Year 4 Mathematics
©Ezy Math Tutoring | All Rights Reserved
www.ezymathtutoring.com.au
Copyright © 2012 by Ezy Math Tutoring Pty Ltd. All rights reserved. No part of this book shall be
reproduced, stored in a retrieval system, or transmitted by any means, electronic, mechanical,
photocopying, recording, or otherwise, without written permission from the publisher. Although
every precaution has been taken in the preparation of this book, the publishers and authors assume
no responsibility for errors or omissions. Neither is any liability assumed for damages resulting from
the use of the information contained herein.
©Ezy Math Tutoring | All Rights Reserved
www.ezymathtutoring.com.au
Learning Strategies
Mathematics is often the most challenging subject for students. Much of the trouble comes from the
fact that mathematics is about logical thinking, not memorizing rules or remembering formulas. It
requires a different style of thinking than other subjects. The students who seem to be “naturally”
good at math just happen to adopt the correct strategies of thinking that math requires – often they
don’t even realise it. We have isolated several key learning strategies used by successful maths
students and have made icons to represent them. These icons are distributed throughout the book
in order to remind students to adopt these necessary learning strategies:
Talk Aloud Many students sit and try to do a problem in complete silence inside their heads.
They think that solutions just pop into the heads of ‘smart’ people. You absolutely must learn
to talk aloud and listen to yourself, literally to talk yourself through a problem. Successful
students do this without realising. It helps to structure your thoughts while helping your tutor
understand the way you think.
BackChecking This means that you will be doing every step of the question twice, as you work
your way through the question to ensure no silly mistakes. For example with this question:
3 × 2 − 5 × 7 you would do “3 times 2 is 5 ... let me check – no 3 × 2 is 6 ... minus 5 times 7
is minus 35 ... let me check ... minus 5 × 7 is minus 35. Initially, this may seem timeconsuming, but once it is automatic, a great deal of time and marks will be saved.
Avoid Cosmetic Surgery Do not write over old answers since this often results in repeated
mistakes or actually erasing the correct answer. When you make mistakes just put one line
through the mistake rather than scribbling it out. This helps reduce silly mistakes and makes
your work look cleaner and easier to backcheck.
Pen to Paper It is always wise to write things down as you work your way through a problem, in
order to keep track of good ideas and to see concepts on paper instead of in your head. This
makes it easier to work out the next step in the problem. Harder maths problems cannot be
solved in your head alone – put your ideas on paper as soon as you have them – always!
Transfer Skills This strategy is more advanced. It is the skill of making up a simpler question and
then transferring those ideas to a more complex question with which you are having difficulty.
For example if you can’t remember how to do long addition because you can’t recall exactly
how to carry the one:
ାହ଼଼ଽ
ସହ଼଻
then you may want to try adding numbers which you do know how
ାହ
to calculate that also involve carrying the one: ଽ
This skill is particularly useful when you can’t remember a basic arithmetic or algebraic rule,
most of the time you should be able to work it out by creating a simpler version of the
question.
©Ezy Math Tutoring | All Rights Reserved
1
www.ezymathtutoring.com.au
Format Skills These are the skills that keep a question together as an organized whole in terms
of your working out on paper. An example of this is using the “=” sign correctly to keep a
question lined up properly. In numerical calculations format skills help you to align the numbers
correctly.
This skill is important because the correct working out will help you avoid careless mistakes.
When your work is jumbled up all over the page it is hard for you to make sense of what
belongs with what. Your “silly” mistakes would increase. Format skills also make it a lot easier
for you to check over your work and to notice/correct any mistakes.
Every topic in math has a way of being written with correct formatting. You will be surprised
how much smoother mathematics will be once you learn this skill. Whenever you are unsure
you should always ask your tutor or teacher.
Its Ok To Be Wrong Mathematics is in many ways more of a skill than just knowledge. The main
skill is problem solving and the only way this can be learned is by thinking hard and making
mistakes on the way. As you gain confidence you will naturally worry less about making the
mistakes and more about learning from them. Risk trying to solve problems that you are unsure
of, this will improve your skill more than anything else. It’s ok to be wrong – it is NOT ok to not
try.
Avoid Rule Dependency Rules are secondary tools; common sense and logic are primary tools
for problem solving and mathematics in general. Ultimately you must understand Why rules
work the way they do. Without this you are likely to struggle with tricky problem solving and
worded questions. Always rely on your logic and common sense first and on rules second,
always ask Why?
Self Questioning This is what strong problem solvers do naturally when they
get stuck on a problem or don’t know what to do. Ask yourself these
questions. They will help to jolt your thinking process; consider just one
question at a time and Talk Aloud while putting Pen To Paper.
©Ezy Math Tutoring | All Rights Reserved
2
www.ezymathtutoring.com.au
Table of Contents
CHAPTER 1: Number
4
Exercise 1: Representing Numbers
8
Exercise 2: Addition & Subtraction
12
Exercise 3: Multiplication & Division
15
Exercise 4: Number Patterns
18
Exercise 5: Fractions
21
Exercise 6: Decimals & Percentages
25
Exercise 7: Chance
30
CHAPTER 2: Data
33
Exercise 1: Data Tables
35
Exercise 2: Picture Graphs
39
CHAPTER 3: Space
Exercise 1:Tessellation
45
s
49
Exercise 2: Angles
54
Exercise 3: 2D & 3D Shapes
63
CHAPTER 4: Measurement:
66
Exercise 1: Time
69
Exercise 2: Mass
74
Exercise 3: Length, Perimeter & Area
77
Exercise 4: Volume & Capacity
80
©Ezy Math Tutoring | All Rights Reserved
3
www.ezymathtutoring.com.au
Year 4 Mathematics
Number
©Ezy Math Tutoring | All Rights Reserved
4
www.ezymathtutoring.com.au
Useful formulae and hints
Numbers are written in the form “abcd”, where each letter
represents a digit
d is the number of ones in the number
c is the number of tens in the number
b is the number of hundreds in the number
a is the number of thousands in the number
For example: the number 4325 has 4 thousands, 3 hundreds, 2 tens,
and 5 ones. These are called the place values of the digits
To group numbers from largest to smallest, work from the left of the
number. Compare all the three digit numbers first.
For example: comparing 4325, 4346, 4327, 137, 5401, and 153
Of the four digit numbers, there is only one with 5 thousands; that
must be the biggest
If the thousands digit is the same, compare the hundreds digits
If the hundreds digits are the same, compare the tens digits
The next largest number is 4346
If numbers have the same hundreds and tens digits, compare their
units’ digits.
4327 is bigger than 4325
Once all the three digit numbers have been compared, do the same
for the three digit numbers; 153 is greater than 137
©Ezy Math Tutoring | All Rights Reserved
5
www.ezymathtutoring.com.au
Do the same for single digit numbers if there are any
To group smallest to largest, follow the above rules but start with the
single digit numbers, then two digits, then three, then four
When deciding how to solve word problems, look for key words
More than, together means addition
Less than, difference means subtraction
Times means multiplication
Share means division
When looking for number patterns, work out the difference between
two numbers next to each other. See if that rule works for the next
two numbers. If it does, use your rule to complete the pattern
Fractions are in the form
ௌ௢௠௘ ௡௨௠௕௘௥
ௌ௢௠௘ ௡௨௠௕௘௥
The bottom number is called the denominator and shows the total
number of equal parts something is broken up into.
The top number is called the numerator, and shows how many of
these parts we have
ଷ
For example, the fraction shows that something is made up of four
ସ
equal parts, and we have three of these parts
(Think of a cake or pizza)
To change a fraction to a decimal, divide the numerator by the
denominator
To change a percentage to a decimal, remove the percentage sign an
move the decimal point two places to the left
©Ezy Math Tutoring | All Rights Reserved
6
www.ezymathtutoring.com.au
To change a percentage to a fraction, remove the percentage sign,
put the number as a fraction with 100 as the denominator, and
simplify the fraction if necessary
When working out possible events, all possibilities must be listed and
counted.
For example, if there are 3 children in a family there could be
3 girls
2 girls and a boy
2 boys and a girl
3 boys
©Ezy Math Tutoring | All Rights Reserved
7
www.ezymathtutoring.com.au
Exercise 1
Representing Numbers
©Ezy Math Tutoring | All Rights Reserved
8
www.ezymathtutoring.com.au
Chapter 1: Number
1)
Write as numbers
8090
Three hundred and ninety
e)
2010
b)
Eight hundred and eighty
three
f)
1117
g)
0
Seven hundred and ninety
three
d)
Five hundred and six
e)
Nine hundred and nine
Write as numbers
a)
b)
c)
d)
e)
3)
d)
a)
c)
2)
Exercise 1: Representing Numbers
Two thousand two hundred
and three
Seven thousand four
hundred and ninety seven
Eight thousand six hundred
and thirty
Nine thousand and twenty
one
Three thousand and one
Write in words
4)
Write down the number that
comes before each of these
numbers
a)
331
b)
156
c)
905
d)
120
e)
1710
f)
1100
g)
2442
h)
1900
i)
9001
j)
3006
a)
2713
k)
1234
b)
2097
l)
10000
c)
3330
©Ezy Math Tutoring | All Rights Reserved
9
www.ezymathtutoring.com.au
Chapter 1: Number
5)
6)
Write the number that comes after
each of these numbers
2114
819
d)
4027
b)
1090
e)
4
c)
8881
f)
1040
d)
4223
g)
2047
e)
8010
f)
711
g)
1999
a)
1234, 2134
h)
3009
b)
9821, 9281
c)
8005, 8015
d)
1023, 103
e)
970, 907
f)
1099, 1089
Put these numbers in order from
smallest to largest
Put these numbers in order from
largest to smallest.
2015, 2004, 4020, 1912, 1911,
2333, 3322, 2921, 2221, 4121,
3004
8)
c)
a)
1325, 1101, 1123, 3000, 2946,
2121, 1015, 2221, 2323, 9104, 694
7)
Exercise 1: Representing Numbers
What is the value of the number 4
in each of these numbers?
9)
Use the > or < sign to show the
relationship between the following
pairs of numbers
10) Write the number that is 10 less
than the number shown. Repeat 4
times
a)
675
b)
555
a)
1034
c)
390
b)
1435
d)
442
©Ezy Math Tutoring | All Rights Reserved
10
www.ezymathtutoring.com.au
Chapter 1: Number
12) Round the following numbers to
e)
530
f)
401
g)
h)
i)
j)
k)
Exercise 1: Representing Numbers
112
220
1039
1050
908
11) Write the number that is 10 more
than the number shown. Repeat
four times
a)
1121
b)
2020
c)
3175
d)
1099
e)
803
f)
960
g)
999
h)
100
i)
1251
©Ezy Math Tutoring | All Rights Reserved
the nearest thousand, hundred
and ten
a)
1263
b)
926
c)
101
d)
4565
e)
8555
f)
7550
g)
6005
h)
1111
11
www.ezymathtutoring.com.au
Exercise 2
Addition & Subtraction
©Ezy Math Tutoring | All Rights Reserved
12
www.ezymathtutoring.com.au
Chapter 1: Number
1)
2)
Exercise 2: Addition & Subtraction
Add these numbers
e)
8122 + 110
f)
9334 + 73
a)
632 + 114
b)
247 + 319
c)
621 + 535
a)
816 - 412
d)
877 + 223
b)
594 - 482
e)
135 + 175
c)
756 -511
f)
414 + 441
d)
929 - 353
e)
504 - 127
f)
865 – 821
g)
9026 – 312
h)
6111 -- 3227
Add these numbers
a)
b)
c)
d)
2225 + 529
4302 + 410
8009 + 377
3)
Subtract these numbers
4335 + 323
4)
Peter has 840 stamps, John has 275 stamps. How many stamps do they have
between them?
5)
Alan weighs 145 kg, Chris weighs 148 kg. How much do they weigh together?
6)
There were 1510 more people at the football game than at the rugby. If there were
4600 people at the football how many people were at the rugby?
7)
Tom and Jerry have read 410 books between them. If Tom has read 318 books, how
many books has Jerry read?
8)
138 students passed a test, 112 failed, and 35 were absent. How many students are
in the school?
9)
What number is 299 less than 6075?
©Ezy Math Tutoring | All Rights Reserved
13
www.ezymathtutoring.com.au
Chapter 1: Number
10)
Exercise 2: Addition & Subtraction
What is the difference between 2710 and 3244?
©Ezy Math Tutoring | All Rights Reserved
14
www.ezymathtutoring.com.au
Exercise 3
Multiplication & Division
©Ezy Math Tutoring | All Rights Reserved
15
www.ezymathtutoring.com.au
Chapter 1: Number
1)
Calculate the following
a)
b)
c)
d)
e)
f)
5 × 20
d)
40 × 5
f)
e)
5 × 30
60 × 5
20 × 7
6 × 15
7 × 15
9 × 15
From your answers, state a
method for quickly
multiplying any number by
15
4)
How many fours in 24?
60 × 7
b)
What is 24 × 25?
Calculate the following
d)
h)
i)
a)
b)
c)
d)
e)
f)
3)
c)
5 × 10
a)
g)
2)
Exercise 3: Multiplication & Division
40 × 7
60 × 9
c)
8 × 13
e)
11 × 7
g)
17 × 8
32 × 6
45 × 9
Calculate the following
a)
b)
f)
16 × 9
15 × 6
15 × 8
©Ezy Math Tutoring | All Rights Reserved
5)
How many fours in 28?
What is 28 × 25?
How many fours in 32?
What is 32 × 25?
Use your answers to parts a
to f to state a method for
quickly multiplying any
number by 25
Calculate the following
a)
b)
c)
24 ÷ 5
33 ÷ 8
15 ÷ 4
16
www.ezymathtutoring.com.au
Chapter 1: Number
d)
e)
f)
g)
h)
i)
j)
6)
Exercise 3: Multiplication & Division
35 ÷ 7
d)
7
24 ÷ 7
e)
74 ÷ 7
f)
4
37 ÷ 5
g)
49 ÷ 8
h)
21 ÷ 4
i)
1
64
100
22
82 ÷ 8
Write the factors of the following
a)
b)
c)
9
15
24
7)
Mary has 40 lollies. If she gives each of her 6 friends an equal amount of lollies, how
many will she have left over for herself? (She gives each friend the most that she
can)
8)
Alan buys 5 pens and gets 5 cents change from his dollar. How much was each pen?
9)
Kathy is having a birthday party and wants each friend to get five lollies in their party
bag. If there are 8 friends coming to the party, how many lollies will be left over
from a bag of 50?
10)
Tom has $5 left after giving an equal amount of money to a number of charities. If
he started with $35, list how many charities he may have given money to, and how
much he would have given to each.
©Ezy Math Tutoring | All Rights Reserved
17
www.ezymathtutoring.com.au
Exercise 4
Number Patterns
©Ezy Math Tutoring | All Rights Reserved
18
www.ezymathtutoring.com.au
Chapter 1: Number
1)
2)
3)
Exercise 4: Number Patterns
Find the sixth term in the following
sequences
a)
3, 6, 9, 12
b)
2, 4, 6
b)
c)
d)
c)
5, 10, 15
d)
7, 14, 21
e)
4, 8, 12
f)
f)
9, 18, 27
g)
Find the fifth term in the following
sequences
a)
25, 20, 15
b)
40, 32, 24
c)
63, 54, 45,
d)
63, 60, 57
e)
14, 11, 8, ___, ___
e)
4)
11 x
= 44
7+
= 15
x 3 = 21
+ 10 = 15
ଵ ଵ ଷ
a) ସ , ଶ , ସ, ___, ____
ଵ ଶ
b) ଷ , ଷ , 1, ____, ____
c)
ଵ ଶ ଷ
, , , ____, ____
ହ ହ ହ
ହ ସ
d) ଷ , ଷ , 1, ____,____
e)
f)
+ 12 = 20
x 5= 30
Complete the following sequences
Find the missing numbers
a)
+ 10 = 20
ଵ଴ ଽ ଼
଻
, , , ____,____
ଽ଻
଻ ଻
,
ଽ଼
,
ଽଽ
ଵ଴଴ ଵ଴଴ ଵ଴଴
, ____,____
5)
Peter wants to give 8 people $5 each. If he has $32 how much more money does he
need to be able to do this?
6)
There are 9 tables in a restaurant. Each table has 6 chairs around them. If there are
70 people coming to the restaurant at one time, how many more chairs are needed?
©Ezy Math Tutoring | All Rights Reserved
19
www.ezymathtutoring.com.au
Chapter 1: Number
7)
8)
Exercise 4: Number Patterns
Every minute 5 ants crawl out of an ant hill.
a)
How many ants have crawled out after 4 minutes?
b)
There are 50 ants out of the ant hill. How many more minutes will go by until
there are 75 ants out of the ant hill?
After 4 hours there were 24 cars in a car park. If the same number of cars park each
hour
a)
How many cars will be in the car park after 7 hours?
b)
How many hours will have passed until there are 54 cars in the car park?
c)
If the car park holds 96 cars, how long until it is full from when it first
opened?
©Ezy Math Tutoring | All Rights Reserved
20
www.ezymathtutoring.com.au
Exercise 5
Fractions
©Ezy Math Tutoring | All Rights Reserved
21
www.ezymathtutoring.com.au
Chapter 1: Number
1)
One fifth
b)
One tenth
c)
Two fifths
d)
One hundredth
e)
Three fifths
f)
Three tenths
g)
Seventeen hundredths
h)
Four fifths
i)
Nine tenths
Write the following in words
a)
b)
c)
7)
d)
Write the following as a fraction
a)
2)
Exercise 5: Fractions
e)
f)
g)
3)
4)
5)
ଵ
ହ
ଵ
ଵ଴଴
ଷ
ଵ଴
6)
ଵଵ
ଵ଴଴
଻
ଵ଴
ସ
ହ
ଽଽ
ଵ଴଴
Put these fractions in order from
smallest to largest
3 2 4 1
, , ,
5 5 5 5
Put these fractions in order from
largest to smallest
5 1 7 2 6
, , , ,
10 10 10 10 10
Fill in the missing numbers
97 95 93 91
,
,
,
, ___, ___
100 100 100 100
Fill in the missing numbers
11 14
20
, , ___, , ___, ___
5 5
5
What fraction is shaded in the following diagrams?
a)
©Ezy Math Tutoring | All Rights Reserved
22
www.ezymathtutoring.com.au
Chapter 1: Number
Exercise 5: Fractions
b)
c)
d)
e)
©Ezy Math Tutoring | All Rights Reserved
23
www.ezymathtutoring.com.au
Chapter 1: Number
Exercise 5: Fractions
ଵ
ଵ ଶ଴
ଶ
଻
଻ହ
ସ
ଽହ
8)
Place the fractions
9)
Tim has one fifth of his lollies left, while Jack has eaten two fifths. Who has more
lollies left?
,
, ,
,
, ,
ଵ଴ ହ ଵ଴଴ ହ ଵ଴ ଵ଴଴ ହ ଵ଴଴
on a number line
10)
Peter had $100 and spent $50. Jack had $10 and spent only $3. Who spent the
bigger fraction of their money?
11)
A fly spray kills two fifths of the flies in a room, whilst another kills three tenths of
them. Which fly spray works better?
©Ezy Math Tutoring | All Rights Reserved
24
www.ezymathtutoring.com.au
Exercise 6
Decimals & Percentages
©Ezy Math Tutoring | All Rights Reserved
25
www.ezymathtutoring.com.au
Chapter 1: Number
1)
2)
Exercise 6: Decimals & Percentages
Round the following decimals to
the nearest whole number
3.7
a)
1.48
d)
5.8
b)
11.05
e)
10.2
c)
13.74
f)
1.36
d)
0.22
g)
2.45
e)
1.55
h)
6.22
f)
22.51
i)
8.49
j)
15.43
Express the following fractions and
mixed numbers as decimals
a)
b)
4)
ଷ
ଵ଴
1.52
b)
2.75
c)
4.26
d)
8.04
଻
e)
13.11
଻଻
f)
8.6
g)
7.2
h)
4.3
i)
1.2
ଵ଴଴
c) 3 ଵ଴
଻
d) 1 ଵ଴
e) 1 ଵ଴଴
f) 1 ଵ଴଴
Multiply each of the following by
10
a)
b)
Multiply each of the following by
100
a)
ଵହ
ଵ
3)
c)
1.4
2.5
©Ezy Math Tutoring | All Rights Reserved
26
www.ezymathtutoring.com.au
Chapter 1: Number
5)
6)
7)
Write the following as a decimal
b)
10.8
a)
30%
c)
9.6
b)
15%
d)
7.2
c)
20%
e)
3.3
d)
10%
f)
1
e)
75%
f)
90%
a)
152.5
g)
100%
b)
143.2
c)
131.9
8)
Write the following as a fraction
Divide each of the following by 100
a)
50%
d)
106.5
b)
25%
e)
98.9
c)
10%
f)
90.2
g)
66.6
h)
9.25
Divide each of the following by 10
a)
9)
Exercise 6: Decimals & Percentages
13.2
Alex has $14.25 in his bank account. Tom has ten times as much. How much money
does Tom have?
10)
John runs 30km and Jill runs 50% of that distance. How far did Jill run?
11)
Place the following decimals on a number line
0.7, 0.65, 0.8, 0.1, 0.25, 0.4, 0.5, 0.9, 0.45
©Ezy Math Tutoring | All Rights Reserved
27
www.ezymathtutoring.com.au
Chapter 1: Number
Exercise 6: Decimals & Percentages
12)
Express the following as a
decimal
a)
b)
c)
d)
e)
13)
15)
ହଵ
ଵ଴଴଴
଻ସ
14)
f)
7.4 + 2.22
g)
8.1 + 3.05
Calculate the following
ଵ଴଴଴
a)
ଵ଻
ଵ଴଴଴
b)
ଵ଴଴଴
଻
c)
ଵ
d)
ଵ଴଴଴
Calculate the following
e)
a)
1.2 + 3.4
f)
b)
3.6 + 4.3
g)
c)
10.2 + 5.3
h)
d)
1.25 + 3.1
i)
e)
2.56 + 5.2
j)
7.4 − 2.3
9.6 − 3.1
10.7 − 9.6
8.4 − 4.8
3.2 − 2.5
7.65 − 4.3
3.43 − 2.3
5.69 − 3.06
7.32 − 5.61
8.19 − 5.43
Jake has $14.70 and spends $12.35. How much money does he have left?
16)
Paul has $12.35 and his grandfather gives him $11.15. How much money does Paul
now have?
17)
Barbara wants to save up to buy a new dress that costs $35.30. At the moment she
has $16.10. How much more money does she need to be able to buy the dress?
©Ezy Math Tutoring | All Rights Reserved
28
www.ezymathtutoring.com.au
Exercise 7
Chance
©Ezy Math Tutoring | All Rights Reserved
29
www.ezymathtutoring.com.au
Chapter 1: Number
Exercise 7: Chance
1)
2)
3)
4)
5)
6)
b)
Alan tosses two coins. List the
possible combinations they could
land on
What colour lolly could he
not get?
c)
Peter rolls two dice and adds the
two numbers. List all the numbers
that he could get
If he pulls out a red lolly
first time, will he definitely
get a red lolly next time?
d)
Could he pull out 20 red
lollies in a row?
e)
If he did this, which colour
would he be more likely to
pull out in his next turn?
List what the two dice from
question 2 could show to get a
total of 7
List what the two dice from
question 2 could show to get a
total of 12
There are 6 red shirts, 6 blue shirts
and 6 yellow shirts in a draw. If a
boy pulls a shirt out without
looking:
7)
In a jar there are 20 blue buttons.
In another jar there are 20 blue
and 20 yellow buttons.
a)
Which jar has more blue
buttons?
b)
From which jar is he more
likely to pull out a blue
button?
c)
Is he more likely to pull a
yellow or blue button from
the second jar?
a)
List what colour shirt he
might pull out
b)
Which colour shirt will he
probably pull out?
c)
Could he pull out 6 yellow
shirts in a row?
d)
There are 20 red, 20 blue and 20
green lollies in a jar. If Jack closes
his eyes and chooses one:
Could he pull 20 yellow
buttons in a row from the
second jar
e)
If he did this, from which
jar would he then have
more chance of pulling a
blue button from?
a)
What colour lolly will he
probably choose?
©Ezy Math Tutoring | All Rights Reserved
30
www.ezymathtutoring.com.au
Chapter 1: Number
Exercise 7: Chance
8)
Tom rolls two normal 6 sided dice and adds the numbers. Which total is he most
likely to get?
9)
Alan tosses two coins; are they more likely to land on two heads or two tails?
10)
Peter spins a spinner with 3 red and 3 white faces. If he spins it twice, list all the
combinations of colours he could get
©Ezy Math Tutoring | All Rights Reserved
31
www.ezymathtutoring.com.au
Year 4 Mathematics
Data
©Ezy Math Tutoring | All Rights Reserved
32
www.ezymathtutoring.com.au
Useful formulae and hints
Data tables are used to summarize findings from research or
questioning, and are usually used to show information in categories
They are often useful at this level for comparing scores or
preferences from two or more groups (e.g. men and women), or
comparing data over time
Graphs can show
 Changes over time
 Records of certain events (for example number of students
getting 60% on a test)
 Quantities at a point in time
Graphs and tables can often show the same information; visually in
the case of graphs or as a summary in the case of tables. Different
types of graphs are more suitable than others depending on the
information to be shown
Picture graphs are a type of graph that shows information on groups
of people or items, where a symbol represents a certain quantity.
For example if one * represents 5 people, then **** would represent
20 people (4 x 5)
©Ezy Math Tutoring | All Rights Reserved
33
www.ezymathtutoring.com.au
Exercise 1
Data Tables
©Ezy Math Tutoring | All Rights Reserved
34
www.ezymathtutoring.com.au
Chapter 2: Data
1)
Exercise 1: Data Tables
Tom made a table that shows how many of his classmates have each colour as their
favourite
Girls
Boys
2)
Green
4
5
Yellow
1
0
Blue
1
8
White
6
4
Black
2
4
a)
How many children in Tom’s class?
b)
Which colour was most popular?
c)
Which colour was most popular for boys?
d)
Which colours had equal numbers of children voting for it?
e)
Which colour or colours had equal number of boys voting for it?
A group of people was asked to vote for one day as their favourite day of the week
Men
Women
Monday
1
3
Tuesday Wednesday Thursday
3
5
10
0
2
5
Friday
5
11
Saturday
6
3
Sunday
15
15
a)
How many people were asked?
b)
What was most people’s favourite day?
c)
Which day was the least favourite of women?
d)
Which day had the biggest difference in the number of men and women
voting for it?
©Ezy Math Tutoring | All Rights Reserved
35
www.ezymathtutoring.com.au
Chapter 2: Data
3)
A man made a list of the cost of a type of blanket and a fan at different times of the
year
Blankets
Fans
4)
Exercise 1: Data Tables
January
$3.50
$20
March
$4
$18
May
$5
$15
July
$6.50
$10
September
$5
$12
November
$4
$14
a)
In which of the months was the blanket the cheapest?
b)
In which month was the fan dearest?
c)
What was the difference in its price between a fan and a blanket in
September?
d)
In which month were the prices closest?
e)
Explain why the prices changed so much during the year?
Show the following data in a two way table

100 people were surveyed as to their favourite car

Everyone had a choice of 4 cars

10 men said they like Holden best

15 women preferred Toyota

5 more men than women preferred Nissan

10 more women than men preferred Ford

20 men preferred Nissan

12 women preferred Ford

Equal numbers of men and women were surveyed
©Ezy Math Tutoring | All Rights Reserved
36
www.ezymathtutoring.com.au
Chapter 2: Data
5)
Exercise 1: Data Tables
The graphs show the number of people that own a certain colour car
Number of men driving each colour
car
14
12
10
8
6
4
2
0
Red
Blue
Green
Black
White
Pink
Yellow
Number of women driving each colour
car
10
9
8
7
6
5
4
3
2
1
0
Red
Blue
Green
Black
a)
Show the information in a two way table
b)
How many people were surveyed?
©Ezy Math Tutoring | All Rights Reserved
White
Pink
Yellow
37
www.ezymathtutoring.com.au
Exercise 2
Picture Graphs
©Ezy Math Tutoring | All Rights Reserved
38
www.ezymathtutoring.com.au
Chapter 2: Data
1)
Exercise 2: Picture Graphs
The picture graph below shows a sport and the number of children for whom it is
their favourite
Each “face” represents 5 people
Game Number
Attendance
Football
Rugby
Soccer
Basketball
Hockey
Swimming
Tennis
Golf
Bowling
Baseball
a)
Which sport is most popular?
b)
For how many people is it their favourite?
c)
For how many people is swimming their favourite sport?
d)
How many people were asked?
e)
Is swimming or hockey more popular?
©Ezy Math Tutoring | All Rights Reserved
39
www.ezymathtutoring.com.au
Chapter 2: Data
2)
Exercise 2: Picture Graphs
Some people were asked how many times they ate fish. The picture graph shows
their answers. Each fish represents 15 days of the year
Name
Tom
Benny
Jane
Julie
Karen
Brian
Richard
Ray
Daniel
Craig
Number of days eating fish
a)
Who eats fish the most days of the year?
b)
How many days a year do they eat fish?
c)
Who eats fish on the least number of days?
d)
How many days do they eat fish on?
e)
If someone ate fish on 50 days of the year, how could you show this on the
graph? Can you think of a better way to show numbers of days that are not
groups of 15?
©Ezy Math Tutoring | All Rights Reserved
40
www.ezymathtutoring.com.au
Chapter 2: Data
3)
4)
Exercise 2: Picture Graphs
The graph below shows the number of kilos of each fruit bought in a week by a cafe.
Bananas were $2.50, apples $2, oranges $3, watermelon $1.50 and strawberries $4
per kilo
a)
On which fruit did the cafe spend most money?
b)
What fruit did the cafe buy least of?
of
c)
How many kilos of fruit were bought in total?
total
d)
How much did the cafe spend on fruit in total?
total
Draw a picture graph that shows the number
number of people that voted for their favourite
animal
Animal
Dog
Cat
Rabbit
Horse
Mouse
Chicken
Lion
Tiger
Snake
Monkey
©Ezy Math Tutoring | All Rights Reserved
Number of men
10
8
2
4
5
4
5
3
1
0
Number of women
4
5
8
2
0
6
3
1
0
1
41
www.ezymathtutoring.com.au
Chapter 2: Data
5)
Exercise 2: Picture Graphs
The following picture graph shows the number of children that get to school in
different ways. Each picture represents 10 children. Show the same information in a
column graph
©Ezy Math Tutoring | All Rights Reserved
42
www.ezymathtutoring.com.au
Chapter 2: Data
©Ezy Math Tutoring | All Rights Reserved
Exercise 2: Picture Graphs
43
www.ezymathtutoring.com.au
Year 4 Mathematics
Space
©Ezy Math Tutoring | All Rights Reserved
44
www.ezymathtutoring.com.au
Useful formulae and hints
Tessellation is the process of making patterns from shapes by
combining them is special ways. In this unit, we are looking to
tessellate congruent shapes. That is only using the same size
and type shape to tessellate.
Tessellations between these types of shapes are successful if no
space is left between them, that is they fit together perfectly
There are 3 methods of treating shapes that may allow them to
tessellate.
 Rotation involves revolving a shape around a fixed point
on its perimeter
 Reflection involves making a mirror image of the shape
 Translation involves sliding a shape in a particular
direction.
By using one or a combination of these techniques, shapes can
be tested to see if they tessellate
In this unit we are looking at angles that are either right angles
(also called perpendicular), and those that are more or less
than right angles
An angle is made up of two line segments that meet at a point
called a vertex
Some 3 dimensional shapes in this unit are
 Cylinders
©Ezy Math Tutoring | All Rights Reserved
45
www.ezymathtutoring.com.au
 Pyramids (square and triangular based)
 Prisms (Triangular and rectangular)
 Cones
Different views of these shapes should be able to be drawn.
The net of a shape is the 2D (flat) representation of it. It is the
model of the shape as if it were undone and flattened.
Net of a cube
A cross section parallel to the base of a shape is the top view of
a cut that goes across the shape
View of the parallel cross section of a rectangular prism
©Ezy Math Tutoring | All Rights Reserved
46
www.ezymathtutoring.com.au
View of the perpendicular cross section of a rectangular prism
A cross section perpendicular to the base is the side view of a
cut that goes down the shape
Both cross sections produce a 2 dimensional shape (e.g. a
rectangle)
A line of symmetry is a line drawn from one point on the
perimeter of a shape to another, such that the two halves
produced are identical
Line of symmetry
Not a line of symmetry
©Ezy Math Tutoring | All Rights Reserved
47
www.ezymathtutoring.com.au
Exercise 1
Tessellations
©Ezy Math Tutoring | All Rights Reserved
48
www.ezymathtutoring.com.au
Chapter 3: Space
1)
Exercise 1: Tessellations
Which of the following shapes tessellate?
a)
b)
c)
d)
©Ezy Math Tutoring | All Rights Reserved
49
www.ezymathtutoring.com.au
Chapter 3: Space
Exercise 1: Tessellations
e)
2)
In the space in the table, write down how many of each shape is necessary to
completely tessellate around a point
Equilateral Triangle
Square
Regular Pentagon
Regular Hexagon
3)
Explain in your own words why you need different numbers of certain shapes to be
able to tessellate them
4)
The side lengths of the triangle are all different. By rotating the triangle, construct a
tessellation, and identify the side names in each triangle
A
B
C
5)
Using the triangle above, form a tessellation by using a combination of rotations and
a reflection?
6)
By using rotations, construct a tessellation from the following quadrilateral
©Ezy Math Tutoring | All Rights Reserved
50
www.ezymathtutoring.com.au
Chapter 3: Space
Exercise 1: Tessellations
7)
By using a translation (sliding), form a tessellation from the following shape
8)
What technique(s) would you use to tessellate the following shapes?
a)
b)
c)
©Ezy Math Tutoring | All Rights Reserved
51
www.ezymathtutoring.com.au
Chapter 3: Space
Exercise 1: Tessellations
d)
e)
©Ezy Math Tutoring | All Rights Reserved
52
www.ezymathtutoring.com.au
Exercise 2
Angles
©Ezy Math Tutoring | All Rights Reserved
53
www.ezymathtutoring.com.au
Chapter 3: Shapes
1)
Exercise 2: Angles
Which of the following pairs of lines are perpendicular?
a)
b)
c)
d)
©Ezy Math Tutoring | All Rights Reserved
54
www.ezymathtutoring.com.au
Chapter 3: Shapes
2)
Exercise 2: Angles
In the following diagram name all the perpendicular pairs of lines
H
I
G
J
F
A
B
D
C
3)
E
Which letter denotes the vertex in each of the following angles?
a)
B
A
C
b)
X
Q
A
©Ezy Math Tutoring | All Rights Reserved
55
www.ezymathtutoring.com.au
Chapter 3: Shapes
c)
Exercise 2: Angles
D
S
P
d)
L
M
R
e)
M
C
T
f)
A
J
X
©Ezy Math Tutoring | All Rights Reserved
56
www.ezymathtutoring.com.au
Chapter 3: Shapes
4)
Exercise 2: Angles
Describe each of the following angles as less than right-angled, more than right
angled or right-angled
a)
b)
c)
d)
©Ezy Math Tutoring | All Rights Reserved
57
www.ezymathtutoring.com.au
Chapter 3: Shapes
Exercise 2: Angles
e)
f)
5)
State whether each pair of angles are the same size
a)
b)
©Ezy Math Tutoring | All Rights Reserved
58
www.ezymathtutoring.com.au
Chapter 3: Shapes
Exercise 2: Angles
c)
d)
©Ezy Math Tutoring | All Rights Reserved
59
www.ezymathtutoring.com.au
Chapter 3: Shapes
6)
Exercise 2: Angles
Identify what parts of the following objects form angles
a)
b)
c)
d)
©Ezy Math Tutoring | All Rights Reserved
60
www.ezymathtutoring.com.au
Chapter 3: Shapes
Exercise 2: Angles
e)
f)
©Ezy Math Tutoring | All Rights Reserved
61
www.ezymathtutoring.com.au
Exercise 3
2D and 3D Shapes
©Ezy Math Tutoring | All Rights Reserved
62
www.ezymathtutoring.com.au
Chapter 3: Shapes
1)
2)
3)
4)
Exercise 3: 2D and 3D Shapes
Sketch the following shapes
b)
Triangular pyramid
a)
Cylinder
c)
Cylinder
b)
Triangular prism
d)
Cone
c)
Triangular pyramid
d)
Rectangular prism
e)
Cone
f)
Triangular prism
5)
Sketch a cylinder from the
following views
a)
Side
b)
Above
c)
Below
6)
Sketch a triangular prism from the
following views
Draw and describe the shape
formed when a cross section
parallel to the base is taken of the
following
a)
Cylinder
b)
Rectangular prism
c)
Triangular pyramid
d)
Cone
Draw and describe the shape
formed when a cross section
perpendicular to the base is taken
of the following
a)
Cone
a)
Side
b)
Triangular prism
b)
Below
c)
Square pyramid
c)
End
d)
Cylinder
d)
Above
a)
Draw the lines of symmetry
of a rectangle
Draw a net of the following shapes
a)
7)
Rectangular prism
©Ezy Math Tutoring | All Rights Reserved
63
www.ezymathtutoring.com.au
Chapter 3: Shapes
b)
Exercise 3: 2D and 3D Shapes
Draw a line through a
rectangle that is not a line
of symmetry
8)
Draw a triangle that has all sides of
equal length and draw all its lines
of symmetry
9)
Draw a triangle that has 2 of its
sides having equal length, and
draw all its lines of symmetry
10)
Draw a triangle that has no sides
of equal length and draw all its
lines of symmetry
11)
Draw a square and also draw all
its lines of symmetry
12)
Draw a four sided shape that has
no sides of equal length and draw
all its lines of symmetry
©Ezy Math Tutoring | All Rights Reserved
64
www.ezymathtutoring.com.au
Year 4 Mathematics
Measurement
©Ezy Math Tutoring | All Rights Reserved
65
www.ezymathtutoring.com.au
Useful formulae and hints
Digital clocks are read as if the numbers were words. For example,
the time on a digital clock reading 9:12 is read as “nine twelve”
(twelve minutes past nine)
Also anything past thirty minutes can also be read as a number of
minutes to the next hour. To calculate this, subtract the number of
minutes showing from sixty
For example: 8:42 is read as “eight forty two” or as forty two minutes
past eight
It can also be read as (60 – 42=) eighteen minutes to 9
There are 60 minutes in one hour, and 60 seconds in one minute
There are 1000 grams in 1 kg
To change grams to kg, divide by 1000
3200 g = 3200 ÷ 1000 = 3.2 kg
To change kg to grams, multiply by 1000
4.3 kg = 4.3 × 1000 = 4300 grams
Example of strategy for solving word problems:
Wire is 200grams for 20 cents. How much could you buy for $5?
Answer: $5 is 25 lots of 20 cents (500 ÷ 20 = 25)
So you could buy 25 lots of 200 grams
25 × 200 = 5000 grams = 5 kg of wire
©Ezy Math Tutoring | All Rights Reserved
66
www.ezymathtutoring.com.au
There are 100 cm in 1 metre
To convert cm to m, divide by 100
500 cm= 500 ÷ 100 = 5m
To convert m to cm, multiply by 100
7.4 m = 7.4 × 100 = 740 cm
The perimeter of a shape is the distance around the outside of it (all
distances must be the same unit)
If the four sides of a rectangle are 50 cm, 1 m, 50 cm, and 1 m, the
perimeter is 0.5 m +1 m + 0.5 m +1 m = 3 m (or 300 cm)
The area of a rectangle is equal to the length of the rectangle
multiplied by its width (all distances must be the same unit)
For the rectangle above, the area is 0.5 x 1 = 0.5 m2, (or 50 x 100
=5000 cm2)
The litre is the unit of volume. One litre = 1000 millilitres (mL)
The volume of a 3D shape (how much space it takes up) is measured
in cm3 (or m3), and its capacity (how much liquid it can hold) is
measured in mL (or litres)
1 cm3 = 1 millilitre
©Ezy Math Tutoring | All Rights Reserved
67
www.ezymathtutoring.com.au
Exercise 1
Time
©Ezy Math Tutoring | All Rights Reserved
68
www.ezymathtutoring.com.au
Chapter 4: Measurement
1)
Exercise 1: Time
Write the following times in words
a)
b)
c)
©Ezy Math Tutoring | All Rights Reserved
69
www.ezymathtutoring.com.au
Chapter 4: Measurement
Exercise 1: Time
d)
2)
Write the following times in two different ways. (For example seven forty-five,
quarter to 8)
a)
b)
©Ezy Math Tutoring | All Rights Reserved
70
www.ezymathtutoring.com.au
Chapter 4: Measurement
Exercise 1: Time
c)
d)
3)
Convert the following to minutes
4)
Convert the following to seconds
a)
1 hour
a)
One minute
b)
2 hours
b)
Two minutes
c)
1 and a half hours
c)
Five minutes
d)
Ten hours
d)
Two and a half minutes
e)
2 hours and fifteen minutes
e)
Six minutes and 20 seconds
f)
4 hours and ten minutes
f)
1 hour
©Ezy Math Tutoring | All Rights Reserved
71
www.ezymathtutoring.com.au
Chapter 4: Measurement
5)
Write each of these times as they
would appear on a digital clock
a)
Eight thirty
b)
Six forty five
c)
Quarter past three
d)
Half past nine
e)
Ten minutes to one
f)
Quarter to 8
g)
Noon
6)
The main movie at the theatre
shows every 2 and a half hours. If
it started at seven thirty, when
would the next showing begin?
7)
A bus goes from the city to John’s
street every fifteen minutes. If the
last bus for the night leaves at nine
o’clock, when did the second last
bus leave?
8)
A magazine is published every 2
weeks. If t was published on May
1st, when is the next time it would
be published?
9)
The American Civil War started in
1860 and went until 1865. How
long did it last for?
Exercise 1: Time
on January 1st 2010, when did he
return?
10)
It took Alan one and a half years
to sail around the world. If he left
©Ezy Math Tutoring | All Rights Reserved
72
www.ezymathtutoring.com.au
Exercise 2
Mass
©Ezy Math Tutoring | All Rights Reserved
73
www.ezymathtutoring.com.au
Chapter 4: Measurement
1)
Convert the following to grams
a)
b)
2)
3)
Half a kilogram
One quarter of a kilogram
c)
One fifth of a kilogram
d)
Three quarters of a
kilogram
e)
Exercise 2: Mass
a)
500 grams
b)
750 grams
d)
e)
f)
g)
a)
500g + 500g
b)
700g + 700g + 600g
c)
200g + 800g
d)
One and a half kg plus half
a kg
e)
750g + 750g
f)
One and a half kg plus one
and a half kg
One third of a kilogram
Convert the following to kilograms
c)
Add the following giving your
answer in kg
250 grams
100 grams
1500 grams
1250 grams
4)
Write the following in kg
a)
Four lots of 500g
b)
Three lots of 500g
c)
Half of 4kg
d)
Five and a half kg subtract
two and a half kg
e)
One half of 5kg
3500 grams
5)
Eric has a bag of marbles. Each marble weighs 200g and he has 10 of them. If John’s
marbles each weigh 400g, how many does he need to have the same weight of
marbles as Eric?
6)
Four men each carry a bag of rocks weighing 250g. How many kg do they carry
between them?
©Ezy Math Tutoring | All Rights Reserved
74
www.ezymathtutoring.com.au
Chapter 4: Measurement
Exercise 2: Mass
7)
John has $5 and wants to buy as much paper as he can. Each 100g of paper costs 50
cents. How much paper can he buy?
8)
Three books weigh 250g, 300g and 600g. How much do the books weigh together?
9)
Peter has three weights: two of them weigh 400g and the other weighs 700g. Alan
has two weights: one weighs 1kg and the other 500g. Who has more weight?
10)
Thomas eats 500g of a 750 g steak, while his Dad leaves 100g of his. How much
steak is left in total?
©Ezy Math Tutoring | All Rights Reserved
75
www.ezymathtutoring.com.au
Exercise 3
Length, Perimeter & Area
©Ezy Math Tutoring | All Rights Reserved
76
www.ezymathtutoring.com.au
Chapter 4: Measurement
1)
2)
3)
4)
Convert the following to metres
(e.g. 1m 50cm = 1.5m)
a)
1 m 25cm
b)
½m
c)
2 m 50cm
d)
3m 60cm
e)
2m 75cm
f)
80cm
Exercise 3: Length, Perimeter & Area
5)
Convert the following to m and cm
(e.g. 1.5m = 1m 50cm)
a)
1.25m
b)
600 cm
Would the area of the following be
approximately equal to 1 square
metre, less than 1 square metre,
or more than 1 square metre?

The floor of a kitchen

A window

A stamp

A coffee table

A lawn

A field

A car door
6)
Describe how to calculate the
perimeter of a shape
7)
Calculate the perimeter of each of
the following rectangles
c)
2.75m
d)
0.5m
a)
Side lengths 1m and 2m
e)
4.2m
b)
Side lengths 2m and 3m
f)
1.05m
c)
Side lengths 5m and 4m
d)
Side lengths 1.5m and 2m
e)
Side lengths 1m 50cm and
2m
f)
Side lengths 50cm and 1m
Graham is 1.6m tall, while his dad
is 2 metres. How much taller is
Graham’s dad in metres?
A square has side length of 1
metre, what is its area?
©Ezy Math Tutoring | All Rights Reserved
77
www.ezymathtutoring.com.au
Chapter 4: Measurement
8)
9)
Exercise 3: Length, Perimeter & Area
Calculate the area of each of the
following rectangles
a)
Side lengths 1m and 2m
b)
Side lengths 2m and 3m
c)
Side lengths 5m and 4m
d)
Side lengths 1.5m and 2m
e)
Side lengths 1m 50cm and
2m
f)
Side lengths 50cm and 1m
There are two pieces of wood on
the ground. One has a length of
1m and a width of 4m, the other is
a square piece of side length 2m.
Which piece of wood has a bigger
area? Which piece of wood has
the bigger perimeter?
10)
A man walked around a lounge
room that was 3m long and 2m
wide. How far did he walk??
11)
The man from question 10 wishes
to carpet his lounge room. How
many square metres of carpet will
he need?
©Ezy Math Tutoring | All Rights Reserved
78
www.ezymathtutoring.com.au
Exercise 4
Volume & Capacity
©Ezy Math Tutoring | All Rights Reserved
79
www.ezymathtutoring.com.au
Chapter 4: Measurement
1)
2)
3)
Exercise 4: Volume & Capacity
Estimate the capacity in litres of
each of the following?

A milk carton

A car’s petrol tank

A bath

A large bottle of soft drink

A swimming pool

A kitchen sink
e)
4)
How much liquid is wasted if
500mL is added to a 1 litre
container that already contains
750mL?
5)
To fill a 2L container, how much
liquid needs to be added if it
currently contains 1.4 litres?
6)
Bill poured 600mL of water into a
bowl, Tom poured a further 500mL
and Peter poured 900mL. How
much water was in the container?
7)
A 1 litre container is filled to the
top with water. One hundred
1cm3 blocks are thrown into the
container and water overflows as a
result of this. How much water is
left in the container?
Convert the following to mL
a)
1.25 L
b)
2.6L
c)
0.75L
d)
3.9L
e)
2.24L
f)
8L
10000mL
Convert the following to Litres
a)
4000mL
b)
2500mL
c)
1250mL
d)
4750mL
©Ezy Math Tutoring | All Rights Reserved
80
www.ezymathtutoring.com.au
Chapter 4: Measurement
Exercise 4: Volume & Capacity
8)
How much liquid is in the following cylinders?
9)
Stacks of 1 cm blocks are built. How much water would they displace from a
container if they were dropped in?
a)
2 rows and 3 columns
b)
4 rows and 5 columns
c)
6 rows and 3 columns
d)
3 rows and 6 columns
e)
10 rows and 10 columns
f)
30 rows and 30 columns
10)
In a fridge there were five 250 mL cans of soft drink. How much soft drink was
there altogether?
©Ezy Math Tutoring | All Rights Reserved
81
www.ezymathtutoring.com.au
Year 4 Mathematics
Solutions
©Ezy Math Tutoring | All Rights Reserved
www.ezymathtutoring.com.au
Copyright © 2012 by Ezy Math Tutoring Pty Ltd. All rights reserved. No part of this book shall be
reproduced, stored in a retrieval system, or transmitted by any means, electronic, mechanical,
photocopying, recording, or otherwise, without written permission from the publisher. Although
every precaution has been taken in the preparation of this book, the publishers and authors assume
no responsibility for errors or omissions. Neither is any liability assumed for damages resulting from
the use of the information contained herein.
©Ezy Math Tutoring | All Rights Reserved
www.ezymathtutoring.com.au
Learning Strategies
Mathematics is often the most challenging subject for students. Much of the trouble comes from the
fact that mathematics is about logical thinking, not memorizing rules or remembering formulas. It
requires a different style of thinking than other subjects. The students who seem to be “naturally”
good at math just happen to adopt the correct strategies of thinking that math requires – often they
don’t even realise it. We have isolated several key learning strategies used by successful maths
students and have made icons to represent them. These icons are distributed throughout the book
in order to remind students to adopt these necessary learning strategies:
Talk Aloud Many students sit and try to do a problem in complete silence inside their heads.
They think that solutions just pop into the heads of ‘smart’ people. You absolutely must learn
to talk aloud and listen to yourself, literally to talk yourself through a problem. Successful
students do this without realising. It helps to structure your thoughts while helping your tutor
understand the way you think.
BackChecking This means that you will be doing every step of the question twice, as you work
your way through the question to ensure no silly mistakes. For example with this question:
3 × 2 − 5 × 7 you would do “3 times 2 is 5 ... let me check – no 3 × 2 is 6 ... minus 5 times 7
is minus 35 ... let me check ... minus 5 × 7 is minus 35. Initially, this may seem timeconsuming, but once it is automatic, a great deal of time and marks will be saved.
Avoid Cosmetic Surgery Do not write over old answers since this often results in repeated
mistakes or actually erasing the correct answer. When you make mistakes just put one line
through the mistake rather than scribbling it out. This helps reduce silly mistakes and makes
your work look cleaner and easier to backcheck.
Pen to Paper It is always wise to write things down as you work your way through a problem, in
order to keep track of good ideas and to see concepts on paper instead of in your head. This
makes it easier to work out the next step in the problem. Harder maths problems cannot be
solved in your head alone – put your ideas on paper as soon as you have them – always!
Transfer Skills This strategy is more advanced. It is the skill of making up a simpler question and
then transferring those ideas to a more complex question with which you are having difficulty.
For example if you can’t remember how to do long addition because you can’t recall exactly
how to carry the one:
ାହ଼଼ଽ
ସହ଼଻
then you may want to try adding numbers which you do know how
ାହ
to calculate that also involve carrying the one: ଽ
This skill is particularly useful when you can’t remember a basic arithmetic or algebraic rule,
most of the time you should be able to work it out by creating a simpler version of the
question.
©Ezy Math Tutoring | All Rights Reserved
1
www.ezymathtutoring.com.au
Format Skills These are the skills that keep a question together as an organized whole in terms
of your working out on paper. An example of this is using the “=” sign correctly to keep a
question lined up properly. In numerical calculations format skills help you to align the numbers
correctly.
This skill is important because the correct working out will help you avoid careless mistakes.
When your work is jumbled up all over the page it is hard for you to make sense of what
belongs with what. Your “silly” mistakes would increase. Format skills also make it a lot easier
for you to check over your work and to notice/correct any mistakes.
Every topic in math has a way of being written with correct formatting. You will be surprised
how much smoother mathematics will be once you learn this skill. Whenever you are unsure
you should always ask your tutor or teacher.
Its Ok To Be Wrong Mathematics is in many ways more of a skill than just knowledge. The main
skill is problem solving and the only way this can be learned is by thinking hard and making
mistakes on the way. As you gain confidence you will naturally worry less about making the
mistakes and more about learning from them. Risk trying to solve problems that you are unsure
of, this will improve your skill more than anything else. It’s ok to be wrong – it is NOT ok to not
try.
Avoid Rule Dependency Rules are secondary tools; common sense and logic are primary tools
for problem solving and mathematics in general. Ultimately you must understand Why rules
work the way they do. Without this you are likely to struggle with tricky problem solving and
worded questions. Always rely on your logic and common sense first and on rules second,
always ask Why?
Self Questioning This is what strong problem solvers do naturally when they
get stuck on a problem or don’t know what to do. Ask yourself these
questions. They will help to jolt your thinking process; consider just one
question at a time and Talk Aloud while putting Pen To Paper.
©Ezy Math Tutoring | All Rights Reserved
2
www.ezymathtutoring.com.au
Table of Contents
CHAPTER 1: Number
4
Exercise 1: Representing Numbers
5
Exercise 2: Addition & Subtraction
11
Exercise 3: Multiplication & Division
14
Exercise 4: Number Patterns
19
Exercise 5: Fractions
23
Exercise 6:Decimals & Percentages
28
Exercise 7: Chance
35
CHAPTER 2: Data
39
Exercise 1: Data Tables
40
Exercise 2: Picture Graphs
46
CHAPTER 3: Space
53
Exercise 1: Tessellations
54
Exercise 2: Angles
59
Exercise 3: 2D & 3D Shapes
70
CHAPTER 4: Measurement
75
Exercise 1: Time
76
Exercise 2: Mass
82
Exercise 3: Length, Perimeter & Area
86
Exercise 4: Volume & Capacity
91
©Ezy Math Tutoring | All Rights Reserved
3
www.ezymathtutoring.com.au
Year 4 Mathematics
Number
©Ezy Math Tutoring | All Rights Reserved
4
www.ezymathtutoring.com.au
Exercise 1
Representing Numbers
©Ezy Math Tutoring | All Rights Reserved
5
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
1)
Exercise 1: Representing Numbers
c)
Write as numbers
a)
Three hundred and ninety
8630
390
b)
d)
Eight hundred and eighty
three
d)
e)
Seven hundred and ninety
three
793
Five hundred and six
Nine hundred and nine
Three thousand and one
3001
3)
Write in words
a)
506
e)
Nine thousand and twenty
one
9021
883
c)
Eight thousand six hundred
and thirty
2713
Two thousand seven
hundred and thirteen
b)
2097
909
2)
Two thousand and ninety
seven
Write as numbers
a)
Two thousand two hundred
and three
c)
Three thousand three
hundred and thirty
2203
b)
Seven thousand four
hundred and ninety seven
7497
3330
d)
8090
Eight thousand and ninety
e)
2010
Two thousand and ten
©Ezy Math Tutoring | All Rights Reserved
6
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
f)
Exercise 1: Representing Numbers
g)
1117
One thousand one hundred
and seventeen
g)
2442
2441
h)
1900
0
1899
Zero
4)
i)
Write down the number that
comes before each of these
numbers
a)
9001
9000
j)
3006
331
3005
330
b)
k)
1234
156
1233
155
c)
l)
10000
905
9999
904
d)
5)
120
119
e)
a)
b)
1100
1099
819
820
1710
1709
f)
Write the number that comes after
each of these numbers
1090
1091
c)
8881
8882
©Ezy Math Tutoring | All Rights Reserved
7
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
d)
4223
Exercise 1: Representing Numbers
8)
What is the value of the number 4
in each of these numbers?
4224
e)
a)
1034
8010
Ones
8011
f)
b)
1435
711
Hundreds
712
g)
c)
2114
1999
Units
2000
h)
d)
4027
3009
Thousands
3010
6)
e)
Put these numbers in order from
smallest to largest
Units
f)
1325, 1101, 1123, 3000, 2946,
2121, 1015, 2221, 2323, 9104, 694
g)
Put these numbers in order from
largest to smallest.
2015, 2004, 4020, 1912, 1911,
2333, 3322, 2921, 2221, 4121,
3004
4121, 4020, 3322, 3004, 2921,
2333, 2221, 2015, 2004, 1912,
1911
©Ezy Math Tutoring | All Rights Reserved
1040
Tens
694, 1015, 1101, 1123, 1325, 2121,
2221, 2323, 2946, 3000, 9104
7)
4
2047
Tens
9)
Use the > or < sign to show the
relationship between the following
pairs of numbers
a)
1234 < 2134
b)
9821 > 9281
8
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
c)
8005 < 8015
d)
1023 > 103
e)
970 > 907
f)
1099 > 1089
10) Write the number that is 10 less
than the number shown. Repeat 4
times
a)
390,
380, 370, 360, 350, 340
d)
e)
i)
j)
k)
391, 381, 371, 361, 351
g)
908
898, 888, 878, 868, 858
11) Write the number that is 10 more
than the number shown. Repeat
four times
a)
1121
1131, 1141, 1151, 1161,
1171
b)
530
401
1050
1040, 1030, 1020, 1010,
1000
2020
2030, 2040, 2050, 2060,
2070
520, 510, 500, 490, 480
f)
1039
1029, 1019, 1009, 999, 989
442
432, 422, 412, 402, 392
220
210, 200, 190, 180, 170
555
545, 535, 525, 515, 505
c)
h)
675
665, 655, 645, 635, 625
b)
Exercise 1: Representing Numbers
c)
3175
3185, 3195, 3205, 3215,
3223
112
102, 92, 82, 72, 62
©Ezy Math Tutoring | All Rights Reserved
9
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
d)
1099
Exercise 1: Representing Numbers
c)
1109, 1119, 1129, 1139,
1149
e)
803
0, 100, 100
d)
813, 823, 833, 843, 853
f)
960
999
e)
8555
9000, 8600, 8560
f)
1009, 1019, 1029, 1039,
1049
h)
4565
5000, 4600, 4560
970, 980, 990, 1000, 1010
g)
101
7550
8000, 7600, 7550
g)
6005
100
6000, 6000, 6000
110, 120, 130, 140, 150
i)
h)
1111
1251
1000, 1100, 1110
1261, 1271, 1281, 1291,
1301
12) Round the following numbers to
the nearest thousand, hundred
and ten
a)
1263
1000, 1300, 1260
b)
926
1000, 900, 930
©Ezy Math Tutoring | All Rights Reserved
10
www.ezymathtutoring.com.au
Exercise 2
Addition & Subtraction
©Ezy Math Tutoring | All Rights Reserved
11
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
1)
Exercise 2: Addition & Subtraction
Add these numbers
a)
4658
632 + 114
e)
746
b)
8232
247 + 319
f)
566
c)
621 + 535
1156
d)
e)
f)
Subtract these numbers
a)
b)
c)
b)
d)
c)
8009 + 377
929 – 353
576
e)
4302 + 410
4712
756 -511
245
2225 + 529
2754
594 – 482
112
Add these numbers
a)
816 – 412
404
414 + 441
855
2)
3)
135 + 175
310
9334 + 73
9407
877 + 223
1100
8122 + 110
504 – 127
377
f)
865 – 821
44
8386
d)
4335 + 323
©Ezy Math Tutoring | All Rights Reserved
12
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
g)
Exercise 2: Addition & Subtraction
9026 – 312
8714
4)
5)
6)
7)
8)
9)
h)
6111 – 3227
2884
Peter has 840 stamps, John has 275 stamps. How many stamps do they have
between them?
840 + 275 = 1115 stamps
Alan weighs 145 kg, Chris weighs 148 kg. How much do they weigh together?
145 + 148 = 293 kg
There were 1510 more people at the football game than at the rugby. If there were
4600 people at the football how many people were at the rugby?
4600 − 1510 = 3090 people at the rugby
Tom and Jerry have read 410 books between them. If Tom has read 318 books, how
many books has Jerry read?
410 − 318 = 92 books
138 students passed a test, 112 failed, and 35 were absent. How many students are
in the school?
138 + 112 + 35 = 285 students
What number is 299 less than 6075?
6075 − 299 = 5776
10)
What is the difference between 2710 and 3244?
3244 − 2710 = 534
©Ezy Math Tutoring | All Rights Reserved
13
www.ezymathtutoring.com.au
Exercise 3
Multiplication & Division
©Ezy Math Tutoring | All Rights Reserved
14
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
1)
Calculate the following
a)
Exercise 3: Multiplication & Division
2)
5 × 10
Calculate the following
a)
50
8 × 13
104
b)
5 × 20
b)
100
16 × 9
144
c)
5 × 30
c)
150
11 × 7
77
d)
40 × 5
d)
200
17 × 8
126
e)
60 × 5
e)
300
32 × 6
192
f)
20 × 7
f)
140
45 × 9
405
g)
40 × 7
3)
Calculate the following
280
h)
a)
60 × 7
15 × 6
90
420
i)
b)
60 × 9
15 × 8
120
540
c)
6 × 15
90
©Ezy Math Tutoring | All Rights Reserved
15
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
d)
Exercise 3: Multiplication & Division
f)
7 × 15
What is 32 × 25?
800
105
e)
g)
9 × 15
135
f)
From your answers, state a
method for quickly
multiplying any number by
15
The answer is ten times the
number plus half of the
result
The answer is the amount
of fours in the number
times one hundred
5)
Calculate the following
a)
4)
a)
How many fours in 24?
b)
6
b)
What is 24 × 25?
600
c)
d)
What is 28 × 25?
700
e)
c)
How many fours in 28?
7
How many fours in 32?
8
©Ezy Math Tutoring | All Rights Reserved
Use your answers to parts a
to f to state a method for
quickly multiplying any
number by 25
d)
e)
24 ÷ 5
4
4
5
33 ÷ 8
4
1
8
15 ÷ 4
3
3
4
35 ÷ 7
5
24 ÷ 7
3
3
7
16
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
f)
g)
h)
i)
j)
6)
74 ÷ 7
10
4
7
37 ÷ 5
7
2
5
49 ÷ 8
6
1
8
Exercise 3: Multiplication & Division
c)
1, 2, 3, 4, 6, 8, 12, 24
d)
1
4
82 ÷ 8
10
2
1
= 10
8
4
e)
9
1, 3, 9
b)
4
1, 2, 4
f)
1
1
g)
64
1, 2, 4, 8, 16, 32, 64
h)
100
1, 2, 4, 5, 10, 20, 25, 50,
100
Write the factors of the following
a)
7
1, 7
21 ÷ 4
5
24
i)
22
1, 2, 11, 22
15
1, 3, 5, 15
7)
Mary has 40 lollies. If she gives each of her 6 friends an equal amount of lollies, how
many will she have left over for herself? (She gives each friend the most that she
can)
The number closest to 40 that is a multiple of 6 is 36; this leaves 4 lollies for Mary
©Ezy Math Tutoring | All Rights Reserved
17
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
8)
Alan buys 5 pens and gets 5 cents change from his dollar. How much was each pen?
$1 – 5 cents = 95 cents. Each pen was
9)
Exercise 3: Multiplication & Division
ଽହ
ହ
= 19 cents
Kathy is having a birthday party and wants each friend to get five lollies in their party
bag. If there are 8 friends coming to the party, how many lollies will be left over
from a bag of 50?
Each friend gets 5 lollies x 8 friends = 40 lollies. This leaves 10 lollies.
10)
Tom has $5 left after giving an equal amount of money to a number of charities. If
he started with $35, list how many charities he may have given money to, and how
much he would have given to each.
He gave 35 − 5 = $30. He could have given any combination that makes $30
1 charity x $30
2 charities x $15
3 charities x $10
4 charities x $7.50
5 charities x $6
6 charities x $5
8 charities x $3.75
10 charities x $3
12 charities x $2.50
15 charities x $2
20 charities x $1.50
24 charities x $1.25
©Ezy Math Tutoring | All Rights Reserved
18
www.ezymathtutoring.com.au
Exercise 4
Number Patterns
©Ezy Math Tutoring | All Rights Reserved
19
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
1)
Find the sixth term in the following
sequences
a)
Exercise 4: Number Patterns
2)
Find the fifth term in the following
sequences
a)
3, 6, 9, 12
Add 3 each time, so 5th
term is 15, 6th term is 18
b)
Subtract 5 each time, so 4th
term is 10, 5th term is 5
b)
2, 4, 6
Add 2 each time, so 4th
term is 8, 5th term is 10, 6th
term is 12
c)
c)
5, 10, 15
d)
f)
e)
14, 11, 8, ___, ___
Subtract 3 each time, so 4th
term is 5, 5th term is 2
4, 8, 12
3)
Find the missing numbers
a)
9, 18, 27
Add 9 each time, so 4th
term is 36, 5th term is 45,
6th term is 54
63, 60, 57
Subtract 3 each time, so 4th
term is 54, 5th term is 51
7, 14, 21
Add 4 each time, so 4th
term is 16, 5th term is 20,
6th term is 24
63, 54, 45
Subtract 9 each time, so 4th
term is 36, 5th term is 27
Add 7 each time, so 4th
term is 28, 5th term is 35,
6th term is 42
e)
40, 32, 24
Subtract 8 each time, so 4th
term is 16, 5th term is 8
Add 5 each time, so 4th
term is 20, 5th term is 25,
6th term is 30
d)
25, 20, 15
b)
8
10
©Ezy Math Tutoring | All Rights Reserved
+ 12 = 20
+ 10 = 20
20
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
c)
d)
e)
f)
g)
4)
6
x 5= 30
11 x
5
c)
, , , ____, ____
ହ ହ ହ
ସ ହ
two terms are ହ , ହ
= 15
ହ ସ
d) ଷ , ଷ , 1, ____,____
ଷ
x 3 = 21
ଵ
1 = ଷ, so subtract ଷ each
time, so next two terms are
ଶ ଵ
,
ଷ ଷ
+ 10 = 15
e)
ଵ଴ ଽ ଼
଻
, , , ____,____
଻ ଻
ଵ
Subtract
Complete the following sequences
ଵ ଵ ଷ
ଵ
Add ସ each time, so next
ହ ଻
two terms are ସ , ସ
ଵ ଶ
6)
ଵ ଶ ଷ
Add ହ each time, so next
a) ସ , ଶ , ସ, ___, ____
5)
ସ ହ
two terms are ଷ , ଷ
ଵ
7+
7
ଵ
Add ଷ each time so next
= 44
4
8
Exercise 4: Number Patterns
b) ଷ , ଷ , 1, ____, ____
f)
଻
each time, so
଻ ଺
next two terms are ଻ , ଻
ଽ଻
,
ଽ଼
,
ଽଽ
ଵ଴଴ ଵ଴଴ ଵ଴଴
ଵ
, ____,____
Add ଵ଴଴ each time, so next
ଵ଴଴ ଵ଴ଵ
two terms are ଵ଴଴ , ଵ଴଴
Peter wants to give 8 people $5 each. If he has $32 how much more money does he
need to be able to do this?
8 ‫ ݔ‬$5 = $40 so he needs an extra $8
There are 9 tables in a restaurant. Each table has 6 chairs around them. If there are
70 people coming to the restaurant at one time, how many more chairs are needed?
©Ezy Math Tutoring | All Rights Reserved
21
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
7)
Exercise 4: Number Patterns
9‫ݔ‬6 = 54, so will need another 16 chairs
Every minute 5 ants crawl out of an ant hill.
a)
b)
How many ants have crawled out after 4 minutes?
4 × 5 = 20 ants.
There are 50 ants out of the ant hill. How many more minutes will go by until
there are 75 ants out of the ant hill?
25 more ants will crawl out in 5 minutes
8)
After 4 hours there were 24 cars in a car park. If the same number of cars park each
hour
a)
b)
c)
How many cars will be in the car park after 7 hours?
24 ÷ 4 = 6 so 6 cars park each hour. 7‫ݔ‬6 = 42 cars
How many hours will have passed until there are 54 cars in the car park?
54 ÷ 6 = 9 hours
If the car park holds 96 cars, how long until it is full from when it first
opened?
96 ÷ 6 = 16 hours
©Ezy Math Tutoring | All Rights Reserved
22
www.ezymathtutoring.com.au
Exercise 5
Fractions
©Ezy Math Tutoring | All Rights Reserved
23
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
1)
Exercise 5: Fractions
Write the following as a fraction
a)
b)
c)
d)
e)
f)
g)
h)
i)
One fifth
1
5
2)
9
10
Write the following in words
One tenth
1
10
Two fifths
a)
1
100
Three fifths
3
5
Three tenths
3
10
Seventeen hundredths
17
100
Four fifths
4
5
©Ezy Math Tutoring | All Rights Reserved
ଵ
ହ
One fifth
b)
2
5
One hundredth
Nine tenths
ଵ
ଵ଴଴
One hundredth
c)
ଷ
ଵ଴
Three tenths
d)
ଵଵ
ଵ଴଴
Eleven hundredths
e)
଻
ଵ଴
Seven tenths
f)
ସ
ହ
Four fifths
g)
ଽଽ
ଵ଴଴
Ninety nine hundredths
24
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
3)
Exercise 5: Fractions
Put these fractions in order from
smallest to largest
5)
97 95 93 91
,
,
,
, ___, ___
100 100 100 100
3 2 4 1
, , ,
5 5 5 5
4)
Each fraction reduces by
1 2 3 4
, , ,
5 5 5 5
next two terms are
Put these fractions in order from
largest to smallest
6)
଼ଽ
,
ଶ
ଵ଴଴
, so
଼଻
ଵ଴଴ ଵ଴଴
Fill in the missing numbers
11 14
20
, , ___, , ___, ___
5 5
5
5 1 7 2 6
, , , ,
10 10 10 10 10
7 6 5 2 1
, , , ,
10 10 10 10 10
7)
Fill in the missing numbers
What fraction is shaded in the following diagrams?
a)
ଵ
b)
One part out of five = ହ
©Ezy Math Tutoring | All Rights Reserved
25
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
Exercise 5: Fractions
ଵ
c)
d)
One part out of ten= ଵ଴
ଷ
Three parts out of ten = ଵ଴
ସ
e)
Four parts out of five = ହ
଻
Seven parts out of ten = ଵ଴
©Ezy Math Tutoring | All Rights Reserved
26
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
8)
Place the fractions
1/10
ଵ
Exercise 5: Fractions
,
ଵ ଶ଴
ଶ
, ,
଻
,
଻ହ
ସ
, ,
ଽହ
ଵ଴ ହ ଵ଴଴ ହ ଵ଴ ଵ଴଴ ହ ଵ଴଴
on a number line
75/100
2/5
1/5
7/10
4/5
95/100
20/100
9)
Tim has one fifth of his lollies left, while Jack has eaten two fifths. Who has more
lollies left?
ଶ
If Jack has eaten ହ, then he has 1 −
10)
ଶ
ହ
ଷ
= of his lollies left, which is more than
ହ
ଵ
ହ
Peter had $100 and spent $50. Jack had $10 and spent only $3. Who spent the
bigger fraction of their money?
ଵ
ଷ
ଵ
ଷ
Peter spent ଶ of his money, Jack spentଵ଴. On a number line ଶ > ଵ଴ so Peter spent the
bigger fraction
11)
A fly spray kills two fifths of the flies in a room, whilst another kills three tenths of
them. Which fly spray works better?
ଶ
ଷ
On a number line ହ > ଵ଴ so the first fly spray works better
©Ezy Math Tutoring | All Rights Reserved
27
www.ezymathtutoring.com.au
Exercise 6
Decimals & Percentages
©Ezy Math Tutoring | All Rights Reserved
28
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
1)
Exercise 6: Decimals & Percentages
ଵ
c) 3 ଵ଴
Round the following decimals to
the nearest whole number
a)
3.1
1.48
଻
d) 1 ଵ଴
1
b)
1.7
11.05
଻
11
c)
e) 1 ଵ଴଴
13.74
1.07
14
d)
଻଻
f) 1 ଵ଴଴
0.22
1.77
0
e)
3)
1.55
2
f)
a)
22.51
23
2)
Multiply each of the following by
10
14
b)
Express the following fractions and
mixed numbers as decimals
a)
ଷ
b)
ଵହ
ଵ଴଴
2.5
25
c)
ଵ଴
0.3
1.4
3.7
37
d)
5.8
58
0.15
©Ezy Math Tutoring | All Rights Reserved
29
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
e)
Exercise 6: Decimals & Percentages
d)
10.2
102
f)
804
e)
1.36
13.6
g)
f)
2.45
g)
6.22
h)
8.49
i)
15.43
Multiply each of the following by
100
a)
4.3
430
154.3
4)
7.2
720
84.9
j)
8.6
860
62.2
i)
13.11
1311
24.5
h)
8.04
1.2
120
5)
Write the following as a decimal
a)
30%
1.52
0.3
152
b)
b)
15%
2.75
0.15
275
c)
c)
20%
4.26
0.2
426
©Ezy Math Tutoring | All Rights Reserved
30
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
d)
Exercise 6: Decimals & Percentages
10%
1.08
0.1
e)
c)
75%
0.96
0.75
f)
d)
90%
e)
100%
b)
c)
7)
f)
Write the following as a fraction
a)
50%
1
2
Divide each of the following by 10
a)
8)
Divide each of the following by 100
a)
13.2
152.5
1.525
b)
143.2
1.432
10%
1
10
1
0.1
25%
1
4
3.3
0.33
1.0
6)
7.2
0.72
0.9
g)
9.6
c)
131.9
1.319
d)
106.5
1.065
1.32
b)
10.8
©Ezy Math Tutoring | All Rights Reserved
31
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
e)
Exercise 6: Decimals & Percentages
0.666
98.9
h)
0.989
9)
f)
90.2
0.902
g)
66.6
9.25
0.925
Alex has $14.25 in his bank account. Tom has ten times as much. How much money
does Tom have?
$14.25 × 10 = $142.50
10)
John runs 30km and Jill runs 50% of that distance. How far did Jill run?
50% × 30݇݉ = 15݇݉
11)
Place the following decimals on a number line
0.7, 0.65, 0.8, 0.1, 0.25, 0.4, 0.5, 0.9, 0.45
0.45
0.1
0.25
©Ezy Math Tutoring | All Rights Reserved
0.4
0.7
0.5
0.65
0.8
0.9
32
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
Exercise 6: Decimals & Percentages
12)
Express the following as a
decimal
a)
d)
ହଵ
4.35
ଵ଴଴଴
e)
0.051
b)
f)
଻
ଵ଴଴଴
0.007
e)
ଵ
g)
14)
Calculate the following
a)
ଵ଴଴଴
Calculate the following
8.1 + 3.05
11.15
7.4 − 2.3
5.1
0.001
13)
7.4 + 2.22
9.62
ଵ଻
ଵ଴଴଴
0.017
d)
2.56 + 5.2
7.76
଻ସ
ଵ଴଴଴
0.074
c)
1.25 + 3.1
b)
9.6 − 3.1
6.5
a)
1.2 + 3.4
4.6
c)
10.7 − 9.6
1.1
b)
3.6 + 4.3
d)
7.9
8.4 − 4.8
3.6
c)
10.2 + 5.3
15.5
e)
3.2 − 2.5
0.7
©Ezy Math Tutoring | All Rights Reserved
33
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
f)
7.65 − 4.3
Exercise 6: Decimals & Percentages
35.30 − 16.10 = $19.20
3.35
g)
3.43 − 2.3
1.13
h)
5.69 − 3.06
2.63
i)
7.32 − 5.61
1.71
j)
8.19 − 5.43
2.76
15)
Jake has $14.70 and spends
$12.35. How much money does he
have left?
14.7 − 12.25 = $2.35
16)
Paul has $12.35 and his
grandfather gives him $11.15.
How much money does Paul now
have?
12.35 + 11.15 = $23.50
17)
Barbara wants to save up to buy
a new dress that costs $35.30. At
the moment she has $16.10. How
much more money does she need
to be able to buy the dress?
©Ezy Math Tutoring | All Rights Reserved
34
www.ezymathtutoring.com.au
Exercise 7
Chance
©Ezy Math Tutoring | All Rights Reserved
35
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
1)
Alan tosses two coins. List the
possible combinations they could
land on
Exercise 7: Chance
5)
There are 6 red shirts, 6 blue shirts
and 6 yellow shirts in a draw. If a
boy pulls a shirt out without
looking:
Both coins heads
a)
First coin heads, second coin tails
First coin tails, second coin heads
Red, blue or yellow
Both coins tails
2)
b)
Peter rolls two dice and adds the
two numbers. List all the numbers
that he could get
c)
List what the two dice from
question 2 could show to get a
total of 7
First dice 1 + second dice 6
First dice 2 + second dice 5
First dice 3 + second dice 4
6)
There are 20 red, 20 blue and 20
green lollies in a jar. If Jack closes
his eyes and chooses one:
a)
List what the two dice from
question 2 could show to get a
total of 12
What colour lolly will he
probably choose?
Could choose red, blue or
green
First dice 5 + second dice 2
4)
Could he pull out 6 yellow
shirts in a row?
Yes, there are 6 yellow
shirts so he could pull all of
them out in a row
First dice 4 + second dice 3
First dice 6 + second dice 1
Which colour shirt will he
probably pull out?
Could pull any colour
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
3)
List what colour shirt he
might pull out
b)
What colour lolly could he
not get?
Any colour but the above
First dice 6 + second dice 6
©Ezy Math Tutoring | All Rights Reserved
36
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
c)
Exercise 7: Chance
c)
If he pulls out a red lolly
first time, will he definitely
get a red lolly next time?
No: he could get a red
lolly, but not definitely
d)
e)
Either is equally likely
d)
Could he pull out 20 red
lollies in a row?
Could he pull 20 yellow
buttons in a row from the
second jar
Yes: there are 20 red lollies
in the jar so he could pull
them all out in a row
Yes, there are 20 yellow
lollies in the jar so he could
pull 20 out in a row
e)
If he did this, which colour
would he be more likely to
pull out in his next turn?
Could then pull out blue or
green
7)
In a jar there are 20 blue buttons.
In another jar there are 20 blue
and 20 yellow buttons.
a)
Which jar has more blue
buttons?
If he did this, from which
jar would he then have
more chance of pulling a
blue button from?
Both jars would have only
20 buttons so both would
have equal chance
8)
Of the following events, which are
certain to happen, impossible, or
could happen?
a)
Each jar has the same
number of blue buttons
b)
Is he more likely to pull a
yellow or blue button from
the second jar?
The sun will rise tomorrow
Certain
From which jar is he more
likely to pull out a blue
button?
b)
The jar with only blue
buttons
c)
You will eat food
Certain
You will go to school
Could happen (if not
holidays or a weekend etc)
©Ezy Math Tutoring | All Rights Reserved
37
www.ezymathtutoring.com.au
Chapter 1: Number: Solutions
d)
You will get every maths
question right
Exercise 7: Chance
f)
Everyone in your class will
win a million dollars
tomorrow
Could happen
Impossible
e)
You will turn 45 years old
tomorrow
Could happen
9)
g)
You will ride a bicycle
Could happen
Tom rolls two normal 6 sided dice and adds the numbers. Which total is he most
likely to get?
There are more ways to get a total of 7 than any other number
10)
Alan tosses two coins; are they more likely to land on two heads or two tails?
Either combination is equally likely
11)
Peter spins a spinner with 3 red and 3 white faces. If he spins it twice, list all the
combinations of colours he could get
A red and a red
A red and a white
A white and a red
A white and a white
©Ezy Math Tutoring | All Rights Reserved
38
www.ezymathtutoring.com.au
Year 4 Mathematics
Data
©Ezy Math Tutoring | All Rights Reserved
39
www.ezymathtutoring.com.au
Exercise 1
Data Tables
©Ezy Math Tutoring | All Rights Reserved
40
www.ezymathtutoring.com.au
Chapter 2: Data: Solutions
1)
Exercise 1: Data Tables
Tom made a table that shows how many of his classmates have each colour as their
favourite
Girls
Boys
a)
Green
4
5
Yellow
1
0
Blue
1
8
White
6
4
Black
2
4
How many children in Tom’s class?
Adding all the numbers gives 14 girls and 21 boys equals 35 in total
b)
Which colour was most popular?
White had 10 votes
c)
Which colour was most popular for boys?
Blue (8 votes)
d)
Which colours had equal numbers of children voting for it?
Green and blue (9 votes)
e)
Which colour or colours had equal number of boys voting for it?
White and black (4 votes)
2)
A group of people was asked to vote for one day as their favourite day of the week
Men
Women
a)
Monday
1
3
Tuesday Wednesday Thursday
3
5
10
0
2
5
Friday
5
11
Saturday
6
3
Sunday
15
15
How many people were asked?
Adding all the numbers gives 84
©Ezy Math Tutoring | All Rights Reserved
41
www.ezymathtutoring.com.au
Chapter 2: Data: Solutions
b)
Exercise 1: Data Tables
What was most people’s favourite day?
Sunday (30 votes)
c)
Which day was the least favourite of women?
Tuesday (0 votes)
d)
Which day had the biggest difference in the number of men and women
voting for it?
Friday (5 men 11 women)
3)
A man made a list of the cost of a type of blanket and a fan at different times of the
year
Blankets
Fans
a)
January
$3.50
$20
March
$4
$18
May
$5
$15
July
$6.50
$10
September
$5
$12
November
$4
$14
In which of the months was the blanket the cheapest?
January ($3.50)
b)
In which month was the fan dearest?
January ($20)
c)
d)
e)
What was the difference in its price between a fan and a blanket in
September?
($12 − $5 = $7)
In which month were the prices closest?
July ($10 − $6.50 = $3.50)
Explain why the prices changed so much during the year?
©Ezy Math Tutoring | All Rights Reserved
42
www.ezymathtutoring.com.au
Chapter 2: Data: Solutions
Exercise 1: Data Tables
In summer people would buy more fans and fewer blankets, and in winter
the opposite. This makes them dearer or cheaper
4)
Show the following data in a two way table

100 people were surveyed as to their favourite car

Everyone had a choice of 4 cars

10 men said they like Holden best

15 women preferred Toyota

5 more men than women preferred Nissan

10 more women than men preferred Ford

20 men preferred Nissan

12 women preferred Ford

Equal numbers of men and women were surveyed
Holden
Toyota
Nissan
Ford
Men
10
18
20
2
Women
8
15
15
12
©Ezy Math Tutoring | All Rights Reserved
43
www.ezymathtutoring.com.au
Chapter 2: Data: Solutions
5)
Exercise 1: Data Tables
The graphs show the number of people that own a certain colour car
Number of men driving each colour
car
14
12
10
8
6
4
2
0
Red
Blue
Green
Black
White
Pink
Yellow
Number of women drivingeach colour
car
10
9
8
7
6
5
4
3
2
1
0
Red
a)
Blue
Green
Black
White
Pink
Yellow
Show the information in a two way table
Red
Blue
Green
Black
White
Pink
Yellow
Men
12
8
3
2
6
1
3
Women
7
8
5
3
2
9
1
©Ezy Math Tutoring | All Rights Reserved
44
www.ezymathtutoring.com.au
Chapter 2: Data: Solutions
b)
Exercise 1: Data Tables
How many people were surveyed?
70
©Ezy Math Tutoring | All Rights Reserved
45
www.ezymathtutoring.com.au
Exercise 2
Picture Graphs
©Ezy Math Tutoring | All Rights Reserved
46
www.ezymathtutoring.com.au
Chapter 2: Data: Solutions
1)
Exercise 2: Picture Graphs
The picture graph below shows a sport and the number of children for whom it is
their favourite
Each “face” represents 5 people
Game Number
Attendance
Football
Rugby
Soccer
Basketball
Hockey
Swimming
Tennis
Golf
Bowling
Baseball
a)
Which sport is most popular?
Tennis
b)
c)
d)
For how many people is it their favourite?
6 × 5 = 30
For how many people is swimming their favourite sport?
3 × 5 = 15
How many people were asked?
41 × 5 = 205
©Ezy Math Tutoring | All Rights Reserved
47
www.ezymathtutoring.com.au
Chapter 2: Data: Solutions
e)
Exercise 2: Picture Graphs
Is swimming or hockey more popular?
They are equally popular
2)
Some people were asked how many times they ate fish. The picture graph shows
their answers. Each fish represents 15 days of the year
Name
Tom
Benny
Jane
Julie
Karen
Brian
Richard
Ray
Daniel
Craig
a)
Number of days eating fish
Who eats fish the most days of the year?
Jane
b)
c)
How many days a year do they eat fish?
8 × 15 = 120
Who eats fish on the least number of days?
Richard
d)
e)
How many days do they eat fish on?
2 × 15 = 30
If someone ate fish on 50 days of the year, how could you show this on the
graph? Can you think of a better way to show numbers of days that are not
groups of 15?

Could make part of a fish equal to say 5 days
©Ezy Math Tutoring | All Rights Reserved
48
www.ezymathtutoring.com.au
Chapter 2: Data: Solutions


3)
Exercise 2: Picture Graphs
Could show a continuous bar instead of pieces
Could use colours for different
di
numbers
The graph below shows the number of kilos of each fruit bought in a week by a cafe.
Bananas were $2.50, apples $2, oranges $3, watermelon $1.50 and strawberries $4
per kilo
a)
On which fruit did the cafe spend most money?
Strawberries (4kg x $4 per kg = $16)
b)
What fruit did the cafe buy least of?
of
Oranges (2 kg)
c)
How many kilos of fruit were bought in total?
total
17kg
d)
How much did the cafe spend on fruit in total?
total
(5 × $2.50)) + (3 × $2) + (2 × $3) + (3 × $1.50) + (4
( × $4) = $45
©Ezy Math Tutoring | All Rights Reserved
49
www.ezymathtutoring.com.au
Chapter 2: Data: Solutions
4)
Exercise 2: Picture Graphs
Draw a picture graph that shows the number of people that voted for their favourite
animal
Animal
Dog
Cat
Rabbit
Horse
Mouse
Chicken
Lion
Tiger
Snake
Monkey
Number of men
10
8
2
4
5
4
5
3
1
0
Number of men
Number of women
4
5
8
2
0
6
3
1
0
1
Number of women
0
©Ezy Math Tutoring | All Rights Reserved
50
www.ezymathtutoring.com.au
Chapter 2: Data: Solutions
5)
Exercise 2: Picture Graphs
The following picture graph shows the number of children that get to school in
different ways. Each picture represents 10 children. Show the same information in a
column graph
©Ezy Math Tutoring | All Rights Reserved
51
www.ezymathtutoring.com.au
Chapter 2: Data: Solutions
Exercise 2: Picture Graphs
How students get to school
N
u
m
b
e
r
140
s 120
t 100
u
80
d
e 60
n 40
t
20
o
s
f
0
Bus
Ride bike
Get lift
walk
Way of getting to school
©Ezy Math Tutoring | All Rights Reserved
52
www.ezymathtutoring.com.au
Year 4 Mathematics
Space
©Ezy Math Tutoring | All Rights Reserved
53
www.ezymathtutoring.com.au
Exercise 1
Tessellations
©Ezy Math Tutoring | All Rights Reserved
54
www.ezymathtutoring.com.au
Chapter 3: Space
1)
Exercise 1: Tessellations
Which of the following shapes tessellate?
a)
b)
c)
d)
©Ezy Math Tutoring | All Rights Reserved
55
www.ezymathtutoring.com.au
Chapter 3: Space
Exercise 1: Tessellations
e)
All tessellate except shape c
2)
In the space in the table, write down how many of each shape is necessary to
completely tessellate around a point
Equilateral Triangle
Square
Regular Pentagon
Regular Hexagon
3)
6
4
Cannot tessellate
3
Explain in your own words why you need different numbers of certain shapes to be
able to tessellate them
Because the angle inside each shape is a different size depending on which shape is
chosen. So you need more or less of them to fill the same space
4)
The side lengths of the triangle are all different. By rotating the triangle, construct a
tessellation, and identify the side names in each triangle
C
B
A
B
A
C
C
©Ezy Math Tutoring | All Rights Reserved
A
56
www.ezymathtutoring.com.au
Chapter 3: Space
Exercise 1: Tessellations
5)
Using the triangle above, form a tessellation by using a combination of rotations and
a reflection
6)
By using rotations, construct a tessellation from the following quadrilateral
7)
By using a translation (sliding), form a tessellation from the following shape
8)
What technique(s) would you use to tessellate the following shapes?
a)
b)
©Ezy Math Tutoring | All Rights Reserved
57
www.ezymathtutoring.com.au
Chapter 3: Space
Exercise 1: Tessellations
c)
d)
e)
©Ezy Math Tutoring | All Rights Reserved
58
www.ezymathtutoring.com.au
Exercise 2
Angles
©Ezy Math Tutoring | All Rights Reserved
59
www.ezymathtutoring.com.au
Chapter 3: Shapes
1)
Exercise 2: Angles
Which of the following pairs of lines are perpendicular?
a)
b)
c)
d)
B and c
©Ezy Math Tutoring | All Rights Reserved
60
www.ezymathtutoring.com.au
Chapter 3: Shapes
2)
Exercise 2: Angles
In the following diagram name all the perpendicular pairs of lines
H
I
G
J
F
A
B
D
C
AD
BI
AD
CG
JF
3)
E
EG
Which letter denotes the vertex in each of the following angles?
a)
B
A
C
B
©Ezy Math Tutoring | All Rights Reserved
61
www.ezymathtutoring.com.au
Chapter 3: Shapes
Exercise 2: Angles
b)
X
Q
A
A
c)
D
S
P
S
d)
L
M
R
L
e)
M
C
T
T
©Ezy Math Tutoring | All Rights Reserved
62
www.ezymathtutoring.com.au
Chapter 3: Shapes
Exercise 2: Angles
f)
A
J
X
X
4)
Describe each of the following angles as less than right-angled, more than right
angled or right-angled
a)
Less than right angled
b)
Right angled
©Ezy Math Tutoring | All Rights Reserved
63
www.ezymathtutoring.com.au
Chapter 3: Shapes
Exercise 2: Angles
c)
Right angled
d)
Less than right angled
e)
Right angled
f)
More than right angled
©Ezy Math Tutoring | All Rights Reserved
64
www.ezymathtutoring.com.au
Chapter 3: Shapes
5)
Exercise 2: Angles
State whether each pair of angles are the same size
a)
Yes
b)
No
©Ezy Math Tutoring | All Rights Reserved
65
www.ezymathtutoring.com.au
Chapter 3: Shapes
Exercise 2: Angles
c)
Yes
d)
Yes
©Ezy Math Tutoring | All Rights Reserved
66
www.ezymathtutoring.com.au
Chapter 3: Shapes
6)
Exercise 2: Angles
Identify what parts of the following objects form angles
a)
Legs to the base of the chair
Seat to the struts
Struts to the back
Back, seat, legs, struts
b)
Spikes of the fence posts
Rail to the spikes
c)
Door sides, door frame
©Ezy Math Tutoring | All Rights Reserved
67
www.ezymathtutoring.com.au
Chapter 3: Shapes
Exercise 2: Angles
d)
Path
End of path to the house
Windows
Door
Roof
Chimney
e)
Perimeter of the sign
Letter T
White line
©Ezy Math Tutoring | All Rights Reserved
68
www.ezymathtutoring.com.au
Chapter 3: Shapes
Exercise 2: Angles
f)
Base of pyramid to ground
Edges of pyramid
Faces of pyramid to each other and to the ground
©Ezy Math Tutoring | All Rights Reserved
69
www.ezymathtutoring.com.au
Exercise 3
2D and 3D Shapes
©Ezy Math Tutoring | All Rights Reserved
70
www.ezymathtutoring.com.au
Chapter 3: Shapes
1)
Sketch the following shapes
a)
Exercise 3: 2D and 3D Shapes
2)
Cylinder
b)
Triangular prism
c)
Triangular pyramid
3)
d)
e)
Rectangular prism
Cone
©Ezy Math Tutoring | All Rights Reserved
Sketch a cylinder from the
following views
a)
Side
b)
Above
c)
Below
Sketch a triangular prism from the
following views
a)
Side
b)
Below
71
www.ezymathtutoring.com.au
Chapter 3: Shapes
c)
End
d)
Above
Exercise 3: 2D and 3D Shapes
d)
5)
4)
Draw a net of the following shapes
a)
b)
c)
Cone
Draw and describe the shape
formed when a cross section
parallel to the base is taken of the
following
a)
Cylinder
b)
Rectangular prism
c)
Triangular pyramid
d)
Cone
Rectangular prism
Triangular pyramid
Cylinder
All these cross sections are
the same shape as the base
©Ezy Math Tutoring | All Rights Reserved
72
www.ezymathtutoring.com.au
Chapter 3: Shapes
Exercise 3: 2D and 3D Shapes
In shapes with an apex; (e.g. pyramid)
the cross section is smaller than the
base. In prisms the cross section is the
same size as the base
6)
Draw and describe the shape
formed when a cross section
perpendicular to the base is taken
of the following
a)
b)
c)
d)
In shapes that have an apex, the
cross section is a triangle. In
prisms and cylinders the cross
section is a rectangle
7)
a)
Draw the lines of symmetry
of a rectangle
b)
Draw a line through a
rectangle that is not a line
of symmetry
Cone
Triangular prism
8)
Draw a triangle that has all sides of
equal length and draw all its lines
of symmetry
9)
Draw a triangle that has 2 of its
sides having equal length, and
draw all its lines of symmetry
Square pyramid
Cylinder
©Ezy Math Tutoring | All Rights Reserved
73
www.ezymathtutoring.com.au
Chapter 3: Shapes
Exercise 3: 2D and 3D Shapes
10)
Draw a triangle that has no sides
of equal length and draw all its
lines of symmetry
Such a triangle has no lines of
symmetry
11)
Draw a square and also draw all
its lines of symmetry
12)
Draw a four sided shape that has
no sides of equal length and draw
all its lines of symmetry
Any irregular shape has no lines of
symmetry
©Ezy Math Tutoring | All Rights Reserved
74
www.ezymathtutoring.com.au
Year 4 Mathematics
Measurement
©Ezy Math Tutoring | All Rights Reserved
75
www.ezymathtutoring.com.au
Exercise 1
Time
©Ezy Math Tutoring | All Rights Reserved
76
www.ezymathtutoring.com.au
Chapter 4: Measurement
1)
Exercise 1: Time
Write the following times in words
a)
Four twelve
b)
One thirty nine
c)
Nine thirty
©Ezy Math Tutoring | All Rights Reserved
77
www.ezymathtutoring.com.au
Chapter 4: Measurement
Exercise 1: Time
d)
Eight twenty four
2)
Write the following times in two different ways. (For example seven forty-five,
quarter to 8)
a)
Twelve forty five, quarter to one
b)
Ten forty, twenty to eleven
©Ezy Math Tutoring | All Rights Reserved
78
www.ezymathtutoring.com.au
Chapter 4: Measurement
Exercise 1: Time
c)
Eight fifteen, quarter past eight
d)
Six thirty, half past six
3)
Convert the following to minutes
a)
c)
e)
1 and a half hours
90 minutes
©Ezy Math Tutoring | All Rights Reserved
2 hours and fifteen minutes
135 minutes
2 hours
120 minutes
Ten hours
600 minutes
1 hour
60 minutes
b)
d)
f)
4 hours and ten minutes
250 minutes
79
www.ezymathtutoring.com.au
Chapter 4: Measurement
4)
Exercise 1: Time
c)
Convert the following to seconds
a)
3:15
One minute
d)
60 seconds
b)
e)
f)
g)
f)
6)
1 hour
3600 seconds
5)
Write each of these times as they
would appear on a digital clock
a)
7)
Eight thirty
©Ezy Math Tutoring | All Rights Reserved
A bus goes from the city to John’s
street every fifteen minutes. If the
last bus for the night leaves at nine
o’clock, when did the second last
bus leave
Fifteen minutes earlier, which is
8:45
Six forty five
6:45
The main movie at the theatre
shows every 2 and a half hours. If
it started at seven thirty, when
would the next showing begin?
10 0’clock
8:30
b)
Noon
12:00
Six minutes and 20 seconds
380 seconds
Quarter to 8
7:45
Two and a half minutes
150 seconds
e)
Ten minutes to one
12:50
Five minutes
300 seconds
d)
Half past nine
9:30
Two minutes
120 seconds
c)
Quarter past three
8)
A magazine is published every 2
weeks. If t was published on May
80
www.ezymathtutoring.com.au
Chapter 4: Measurement
Exercise 1: Time
1st, when is the next time it would
be published?
May 15th
9)
The American Civil War started in
1860 and went until 1865. How
long did it last for?
1865 --1860 = 5 years
10)
It took Alan one and a half years
to sail around the world. If he left
on January 1st 2010, when did he
return?
July 1st 2011
©Ezy Math Tutoring | All Rights Reserved
81
www.ezymathtutoring.com.au
Exercise 2
Mass
©Ezy Math Tutoring | All Rights Reserved
82
www.ezymathtutoring.com.au
Chapter 4: Measurement
1)
Convert the following to grams
a)
b)
c)
d)
e)
2)
Exercise 2: Mass
Half a kilogram
d)
1
× 1 ݇݃ = 0.5݇݃ = 500݃
2
One quarter of a kilogram
e)
1
× 1݇݃ = 0.25݇݃ = 250݃
2
One fifth of a kilogram
f)
1
× 1݇݃ = 0.2݇݃ = 200݃
5
Three quarters of a
kilogram
3
× 1݇݃ = 0.75݇݃ = 750݃
4
One third of a kilogram
1
× 1݇݃ = 0.33݇݃ = 333.33݃
3
g)
3)
b)
c)
500 grams
750
= 0.75݇݃
1000
250 grams
©Ezy Math Tutoring | All Rights Reserved
100
= 0.1݇݃
1000
1500 grams
1500
= 1.5݇݃
1000
1250 grams
1250
= 1.25݇݃
1000
3500 grams
Add the following giving your
answer in kg
a)
b)
500
= 0.5݇݃
1000
750 grams
100 grams
3500
= 3.5݇݃
1000
Convert the following to kilograms
a)
250
= 0.25݇݃
1000
500g + 500g
= 1000݃ = 1݇݃
700g + 700g + 600g
= 2000݃ = 2݇݃
c)
200g + 800g
= 1000݃ = 1݇݃
83
www.ezymathtutoring.com.au
Chapter 4: Measurement
d)
e)
f)
4)
One and a half kg plus half
a kg
= 1.5݇݃ + 0.5݇݃ = 2݇݃
= 1500݃ = 1.5݇݃
One and a half kg plus one
and a half kg
Write the following in kg
Four lots of 500g
4 × 500݃ = 2000݃ = 2݇݃
5)
b)
c)
750g + 750g
= 1.5݇݃ + 1.5݇݃ = 3݇݃
a)
Exercise 2: Mass
d)
e)
Three lots of 500g
3 × 500݃ = 1500݃ = 1.5݇݃
Half of 4kg
1
‫ݔ‬4݇݃ = 2݇݃
2
Five and a half kg subtract
two and a half kg
5.5݇݃ − 2.5݇݃ = 3݇݃
One half of 5kg
1
× 5݇݃ = 2.5݇݃
2
Eric has a bag of marbles. Each marble weighs 200g and he has 10 of them. If John’s
marbles each weigh 400g, how many does he need to have the same weight of
marbles as Eric?
Eric has 10 × 200݃ = 2000݃ = 2݇݃ of marbles
5 × 400݃ = 2000݃
Therefore John needs five 400g marbles
6)
7)
Four men each carry a bag of rocks weighing 250g. How many kg do they carry
between them?
4 × 250݃ = 1000݃ = 1݇݃
John has $5 and wants to buy as much paper as he can. Each 100g of paper costs 50
cents. How much paper can he buy?
John has 10 lots of 50 cents ($5), so he can buy 10 lots of 100g
©Ezy Math Tutoring | All Rights Reserved
84
www.ezymathtutoring.com.au
Chapter 4: Measurement
Exercise 2: Mass
10 × 100݃ = 1000݃ = 1݇݃
John can buy 1kg of paper
8)
9)
Three books weigh 250g, 300g and 600g. How much do the books weigh together?
250݃ + 300݃ + 600݃ = 1150݃ = 1.15݇݃
Peter has three weights: two of them weigh 400g and the other weighs 700g. Alan
has two weights: one weighs 1kg and the other 500g. Who has more weight?
Peter’s total of weights is 400݃ + 400݃ + 700݃ = 1500݃ = 1.5݇݃
Alan’s total of weights is 1݇݃ + 0.5݇݃ = 1.5݇݃
Peter and Alan have the same weight
10)
Thomas eats 500g of a 750 g steak, while his Dad leaves 100g of his. How much
steak is left in total?
Thomas has 750݃ − 500݃ = 250݃ of his steak left
250݃ + 100݃ = 350݃ of steak left in total
©Ezy Math Tutoring | All Rights Reserved
85
www.ezymathtutoring.com.au
Exercise 3
Length, Perimeter & Area
©Ezy Math Tutoring | All Rights Reserved
86
www.ezymathtutoring.com.au
Chapter 4: Measurement
1)
Exercise 3: Length, Perimeter & Area
Convert the following to metres
(e.g. 1m 50cm = 1.5m)
a)
1 m 25cm
25ܿ݉ =
b)
c)
1
× 1݉ = 0.5݉
2
0.25݉ × 100 = 25ܿ݉
b)
2 m 50cm
c)
d)
3݉ + 0.6݉ = 3.6݉
2m 75cm
80cm
80
80ܿ݉ =
݉ = 0.8݉
100
©Ezy Math Tutoring | All Rights Reserved
600 cm
600ܿ݉ =
2.75m
600
݉ = 6݉
100
0.75݉ = 0.75 × 100ܿ݉
= 75ܿ݉
3m 60cm
2݉ + 0.75݉ = 2.75,
1.25݉ = 1݉ 25ܿ݉
2.75݉ = 2݉ + 0.75݉
2݉ + 0.5݉ = 2.5݉
60
݉ = 0.6݉
100
1.25m
1.25݉ = 1݉ + 0.25݉
½m
75
75ܿ݉ =
݉ = 0.75݉
100
f)
a)
1݉ + 0.25݉ = 1.25݉
60ܿ݉ =
e)
Convert the following to m and cm
(e.g. 1.5m = 1m 50cm)
25
݉ = 0.25݉
100
50
50ܿ݉ =
݉ = 0.5݉
100
d)
2)
e)
2.75݉ = 2݉ 75ܿ݉
0.5m
0.5݉ = 0.5 × 100ܿ݉
= 50ܿ݉
4.2m
4.2݉ = 4݉ + 0.2݉
0.2݉ = 0.2 × 100ܿ݉
= 20ܿ݉
4.2݉ = 4݉ 20ܿ݉
87
www.ezymathtutoring.com.au
Chapter 4: Measurement
f)
Exercise 3: Length, Perimeter & Area
1.05m

1.05݉ = 1݉ + 0.05݉
More
0.05݉ = 0.05 × 100ܿ݉
= 5ܿ݉
3)
4)
5)

1.05݉ = 1݉ 5ܿ݉

Would the area of the following be
approximately equal to 1 square
metre, less than 1 square metre,
or more than 1 square metre?

6)

Describe how to calculate the
perimeter of a shape
Measure the distance around the
outside of the shape
7)
Calculate the perimeter of each of
the following rectangles
a)
The floor of a kitchen
More
b)
A window
About equal

A stamp
Less

A coffee table
A car door
About equal
A square has side length of 1
metre, what is its area?
1݉ × 1݉ = 1݉ଶ
A field
More
Graham is 1.6m tall, while his dad
is 2 metres. How much taller is
Graham’s dad in metres?
2݉ − 1.6݉ = 0.4݉
A lawn
c)
Side lengths 1m and 2m
1݉ + 2݉ + 1݉ + 2݉
= 6݉
Side lengths 2m and 3m
2݉ + 3݉ + 2݉ + 3݉
= 10݉
Side lengths 5m and 4m
5݉ + 4݉ + 5݉ + 4݉
= 18݉
About equal
©Ezy Math Tutoring | All Rights Reserved
88
www.ezymathtutoring.com.au
Chapter 4: Measurement
d)
e)
Exercise 3: Length, Perimeter & Area
e)
Side lengths 1.5m and 2m
1.5݉ + 2݉ + 1.5݉ + 2݉
= 7݉
1݉ 50ܿ݉ = 1.5݉
Rectangle and hence area
is same as previous
question
Side lengths 1m 50cm and
2m
1݉ 50ܿ݉ = 1.5݉
f)
Rectangle and hence
answer are same as
previous question
f)
Side lengths 50cm and 1m
50ܿ݉ = 0.5݉
8)
0.5݉ + 1݉ + 0.5݉ + 1݉
= 3݉
Calculate the area of each of the
following rectangles
Side lengths 1m 50cm and
2m
Side lengths 50cm and 1m
50ܿ݉ = 0.5݉
9)
0.5݉ × 1݉ = 0.5݉ଶ
There are two pieces of wood on
the ground. One has a length of
1m and a width of 4m, the other is
a square piece of side length 2m.
Which piece of wood has a bigger
area? Which piece of wood has
the bigger perimeter?
Area of first piece =
a)
b)
c)
d)
Side lengths 1m and 2m
1݉ × 2݉ = 2݉ଶ
Side lengths 2m and 3m
2݉ × 3݉ = 6݉ଶ
Side lengths 5m and 4m
5݉ × 4݉ = 20݉ଶ
1݉ × 4݉ = 4݉ଶ
Area of second piece =
2݉ × 2݉ = 4݉ଶ
The two pieces have the same area
Perimeter of first piece =
Side lengths 1.5m and 2m
1݉ + 4݉ + 1݉ + 4݉ = 10݉
1.5݉ × 2݉ = 3݉ଶ
2݉ + 2݉ + 2݉ + 2݉ = 8݉
©Ezy Math Tutoring | All Rights Reserved
Perimeter of second piece =
89
www.ezymathtutoring.com.au
Chapter 4: Measurement
Exercise 3: Length, Perimeter & Area
First piece has larger perimeter
10)
A man walked around a lounge
room that was 3m long and 2m
wide. How far did he walk?
Perimeter =
3݉ + 2݉ + 3݉ + 2݉ = 10݉
11)
The man from question 10 wishes
to carpet his lounge room. How
many square metres of carpet will
he need?
Area = 3݉ × 2݉ = 6݉ଶ
©Ezy Math Tutoring | All Rights Reserved
90
www.ezymathtutoring.com.au
Exercise 4
Volume & Capacity
©Ezy Math Tutoring | All Rights Reserved
91
www.ezymathtutoring.com.au
Chapter 4: Measurement
1)
Exercise 4: Volume & Capacity
Estimate the capacity in litres of
each of the following?
b)
NOTE the following are estimates
only

A milk carton
c)
Usually 1 litre

A car’s petrol tank
Anywhere from 50 to 100
litres

d)
A bath
Around 200 litres

e)
A large bottle of soft drink
2 litres

Depends on type of pool:
a backyard pool could be
around 250,000 litres to
an Olympic pool that has
a capacity of around 5
million litres

f)
A swimming pool
3)
a)
1.25 L
©Ezy Math Tutoring | All Rights Reserved
2.6݈ = 2.6 × 1000݈݉
= 2600݈݉
0.75L
0.75݈ = 0.75 × 1000݈݉
= 750݈݉
3.9L
3.9݈ = 3.9 × 1000݈݉
= 3900݈݉
2.24L
2.24݈ = 2.24 × 1000݈݉
= 2240݈݉
8L
Convert the following to Litres
a)
A kitchen sink
Convert the following to mL
2.6L
8݈ = 8 × 1000݈݉
= 8000݈݉
Around 20 litres
2)
1.25݈ = 1.25 × 1000݉‫ܮ‬
= 1250݈݉
b)
4000mL
4000݉ = (4000 ÷ 1000)݈
= 4݈
2500mL
2500݉ = (2500 ÷ 1000)݈
= 2.5݈
92
www.ezymathtutoring.com.au
Chapter 4: Measurement
c)
d)
e)
4)
1250mL
1250݉ = (1250 ÷ 1000)݈
= 1.25݈
4750mL
4750݉ = (4750 ÷ 1000)݈
= 4.75݈
10000mL
10000݈݉ = (10000 ÷ 1000)݈
= 10݈
Exercise 4: Volume & Capacity
7)
A 1 litre container is filled to the
top with water. One hundred
1cm3 blocks are thrown into the
container and water overflows as a
result of this. How much water is
left in the container?
100 × 1ܿ݉ଷ = 100ܿ݉ଷ
100ܿ݉ଷ = 100݈݉
Therefore there is 900݈݉ of water
left in the container
How much liquid is wasted if
500mL is added to a 1 litre
container that already contains
750mL?
750݈݉ + 500݈݉ = 1250݈݉
5)
The container overflows by 250݈݉
To fill a 2L container, how much
liquid needs to be added if it
currently contains 1.4 litres?
2݈ − 1.4݈ = 0.6݈ = 600݈݉
6)
600݈݉ should be added
Bill poured 600mL of water into a
bowl, Tom poured a further 500mL
and Peter poured 900mL. How
much water was in the container?
600݈݉ + 500݈݉ + 900݈݉
= 2000݈݉ = 2݈
©Ezy Math Tutoring | All Rights Reserved
93
www.ezymathtutoring.com.au
Chapter 4: Measurement
8)
How much liquid is in the following cylinders?
500݈݉
9)
Exercise 4: Volume & Capacity
1400݈݉ = 1.4݈
1500݈݉ = 1.5݈
1݈
2݈
700݈݉ = 0.7݈
1300݈݉ = 1.3݈
100݈݉ = 0.1݈
Stacks of 1 cm blocks are built. How much water would they displace from a
container if they were dropped in?
(Each block is 1ܿ݉ଷ )
a)
b)
c)
2 rows and 3 columns
2 × 3 = 6 ܾ݈‫ = ݏ݇ܿ݋‬6ܿ݉ଷ = 6݈݉
4 rows and 5 columns
4 × 5 = 20 ܾ݈‫ = ݏ݇ܿ݋‬20ܿ݉ଷ = 20݈݉
6 rows and 3 columns
6 × 3 = 18 ܾ݈‫ = ݏ݇ܿ݋‬18ܿ݉ଷ = 18݈݉
©Ezy Math Tutoring | All Rights Reserved
94
www.ezymathtutoring.com.au
Chapter 4: Measurement
d)
e)
f)
10)
Exercise 4: Volume & Capacity
3 rows and 6 columns
3 × 6 = 18 ܾ݈‫ = ݏ݇ܿ݋‬18ܿ݉ଷ = 18݈݉
10 rows and 10 columns
10 × 10 = 100 ܾ݈‫ = ݏ݇ܿ݋‬100ܿ݉ଷ = 100݈݉
30 rows and 30 columns
30 × 30 = 900 ܾ݈‫ = ݏ݇ܿ݋‬900ܿ݉ଷ = 900݈݉
In a fridge there were five 250 mL cans of soft drink. How much soft drink was
there altogether?
5 × 250݈݉ = 1250݈݉ = 1.25݈
©Ezy Math Tutoring | All Rights Reserved
95
www.ezymathtutoring.com.au