92093147.F Multiplication Student

F
Series
Student
Multiplication
and Division
My name
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First edition printed 2009 in Australia.
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ISBN 978-1-921860-78-2
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Series F – Multiplication and Division
Contents
Topic 1 – Mental multiplication strategies (pp. 1–10) Date completed
• doubling strategy_______________________________________ / /
• multiply by 10s, 100s and 1 000s__________________________ / /
• split strategy__________________________________________ / /
• compensation strategy__________________________________ / /
• factors and multiples____________________________________ / /
Topic 2 – Mental division strategies (pp. 11–19)

• use multiplication facts__________________________________ / /
• divide by 10s, 100s and 1 000s____________________________ / /
• halving strategy________________________________________ / /
• split strategy__________________________________________ / /
• tests of divisibility______________________________________ / /
Topic 3 – Written methods (pp. 20–28)

• contracted multiplication________________________________ / /
• extended multiplication__________________________________ / /
• short division__________________________________________ / /
• short division with remainders____________________________ / /
• solving problems_______________________________________ / /
Topic 4 – Puzzles and investigations (pp. 29–32)

• crack the code – apply___________________________________ / /
• smart buttons – apply___________________________________ / /
• bugs – investigate______________________________________ / /
• puzzles – apply_________________________________________ / /
Series Authors:
Rachel Flenley
Nicola Herringer
Copyright ©
Mental multiplication strategies – doubling strategy
Doubling is a useful strategy to use when multiplying.

To multiply a number by four, double it twice. To multiply a number by eight, double it three times.
15 × 4 double 13 × 8 double > double twice = 60 double twice = 52
double three times = 104
1 Warm up with some doubling practice:
a b c
2 40
1 4 10 20 6 12
3 6 15 30 9 24
D D D
5 9 25 40 96 8
2 7 35 50 32 16
2 Finish the doubling patterns:
a 4 8
__________ 16
___________ __________ 64
___________ __________
b 3 __________ ___________ __________ ___________ 96

__________
c 5 __________ ___________ 40
__________ ___________ __________
d 25 50
__________ ___________ __________ ___________ __________
e 7 __________ 28
___________ __________ ___________ 224
__________
f 75 __________ 300
___________ __________ ___________ __________
3 Choose a number and create your own doubling pattern. How high can you go? What patterns can you
see within your pattern?
4 Two sets of twins turn 12. They decide to have a joint birthday party with 1 giant cake but they all want
their own candles. How many candles will they need?
Multiplication and Division

Copyright © 3P Learning
F 1 1
SERIES TOPIC
Mental multiplication strategies – doubling strategy
5 Use the doubling strategy to solve these:
To multiply by 4, double
×2 ×4 twice. To multiply by 8,
double three times.
a 13 × 4 26
___________ 52
___________
b 16 × 4 ___________ ___________
c 24 × 4 ___________ ___________
d 25 × 4 ___________ ___________
e 32 × 4 ___________ ___________
f 21 × 4 ___________ ___________
g 35 × 4 ___________ ___________
6 Use the doubling strategy to solve these:
×2 ×4 ×8
a 12 × 8 24
_____________ ____________ 96
____________
b 14 × 8 _____________ ____________ 112

____________
c 25 × 8 _____________ ____________ ____________
d 21 × 8 _____________ 84
____________ ____________
e 13 × 8 _____________ ____________ ____________
f 16 × 8 32
_____________ ____________ ____________
7 Work out the answers in your head using the appropriate doubling strategy. Use a table like the one
above if it helps.
a 18 × 4 = b 16 × 4 = c 26 × 4 =
d 24 × 8 = e 15 × 8 = f 22 × 8 =
8 Nick’s dad offered him two methods of payment for helping with a 5 week landscaping project.
Method 1: $24 a week for 5 weeks.

Method 2: $8 for the first week, then double the payment each week.
Which method would earn Nick the most money? Why?
2 F 1 Multiplication and Division

SERIES TOPIC
Mental multiplication strategies – multiply by 10s, 100s and 1 000s
When we multiply by 10 we move the number one place value to the left.
When we multiply by 100 we move the number two place values to the left.
When we multiply by 1 000 we move the number three place values to the left.
Look at how this works with the number 45:
Ten Thousands Thousands Hundreds Tens Units

4 5
4 5 0 × 10
4 5 0 0 × 100
4 5 0 0 0 × 1 000
1 Multiply the following numbers by 10, 100 and 1 000:
a T Th Th H T U b T Th Th H T U
1 7 4 3
× 10 × 10
× 100 × 100
× 1 000 × 1 000
c T Th Th H T U d T Th Th H T U
8 5 9 9
× 10 × 10
× 100 × 100
× 1 000 × 1 000
2 Try these:
a 14 × 10 = b 14 × 100 = c 14 × 1 000 =
d 92 × 10 = e 92 × 1 000 = f 92 × 100 =
g 11 × 1 000 = h 11 × 100 = i 11 × 10 =
3 You’ll need a partner and a calculator for this activity. Take turns giving each other problems such as
�Show me 100 × 678�. The person whose turn it is to solve the problem, writes down their prediction
and you both check it on the calculator. 10 points for each correct answer, and the first person to
50 points wins.

F 1 3
SERIES TOPIC
Mental multiplication strategies – multiply by 10s, 100s and 1 000s
It is also handy to know how to multiply multiples of 10 such as 20 or 200 in our heads.
4 × 2 helps us work out 4 × 20: 4 × 2 = 8 4 × 20 = 80
We can express this as 4 × 2 × 10 = 80 How would you work out 4 × 200?
4 Use patterns to help you solve these:
a 5 × 2 _____________ 5 × 20 _____________ 5 × 200 ___________
b 2 × 9 _____________ 2 × 90 _____________ 2 × 900 ___________
c 6 × $4 _____________ 6 × $40 _____________ 6 × $400 ___________
d 8 × 3 _____________ 8 × 30 _____________ 8 × 300 ___________
e 3 × $7 _____________ 3 × $70 _____________ 3 × $700 ___________
f 2 × 8 _____________ 20 × 8 _____________ 200 × 8 ___________
g 3 × 9 _____________ 30 × 9 _____________ 300 × 9 ___________
5 Answer these problems: If you’re struggling with

a Jock runs 50 km per week. How far does he run over 10 weeks? your tables, get onto Live
Mathletics and practise!
b Huy earns $20 pocket money per week. If he saves half of this, how much
will he have saved at the end of 8 weeks?
c The sum of two numbers is 28. When you multiply them together, the
answer is 160. What are the numbers?
6 Finish these counting patterns:
a 10 20 30
__________ __________ ___________ 60
__________
b 20 40 __________ 80
__________ ___________ __________
c 30 60 __________ __________ 150
___________ __________
d 40 80 __________ __________ 200
___________ 240
__________
e 50 100 150
__________ __________ ___________ __________
f 100 200 __________ 400
__________ ___________ __________
g 200 400 __________ __________ ___________ 1 200
__________

SERIES TOPIC
Mental multiplication strategies – split strategy
Sometimes it’s easier to split a number into parts and work with the parts separately.
Look at 64 × 8
Split the number into 60 and 4
Work out (60 × 8) and then (4 × 8)
Add the answers together 480 + 32 = 512
1 Use the split strategy to answer the questions:
a 46 × 4 b 74 × 5 c 48 × 4
(40 × 4) + (6 × 4) (___ × ___) + (___ × ___) (___ × ___) + (___ × ___)
_______ + _______ _______ + _______ _______ + _______
= = =
d 37 × 7 e 62 × 8 f 91 × 5
(___ × ___) + (___ × ___) (___ × ___) + (___ × ___) (___ × ___) + (___ × ___)
_______ + _______ _______ + _______ _______ + _______
= = =
2 Use the split strategy to answer the questions. This time see if you can do the brackets in your head:
a 48 × 8 = __________ + __________ = It's a good thing I

know how to work
b 52 × 7 = __________ + __________ = with multiples of
ten in my head!
c 9 × 43 = __________ + __________ =
d 8 × 29 = __________ + __________ =
e 86 × 7 = __________ + __________ =
3 These problems have been worked out incorrectly. Circle where it all went wrong.
a 37 × 6 b 17 × 5 c 32 × 9
(30 × 6 ) + (7 × 6) (10 × 5) + (7 × 5) (30 × 9) + (2 × 9)
180 + 13 70 + 35 27 + 18
= 193 = 105 = 45

F 1 5
SERIES TOPIC
Mental multiplication strategies – split strategy
4 Each trail contains 2 multiplication problems and steps to solve them. Only one trail has been solved
correctly. There are errors in the other two. Find and colour the winning trail.
FINISH
78
291 114
(30 × 9) + (3 × 9) (10 × 6) + (3 × 6) (10 × 9) + (6 × 9)
13 × 6 33 × 9 16 × 9
464 294 51
(40 × 7) + (2 × 7) 400 + 64 30 + 21
42 × 7 58 × 8 17 × 3
START

SERIES TOPIC
Mental multiplication strategies – compensation strategy
When multiplying we can round to an easier number and then adjust.

Look how we do this with 4 × 29
29 is close to 30. We can do 4 × 30 in our heads because we know 4 × 3 = 12
4 × 30 = 120
We have to take off 4 because we used one group of 4 too many: 120 – (1 × 4) = 116
4 × 29 = 116
1 Use the compensation strategy to answer the questions. The first one has been done for you.
20
a 19 × 3 = ________ 3
× ________ 3
– ________ = 57
b 8 × 29 = ________ × ________ – ________ =
c 18 × 6 = ________ × ________ – ________ =
d 7 × 39 = ________ × ________ – ________ =
e 28 × 5 = ________ × ________ – ________ =
We can also adjust up. Look how we do this with 6 × 62:

62 is close to 60. We can do 6 × 60 in our heads because we know 6 × 6 = 36
6 × 60 = 360
We have to then add 2 more lots of 6: 360 + 12 = 372
6 × 62 = 372
2 Use the compensation strategy and adjust up for these. The first one has been done for you.
Would I use the compensation

40
a 41 × 3 = ________ 3
× ________ 3
+ ________ = 123 strategy with numbers such as
56 or 84? Why or why not?
b 81 × 4 = ________ × ________ + ________ =
c 22 × 9 = ________ × ________ + ________ =
d 32 × 9 = ________ × ________ + ________ =
e 7 × 62 = ________ × ________ + ________ =

F 1 7
SERIES TOPIC
Mental multiplication strategies – compensation strategy
3 In this activity you’ll work alongside a partner. You’ll each need two dice and your own copy
of this page. For each line, roll the dice to find the tens digit and then roll it again to find the
multiplier. Your partner will do the same. Use the compensation strategy to mentally work
out the answers to the problems. copy
Tens Units Multiplier Answer
1 × =
9 × =
2 × =
1 × =
8 × =
1 × =
9 × =
8 × =
2 × =
1 × =
a Check each other’s calculations. You may want to use a calculator.

b Now, use the calculator to add your answers. The person with the highest score wins.

SERIES TOPIC
Mental multiplication strategies – factors and multiples
Factors are the numbers we multiply together to get to another number:

factor × factor = whole number
How many factors does the number 12 have? 4 × 3 = 12, 6 × 2 = 12, 1 × 12 = 12

4, 3, 6, 2, 1 and 12 are all factors of 12.
1 List the factors of these numbers:
a 18 b 25
c 14 d 9
e 16 f 15
g 30 h 42
2 Fill the gaps in these sentences. The first one has been done for you.
1 or _____
a _____ 16 or _____
2 or _____
8 or _____
4 people can share 16 lollies evenly.
b _____ or _____ or _____ or _____ or _____ or _____ people can share 20 slices of pie evenly.
c _____ or _____ or _____ or _____ or _____ or _____ or _____ or _____ people can share 24 cherries.
d _____ or _____ or _____ or _____ or _____ or _____ or _____ or _____ people can share 30 pencils.
e _____ or _____ people can share 5 balls evenly.
3 Use a calculator to help you find as many factors of 384 as you can:
A factor divides into

a number evenly
with no remainder.

F 1 9
SERIES TOPIC
Mental multiplication strategies – factors and multiples
Multiples are the answers we get when we multiply 2 factors.

Think about the 3 times tables where 3 is always a factor.
What are the multiples of 3?
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33 and 36 … 3 × factor = multiple
4 Fill in the gaps on these multiple boards:
a 4 b 5 c 9 d 7
8 10
16
35
63
Numbers can be either factors or multiples depending on where they sit in the number sentence.
5 Choose 2 numbers between 2 and 5 and put them in the first frame as factors. Your answer is the
multiple. Now take that multiple and make it a factor in another number sentence. Write in the other
factor and solve the problem. Then make the answer a factor again. Can you fill the grid? Use a calculator
for the larger problems. The first one has been done for you.
a 3 × 4 = 12 12 × 2 = 24 24 × 2 = 48

b × = × = × =

c × = × = × =

d × = × = × =


SERIES TOPIC
Mental division strategies – use multiplication facts
Knowing our multiplication facts helps us with division as they do the reverse of each other.
They are inverse operations.
3 × 5 = 15 15 ÷ 5 = 3
1 Use your knowledge of multiplication facts to help answer these division questions:
a 56 ÷ 7 8
________ × 7 = 56 56 ÷ 7 =
b 121 ÷ 11 ________ × 11 = 121 121 ÷ 11 =
c 72 ÷ 8 ________ × 8 = 72 72 ÷ 8 =
d 49 ÷ 7 ________ × 7 = 49 49 ÷ 7 =
e 36 ÷ 9 ________ × 9 = 36 36 ÷ 9 =
f 64 ÷ 8 ________ × 8 = 64 64 ÷ 8 =
g 108 ÷ 12 ________ × 12 = 108 108 ÷ 12 =
2 Now try these: Doing maths

without knowing
your multiplication
a 81 ÷ 9 = b 40 ÷ 5 = facts is hard.
Learning them
c 21 ÷ 3 = d 54 ÷ 6 = makes your life
much easier. It’s
e 42 ÷ 7 = f 63 ÷ 9 = worth persevering
to conquer them!
g 36 ÷ 4 = h 45 ÷ 9 =
i 39 ÷ 3 = j 24 ÷ 6 =
3 Fill in the division wheels. Use multiplication facts to help you.
a b c
36 24 81 9 36 16
60 6 54 18 28 40
÷6 ÷9 ÷4
42 48 72 36 44 24
30 18 63 45 32 8

F 2 11
SERIES TOPIC
Mental division strategies – use multiplication facts
Knowing our families of facts is also helpful.

3 × 5 = 15 5 × 3 = 15 15 ÷ 5 = 3 15 ÷ 3 = 5
4 Complete the following patterns. How many more multiplication and division facts can you find, given the
first fact?
a 7 × 8 = 56 b 8 × 9 = 72 c 7 × 9 = 63
8 × 7 = 9 × 8 = 9 × 7 =
56 ÷ = 8 72 ÷ =9 63 ÷ = 9
÷ 8 = 7 ÷ 9 = 8 ÷ 9 = 7
5 Write down another multiplication fact and two division facts for each question.
a 6 × 7 = 42 b 5 × 9 = 45 c 9 × 6 = 54
d 17 × 8 = 136 e 12 × 8 = 96 f 11 × 21 = 231
6 Look at these two division facts: 20 ÷ 5 = 4 and 20 ÷ 4 = 5
Imagine you’re explaining to a younger child how they’re related yet different. How would you do it?
What would you say/write/draw?

SERIES TOPIC
Mental division strategies – divide by 10s, 100s and 1 000s
When we divide by 10 we move the number one place value to the right.
When we divide by 100 we move the number two place values to the right.
When we divide by 1 000 we move the number three place values to the right.
Look what happens to 45 000 when we apply these rules:
Ten Thousands Thousands Hundreds Tens Units

4 5 0 0 0
4 5 0 0 ÷ 10
4 5 0 ÷ 100
4 5 ÷ 1 000
1 Divide the following numbers by 10, 100 and 1 000:
a T Th Th H T U b T Th Th H T U
4 5 0 0 0 4 3 0 0 0
÷ 10 ÷ 10
÷ 100 ÷ 100
÷ 1 000 ÷ 1 000
c T Th Th H T U d T Th Th H T U
8 5 0 0 0 8 8 0 0 0
÷ 10 ÷ 10
÷ 100 ÷ 100
÷ 1 000 ÷ 1 000
2 Draw lines to match the answers with the questions:
a What number is one thousand times smaller than 32 000? 9 500
b What number is one hundred times smaller than 32 000? 88
c What number is one hundred times smaller than 95 000?

950
d What number is ten times smaller than 95 000? 880
e What number is one hundred times smaller than 8 800?

320
f What number is ten times smaller than 8 800? 32

F 2 13
SERIES TOPIC
Mental division strategies – halving strategy
When the two numbers seem too large to work with in our heads, we can halve them till we get to
a division fact we recognise. Both numbers must be even for this to work.
126 ÷ 14
(half 126) ÷ (half 14)
63 ÷ 7 = 9
1 Practise your halving. The first one has been done for you.
a 32 16 b 24 c 50

56 48 500

36
halve
72
halve
1 000
halve
84 144 250

96 192 100

2 Halve each number to get to a recognisable division fact. The first one has been done for you.
a 112 ÷ 14 56
________ 7
÷ ________ = 8
b 144 ÷ 16 ________ ÷ ________ =
c 96 ÷ 12 ________ ÷ ________ =
d 220 ÷ 4 ________ ÷ ________ =
e 162 ÷ 18 ________ ÷ ________ =
3 Match the problems with their halved equivalents. Then solve the problem. The first one has been done
for you.
a 90 ÷ 18 60 ÷ 6 = 5
b 64 ÷ 16 24 ÷ 8 =
c 120 ÷ 12 35 ÷ 7 =
d 70 ÷ 14 45 ÷ 9 =
e 144 ÷ 24 72 ÷ 12 =
f 48 ÷ 16 32 ÷ 8 =

SERIES TOPIC
Mental division strategies – halving strategy
Sometimes we need to keep halving until we reach an easy division fact.

144 ÷ 36 72 ÷ 18 36 ÷ 9 = 4
4 Keep halving until you get to a fact you can work with. If you can do it in your head, just fill in the last
box. Otherwise, use the lines to help you.
a 216 ÷ 36 = ________ ÷ ________ = ________ ÷ ________ =
b 196 ÷ 28 = ________ ÷ ________ = ________ ÷ ________ =
c 224 ÷ 32 = ________ ÷ ________ = ________ ÷ ________ =
d 168 ÷ 24 = ________ ÷ ________ = ________ ÷ ________ =
e 144 ÷ 36 = ________ ÷ ________ = ________ ÷ ________ =
f 288 ÷ 72 = ________ ÷ ________ = ________ ÷ ________ =
5 Draw lines to connect numbers that could be doubled or halved to reach each other.
10 16
48 40
32 25 64
20
60 96
30
128
256 192
120
125 250
50
80
100
6 Work with a partner to solve this problem using halving:

You have an after school job at the local lolly shop, making up the mixed lolly bags. Today, you have to evenly
share 288 freckles among 48 bags. How many freckles will you put in each bag? Show each halved sum.

F 2 15
SERIES TOPIC
Mental division strategies – split strategy
Division problems also become easier if you split the number to be divided into recognisable facts.
Look at the problem 144 ÷ 9 144 ÷ 9
Can we divide 144 into 2 multiples of 9? 90 54

÷ 9 ÷9
We can divide it into 54 and 90. These are both easily
divided by 9. Then we add the two answers together. 10 + 6 = 16
1 Use the split strategy to divide these numbers. Use the clues to guide you:
a 112 ÷ 8 b 85 ÷ 5 c 78 ÷ 6
80
_____ 32
_____ 50
_____ _____ 18
_____ _____
÷ 8 ÷8 ÷ 5 ÷5 ÷ 6 ÷6
_____ + _____ = 7
_____ + _____ = 10 + _____ =
_____
d 64 ÷ 4 e 91 ÷ 7 f 144 ÷ 8
24
_____ _____ 21
_____ _____ 80
_____ 64
_____
÷ 4 ÷4 ÷ 7 ÷7 ÷ 8 ÷8
_____ + _____ = _____ + _____ = _____ + _____ =
2 Now try these:

Hmmm … 91 ÷ 7.
60 ÷ ______
______ 6 The unit digit helps
a 90 ÷ 6 = me here. What
30 ÷ ______
______ 6 multiple of 7 ends
in 1? I know, 21.
So that makes the
70 ÷ ______
______ other number 70!
b 105 ÷ 7 =
______ ÷ ______
______ ÷ ______
c 72 ÷ 4 =
24 ÷ ______
______
______ ÷ ______
d 144 ÷ 8 =
96 ÷ ______
______

SERIES TOPIC
Mental division strategies – split strategy
3 Play this game with a partner. Use one copy of this page between you. Cut out the problems
on the left and stack them face up. Cut out and spread the other cards face up. Work
together (or race) to find two numbers you could divide to solve the problem on the top
card of the pile. One card in the pair will be grey, the other white. For example, if the copy
problem was 76 ÷ 4, you could locate 36 and 40.
96 ÷ 4 45 90
75 ÷ 5 25 21
87 ÷ 3 60 50
98 ÷ 7 80 70
135 ÷ 9 55 36
78 ÷ 6 30 60
112 ÷ 8 60 60
51 ÷ 3 27 32
95 ÷ 5 24 40
84 ÷ 6 28 18
F 2 17
SERIES TOPIC
Mental division strategies – tests of divisibility
Divisibility tests tell us if a number can be divided evenly by another (that is with no remainders).
1 Use the rules to test out the numbers in the last column. The first two have been done for you:
Divisible by Rule Test

Is 458 divisible by 2?
Yes, because it ends in an
A number is divisible by 2 if it’s even
2 even number.
(ends in 0, 2, 4, 6 or 8).
Is 7 281 divisible by 3?
A number is divisible by 3 if the sum of 7 + 2 + 8 + 1 = 18

3
its digits is divisible by 3. Yes, because 18 is divisible by 3.
A number is divisible by 4 if the number

4
made by the last 2 digits is divisible by 4.
Is 455 divisible by 5?
A number is divisible by 5 if there’s

5
a 0 or 5 in the units place.
A number is divisible by 8 if the last

8
3 digits are divisible by 8.
A number is divisible by 9 if the sum of

9
its digits is divisible by 9.
A number is divisible by 10 if there is

10
a zero in the units place.

SERIES TOPIC
Mental division strategies – tests of divisibility
2 These numbers can all be divided with no remainders. Work with a partner to find the rule/s that can be
used to divide them. Fill in the tables.
36 90 84 99 50 72
456 330 888 120 981 548
1 025 3 486 6 993 1 256 9 050 10 072
÷4 ÷5
÷9 ÷3
÷8
Numbers may go onto

more than 1 table!

F 2 19
SERIES TOPIC
Written methods – contracted multiplication
Contracted multiplication is one way to solve a multiplication problem.

First we use our mental strategies to estimate an easier problem:
H T U 3 × 150 = 450. The answer will be around 450.
1 1
1 5 6 We start with the units. 3 × 6 is 18 units. We rename this as 1 ten and 8 units.
× 3 We put 8 in the units column and carry the 1 to the tens column.
3 × 5 plus the carried 1 is 16 tens. We rename this as 1 hundred and 6 tens.
4 6 8
We put 6 in the tens column and carry the 1 to the hundreds column.
3 × 1 plus the carried 1 is 4 hundreds. We put 4 in the hundreds column.
1 Solve these problems using contracted multiplication. Estimate first:
e: e: e:
a H T U b H T U c H T U
3 2 7 2 4 7 1 5 4
× 3 × 4 × 5
e: e: e:
d H T U e H T U f H T U
3 1 5 2 8 6 1 9 4
× 3 × 2 × 5
2 Solve these word problems. Show how you worked them out:
a Dan’s dad has resorted to bribery to counteract

Dan’s PlayStation addiction. For every evening, Dan
spends away from the PlayStation, his dad pays
him $3. So far, Dan has racked up an impressive 27
nights (though he looks like breaking any day now).
How much money does this equate to?
b Dan’s mum thinks she might get in on the action

too and pays Dan $4 for every week that he puts
his dishes in the dishwasher and his dirty clothes
in the basket. Dan is less keen on this plan but
does manage 33 weeks in 1 year. How much has
he made out of this scheme?

SERIES TOPIC
Written methods – contracted multiplication
3 Below are Jess and Harry’s tests. Check them and give them a mark out of 5. If they made mistakes,
give them some feedback as to where they went wrong.
Jess Harry
1 1 1 1
3 8 7 3 8 7
× 2 × 2
7 7 4 7 7 4
1 6
1 1 9 1 1 9
× 7 × 7
7 7 3 8 3 3
2 0 3 2 0 3
× 3 × 3
6 0 9 6 9
1 1 1
4 3 6 4 3 6
× 3 × 3
1 2 0 8 1 3 0 8
4 0 1 4 0 1
× 7 × 7
2 8 0 7 2 8 7

F 3 21
SERIES TOPIC
Written methods – extended multiplication
H T U
2 3 4
× 3 Extended multiplication is another way of solving
problems. In extended multiplication we multiply
1 2 (3 × 4)
the units, tens and hundreds separately then add
9 0 (3 × 30)
the answers together.
6 0 0 (3 × 200)
7 0 2
1 Use a calculator to help you work out the values you could expect when
2 × 2 would give
multiplying the following. Tick the columns: me a unit only. But
8 × 6 would give me
T TH TH H T U tens and units. I’ll
tick both columns.
a a unit by a unit 9 × 7
b a ten by a unit 43 × 5
c a hundred by a unit 126 × 7
d a ten by a ten 13 × 72
e a ten by a hundred 55 × 120
2 Complete using extended multiplication. Estimate first:
e: e: e:
a 2 4 5 b 4 5 2 c 3 2 7
× 2 × 7 × 8
(2 × 5) (7 × 2) (8 × 7)
(2 × 40) (7 × 50) (8 × 20)
(2 × 200) (7 × 400) (8 × 300)
e: e:
d 2 7 9 e 4 1 2
× 2 × 9
(2 × _____) (9 × _____)
(2 × _____) (9 × _____)
(2 × _____) (9 × _____)

SERIES TOPIC
Written methods – extended multiplication
3 Use extended multiplication to solve these problems:
a Jack and his 2 friends bought tickets to the b Jack has a paper round and earns $7 per day. He
World Cup. Each ticket costs $124. How much works for 18 days and saves it all. Has he earned
did they spend altogether? enough to pay for his World Cup ticket?
e: e:
c Yusuf’s highest Level 1 Live Mathletics score is d Kyra’s class of 24 all had to stay in for 11 minutes
112. Yep, he’s fast. If he scores this 7 times in a of their recess. Something to do with too much
row, how many correct answers has he achieved? talking. How many minutes is this in total?
e: e:
4 Once you have the hang of extended multiplication, you can apply it to larger numbers. Try these:
a 2 4 5 b 3 2 9 c 2 3 8
× 3 2 × 4 3 × 5 2
(2 × 5) (3 × 9) (2 × 8)
(2 × 40) (3 × 20) (2 × 30)
(2 × 200) (3 × 300) (2 × 200)
(30 × 5) (40 × 9) (50 × 8)
(30 × 40) (40 × 20) (50 × 30)
(30 × 200) (40 × 300) (50 × 200)

F 3 23
SERIES TOPIC
Written methods – short division
In short division, we use our knowledge of multiplication to help us. We can split 936 into 900 + 30 + 6.
900 divided by 3 is 300, so we put a 3 in the hundreds place.
3 1 2
30 divided by 3 is 10, so we put a 1 in the tens place.
3 9 3 6 6 divided by 3 is 2, so we put a 2 in the units place. 936 ÷ 3 = 312
1 Divide these numbers:
a b c
4 8 4 5 5 5 3 9 3
d e f
9 9 9 0 4 4 8 4 6 6 6 6
g h i
3 9 9 9 2 4 6 2 3 6 9 3
In these problems, if there

Sometimes it’s easier to split the numbers differently. We can also are no tens in a number we
split 936 into 900 + 36. put a 0 in to show this and
also to hold the place of
900 divided by 3 is 300 so we put a 3 in the
the other numbers!
3 1 2 hundreds place
36 divided by 3 is 12. We put the 1 in the tens
3 9 3 6
place and the 2 in the units place.
936 ÷ 3 = 312
2 Decide how you’ll split these numbers and then divide. Remember
to put in zeros as needed.
a b
5 5 1 5 3 6 6 9
c d e
9 9 2 7 4 8 0 4 4 8 1 2

SERIES TOPIC
Written methods – short division with remainders
Sometimes numbers don’t divide evenly. The amount left over is called the remainder.
Look at 527 divided by 5.
500 divided by 5 is 100.
1 0 5 r2
27 divided by 5 is 5 with 2 left over (this is the remainder).
5 5 2 7
This can be written as r 2.
527 ÷ 5 = 105 r 2.
1 Divide these 2 digit numbers. Each problem will have a remainder.
a r b r c r
9 7 5 4 4 7 6 3 8
d r e r f r
5 6 3 4 4 9 6 6 2
2 Divide these 3 digit numbers. Each problem will have a remainder.
a r b r c r
5 5 5 7 3 6 6 1 4 4 8 1
d r e r f r
9 9 9 4 4 8 4 5 6 6 3 8
3 Solve these problems:

a Giovanni’s Nonna has given him a bag of gold coins to share among him and his two sisters.
There are 47 gold coins altogether. How many does each child get if they’re shared evenly?
How would you suggest they deal with the remainder?
___________________________________________________________________________
b You have 59 jubes to add to party bags. Each bag gets 5 jubes. How many full party bags
can you make?

F 3 25
SERIES TOPIC
Written methods – short division with remainders
There are 3 ways of expressing remainders. How we do it depends 1 0 5 r2

on how we’d deal with the problem in the real world. Look at: 5 5 2 7
4 One way is to write r 2 as in the example above. We use this when we don’t care about being absolutely
precise and when the remainder can’t be easily broken up. An example would be sharing 527 jelly beans
among 5 people. Solve these problems expressing the remainders as r.
a Share 126 blue pencils among 4 people. b Share 215 paper clips among 7 people.
5 We can also express a remainder as a fraction. We do this when we can 1

6 3
easily share the remainder. For example, 19 cakes shared among 3 people
is 6 and one third each. Solve these problems expressing the remainder 3 1 9
as a fraction:
a Share 13 pizzas among 4 people. b

Share 50 sandwiches among
3 people.
6 We express remainders as decimals when we must be absolutely precise. 27 divided by 2 is 13.

Sharing dollar amounts is a good example of this. We add the cents after Now we have one dollar
the decimal point to help us. Try these: left. How how many cents
is half of one dollar?
a Share 12 dollars among 4 people. b
Share 27 dollars between
2 people.
4 1 2 0 0 2 2 7 0 0

SERIES TOPIC
Written methods – solving problems
We regularly come across multiplication and division problems in our everyday life. It doesn’t
matter which strategy we use to solve them, we can choose the one that suits us or the problem best.
1 One real-life problem is comparing prices to find the best deal. It’s easy if the prices and amounts are the
same but what if the amounts are different? Use a strategy to help you find the best deal on these:
a b
100 g 300 g
$1.95 $5.43 $3.95 $8.50
Best deal is __________________________ Best deal is __________________________
c d
10 pack CD Single CD
500 ml 2 litres
$22.90 $2.75 $1.40 $2.80
Best deal is __________________________ Best deal is __________________________
2 You go to the service station with your weekly pocket money of $5. When you take a $1.75 chocolate bar
to the counter, they offer you the special of 3 bars for $4.50. Which is a better deal? Show why.

F 3 27
SERIES TOPIC
Written methods – solving problems
3 You’re planning a trip to the Wet and Wild theme park and
there are many ticket options. Use a strategy of your choice
and the price list below to answer the following questions:
Entry Extras
1-day pass $32 5-minute helicopter ride $42
2-day pass $48 10-minute helicopter ride $74
Annual pass $99 30-minute helicopter ride $209
Individual rides $12 Sunset cruise $12
10-ride pass $95 Lunch cruise $22
Order online $5 discount Swim with the dolphins $75
a If you buy a 2-day pass, what is the cost per day?
b How much cheaper is this option than buying two 1-day passes?
c If you bought an annual pass, how many times would you need to visit to make it
a better option than buying either a 1-day or 2-day pass?
d What if you choose just the rides? How much would you save if you bought the
10-ride pass instead of the individual rides?
e If you took a 5-minute helicopter ride, what would be the cost per minute?
f What about if you chose the 10-minute flight option? What would be the cost per minute?
g Plan a day’s itinerary for you and a partner. How much will this cost?

SERIES TOPIC
Crack the code apply
What
to do Use the code below to work out the hidden message.
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __
2 1 3 6 4 5 3 8 7 9 8 9 10 12 11
Once I work out the first

A × A = A A is ______ F = H + L F = ______
couple, the rest come easily!
M × M = M + M M is ______ E = F ÷ 2 E = ______
T – M = A T is ______ 2 × L = I I = ______
T + T = H H is ______ (2 × L) – A = C C = ______
H – M = L L is ______ F + A = N N = ______
3 × L = U U is ______ 3 × T = S S = ______
What
to do Try this one:
__ __ __ __ __ __ __ __ __ __ __ __ __
2 9 4 12 13 8 2 7 4 9 2 12 3
__ __ __ __ __ __ __ __ __ __ __ __ __
4 2 6 6 3 12 0 8 9 1 2 5 3
A × A = A + A A is ______ L + E = S S is ______
A + A = T T is ______ N – N = I I is ______
If two letters
are together, T × 2 = N N is ______ U – A = C C is ______
we read
them as a AT ÷ N = E E is ______ S – (2 × T) = P P is ______
tens digit and
a units digit. 2 × E = L L is ______ 2 × U – P = O O is ______
E + T = U U is ______ S + E = R R is ______

F 4 29
SERIES TOPIC
Smart buttons apply
Getting In this activity, you’ll use your knowledge of multiplication, division, subtraction and
ready
addition to find as many number statements you can to create one number.
What Using ONLY the number 2, +, ×, – and ÷ keys on your calculator,

to do find as many ways as you can to create the number 13.
For example, you could make:
22 + 2 + 2 = 26 ÷ 2 = 13
Record your statements on a piece of paper.
Now, compare your answers with a partner’s. How many did they find?
Can you supplement each other’s lists?
What’s the longest statement? What’s the shortest?
Choose another number to make and see how many statements you can find or
What challenge a partner to a competition. Set a time limit and see who can find the most
to do
ways to make 15 within the time span.
Bugs investigate
Getting
ready Use your knowledge of multiples to help you work out how many boy bugs and
girl bugs there are in the problem below. Listing all the multiples is a strategy that
would help.
What Girl bugs have 4 splodges on their backs, boy bugs have 9.
to do
Altogether there are 48 splodges. Work out how many girl
bugs and how many boy bugs there are.
What to
do next What if girl bugs have 8 splodges and boy bugs have 6 and there are 120 splodges
altogether? How many different answers can you find?

SERIES TOPIC
Puzzles apply
What Use your knowledge of multiplication to work out the missing values:
to do
a 2 8 b 7 c 7
× 3 × 4 × 5
8 2 8 8 2 3 5
d 8 e 6 8 f 2 3
× 9 × ×
7 2 9 2 0 4 6 5 8 4
g 2 6 1 h 4 2 i 5 6
× × 3 × 2 7
4 4 1 2 6 3 9 2
6 8 0
What
to do
Fill in the multiplication and division tables by × 3
working out the missing digits. The arrows show
you some good starting places. 4 32
14
45 27
× 7 6 × 8 9
12 24
20 16 14 12 24
5 40 3 12 × 9
36 14 6
3 30 54 11 33 44
63
8 64

F 4 31
SERIES TOPIC
Puzzles apply
What Complete this crossnumber puzzle:

to do
1 2 Across Down
1 60 ÷ 5 1 11 × 11
3
2 25 × 5 2 12 × 10
4 5
3 7 × 6 3 7 × 7
6 7 4 15 × 6 5 66 ÷ 6
8
7 7 × 3 6 12 × 12
9 9 × 6 8 39 ÷ 3
9 10
10 6 × 50
What
to do Test your speed and accuracy. Race against a partner or the clock to complete each table:
÷8 ÷3 ÷7
56 9 21
16 6 7
64 18 14
80 12 70
32 24 49
72 30 28
24 27 42
8 33 35
Time: Time: Time:
If the decimals are confusing

What me, I can change the amounts
to do Use the “guess, check and improve” strategy to to 310 cents and 295 cents.
solve this problem. You could use a calculator
to help if you wish.
Tracey paid $3.10 for 7 lolly snakes and 4 sherbets. Madison
paid $2.95 for 4 lolly snakes and 7 sherbets. How much does
one lolly snake cost? How much does one sherbet cost?

SERIES TOPIC

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Published 3P Learning Ltd

Designed 3P Learning Ltd

• multiply by 10s, 100s and 1 000s__________________________ / /

• factors and multiples____________________________________ / /

Topic 2 – Mental division strategies (pp. 11–19)

• divide by 10s, 100s and 1 000s____________________________ / /

Topic 3 – Written methods (pp. 20–28)

• short division with remainders____________________________ / /

Topic 4 – Puzzles and investigations (pp. 29–32)

• smart buttons – apply___________________________________ / /

Doubling is a useful strategy to use when multiplying.

1 Warm up with some doubling practice:

2 Finish the doubling patterns:

b 3 __________ ___________ __________ ___________ 96

Multiplication and Division

6 Use the doubling strategy to solve these:

b 14 × 8 _____________ ____________ 112

c 25 × 8 _____________ ____________ ____________

e 13 × 8 _____________ ____________ ____________

Method 1: $24 a week for 5 weeks.

2 F 1 Multiplication and Division

Ten Thousands Thousands Hundreds Tens Units

1 Multiply the following numbers by 10, 100 and 1 000:

Multiplication and Division

4 Use patterns to help you solve these:

a 5 × 2 _____________ 5 × 20 _____________ 5 × 200 ___________

b 2 × 9 _____________ 2 × 90 _____________ 2 × 900 ___________

c 6 × $4 _____________ 6 × $40 _____________ 6 × $400 ___________

d 8 × 3 _____________ 8 × 30 _____________ 8 × 300 ___________

e 3 × $7 _____________ 3 × $70 _____________ 3 × $700 ___________

f 2 × 8 _____________ 20 × 8 _____________ 200 × 8 ___________

g 3 × 9 _____________ 30 × 9 _____________ 300 × 9 ___________

5 Answer these problems: If you’re struggling with

6 Finish these counting patterns:

4 F 1 Multiplication and Division

1 Use the split strategy to answer the questions:

(40 × 4) + (6 × 4) (___ × ___) + (___ × ___) (___ × ___) + (___ × ___)

_______ + _______ _______ + _______ _______ + _______

_______ + _______ _______ + _______ _______ + _______

a 48 × 8 = __________ + __________ = It's a good thing I

Multiplication and Division

(30 × 9) + (3 × 9) (10 × 6) + (3 × 6) (10 × 9) + (6 × 9)

6 F 1 Multiplication and Division

When multiplying we can round to an easier number and then adjust.

b 8 × 29 = ________ × ________ – ________ =

c 18 × 6 = ________ × ________ – ________ =

d 7 × 39 = ________ × ________ – ________ =

e 28 × 5 = ________ × ________ – ________ =

We can also adjust up. Look how we do this with 6 × 62:

Would I use the compensation

c 22 × 9 = ________ × ________ + ________ =

d 32 × 9 = ________ × ________ + ________ =

e 7 × 62 = ________ × ________ + ________ =

Multiplication and Division

a Check each other’s calculations. You may want to use a calculator.

8 F 1 Multiplication and Division

Factors are the numbers we multiply together to get to another number:

How many factors does the number 12 have? 4 × 3 = 12, 6 × 2 = 12, 1 × 12 = 12

b 3 ____ _ _____ 96

b 14 × 8 _ 112

c 25 × 8 _

e 13 × 8 _

a 5 × 2 _______ 5 × 20 _ 5 × 200 _____

b 2 × 9 _______ 2 × 90 _ 2 × 900 _____

c 6 × $4 _______ 6 × $40 _ 6 × $400 _____

d 8 × 3 _______ 8 × 30 _ 8 × 300 _____

e 3 × $7 _______ 3 × $70 _ 3 × $700 _____

f 2 × 8 _______ 20 × 8 _ 200 × 8 _____

g 3 × 9 _______ 30 × 9 _ 300 × 9 _____

(40 × 4) + (6 × 4) (_ × _) + (_ × _) (_ × _) + (_ × _)

___ + _ _ + _ _ + ___

___ + _ _ + _ _ + ___

a 48 × 8 = + = It's a good thing I

b 8 × 29 = × – =

c 18 × 6 = × – =

d 7 × 39 = × – =

e 28 × 5 = × – =

c 22 × 9 = × + =

d 32 × 9 = × + =

e 7 × 62 = × + =

e _ or _ people can share 5 balls evenly.

b 144 ÷ 16 ÷ =

d 220 ÷ 4 ÷ =

e 162 ÷ 18 ÷ =

a 216 ÷ 36 = ÷ = ÷ =

b 196 ÷ 28 = ÷ = ÷ =

c 224 ÷ 32 = ÷ = ÷ =

d 168 ÷ 24 = ÷ = ÷ =

e 144 ÷ 36 = ÷ = ÷ =

f 288 ÷ 72 = ÷ = ÷ =

___ + _ = _ + _ = _ + ___ =

a Dan’s dad has resorted to bribery to counteract

b Dan’s mum thinks she might get in on the action