11 NCM7 2nd ed SB TXT -...

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MEASUREMENT

Measuring is important in our lives: ‘How long until my birthday?’ ‘How heavy is my school bag?’ ‘How much water to fill the swimming pool?’ If you worked in a kitchen, you would be continually measuring: ‘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.

11 NCM7 2nd ed SB TXT.fm Page 378 Saturday, June 7, 2008 6:17 PM

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In this chapter you will: Wordbank

• 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 cm

3

=

1 mL, and 1 m

3

=

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• convert between units of time (seconds, minutes,

hours and days)• add and subtract times and calculate time

differences• use time zones to calculate time differences

between major cities• interpret and use timetables.

•

capacity

The amount of fluid (liquid or gas) contained by an object.

•

cubic metre

The volume of a cube with side length 1 metre.

•

Eastern Standard Time

The time zone for the eastern states of Australia.

•

time zone

A region of the world in which all places experience the same time of day.

•

tonne

A measuring unit of mass for heavy objects, equal to 1000 kg.

•

volume

The amount of space occupied by an object.


380

NEW CENTURY MATHS 7

Start up

1

Each cube in these drawings represents one cubic centimetre (1 cm

3

). Find the volume of each figure.

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).

Worksheet11-01

Brainstarters 11 a b c d

e f g h

i j k l

a b c

d e f12

2

3

4567

8

9

1011 1 12

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 112

2

3

4567

8

9

1011 1

Skillsheet11-01

Units of time

Skillsheet11-02

Telling the time

13 :20 20 :17

a b c

04:15Worksheet11-02

TV times

Skillsheet11-03

24-hour time

11 NCM7 2nd ed SB TXT.fm 80 Saturday, June 7, 2008 6:17 PM

381

CHAPTER 11

VOLUME, MASS AND TIME

4

Write these as 24-hour times.

a

4:00pm

b

1:00am

c

3:30am

d

5:15am

e

6:38pm

f

12:30pm

g

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 hours

d

0530 hours

e

1330 hours

f

1915 hours

g

1930 hours

h

2005 hours

i

2145 hours

j

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 endingin 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 there are between 1949 and 1983.

b

How many leap years are there between 1991 and 2021?

8

Calculate the following.

a

5

×

100

b

26

×

1000

c

1800

÷

10

d

7000

÷

1000

e

350

×

100

f

2.4

×

100

g

6.01

÷

10

h

4.05

÷

100

i

13.71

×

1000

Skillsheet8-01

Multiplying by 10, 100, 1000

Working mathematically

Comparing volumesTo complete this activity you will need measuring equipment such as a measuring cylinder, cup or jug.

1 Bring to school as many different containers as you can find. 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 filling the containers with either water or sand and comparing results.

4 Discuss your results with your teacher.

Applying strategies


382

NEW CENTURY MATHS 7

11-01 Volume

Often, informal (everyday) units are used to refer to volume. For example:• a

cup

of flour• a

cup

of milk

Standard units of volume

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 cm

3

.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 isone cubic millimetre, or 1 mm

3

. 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 m

3

. A washing machine is about half a cubic metre. There are 1 000 000 cubic centimetres in one cubic metre. The diagram below illustrates this.

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

1 cm1 cm

1 cm

1 cm3

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

10 mm

1000 mm3

10 mm

10 mm1 cm

1 cm

1 cubic millimetre

1 cm

1 cubic centimetre

L 164

Inside a cubic metre

TLF

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)


383

CHAPTER 11

VOLUME, MASS AND TIME

The diagram below will help you convert units.

1

Write an example of the items that could be measured by each informal unit of volume.

a

cup(s)

b

box(es)

c

handful

d

pinch

e

bucket(s)

f

packet

g

capsule(s)

h

can(s)

i

teaspoon

j

wheelbarrow

k

carton

l

capful

2

What unit of volume would you use when measuring the volume of:

a

a textbook?

b

a backpack?

c

the carton for a large TV?

d

a large suitcase?

e

a match box?

f

a room?

3

Copy and complete the following.

a

3 cm

3

=

mm

3

b

5 m

3

=

cm

3

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 11-01

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.

Solution12 000 mm3 = (12 000 ÷ 1000) cm3

= 12 cm3

2 Convert 48 m3 into cm3.

Solution48 m3 = (48 × 1 000 000) cm3

= 48 000 000 cm3

cm3 mm3

÷ 1000

m3 cm3

× 1 000 000

Ex 1


384 NEW CENTURY MATHS 7

4 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.

5 What is the approximate volume of a brick? Select from A, B, C or D. A 1000 cm2 B 20 cm2 C 1600 cm3 D 2100 cm3

6 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 classroom E 20 000 mm3

f a school hall F 250 cm3 g a cereal package G 2200 cm3


Building a cubic metreAs a group activity, construct your own cubic metre. Write a short report on how you did this.

Volumes of rectangular prisms1 The rectangular prisms at the top of the next page are made up of 1 cm cubes. Copy

and complete the following table.

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

a

b

c

d

e

f

Applying strategies


385CHAPTER 11 VOLUME, MASS AND TIME

2 Copy and complete this table for the rectangular prisms in Question 1.

3 What is the relationship between the length, breadth and height of a rectangular prism and its volume?

4 Write the relationship as a rule:Volume of a rectangular prism = × ×

Shape Length (cm) Breadth (cm) Height (cm) Volume (cm3)

a 4 4 1 16

b

c

d

e

f

a b

c

d

e f

length

height

breadth



11-02 Volume of a rectangular prism

1 Find the volume of each of these rectangular prisms.

Exercise 11-02

Worksheet11-03

Volume

The volume of the rectangular prism is V = length × breadth × heightV = l × b × h!

Example 2

Find the volume of the rectangular prism on the right.

SolutionV = l × b × h

= 18 × 12 × 8= 1728

The volume is 1728 cm3.

8 cm

18 cm12 cm

Ex 2

9 cm

5 cm

5 cm17 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



2 Find the missing measurements for the rectangular prisms in the table.

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

Prism Length Breadth Height Volume

a 50 cm 50 cm 50 cm

b 5 cm 10 cm 18 cm

c 4 m 2.5 m 1.4 m

d 24 mm 16 mm 11 mm

e 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 mm

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

10 cm

24 c

m

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 m

m

10 cm

28 cm



4 Find the volume of each of these rectangular prisms. (Hint: make sure that all the measurements you use are in the same units.)

1.5 m

2 m

3 m

50 cm

15 mm

15 mm

2.5 cm

a b c

d e

80 cm

10 cm

0.5 m

10 cm

10 cm40 mm

5 cm

500 mm


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 find 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 find 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

Applying strategies and communicating



11-03 Capacity‘What is the capacity of the water tank?’Capacity is the amount of fluid (liquid or gas) in a container.The standard units of capacity are the litre (L), the millilitre (mL) and the kilolitre (kL). 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.

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

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

Exercise 11-03

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

!

1 mL

÷ 1000 ÷ 1000

× 1000 × 1000

1 L1 kL

1 cm3 contains 1 mL

1 m3 contains 1 kL !

1 m3 = 1 kL

1 mL

1 cm3 × 1 000 000 =



2 State what unit of capacity you would use when measuring:a a glass of milk b a dam c a petrol tankd a bottle of medicine e the amount of soft drink consumed in a week

3 Copy and complete the following.a 7000 mL = L b 2 L = mL

c 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

4 Select A, B, C or D to complete this statement.The capacity of a bottle of cough medicine is approximately equal to:

A 200 mL B 500 mL C 1500 mL D 2000 mL

5 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 9 Li teaspoon I 375 mLj water storage tank J 180 L

6 A jug holds 2 L of water. How many 250 mL glasses could be filled from it?

7 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?

8 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?

9 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?

10 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 taketo fill a 1.25 L soft drink bottle?

11 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 fit in the lunch box?

12---



12 Gina’s swimming pool is 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 fill the pool? (Hint: 1 m3 holds 1 kL.)

13 A fish tank is a rectangular prism 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?

Just for the record

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 flush) 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• Campbelltown swimming pool (Olympic 50 m) uses 1870 kL

On 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 flushed in a toilet.

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




Volume by displacementArchimedes, a mathematician and inventor from ancient Greece, discovered that the volume of an object fully immersed in a fluid equals the volume of the displaced fluid. (‘Displaced’ means moved from its position.)

1 Fill a measuring jug with 500 mL of water.2 Choose at least five 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 afterputting object in

Difference in water level

Volume of object in cm3

500 mL

500 mL

500 mL

500 mL

500 mL

Applying strategies and reasoning

Using technology

Comparing volume and capacity of two damsBrogo Dam is situated near Bega on the south coast of NSW. Windamere Dam, which is larger in comparison, is situated between Dubbo and Newcastle. Some data for the dams is shown below.

Source: www.waterinfo.nsw.gov.au



11-04 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.

1 Copy the table on the previous page into a spreadsheet. (Note: ML = Megalitres.)

2 In the spreadsheet, ‘Capacity’ refers to the total capacity of a dam. ‘Volume’ means the amount of water in the dam and ‘% Capacity’ calculates that volume as a percentage of the total capacity. To find the percentage capacity on 11 July 2006, enter =B4/$C$1 in cell C4 and click %.

3 Fill Down the formula from cell C4 to C16. Notice that, by using an absolute cell reference ($C$1), each volume is divided by the same number (the total capacity).

4 Repeat the steps above to calculate Windamere Dam’s percentage capacity, in cells H4 to H16.

5 Answer the following questions in the given cells:a In cell A18, explain (in one sentence) why it is inappropriate to graph the data for

both dams on a single graph.b State the driest month for:

i Brogo Dam (answer in cell A19) ii Windamere Dam (B19).c State the wettest month for:

i Brogo Dam (A20) ii Windamere Dam (B20).d Use the ‘% Capacity’ column to find the month which shows the lowest dam level

for each dam. Answer in cell A21 (Brogo) and B21 (Windamere).e Which area is more suitable for the development of a new town? Begin your

answer in cell A22. Give reasons to support your answer.f Which dam is located in an area more likely to receive rain? Give reasons to

support your answer. Answer in cell A25.



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.

The diagram below will help you convert units.

Note: You will need a variety of weighing scales.1 What unit of mass would you use when measuring:

a a piece of fruit? b an elephant? c a schoolbag?d a car? e a television?

Exercise 11-04

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


Mass of household objectsEach member of the group must find 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 the one below.

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

Reflecting



2 Measure the mass of:a this textbook b your lunchbox c your schoolbagd a shoe e a pencil case f yourselfg a jumper h a brick i an apple

3 Copy and complete the following.a 3000 g = kg b 2 t = kg c 4 kg = gd 9000 kg = t e 7.5 t = kg f 10 000 mg = gg 1.5 kg = g h 3800 kg = t i 3 g = mg

4 Select A, B, C or D to complete the following statement.A tub of margarine weighing 500 g has a mass greater than:

A 2.5 kg B 0.01 tonnes C 60 000 mg D 0.8 kg

5 Copy and complete the following, using a �, � or = sign.a 700 g 0.6 kg b 0.8 g 95 mg c 3500 kg 3.5 td 1.7 kg 1700 g e 0.007 t 7 kg f 640 mg 0.7 gg 4000 mg 0.04 kg h 0.03 kg 3 g

6 Match the items given (a to j) with the masses listed (A to J). 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

7 Measure the mass of 1 L of water. Write a report on how you did it.


Investigating mass1 Investigate the sport of weight-lifting.

2 a Obtain a schedule of postal charges from the post office. Imagine that you have five pen-friends in different countries (you choose the countries) and want to send a present to each. Choose the presents, work out the mass of each when wrapped to send, and calculate the cost of sending each one by airmail and by sea.

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

3 Library or Internet researcha Choose 10 animals and estimate their masses. Then compare your estimates with

data you find at the library or on the Internet.b Find 10 world records that have something to do with mass; for example, the

heaviest man, the lightest baby, etc.

Applying strategies



Mental skills 11

24-hour time

To convert from 24-hour time to 12-hour (am/pm) time, look at the first two digits.• If they are 00, then it is just after 12:00 midnight.• If they are less than 12, then it is ‘am’ (morning) time. Write ‘am’.• If they are 12 or more, it is ‘pm’ (afternoon/evening) time. Subtract 12 and write ‘pm’. Then insert a colon (:) before the last two digits.

1 Consider these examples.a Convert 1850 hours to 12-hour time.

The first two digits are 18.18 is more than 12, so it is ‘pm’ time, and we need to subtract 12. 18 − 12 = 6∴ 1850 hours = 6:50pm

b Convert 0430 hours to 12-hour time.The first two digits are 04.04 is less than 12, so it is ‘am’ time.∴ 0430 hours = 4:30am

c Convert 0015 hours to 12-hour time.The first two digits are 00.00 is 12:00 midnight, so it is just after midnight∴ 0015 hours = 12:15am

d Convert 2223 hours to 12-hour time.The first two digits are 22.22 is more than 12, so it is ‘pm’ time, and we need to subtract 12. 22 − 12 = 10∴ 2223 hours = 10:23pm

24-hour time 12-hour time 24-hour time 12-hour time

0000 hours 12:00 midnight 1200 hours 12:00 midday

0100 hours 1:00am 1300 hours 1:00pm









1000 hours 10:00am 2200 hours 10:00pm

1100 hours 11:00am 2300 hours 11:00pm

Maths without calculators

Skillsheet11-03

24-hour time

L 347

Rainforest: book a flight

TLF



11-05 TimelinesTimelines record events in the order in which they happen, along a regular scale. A timeline for a puppy’s first 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 (unit) represents 4 weeks.

2 Now convert these examples to 12-hour time.a 0845 hours b 1320 hours c 1750 hours d 0017 hourse 2105 hours f 1832 hours g 1115 hours h 0238 hoursi 1440 hours j 0320 hours k 1655 hours l 2331 hoursm 0108 hours n 1018 hours o 2000 hours p 0643 hours

We can also convert from 12-hour time to 24-hour time:• If it is 12:00 midnight, change the 12 to 00.• If it is ‘am’ time or 12:00 midday, then keep the hour as it is, but make sure it has

two digits (for example 02, 09).• If it is 1:00pm or later, then add 12 to the hour.Then remove the colon (:) before the last two digits.3 Consider these examples:

a Convert 4:10am to 24-hour time.It is ‘am’ time, so keep the hour (4), then insert a ‘0’ so it has two digits, (04).∴ 4:10am = 0410 hours.

b Convert 4:10pm to 24-hour time.It is ‘pm’ time, so add 12 to the hour. 4 + 12 = 16∴ 4:10pm = 1610 hours.

c Convert 12:47am to 24-hour time.It is just after 12:00 midnight, so change the 12 to 00.∴ 12:47am = 0047 hours.

d Convert 12:47pm to 24-hour time.It is just after 12:00 midday, so leave the 12 as it is.∴ 12:47pm = 1247 hours.

4 Now convert each of these to 24-hour time.a 6:35pm b 8:05am c 11:45am d 11:20pme 2:21am f 12:30pm g 3:48pm h 7:11pmi 9:08am j 9:50pm k 12:42am l 7:39amm 1:59am n 10:18pm o 10:46am p 5:23pm

Worksheet11-04

History of the calendar

Weeks0 328 16 24

opened eyes

leftmother

learnt to play fetch

dug up new plants

ate cake from table

made a mess on

the carpetate a

slipperchased first cat



From the timeline, you can see that, at 24 weeks, the puppy chased its first cat. It left its mother at about 6 weeks and at 20 weeks it started digging up the garden.

1 a Copy this timeline.

b How many years does each interval (unit) 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 Count’544 BC Date recorded as the birth of BuddhaAD 1792 Declaration of the 1st French RepublicAD 622 Traditional date for the flight of Muhammad

2

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

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 Port Jackson1982 Brisbane hosted the Commonwealth Games1901 The Federation of the Australian States to form the Commonwealth of

Australia

Exercise 11-05

3000 BC 2000 BC 1000 BC 1000 AD

1770 1870 1970

G A

E D H

C F B



3 The table below shows the names of Australia’s Governors-General and the year they each took office, from 1960 to 2003.

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

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

4 Draw a timeline to show these events for the period between 1945 and 2010.1969 Astronauts first walked on the moon1945 World War II ended1989 Wayne Gardner won his first 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 America’s Cup1956 The first television transmission in Australia occurred2000 The Olympic Games were held in Sydney2002 Steve Fossett flew solo around the world in a balloon2006 The Crocodile Hunter, Steve Irwin, died20__ (Enter your own important event.)

5 Draw a timeline to display these famous Australian inventions and discoveries.1906 The surf-lifesaving reel for use at Bondi Beach was invented1919 The preferential voting system was first used for the House of Representatives1922 Vegemite was developed by Dr Cyril Callister1930 The world’s first 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 Richardson

Name Year

A Viscount Dunrossil 1960

B Lord Casey 1965

C Sir Zelman Cowen 1977

D Viscount De L’Isle 1961

E Right Reverend Dr Peter Hollingworh 2001

F Sir William Deane 1996

G Sir Paul Hasluck 1969

H Sir John Kerr 1974

I William Hayden 1989

J Sir Ninian Stephen 1982

K Major-General Michael Jeffery 2003

1960 1972 2008

A C

1984 1996



1979 Race-cam was first 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 first released

6 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.

11-06 Converting units of time


Timeline displayBy yourself, or with a partner, create 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 • A topic approved by your teacher

Communicating

Worksheet11-05

Metric units

Unit Abbreviation Conversionsecond s minute min 1 min = 60 shour h 1 h = 60 min = 3600 sday day 1day = 24 h

!

day h min

÷ 24 ÷ 60

× 24 × 60

s

÷ 60

× 60

× 3600

÷ 3600

Example 3

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 6 seconds

Solutiona 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 1 hour. b 12 h 19 min ≈ 12 h (round down because 19 min � 30 min)c 2 h 43 min 6 s ≈ 3 h (round up because 43 min � 30 min)



Most scientific calculators have a degrees-minutes-seconds key, or , that isuseful 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 5 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.

1 State which unit of time (hours, minutes, or days) would be used to measure each event.a snapping your fingers five times, as fast as possibleb a day-night cricket match c running once around the school ovald building a house e flying from Sydney to Broken Hillf watching a DVD from beginning to end g the life span of a grasshopper

Exercise 11-06

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 seconds

Solutiona 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)

Example 4

1 Convert 7 minutes into seconds.

Solution7 minutes = 7 × 60 seconds

= 420 seconds

2 Convert 91 days into weeks.

Solution91 days = 91 ÷ 7 weeks

= 13 weeks

Example 5

Convert 275 minutes into hours and minutes.

SolutionThere are 60 minutes in 1 hour.

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

° ' " DMS

° ' "



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 minutes

i 8.5 days to hours j 10 minutes to seconds

k 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.

Ex 3

Ex 4

12---

Ex 5

Just for the record

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.



11-07 Time 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?

Exercise 11-07

Worksheet11-06

Time calculations

Example 6

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. 11:52pm

+ 7 h

6:52am 7:32am

+ 8 min + 32 min

7am

Example 7

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 Convert to 24-hour time first. Then use the calculator’s or key to

enter hours and minutes, and subtract the times.

8:35am

+ 6 h

3:10pm

+ 10 min

3pm9am

25 min

° ' " DMS

Example 8

Find 7 h 5 min − 3 h 24 min.

Solution7 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 Use the calculator’s or key to enter hours and minutes, and subtract the times.

° ' " DMS

Ex 06

14---



2 A marathon began at 10:20am. Here are some of the competitors and the times they ran. Write the runners in their order of finishing and the time each crossed the finishing line.

Mike 3:11 (3 h 11 min) Joe 2:23Anna 2:54 Pathena 3:01Ken 2:59 Gail 3:42

3 What is the difference in time between 10:42am and 2:13pm? Select A, B, C or D.A 3 h 31 min B 4 h 55 min C 8 h 29 min D 12 h 55 min

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

11-08 Standard timeWorld 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 (1827–1915), a Canadian civil engineer and scientist. In 1884, scientists from 27 nations met in Washington and devised the time system we now use.

Ex 7

Ex 8

Worksheet11-07

World time zones



The map below shows how times around the world are related. All time is measured in relation to the time at Greenwich (in London), either ahead or behind Greenwich Mean Time (GMT), also known as UTC (Coordinated Universal Time). Australia’s time is ahead of Greenwich Mean Time since Australia is east of Greenwich. America’s time is behind Greenwich Mean Time since America is west of Greenwich.

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, find 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 11-08

180°W 0°90°W 30°W 20°E60°W150°W 120°W 60°E 90°E 120°E 150°E 180°EInternational D

ate Line

International Date L

ine

Greenw

ich Meridian

N

Rio deJaneiro

Honolulu

San FranciscoNew York

GreenwichGeneva

Moscow

Beijing

Hong

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

Athens

Ottawa

(behind GMT) (ahead of GMT)



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 Sydney’s time is 4 hours ahead of India’s?

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 Brisbane is 2 hours behind New Zealand. A plane leaves New Zealand at midday and takes 3 hours to fly to Brisbane. What is the local time in Brisbane when the plane lands? Select A, B, C or D.A 11am B 1pm C 3pm D 5pm

8 Find out what happens if you cross the International Date Line (IDL). Why isn’t the IDL straight?

11-09 Australian standard timeThis map shows the three time zones for Australia.

Note: During daylight saving periods, add 1 hour.

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)

Exercise 11-09

12---

NorthernTerritory

QueenslandWesternAustralia

SouthAustralia

New SouthWales

Victoria

Tasmania

Australian Western Standard Time

(AWST)

Australian Eastern Standard Time

(AEST)

−2 hours10am 11:30am 12noon

− hour12 Zero

Australian Central Standard Time

(ACST)



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 Joe flies from Sydney to Perth, taking 4 hours. If he leaves Sydney at 2pm, what time does he land in Perth? Give your answer as Perth local time.

b When Joe flies home, he leaves Perth at 9am. What time does he land in Sydney? Give your answer as Sydney local time.

6 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?d If it is 12:30pm in Western Australia (not on daylight saving), what time is it in New

South Wales on Eastern Standard Daylight Saving Time?

11-10 Timetables

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

a How long does flight TH503 take from Sydney to Brisbane?b The team plans to meet at Sydney airport at 10:45am. How long will they need to

wait for the next available flight?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 flight the team can catch from Sydney?

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

Exercise 11-10

Flight number Sydney departure time Brisbane arrival time

TH503 0905 1030

TH511 0935 1100

TH038 1005 1130

TH114 1040 1210

TH514 1105 1230

TH051 1135 1300

Worksheet11-08

Tide chart

Journey planner: quickest route 1

L 764TLF



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 Wagga Return: Wagga Wagga to SydneySydney 2:30pm Wagga 7:15amStrathfield 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 Strathfield 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. Below 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 Sofia 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 spendat 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 theExplorer 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 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


Round tripPlan a trip around the world with at least three stopovers (for example, Berlin, London, New York). Obtain some airline timetables so you can give details of departures and arrivals. Work out how much time is actually spent flying. Does it matter if you head east or west when you start? What effect does the International Date Line have on your trip?




Using technology

Graphing winning timesThe table below shows the gold medal winning time of the women’s 400-metre track event in the Olympic Games held from 1972 to 2004.

1 Copy the data, as shown in the table above, into a spreadsheet.

2 Highlight the data, open Chart Wizard (by clicking on or choosing Insert Chart) and select XY (Scatter). Click on the option that shows points joined with

straight lines .

3 Give the graph an appropriate title and axes labels. Click ‘Next’. Save the graph‘As new sheet’.

4 On the graph, position the mouse over a data point. (Do not click on it.) You can view the specific details of the Olympic year and winning time.

5 Use your spreadsheet, graph and the formulas below to answer these questions.a In what year was the fastest gold medal winning time run? In cell A5, enter

=min(B2:J2). In cell B5, enter the year that corresponds to this time.b In cell A6, type the label ‘Average’. In cell B6, use the formula =average(B2:J2)

to calculate the average winning time for this event, from 1972 to 2004.c In cell A7, enter =max(B2:J2) to find the

slowest winning time in this event. In cell B7, enter the year that corresponds to this time.

d In cell A8, enter a formula to find the difference between the fastest and slowest winning times.

e Predict the gold medal time at the 2008 Olympic Games in this event. Justify your answer.

f In cell A9, enter a formula to calculate the speed, in metres per second, of the fastest women’s 400-m runner, from 1972 to 2004.

g Starting in cell A10, write a paragraph describing the changes in winning times for this event between 1972 and 2004.

h In cell A15, suggest reasons why the pattern of gold medal times has changed between 1972 and 2004.

Year 1972 1976 1980 1984 1988 1992 1996 2000 2004

Time (s) 51.08 49.28 48.88 48.83 48.65 48.83 48.25 49.11 49.41




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 find someone’s 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 first 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 first digit of their age from this sum to get the second digit of their age.

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Puzzler 3

The floral 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 finish 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 in our time is a metric hour if:

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

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Power plus

1 The diagram on the right shows a tank. The tank is half-filled 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 children’s pool is in the shape of a cross as shown on the right. Each side is 3 m long. The pool is filled 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 fill the pool?

4 A doctor orders 5.2 litres of fluid each day to be given to a patient in drops. Each 1 mL of fluid is equivalent to 15 drops. How many drops of fluid 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 flying from Perth to Port Augusta. If the flight takes 2 hours and the flight 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

13 cm13 cm2 cm

ba

16 cm

16 cm

8 cm

8 cm

16 cm

20 cm

2 cm

100 cm

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Chapter 11 review

Language of mathscapacity cubic centimetre cubic metrecubic millimetre 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.

Topic overview• Write in your own words what you have learnt about volume, mass and time.• What parts of this topic were new to you?• What parts of this topic did you have difficulty 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.

Worksheet11-09

Measurement crossword

123

4567

8

910

11 12

T ____

VOLUME, MASSand TIME

l × b × h

V _____M _____

• mg• g• kg• t

cm3

m3

C _______• mL• L• kL



Chapter revision1 Copy and complete the following.

a 20 cm3 = mm3 b 0.5 m3 = cm3

c 7500 mm3 = cm3 b 230 000 mm3 = m3

2 Count the cubes in this solid to find its volume. Each cube equals 1 cm3.

3 Find the volume of each of these prisms.

4 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 contained in B9? (1 kL of water will occupy 1 m3.)

5 Copy and complete the following.

a 2000 mL = L b 3 kL = Lc 7 L = mL d 3300 L = kLe 1750 mL = L f 2.5 L = mL

Exercise 11-01

Exercise 11-02

Exercise 11-02

a b

c d

e f

10 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

Exercise 11-02

Exercise 11-03

Topic test 11



6 Select A, B, C or D to complete the following. The mass of an egg is closest to:A 5 g B 50 g C 500 g D 5 kg

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

8 Copy and complete the following.a 5000 g = kg b 2 g = mg

c 1 t = kg d 6500 kg = t

e 4000 mg = g f 1.5 kg = g

9 Make up a timeline for your life from age 0 to 12.

10 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

11 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

12 Copy and complete the following.a 56 days = weeks b 4 h = minc 960 s = min d 5 years = weekse 7 days = h f 750 min = h

13 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?

14 What is the difference in time 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?

15 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

16 If it is 10:00am in Sydney, use the maps on pages 405 and 406 to help you work out the time in:a Perth b Rio de Janeiro c Adelaided Moscow e Hong Kong f San Francisco

17 Use the information on page 406 to answer the following question.When it’s 2am in Sydney, what time is it in:

a Melbourne? b Perth? c Darwin? d Canberra?

18 Use the Countrylink train timetable on page 408 to answer the following.a How long does the 7.45 pm train take to get to Sydney?b What time do you need to catch the train at Moss Vale to be in Sydney by 11 am?

Exercise 11-04

Exercise 11-04

Exercise 11-04

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Exercise 11-05

Exercise 11-06

Exercise 11-06

Exercise 11-06

Exercise 11-07

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Exercise 11-07

Exercise 11-07

Exercise 11-08

Exercise 11-09

Exercise 11-10


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