney to Wagga take?b How long would the trip take without a meal break?c Ali joins the return bus at Jugiong and gets off at Liverpool. How long is his trip?d Find the time taken from Liverpool to Sydney and from Sydney to Liverpool. Suggest

a reason for the difference.3 Countrylink Train Timetable

a Michael has an interview in Sydney on Tuesday at 10:45am. At what time must he catch the train in Goulburn?

b What is the difference in the time taken to travel from Goulburn to Sydney on the 5:08am train and the 8:17am train?

c Georgina travels from Penrose to Yerrinbool, arriving at 4:07pm. How long did the trip take?

d You have been visiting friends in Moss Vale and are returning to Sydney. Decide which train you would catch and explain why.

e A new train is added to the timetable, leaving Goulburn at 11:12am. Write out a timetable for this train if it stops at the same stations as the 6:47pm train.

Forward: Sydney to Wagga Return: Wagga to SydneySydney 2:30pm Wagga 7:15amStratheld 3:00pm Gundagai 8:25amYagoona 3:20pm Jugiong 8:54amLiverpool 3:45pm Yass 9:41amMittagong 4:40pm Goulburn* 10:41amGoulburn* 5:40pm Mittagong 12:10pmYass 7:10pm Liverpool 1:05pmJugiong 7:55pm Yagoona 1:20pmGundagai 8:20pm Stratheld 1:35pmWagga 9:30pm Sydney 2:05pm* 30 minute meal stop at Goulburn

Goulburn to Sydney Monday to Fridayam am am pm pm pm pm pm

GOULBURN 5:08 7:27 8:17 1:47 2:45 4:26 6:47 7:45MARULAN 5:26 7:45 3:03 8:03TALLONG 5:32 7:51 Bookings Bookings 3:09 Bookings Bookings 8:09WINGELLO 5:39 7:58 essential essential 3:16 essential essential 8:16PENROSE 5:44 8:03 3:21 8:21BUNDANOON 5:50 8:09 8:52 2:22 3:27 7:22 8:27EXETER 5:55 8:14 3:32 8:32MOSS VALE 6:05 8:24 9:05 2:35 3:42 5:13 7:35 8:42BURRADOO 6:10 3:47 8:47BOWRAL 6:13 8:30 9:11 2:41 3:50 7:41 8:50MITTAGONG 6:17 8:34 9:16 2:46 3:54 7:46 8:54YERRINBOOL 6:30 4:07 9:07BARGO 6:41 4:18 9:18TAHMOOR 6:48 4:25 9:25PICTON 6:56 9:08 4:33 9:33CAMPBELLTOWN 7:23 9:30 10:11 3:41 5:00 6:13 8:42 10:00STRATHFIELD 10:42 4:17 7:00 9:12SYDNEY 8:12 10:12 10:54 4:29 6:20 7:13 9:24 11:04


4 The Explorer BusThe Explorer Bus operates in Sydney, Canberra and Melbourne. It takes tourists on a tour of the city and allows them to visit places of interest.This is a winter timetable for an Explorer Bus in a capital city:

a How many buses are needed to meet the winter Explorer Bus timetable? Explain how you arrived at your answer.

b Vo, Binh and Vicki came to the city by train, arriving at the station at 11:42am. They caught the Explorer Bus to the zoo. What is the earliest time they could expect to arrive at the zoo? Explain your answer.

c Manuel and Soa are dropped off by car at the City cathedral at 10:25am. They arrange to meet their hosts at the Hall of fame at 2:45pm. They want to spend at least half an hour at the museum, photograph the City square and do some souvenir shopping at the Dockland shops. Plan a list of times for them to catch the Explorer Bus to do these things and meet their hosts on time.

d In summer, extra Explorer tours leave the depot at 11:30am, 1:30pm, and 2:30pm. Make a list of departure times that would appear in the timetable for each of these tours.

DepartExplorer depot 10:00 10:25 10:50 11:15 11:45 12:00 12:25 12:50 1:15City cathedral 10:08 10:33 10:58 11:23 11:53 12:08 12:33 12:58 1:23Railway station 10:15 10:40 11:05 11:30 12:00 12:15 12:40 1:05 1:30Parliament 10:24 10:49 11:14 11:39 12:09 12:24 12:49 1:14 1:39Museum 10:35 11:00 11:25 11:50 12:20 12:35 1:00 1:25 1:50City square 10:45 11:10 11:35 12:00 12:30 12:45 1:10 1:35 2:00Zoo 11:00 11:25 11:50 12:15 12:45 1:00 1:25 1:50 2:15Dockland shops 11:12 11:37 12:02 12:27 12:57 1:12 1:37 2:02 2:27Arts centre 11:19 11:44 12:09 12:34 1:04 1:19 1:44 2:09 2:34Water gardens 11:30 11:55 12:20 12:45 1:15 1:30 1:55 2:20 2:45Hall of fame 11:38 12:03 12:28 12:53 1:23 1:38 2:03 2:28 2:53ArriveExplorer depot 11:50 12:15 12:40 1:05 1:35 1:50 2:15 2:40 3:05

The train timetableUse a spreadsheet to make up a timetable for a new railway line that runs trains on a route with nine stations. Every third train runs express between stations 4 and 8. Allow 2 to 4 minutes between each station. Trains leave the rst station every 15 minutes starting at 7:30am. The last train leaves at 10:30am. Give your stations creative names, or use the names of existing suburbs.

Using technology

Spreadsheet


Applying strategies and reasoning: Time puzzlersTry to solve as many of the following puzzles as you can, on your own or in a group. Record your solution and how you solved the puzzle each time.Try the puzzles out on your family and friends.


Puzzler 1

If it takes 3 minutes to soft boil 1 egg, how long will it take to soft boil 3 eggs?

Puzzler 2Here is a way to nd someones age. Give them the following instructions. Think of any number between 1 and 10. Square it. Subtract 1. Multiply the result by the original

number. Multiply that by 3. Add the digits of the answer. Add your age in years and tell me the

result.Now comes the trick: First you need to guess the rst digit of

their age (that is, are they in their teens, 20s, 50s, etc.?).

Add the digits of the result you have been given.

Subtract the rst digit of their age from this sum to get the second digit of their age.

12---

Puzzler 3

The oral clock shown above gains half a minute during the day due to the warmth of the sun, and loses one-third of a minute during the cool of the night. If the clock was set to the correct time on 1 January, when will it be 5 minutes fast?

Puzzler 4A doctor prescribed 15 pills and told his patient to take one every half-hour. How long would it take the patient to nish the course of pills?(Note: The answer is not 7 hours.)Puzzler 5Some months have 31 days, some have 30 days. How many months have 28 days?

Puzzler 6How long is a metric hour if:

1 minute = 100 secondsand: 1 hour = 100 minutes?

12---


1 The diagram on the right shows a tank. The tank is half-lled with water. Find the amount of water in the tank.

2 A cube has a volume of 512 cm3. Find the length of each side of the cube.

3 A childrens pool is in the shape of a cross as shown on the right. Each side is 3 m long. The pool is lled with water to a depth of 300 mm.a Find the area of the pool surface.b Calculate the volume of water, in cubic

metres (m3).c If water is charged for at $0.80 per kL, how much

does it cost to ll the pool?

4 A doctor orders 5.2 litres of uid each day to be given to a patient in drops. Each 1 mL of uid is equivalent to 15 drops. How many drops of uid per minute are needed for the patient to receive the required dose?

5 The diagram on the right shows a container in the shape of a rectangular prism.a How many cubes of side length 60 cm could be

stacked in the container?b If each cube has a mass of 25 kg, how many

tonnes would the container carry?6 Calculate the volume of each solid below.

7 A rectangular box 40 cm long and 12 cm wide contains 2880 cm3 of sugar. How deep is the sugar in the box if it is spread evenly?

8 South Australia is 1 hours ahead of Western Australia. Anna is ying from Perth to Port Augusta. If the ight takes 2 hours and the ight leaves Perth at 10:00am on Sunday, at what time will the plane land in Port Augusta?

9 What happens if you travel east across the International Date Line?10 If a 1 cm3 container can hold 1 mL, explain why a 1 m3 container can hold 1 kL.

30 cm

14 cm

15 cm

3 m

3 m

3 m

3 m

12 m

3 m

3 m

30 cm

100 cm

13 cm13 cm2 cm

ba

16 cm

16 cm

8 cm

8 cm

16 cm

20 cm

2 cm

12--- 1

2---

Power plus


Topic overview Write in your own words what you have learnt about volume, about mass, and about time. What parts of this topic were new to you? What parts of this topic did you have difculty with? Discuss them with a friend or your

teacher. Give some examples of situations where you would use what you know about volume,

mass and time. Copy this summary into your workbook and complete it. Use colour to help you

remember your summary. Check it with other students and your teacher.

Language of mathsbase capacity cubic centimetre cubic metre Central Standard Time Eastern Standard Time gram Greenwich Mean Time kilogramkilolitre litre massmilligram millilitre timelinetimetable time zone tonne24-hour time volume Western Standard Time

1 What is the difference between volume and capacity?2 Look up the different meanings of capacity in the dictionary. How are these

related to its mathematical meaning?3 Find out the difference between a tonne and a ton.4 What is a megalitre (ML)?5 The word minute can be pronounced differently and has different meanings.

Find how the other meanings relate to a minute meaning a fraction of an hour.6 In Summer, the eastern states of Australia use AEDST instead of AEST. Explain.

Worksheet 11-08

Measurement crossword

123

4567

8

910

1112

T _ _ _

VOLUME, MASSand TIME

123

4567

8

910

1112

T _____

l b h

V _____M _____ mg g kg t

cm3

m3

C _______ mL L kL


Chapter 11 Review Topic testChapter 11

1 Count the cubes in this solid to nd its volume:

2 Find the volume of each of these prisms:

3 The biggest iceberg on record was called B9. It had the same volume as a rectangular prism with dimensions 160 km long, 50 km wide and 250 metres high. When B9 melted, how many litres of water was produced? (1 kL of water will occupy 1 m3.)

Ex 11-03

Each cube = 1 cm3

Ex 11-04

a b

c d

e f10 cm

12 mm8 mm

10 m

6 m

7 mm

6 m

8 m5 m

20 cm

4 cm

4 cm2 m

15 cm

20 cm

15 m

15 m

6 m7 m

5 m

Ex 11-04


4 Copy and complete:a 2000 mL = L b 3 kL = Lc 7 L = mL d 3300 L = kLe 1750 mL = L f 2.5 mL = mL

5 The mass of an orange is closest to:A 5 g B 50 g C 500 g D 5 kg

6 Eighteen trucks, each carrying 12 000 kg of debris, were required to clear a building site. How many tonnes of debris were cleared altogether?

7 Copy and complete:a 5000 g = kg b 2 g = mgc 1 t = kg d 6500 kg = te 4000 mg = g f 1.5 kg = g

8 Write each of these amounts of time correct to the nearest hour:a 9 h 50 min b 3.2 h c 4 h 12 min 49 s

9 Write each of these amounts of time correct to the nearest minute:a 2 min 36 s b 10.5 min c 3 h 23 min 40 s

10 Copy and complete:a 56 days = weeks b 4 h = minc 960 s = min d 5 years = weekse 7 days = h f 750 min = h

11 What is the time:a 5 hours after 10:42pm? b 2 hours 28 minutes after 5:23am?c 55 minutes before 7:15pm? d 7 hours 36 minutes before 1:19am?e 15 hours 34 minutes after 7:00am? f 3 hours after 3:40pm?

12 How much time elapses between:a 5.26am and 9:45am? b 11:56pm and 7:30am?c 1316 hours and 2003 hours? d 0750 hours and 1425 hours?e 2347 hours and 0006 hours? f 1529 hours and 3:28pm?

13 Find:a 6 h 45 min + 3 h 20 min b 3 h 16 min 1 h 26 minc 4 h 33 min + 2 h 24 min d 4 h 19 min 2 h 50 min

14 If it is 10:00am in Sydney, use the maps on pages 378 and 379 to help you work out the time in:a Perth b Rio de Janeiro c Adelaided Moscow e Hong Kong f San Francisco

Ex 11-05

Ex 11-06

Ex 11-06

Ex 11-06

12---

Ex 11-08

Ex 11-08

Ex 11-08

Ex 11-09

14---

Ex 11-09

Ex 11-09

Ex 11-10

Student textImprint pageTable of contentsPrefaceHow to use this bookHow to use the CD-ROMAcknowledgementsSyllabus reference grid1 The history of numbersDifferent number systemsThe HinduArabic number systemPlace valueExpanded notationThe four operationsArithmagonsDividing by a two-digit numberOrder of operationsThe symbols of mathematicsTopic overviewChapter review

2 AnglesNaming anglesComparing angle sizeThe protractorDrawing anglesAngle geometryNaming linesAngles and parallel linesFinding parallel linesTopic overviewChapter review

3 Exploring numbersSpecial number patternsTests for divisibilityFactorsPrime and composite numbersPrime factorsIndex notationSquares, cubes and rootsTopic overviewChapter review

Mixed revision 14 SolidsNaming solidsConvex and non-convex solidsPolyhedraPrisms and pyramidsCylinders, cones and spheresClassifying solidsEulers ruleEdges of a solidThe Platonic solidsDrawing and building solidsDifferent views of solidsTopic overviewChapter review

5 IntegersNumber linesNumbers above and below zeroDirected numbersOrdering directed numbersAdding and subtracting integersMultiplying integersDividing integersThe four operations with integersReading a map gridThe number planeThe number plane with negative numbersTopic overviewChapter review

6 Patterns and rulesNumber rules from geometric patternsUsing pattern rulesThe language of algebraTables of valuesFinding the ruleFinding harder rulesFinding rules for geometric patternsAlgebraic abbreviationsSubstitutionSubstitution with negative numbersTopic overviewChapter review

Mixed revision 27 DecimalsPlace valueUnderstanding the pointOrdering decimalsDecimals are special fractionsAdding and subtracting decimalsMultiplying and dividing by powers of 10Multiplying decimalsCalculating changeDividing decimalsDecimals at workConverting common fractions to decimalsRecurring decimalsRounding decimalsMore decimals at workTopic overviewChapter review

8 Length and areaThe history of measurementThe metric systemConverting units of lengthReading measurement scalesThe accuracy of measuring instrumentsEstimating and measuring lengthPerimeterAreaConverting units of areaArea of squares, rectangles and trianglesAreas of composite shapesMeasuring large areasTopic overviewChapter review

9 Geometric figuresPolygonsClassifying trianglesNaming geometric figuresConstructing trianglesClassifying quadrilateralsConstructing perpendicular and parallel linesConstructing quadrilateralsTopic overviewChapter review

Mixed revision 310 FractionsHighest common factor and lowest common multipleNaming fractionsEquivalent fractionsOrdering fractionsAdding and subtracting fractionsAdding and subtracting mixed numeralsFractions of quantitiesMultiplying fractionsDividing fractionsTopic overviewChapter review

11 Volume, mass and timeVolumeVolume of a rectangular prismCapacity and liquid measureMassTimelinesConverting units of timeTime calculationsWorld standard timesTimetablesTopic overviewChapter review

12 AlgebraAlgebraic expressionsAlgebraic abbreviationsFrom words to algebraic expressionsLike termsMultiplying algebraic termsExpanding an expressionExpanding and simplifyingAlgebraic substitutionTopic overviewChapter review

13 Interpreting graphs and tablesPicture graphsColumn graphs and divided bar graphsSector graphsLine graphsTravel graphs and conversion graphsStep graphsReading tablesTopic overviewChapter review

Mixed revision 4General revisionAnswersIndex

GlossaryABCDEFG HI JK LMNOPQRSTU VW X Y Z

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Chapter11-Volume, Mass and Time