F
Teacher
Student Book
SERIES
Name _____________________________________
Multiplication and Division
Series F – Multiplication and Division
Contents
Topic 1 –1 Mental
Section
– Answers
multiplication
(pp. 1–32) strategies (pp. 1–10)
Date completed
• mental
doublingmultiplication
strategy_______________________________________
strategies__________________________ 1 /
/
• mental
100s and 1 000s__________________________
11 /
multiplydivision
by 10s,strategies______________________________
/
• split
written
strategy__________________________________________
methods_____________________________________ 20 /
/
• compensation
puzzles and investigations______________________________
strategy__________________________________
29 /
/
• factors and multiples____________________________________
/
/
• multiplication
facts___________________________________
33 /
use multiplication
facts__________________________________
/
• mental
multiplication
strategies_________________________
37 /
divide by
10s, 100s and
1 000s____________________________
/
• halving
strategies______________________________ 41 /
mental division
strategy________________________________________
/
methods_____________________________________ 43 /
written
• split
strategy__________________________________________
/
• tests of divisibility______________________________________
/
/
• contracted multiplication________________________________
/
/
• extended multiplication__________________________________
/
/
• short division__________________________________________
/
/
• short division with remainders____________________________
/
/
• solving problems_______________________________________
/
/
• crack the code – apply___________________________________
/
/
• smart buttons – apply___________________________________
/
/
• bugs – investigate______________________________________
/
/
• puzzles – apply_________________________________________
/
/
Section
– Assessment
answers
(pp.
33–44)
Topic 2 –2 Mental
divisionwith
strategies
(pp.
11–19)
Section
– Outcomes
(pp. 45–46)
Topic 3 –3 Written
methods
(pp. 20–28)
Topic 4 – Puzzles and investigations (pp. 29–32)
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 once = 30
13 × 8 double once = 26
double twice = 60 double twice = 52
double three times = 104
1
Warm up with some doubling practice:
a
b
2
6
10
1
3
2
3
40
20
4
6
D
5
4
2
c
8
12
9
7
18
30
50
14
10 20
15
25
30
D
70
60
18
40
35 50
24
12
80
192
100
6
9
96
12
24
D
8
32 16
48
16
32
64
Finish the doubling patterns:
a4
8
__________
16
___________
32
__________
64
___________
128
__________
b3
6
__________
12
___________
24
__________
48
___________
96
__________
c 5
10
__________
20
___________
40
__________
80
___________
160
__________
d 25
50
__________
100
___________
200
__________
400
___________
800
__________
e7
14
__________
28
___________
56
__________
112
___________
224
__________
f 75
150
__________
300
___________
600
__________
1 200
___________
2 400
__________
Choose a number and create your own doubling pattern. How high can you go? What patterns can you
see within your pattern?
Answers will vary.
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?
4 × 12 = 48
Multiplication and Division
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SERIES
TOPIC
1
Mental multiplication strategies – doubling strategy
5
6
7
8
Use the doubling strategy to solve these:
To multiply by 4, double
twice. To multiply by 8,
double three times.
×2
×4
a13 × 4
26
___________
52
___________
b 16 × 4
32
___________
64
___________
c24 × 4
48
___________
96
___________
d 25 × 4
50
___________
100
___________
e32 × 4
64
___________
128
___________
f21 × 4
42
___________
84
___________
g 35 × 4
70
___________
140
___________
Use the doubling strategy to solve these:
×2
×4
×8
a 12 × 8
24
_____________
48
____________
96
____________
b 14 × 8
28
_____________
56
____________
112
____________
c 25 × 8
50
_____________
100
____________
200
____________
d 21 × 8
42
_____________
84
____________
168
____________
e 13 × 8
26
_____________
52
____________
104
____________
f 16 × 8
32
_____________
64
____________
128
____________
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 =
72
b 16 × 4 =
64
c 26 × 4 =
104
d 24 × 8 =
192
e 15 × 8 =
120
f 22 × 8 =
176
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
SERIES
TOPIC
Method 1 = $120
24 x 5 = 120
Method 2 = $248
8 + 16 + 32 + 64 + 128 = 248
Multiplication and Division
Copyright © 3P Learning
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
c
T Th
4
5
0
4
5
0
0
5
0
0
0
T
U
1
7
1
7
0
× 10
1
7
0
0
× 100
1
7
0
0
0
× 1 000
T Th
Th
H
T
U
8
5
8
5
0
× 10
8
5
0
0
× 100
5
0
0
0
× 1 000
8
Th
× 10
× 100
× 1 000
H
b
d
T Th
T
U
4
3
4
3
0
× 10
4
3
0
0
× 100
4
3
0
0
0
× 1 000
T Th
Th
H
T
U
9
9
9
9
0
× 10
9
9
0
0
× 100
9
0
0
0
× 1 000
9
Th
H
Try these:
a 14 × 10
=
140
b 14 × 100 =
1 400
c 14 × 1 000=
14 000
d 92 × 10
=
920
e 92 × 1 000=
92 000
f 92 × 100 =
9 200
11 000
h 11 × 100 =
1 100
g 11 × 1 000=
3
Units
Multiply the following numbers by 10, 100 and 1 000:
a
2
Tens
4
5
4
1
Hundreds
i 11 × 10
=
110
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.
Answers will vary.
Multiplication and Division
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F
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SERIES
TOPIC
3
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
We can express this as 4 × 2 × 10 = 80
4
5
4 × 20 = 80
How would you work out 4 × 200?
Use patterns to help you solve these:
10
a 5 × 2 _____________
5 × 20
100
_____________
5 × 200
1000
___________
18
b 2 × 9 _____________
2 × 90
180
_____________
2 × 900
1800
___________
$24
c 6 × $4 _____________
$240
6 × $40 _____________
24
d 8 × 3 _____________
8 × 30
$21
e 3 × $7 _____________
$210
3 × $70 _____________
16
f 2 × 8 _____________
20 × 8
160
_____________
200 × 8
1 600
___________
27
g 3 × 9 _____________
30 × 9
270
_____________
300 × 9
2 700
___________
240
_____________
$2 400
6 × $400 ___________
8 × 300
2 400
___________
$2 100
3 × $700 ___________
Answer these problems:
a Jock runs 50 km per week. How far does he run over 10 weeks?
500 km
If you’re struggling with
your tables, get onto Live
Mathletics and practise!
bHuy earns $20 pocket money per week. If he saves half of this, how much
will he have saved at the end of 8 weeks?
$80
cThe sum of two numbers is 28. When you multiply them together, the
answer is 160. What are the numbers?
20, 8
6
4
Finish these counting patterns:
a 10
20
30
__________
40
__________
50
___________
60
__________
b 20
40
60
__________
80
__________
100
___________
120
__________
c 30
60
90
__________
120
__________
150
___________
180
__________
d 40
80
120
__________
160
__________
200
___________
240
__________
e 50
100
150
__________
200
__________
250
___________
300
__________
f 100
200
300
__________
400
__________
500
___________
600
__________
g 200
400
600
__________
800
__________
1 000
___________
1 200
__________
F
1
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
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
(40 × 4) + (6 × 4)
5
4 × ___)
5 + (___
70 × ___)
(___
4
8 × ___)
4 + (___
40 × ___)
(___
24
160 + _______
_______
20
350 + _______
_______
160 + _______
32
_______
=
=
=
184
d 37 × 7
2
3
c 48 × 4
370
e 62 × 8
192
f 91 × 5
7
7 × ___)
7 + (___
30 × ___)
(___
8
2 × ___)
60 × ___)
8 + (___
(___
5
1 × ___)
5 + (___
90 × ___)
(___
49
210 + _______
_______
480 + _______
16
_______
450 + _______
5
_______
=
=
=
259
496
455
Use the split strategy to answer the questions. This time see if you can do the brackets in your head:
64
320
+ __________
=
a 48 × 8 = __________
384
14
350
b 52 × 7 = __________
+ __________
=
364
360
27
c 9 × 43 = __________
+ __________
=
387
160
72
d 8 × 29 = __________
+ __________
=
232
42
560
e 86 × 7 = __________
+ __________
=
602
It's a good thing I
know how to work
with multiples of
ten in my head!
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
=
Multiplication and Division
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45
F
1
SERIES
TOPIC
5
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)
13 × 6
464
(40 × 7) + (2 × 7)
42 × 7
(10 × 9) + (6 × 9)
33 × 9
294
16 × 9
51
400 + 64
58 × 8
30 + 21
17 × 3
START
The middle path is correct.
6
F
1
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
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
3
3
× ________
– ________
=
a 19 × 3 = ________
57
8
30
8
b 8 × 29 = ________
× ________
– ________
=
232
20
6
12
c 18 × 6 = ________
× ________
– ________
=
108
7
40
7
d 7 × 39 = ________
× ________
– ________
=
273
10
30
5
e 28 × 5 = ________
× ________
– ________
=
140
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.
40
3
3
a 41 × 3 = ________
× ________
+ ________
=
123
80
4
4
b 81 × 4 = ________
× ________
+ ________
=
324
20
9
18
c 22 × 9 = ________
× ________
+ ________
=
198
30
9
18
d 32 × 9 = ________
× ________
+ ________
=
288
7
60
14
e 7 × 62 = ________
× ________
+ ________
=
434
Multiplication and Division
Copyright © 3P Learning
Would I use the compensation
strategy with numbers such as
56 or 84? Why or why not?
F
1
SERIES
TOPIC
7
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.
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.
bNow, use the calculator to add your answers. The person with the highest score wins.
8
F
1
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
copy
Check
individual
answers.
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
2
List the factors of these numbers:
a 18
1
18
2
9
c 14
1
14
2
7
e 16
1
16
2
8
4
g 30
1
30
2
15
3
3
6
10
5
6
b 25
1
25
5
d
9
1
9
3
f 15
1
15
5
3
h 42
1
42
2
21
3
14
6
7
Fill the gaps in these sentences. The first one has been done for you.
1 or _____
16 or _____
2 or _____
8 or _____
4 people can share 16 lollies evenly.
a _____
1 or _____
20 or _____
2 or _____
10 or _____
4 or _____
5 people can share 20 slices of pie evenly.
b _____
1 or _____
24 or _____
2 or _____
12 or _____
3 or _____
8 or _____
4 or _____
6 people can share 24 cherries.
c _____
1 or _____
30 or _____
2 or _____
15 or _____
3 or _____
10 or _____
5 or _____
6 people can share 30 pencils.
d _____
1 or _____
5 people can share 5 balls evenly.
e _____
3
Use a calculator to help you find as many factors of 384 as you can:
1, 384
8, 48
2, 192
12, 32
3, 128
16, 24
A factor divides into
a number evenly
with no remainder.
4, 96
6, 64
Multiplication and Division
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F
1
SERIES
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9
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
×
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33 and 36 …
4
factor
multiple
=
Fill in the gaps on these multiple boards:
4
a
5
b
9
c
7
d
8
10
18
14
12
15
27
21
16
20
36
28
20
25
45
35
24
30
54
42
28
35
63
49
Numbers can be either factors or multiples depending on where they sit in the number sentence.
5
10
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
b
2
×
5
=
10
c
4
×
2
=
8
d
5
×
4
=
20
F
1
SERIES
TOPIC
12
×
2
=
24
10
×
5
=
50
8
×
3
=
24
20
×
4
=
80
Multiplication and Division
Copyright © 3P Learning
24
×
2
=
50
×
5
= 250
24
×
3
=
80
×
4
= 320
48
72
Sample
answers
– answers
will vary.
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
2
3
Use your knowledge of multiplication facts to help answer these division questions:
a 56 ÷ 7
8
________
× 7 = 56
56 ÷ 7
b 121 ÷ 11 11 × 11 = 121
________
121 ÷ 11 =
c 72 ÷ 8 9
________
× 8 = 72
72 ÷ 8
=
9
d 49 ÷ 7 7
________
× 7 = 49
49 ÷ 7
=
7
e 36 ÷ 9 4
________
× 9 = 36
36 ÷ 9
=
4
f 64 ÷ 8
8
________
× 8 = 64
64 ÷ 8
=
8
g 108 ÷ 12
9
________
× 12 = 108
108 ÷ 12 =
9
8
=
11
Now try these:
a 81 ÷ 9 =
9
b 40 ÷ 5 =
8
c 21 ÷ 3 =
7
d 54 ÷ 6 =
9
e 42 ÷ 7 =
6
f 63 ÷ 9 =
7
g 36 ÷ 4 =
9
h 45 ÷ 9 =
5
i 39 ÷ 3 =
13
j 24 ÷ 6 =
4
Doing maths
without knowing
your multiplication
facts is hard.
Learning them
makes your life
much easier. It’s
worth persevering
to conquer them!
Fill in the division wheels. Use multiplication facts to help you.
a
b
6
10
7
36
60
42
24
÷6
6
48
30 18
5
c
4
3
9
1
8
6
8
1
81
54
72
9
÷9
18
36
63 45
7
9
2
4
5
Multiplication and Division
Copyright © 3P Learning
7
11
4
36 16
28
44
40
÷4
32
8
10
24
8
6
2
F
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11
Mental division strategies – use multiplication facts
Knowing our families of facts is also helpful.
3 × 5 = 15
5 × 3 = 15
4
a
7 × 8 = 56
b
8 × 9 = 72
c
7 × 9 = 63
8 × 7 =
9 × 8 =
9 × 7 =
7
56
56
= 8
÷ 8 = 7
72 ÷
72
8
72
=9
63 ÷
÷ 9 = 8
63
7
63
= 9
÷ 9 = 7
Write down another multiplication fact and two division facts for each question.
a 6 × 7 = 42
7x6
= 42
b 5 × 9 = 45
c 9 × 6 = 54
6 x 9 = 54
9 x 5 = 45
42 ÷ 6 = 7
45 ÷ 9 = 5
54 ÷ 6 = 9
42 ÷ 7 = 6
45 ÷ 5 = 9
54 ÷ 9 = 6
d 17 × 8 = 136
8 x 17 = 136
136 ÷ 8 = 17
136 ÷ 17 = 8
6
15 ÷ 3 = 5
Complete the following patterns. How many more multiplication and division facts can you find, given the
first fact?
56 ÷
5
15 ÷ 5 = 3
Look at these two division facts:
f 11 × 21 = 231
e 12 × 8 = 96
21 x 11 = 231
8 x 12 = 96
231 ÷ 21 = 11
96 ÷ 8 = 12
231 ÷ 11 = 21
96 ÷ 12 = 8
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?
20 ÷ 5 = 4
20 ÷ 4 = 5
Sample answer.
12
F
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TOPIC
Multiplication and Division
Copyright © 3P Learning
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:
1
Thousands
Hundreds
Tens
Units
4
5
4
0
5
4
0
0
5
4
0
0
0
5
÷ 10
÷ 100
÷ 1 000
Divide the following numbers by 10, 100 and 1 000:
a
c
2
Ten Thousands
T Th
Th
H
T
U
4
5
0
0
0
4
5
0
0
÷ 10
4
5
0
÷ 100
4
5
÷ 1 000
b
d
T Th
Th
H
T
U
8
5
0
0
0
8
5
0
0
÷ 10
8
5
0
÷ 100
8
5
÷ 1 000
T Th
Th
H
T
U
4
3
0
0
0
4
3
0
0
÷ 10
4
3
0
÷ 100
4
3
÷ 1 000
T Th
Th
H
T
U
8
8
0
0
0
8
8
0
0
÷ 10
8
8
0
÷ 100
8
8
÷ 1 000
Draw lines to match the answers with the questions:
a
What number is one thousand times smaller than 32 000?
b
What number is one hundred times smaller than 32 000?
c
What number is one hundred times smaller than 95 000?
d
What number is ten times smaller than 95 000?
e
What number is one hundred times smaller than 8 800?
f
What number is ten times smaller than 8 800?
Multiplication and Division
Copyright © 3P Learning
9 500
88
950
880
320
32
F
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TOPIC
13
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
56
36
84
96
2
3
14
32
16
28
halve
18
42
48
b
24
48
72
144
192
12
24
halve
36
72
96
c
50
500
1 000
250
100
25
250
halve
500
125
50
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
8
72
________
÷ ________
=
9
c 96 ÷ 12
48
6
________
÷ ________
=
8
d 220 ÷ 4
110
2
________
÷ ________
=
55
e 162 ÷ 18
81
9
________
÷ ________
=
9
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
=
4
c 120 ÷ 12
35 ÷ 7
=
10
d 70 ÷ 14
45 ÷ 9
=
5
e 144 ÷ 24
72 ÷ 12
=
6
f 48 ÷ 16
32 ÷ 8
=
3
F
2
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
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
5
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.
108
18
54
9
a 216 ÷ 36 = ________
÷ ________
= ________
÷ ________
=
6
14
49
7
98
b 196 ÷ 28 = ________
÷ ________
= ________
÷ ________
=
7
112
16
56
8
c224 ÷ 32 = ________
÷ ________
= ________
÷ ________
=
7
84
12
42
6
d 168 ÷ 24 = ________
÷ ________
= ________
÷ ________
=
7
72
18
36
9
e144 ÷ 36 = ________
÷ ________
= ________
÷ ________
=
4
144
36
72
18
f 288 ÷ 72 = ________
÷ ________
= ________
÷ ________
=
4
Draw lines to connect numbers that could be doubled or halved to reach each other.
16
10
48
25
32
20
40
64
96
60
30
128
256
125
192
250
80
100
6
120
50
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.
288 ÷ 48
144 ÷ 24
72 ÷ 12
36 ÷ 6 = 6
Multiplication and Division
Copyright © 3P Learning
F
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15
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
Can we divide 144 into 2 multiples of 9?
We can divide it into 54 and 90. These are both easily
divided by 9. Then we add the two answers together.
1
90
54
÷ 9
÷9
10 + 6 = 16
Use the split strategy to divide these numbers. Use the clues to guide you:
a
112 ÷ 8
b
85 ÷ 5
c
50
35
_____
_____
18
60
_____
_____
÷ 8
÷8
10 + _____
4
_____
=
d
14
64 ÷ 4
÷ 5
÷5
7
10 + _____
_____
=
e
17
91 ÷ 7
÷ 6
÷6
10 + _____
3
_____
=
f
21
70
_____
_____
80
64
_____
_____
÷ 4
÷4
6
10 =
_____
+ _____
16
÷ 7
÷7
3 + _____
10 =
_____
13
÷ 8
60 ÷ ______
6
______
=
15
=
15
=
18
8
48 ÷ ______
______
d 144 ÷ 8=
96 ÷ ______
8
______
18
b 105 ÷ 7
30 ÷ ______
6
______
7
70 ÷ ______
______
Hmmm … 91 ÷ 7.
The unit digit helps
me here. What
multiple of 7 ends
in 1? I know, 21.
So that makes the
other number 70!
7
35 ÷ ______
______
c 72 ÷ 4
48 ÷ ______
4
______
24 ÷ ______
4
______
F
2
SERIES
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Multiplication and Division
Copyright © 3P Learning
÷8
10 + _____
8
_____
=
Now try these:
a 90 ÷ 6
13
144 ÷ 8
24
40
_____
_____
16
78 ÷ 6
80
32
_____
_____
2
144 ÷ 9
18
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
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
Multiplication and Division
Copyright © 3P Learning
copy
F
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TOPIC
17
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?
2
A number is divisible by 2 if it’s even
(ends in 0, 2, 4, 6 or 8).
Yes, because it ends in an
even number.
Is 7 281 divisible by 3?
3
A number is divisible by 3 if the sum of
its digits is divisible by 3.
7 + 2 + 8 + 1 = 18
Yes, because 18 is divisible by 3.
Is 3 912 divisible by 4?
4
A number is divisible by 4 if the number
made by the last 2 digits is divisible by 4.
Yes, because 12 is divisible by 4.
Is 455 divisible by 5?
5
A number is divisible by 5 if there’s
a 0 or 5 in the units place.
Yes, because 5 is in the units
place.
Is 74 160 divisible by 8?
8
A number is divisible by 8 if the last
3 digits are divisible by 8.
Yes, because 160 ÷ 8 = 20
Is 6 345 divisible by 9?
9
A number is divisible by 9 if the sum of
its digits is divisible by 9.
6 + 3 + 4 + 5 = 18
Yes, because the digits add to 18
and that is divisible by 9.
18 ÷ 9 = 2
Is 5 680 divisible by 10?
10
18
F
2
SERIES
TOPIC
A number is divisible by 10 if there is
a zero in the units place.
Yes, because there is a zero in
the units place.
Multiplication and Division
Copyright © 3P Learning
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
36
456
888
120
÷5
÷9
36
90
99
50
36
120
90
330
72
1 025
548
981
9 050
1 256
72
90
10 072
6 993
330
981
3 486
6 993
÷8
72
84
÷3
Numbers may go onto
more than 1 table!
456
456
888
120
120
99
1 256
84
10 072
888
72
Multiplication and Division
Copyright © 3P Learning
F
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Written methods – contracted multiplication
H
1
1
1
T
U
5
6
×
3
4
1
6
8
Solve these problems using contracted multiplication. Estimate first:
e:
a
H
2
T
U
2
7
×
e:
8
H
3
1
U
1
5
4
5
2
U
4
7
9
8
H
1
2
1
8
6
7
5
4
7
0
1 000
f
H
4
1
2
T
U
9
4
×
2
5
9
7
0
Solve these word problems. Show how you worked them out:
aDan’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?
bDan’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?
20
U
5
e:
U
2
7
2
5
1
T
×
8
T
×
H
2
560
e
750
c
4
e:
3
9
2
T
×
1
T
×
H
1
900
e:
1 000
b
3
9
d
e:
990
3
2
Contracted multiplication is one way to solve a multiplication problem.
First we use our mental strategies to estimate an easier problem:
3 × 150 = 450. The answer will be around 450.
We start with the units. 3 × 6 is 18 units. We rename this as 1 ten and 8 units.
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.
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.
F
3
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
2
2
×
7
3
8
$81
1
1
3
×
3
4
1
3
2
$132
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
1
3
1
Harry
8
1
7
×
2
7
7
4
1
1
9
×
7
3
2
0
3
×
4
1
0
9
3
6
×
7
1
2
0
8
4
0
1
×
8
0
7
6
1
9
8
3
3
2
0
3
×
1
4
1
6
9
3
6
×
3
7
3
1
3
0
8
4
0
1
×
3
3
3
3
7
2
1
4
7
7
7
7
7
×
3
1
8
2
3
3
6
1
×
7
7
3
3
7
2
8
7
7
Forgot to carry.
Did not multiply the zero.
Multiplication and Division
Copyright © 3P Learning
F
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21
Written methods – extended multiplication
H
2
T
3
6
7
1
9
0
0
×
1
U
4
3
2
0
0
2
Extended multiplication is another way of solving
problems. In extended multiplication we multiply
the units, tens and hundreds separately then add
the answers together.
(3 × 4)
(3 × 30)
(3 × 200)
Use a calculator to help you work out the values you could expect when
multiplying the following. Tick the columns:
T TH
2
a
a unit by a unit
9 × 7
b
a ten by a unit
43 × 5
c
a hundred by a unit
d
a ten by a ten
e
a ten by a hundred
126 × 7
13 × 72
3
55 × 120
H
T
U
3
3
3
3
3
3
3
3
3
3
3
3
3
3
Complete using extended multiplication. Estimate first:
e:
a
e:
490
2
4
×
5
2
0 (2 × 5)
8
0 (2 × 40)
4
0
0 (2 × 200)
4
9
0
d
3
SERIES
TOPIC
5
2
2
7
3
7
4 (7 × 2)
3
5
0 (7 × 50)
2
8
0
0 (7 × 400)
3
1
6
4
e:
9
5
6 (8 × 7)
1
6
0 (8 × 20)
2
4
0
0 (8 × 300)
2
6
1
6
1
4
1
×
2
9
1
9
8 (2 × _____)
1
2
8 (9 × _____)
1
4
70
0 (2 × _____)
9
10
0 (9 × _____)
4
0
200
0 (2 × _____)
3
6
0
400
0 (9 × _____)
5
5
8
3
7
0
8
Multiplication and Division
Copyright © 3P Learning
7
8
3 600
e
2
2
×
1
1
2 600
c
560
×
F
4
×
1
e:
3 100
b
e:
22
TH
2 × 2 would give
me a unit only. But
8 × 6 would give me
tens and units. I’ll
tick both columns.
Written methods – extended multiplication
3
Use extended multiplication to solve these problems:
aJack and his 2 friends bought tickets to the
World Cup. Each ticket costs $124. How much
did they spend altogether?
e:
bJack has a paper round and earns $7 per day. He
works for 18 days and saves it all. Has he earned
enough to pay for his World Cup ticket?
e:
360
$
1
2
×
$
4
$
3
×
1
8
7
1
2
(3 × 4)
5
6
(7 × 8)
6
0
(3 × 20)
7
0
(7 × 10)
3
0
0
(3 × 100)
2
6
3
7
2
$
cYusuf’s highest Level 1 Live Mathletics score is
112. Yep, he’s fast. If he scores this 7 times in a
row, how many correct answers has he achieved?
e:
1
×
1
dKyra’s class of 24 all had to stay in for 11 minutes
of their recess. Something to do with too much
talking. How many minutes is this in total?
e:
770
1
4
120
240
2
×
7
1
4
(7 × 2)
7
0
(7 × 10)
7
0
0
(7 × 100)
7
8
4
2
4
1
1
4
(1 × 4)
2
0
(1 × 20)
4
0
(10 × 4)
2
0
0
(10 × 20)
2
6
4
Once you have the hang of extended multiplication, you can apply it to larger numbers. Try these:
a
2
2
9
3
8
4
3
5
2
0 (2 × 5)
2
7 (3 × 9)
1
6 (2 × 8)
8
0 (2 × 40)
6
0 (3 × 20)
6
0 (2 × 30)
4
0
0 (2 × 200)
9
0
0 (3 × 300)
4
0
0 (2 × 200)
1
5
0 (30 × 5)
3
6
0 (40 × 9)
4
0
0 (50 × 8)
1
2
0
0 (30 × 40)
8
0
0 (40 × 20)
1
5
0
0 (50 × 30)
6
0
0
0 (30 × 200)
1
2
0
0
0 (40 × 300)
1
0
0
0
0 (50 × 200)
7
8
4
0
1
4
1
4
7
1
2
3
7
6
×
4
5
3
2
1
b
3
×
Multiplication and Division
Copyright © 3P Learning
c
2
×
F
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23
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
4
d
9
g
3
b
2
1
8
4
1
1
0
9
9
0
3
3
3
9
9
9
5
e
4
h
2
c
1
1
5
5
1
2
1
4
8
4
2
3
1
4
6
2
3
f
6
i
3
9
3
1
1
1
6
6
6
2
3
1
6
9
3
Decide how you’ll split these numbers and then divide. Remember
to put in zeros as needed.
a
5
c
9
24
1
In these problems, if there
are no tens in a number we
put a 0 in to show this and
also to hold the place of
the other numbers!
Sometimes it’s easier to split the numbers differently. We can also
split 936 into 900 + 36.
900 divided by 3 is 300 so we put a 3 in the
hundreds place
3 1 2
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
3
1
0
3
5
1
5
1
0
3
9
2
7
F
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TOPIC
b
3
d
4
2
2
3
6
6
9
2
0
1
8
0
4
Multiplication and Division
Copyright © 3P Learning
e
4
2
0
3
8
1
2
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
8
9
d
7
5
1
2
6
3
5
2
b
1
1
4
7
1
2
4
9
4
e
r3
4
r3
c
0
6
3
8
1
0
6
2
6
f
r1
6
r2
r2
Divide these 3 digit numbers. Each problem will have a remainder.
a
5
d
9
3
r3
1
1
1
5
5
7
1
1
0
9
9
4
r2
b
3
r4
e
4
2
2
0
6
6
1
2
1
1
8
4
5
r1
c
4
r1
f
6
1
2
0
4
8
1
1
0
6
6
3
8
r1
r2
Solve these problems:
aGiovanni’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?
15
Answers will vary.
___________________________________________________________________________
bYou have 59 jubes to add to party bags. Each bag gets 5 jubes. How many full party bags
can you make?
5
1
1
5
9
r4
Multiplication and Division
Copyright © 3P Learning
11 r 4
F
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25
Written methods – short division with remainders
There are 3 ways of expressing remainders. How we do it depends
on how we’d deal with the problem in the real world. Look at:
4
0
5
5
2
7
r2
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.
4
5
5
1
1
3
1
2
6
b Share 215 paper clips among 7 people.
r2
7
2
We can also express a remainder as a fraction. We do this when we can
easily share the remainder. For example, 19 cakes shared among 3 people
is 6 and one third each. Solve these problems expressing the remainder
as a fraction:
a Share 13 pizzas among 4 people.
3
0
1
5
r5
6
3
1
1
3
9
b
Share 50 sandwiches among
3 people.
3
4
6
1
1
4
3
3
1
6
5
0
2
3
We express remainders as decimals when we must be absolutely precise.
Sharing dollar amounts is a good example of this. We add the cents after
the decimal point to help us. Try these:
a Share 12 dollars among 4 people.
b
Share 27 dollars between
2 people.
4
26
1
F
3
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TOPIC
3
0
0
2
0
0
2
1
3
5
0
2
7
0
0
Multiplication and Division
Copyright © 3P Learning
27 divided by 2 is 13.
Now we have one dollar
left. How how many cents
is half of one dollar?
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
2
100 g
300 g
$1.95
$5.43
1
1
9
×
5
3
5
8
or
5
1
3
2
5
8
1
4
3
1
1
3
9
5
×
2
7
9
or
0
2
4
2
5
8
5
0
$5.43 for 300 g
Best deal is __________________________
$3.95 for 500 g
Best deal is __________________________
c
d
10 pack CD
Single CD
500 ml
$2.75
$22.90
2 litres
$2.80
$1.40
$22.90 ÷ 10 = $2.29
or
$2.75 × 10 = $27.50
1
1
1
4
×
0
4
5
10 pack CD
Best deal is __________________________
2
$8.50
$3.95
6
0
or
4
0
7
0
2
8
0
2 litres
Best deal is __________________________
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.
2
1
3
4
5
1
0
or
5
0
1
1
7
×
5
3
5
2
Best deal is 3 bars for $4.50- $1.50 each.
Cheaper than $1.75 each.
5
Multiplication and Division
Copyright © 3P Learning
F
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27
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?
$24
b How much cheaper is this option than buying two 1-day passes?
$16
cIf 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?
dWhat if you choose just the rides? How much would you save if you bought the
10-ride pass instead of the individual rides?
$25
e If you took a 5-minute helicopter ride, what would be the cost per minute?
$8.40
f What about if you chose the 10-minute flight option? What would be the cost per minute?
$7.40
g Plan a day’s itinerary for you and a partner. How much will this cost?
28
5
F
3
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
Answers
will vary.
Crack the code
What
to do
apply
Use the code below to work out the hidden message.
M
A
T
H
L
E
T
I
C
S
__
__
__
__
__
__
__
__
__
__
2
1
3
6
4
5
3
8
7
I
S
__
__
9
8
1
A is ______
F = H + L
10
F = ______
2
M × M = M + M M is______
E = F ÷ 2
5
E = ______
8
I = ______
A × A = A
T – M = A
3
T is ______
2 × L = I
T + T = H
6
H is ______
7
(2 × L) – A = C C = ______
H – M = L
4
L is ______
F + A = N
11
N = ______
3 × L = U
12
U is ______
3 × T = S
9
S = ______
What
to do
9
10
12
11
Once I work out the first
couple, the rest come easily!
Try this one:
A
S
T
R
O
N
A
U
T
S
__
__
__
__
__
__
__
__
__
__
2
9
4
12
13
8
T
A
L
L
E
R
__
__
__
__
__
__
4
F
U
N
__
__
__
2
6
6
3
2
7
4
9
I
N
__
__
12
0
8
2 A × A = A + A A is______
If two letters
are together,
we read
them as a
tens digit and
a units digit.
A
R
E
__
__
__
2
12
3
S
P
A
C
E
__
__
__
__
__
9
1
2
5
3
L + E = S
9
S is______
A + A = T
4 T is ______
N – N = I
0
I is______
T × 2 = N
8 N is______
U – A = C
5
C is______
AT ÷ N = E
3 E is______
1
S – (2 × T) = P P is______
2 × E = L
6 L is ______
13
2 × U – P = O O is______
E + T = U
7 U is______
S + E = R
Multiplication and Division
Copyright © 3P Learning
12
R is______
F
4
SERIES
TOPIC
29
Smart buttons
Getting
ready
What
to do
apply
In this activity, you’ll use your knowledge of multiplication, division, subtraction and
addition to find as many number statements you can to create one number.
Using ONLY the number 2, +, ×, – and ÷ keys on your calculator,
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?
What
to do
Choose another number to make and see how many statements you can find or
challenge a partner to a competition. Set a time limit and see who can find the most
ways to make 15 within the time span.
Answers will vary.
Bugsinvestigate
Getting
ready
What
to do
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.
Girl bugs have 4 splodges on their backs, boy bugs have 9.
Altogether there are 48 splodges. Work out how many girl
bugs and how many boy bugs there are.
3 girl bugs.
4 boy bugs.
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?
Answers will vary.
30
F
4
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
Puzzlesapply
What
to do
a
2
×
Use your knowledge of multiplication to work out the missing values:
8
b
3
8
d
e
1
×
9
g
2
9
2
6
8
6
8
1
4
0
2
f
3
5
8
2
3
×
8
6
5
8
4
5
6
2
7
3
9
2
4
2
4
3
1
2
6
1
6
8
0
1
1
2
0
1
8
0
6
1
5
1
2
×
4
What
to do
5
4
h
7
4
×
3
2
4
0
8
×
×
1
4
2
4
c
2
×
8
7
7
i
×
Fill in the multiplication and division tables by
working out the missing digits. The arrows show
you some good starting places.
8
9
×
5
2
3
8
4
20
8
12
32
7
35
14
21
56
9
45 18
27
72
24
36
96
×
10
8
7
6
×
2
2
20
16
14
12
12
24
96 108 48
5
50
40
35
30
3
6
24
27
12
×
3
4
9
8
6
60
48
42
36
7
14
56
63
28
2
6
8
18
16
3
30
24
21
18
6
12
48
54
24
11
33
44
99
88
7
21
28
63
56
8
24
32
72
64
Multiplication and Division
Copyright © 3P Learning
4
12 60
F
4
SERIES
TOPIC
31
Puzzlesapply
What
to do
Complete this crossnumber puzzle:
1
2
2
1
3
2
4
1
6
What
to do
5
4
2
9
5
0
7
8
2
1
1
1
10
4
5
2
1
4
9
1
3
0
0
Down
1 60 ÷ 5
1 11 × 11
2 25 × 5
2 12 × 10
3 7 × 6
3 7 × 7
4 15 × 6
5 66 ÷ 6
7 7 × 3
6 12 × 12
9 9 × 6
8 39 ÷ 3
10 6 × 50
Test your speed and accuracy. Race against a partner or the clock to complete each table:
÷8
÷3
÷7
56
7
9
3
21
3
16
2
6
2
7
1
64
8
18
6
14
2
80
10
12
4
70
10
32
4
24
8
49
7
72
9
30
10
28
4
24
3
27
9
42
6
8
1
33
11
35
5
Time:
What
to do
Across
Time:
Use the “guess, check and improve” strategy to
solve this problem. You could use a calculator
to help if you wish.
Time:
If the decimals are confusing
me, I can change the amounts
to 310 cents and 295 cents.
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?
1 lolly snake = 30¢
1 sherbet = 25¢
32
F
4
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
Multiplication facts
1
Name_____________________
Using a lead pencil complete the grid facts. Once the grid has been checked, colour all your correct facts.
How many do you know? How many do you still need to learn?
×
4
2
3
7
6
12
5
10
11
1
9
8
2
3
7
6
12
5
10
11
1
9
8
2
4
8
2
Try these sets:
×
4
7
5
10
Skills
Not yet
Kind of
Got it
• 2×
• 4×
• 8×
• 7×
• 5×
• 10 ×
Series F Topic 1 Assessment
Copyright © 3P Learning
33
Multiplication facts
3
Name_____________________
Using a lead pencil complete the grid facts. Once the grid has been checked, colour all your correct facts.
How many do you know? How many do you still need to learn?
×
4
2
3
7
6
12
5
10
11
1
9
8
2
3
7
6
12
5
10
11
1
9
8
3
6
9
4
Try these sets:
×
4
11
12
0
1
Skills
Not yet
Kind of
Got it
• 3×
• 6×
• 9×
• 11 ×
• 12 ×
• 0×
• 1×
34
Series F Topic 1 Assessment
Copyright © 3P Learning
Multiplication facts
1
2
Name_____________________
Using a lead pencil complete the grid facts. Once the grid has been checked, colour all your correct facts.
How many do you know? How many do you still need to learn?
×
4
2
3
7
6
12
5
10
11
1
9
8
2
8
4
6
14
12
24
10
20
22
2
18
16
4
16
8
12
28
24
48
20
40
44
4
36
32
8
32
16
24
56
48
96
40
80
88
8
72
64
Try these sets:
×
4
2
3
7
6
12
5
10
11
1
9
8
7
28
14
21
49
42
84
35
70
77
7
63
56
5
20
10
15
35
30
60
25
50
55
5
45
40
10
40
20
30
70
60
120
50
100
110
10
90
80
Skills
Not yet
Kind of
Got it
• 2×
• 4×
• 8×
• 7×
• 5×
• 10 ×
Series F Topic 1 Assessment
Copyright © 3P Learning
35
Multiplication facts
3
4
Name_____________________
Using a lead pencil complete the grid facts. Once the grid has been checked, colour all your correct facts.
How many do you know? How many do you still need to learn?
×
4
2
3
7
6
12
5
10
11
1
9
8
3
12
6
9
21
18
36
15
30
33
3
27
24
6
24
12
18
42
36
72
30
60
66
6
54
48
9
36
18
27
63
54
108
45
90
99
9
81
72
Try these sets:
×
4
2
3
7
6
12
5
10
11
1
9
8
11
44
22
33
77
66
132
55
110
121
11
99
88
12
48
24
36
84
72
144
60
120
132
12
108
96
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
3
7
6
12
5
10
11
1
9
8
Skills
Not yet
Kind of
Got it
• 3×
• 6×
• 9×
• 11 ×
• 12 ×
• 0×
• 1×
36
Series F Topic 1 Assessment
Copyright © 3P Learning
Mental multiplication strategies
1
Show how you would solve 18 × 4 using:
a
b
the doubling strategy
2
c
the split strategy
the compensation strategy
Use a strategy of your choice to solve the following problems. Show how you arrived at your answer.
a 28 × 4
3
Name_____________________
bIn 2000, a new world record was set when
18 people crammed into a mini. How many
people would fit into 9 minis?
You can choose from the payment methods below for your new after school job as chief taster at an ice
cream shop. You work Monday to Friday, 4 pm to 6 pm. Which method would earn you the most money
in 4 weeks and why?
a Daily payments of $9.
b Weekly payments of $42.
c Fortnightly payments of $75.
Series F Topic 1 Assessment
Copyright © 3P Learning
37
Mental multiplication strategies
4
Multiply these numbers:
a 10 × 43
5
6
7
Name_____________________
b 10 × $92
=
=
c 100 × 43 =
d 100 × $92 =
e 1 000 × 43=
f 1 000 × $92=
Use patterns to help solve these:
a 5 × 2 _____________ 5 × 20 _____________ 5 × 200
_____________
b 2 × 9 _____________ 2 × 90 _____________ 2 × 900
_____________
c 6 × $4 _____________ 6 × $40 _____________ 6 × $400 _____________
What number is:
a 100 times larger than 42?
b 1 000 times larger than 135?
c 30 times larger than 8?
d 200 times larger than 7?
List all the factors of the following numbers:
List the first 5 multiples of:
36
5
24
7
45
4
18
3
Skills
Not yet
Kind of
Got it
• Recognises and uses a range of mental multiplication strategies
doubling
split
compensation
• Solves mental multiplication problems using strategy of choice
• Applies strategies to real life word problems
• Multiplies by numbers ending in zeros
• Names factors and multiples of numbers to 50
38
Series F Topic 1 Assessment
Copyright © 3P Learning
Mental multiplication strategies
1
Show how you would solve 18 × 4 using:
a
b
18 × 4
18 × 2 = 36
36 × 2 = 72
c
18 × 4
(10 × 4) + (8 × 4)
40 + 32
= 72
the doubling strategy
2
the split strategy
18 × 4
= 20 × 4– 8
= 72
the compensation strategy
Use a strategy of your choice to solve the following problems. Show how you arrived at your answer.
a 28 × 4
3
Name_____________________
bIn 2000, a new world record was set when
18 people crammed into a mini. How many
people would fit into 9 minis?
28 × 4 = 112
18 × 9 = 162
Working out will vary.
Working out will vary.
You can choose from the payment methods below for your new after school job as chief taster at an ice
cream shop. You work Monday to Friday, 4 pm to 6 pm. Which method would earn you the most money
in 4 weeks and why?
a Daily payments of $9.
9 × 5 = 45, 45 × 4 = $180
b Weekly payments of $42.
42 × 4 = $168
c Fortnightly payments of $75.
75 × 2 = $150
You would earn the most with daily payments of $9 because you multiply it by days
and weeks.
Series F Topic 1 Assessment
Copyright © 3P Learning
39
Mental multiplication strategies
4
Multiply these numbers:
a 10 × 43
5
6
=
b 10 × $92
430
=
$920
c 100 × 43 =
4 300
d 100 × $92 =
$9 200
e 1 000 × 43=
43 000
f 1 000 × $92=
$92 000
Use patterns to help solve these:
10
a 5 × 2 _____________
100
5 × 20 _____________
5 × 200
1 000
_____________
18
b 2 × 9 _____________
180
2 × 90 _____________
2 × 900
1 800
_____________
$24
c 6 × $4 _____________
$240
6 × $40 _____________
$2 400
6 × $400 _____________
What number is:
a 100 times larger than 42?
4 200
c 30 times larger than 8?
7
Name_____________________
240
List all the factors of the following numbers:
b 1 000 times larger than 135?
d 200 times larger than 7?
135 000
1 400
List the first 5 multiples of:
36
1, 36, 2, 18, 6, 4, 9, 3, 12
5
5
10
15
20
25
24
1, 24, 2, 12, 4, 6, 3, 8
7
7
14
21
28
35
45
1, 45, 5, 9, 3, 15
4
4
8
12
16
20
18
1, 18, 2, 9, 3, 6
3
3
6
9
12
15
Skills
Not yet
Kind of
Got it
• Recognises and uses a range of mental multiplication strategies
doubling
split
compensation
• Solves mental multiplication problems using strategy of choice
• Applies strategies to real life word problems
• Multiplies by numbers ending in zeros
• Names factors and multiples of numbers to 50
40
Series F Topic 1 Assessment
Copyright © 3P Learning
Mental division strategies
1
Name______________________
Solve these division problems:
a 40 ÷ 5
=
b 36 ÷ 6
=
c 21 ÷ 3
=
d 54 ÷ 6
=
e 49 ÷ 7
=
f 48 ÷ 8
=
g 500 ÷ 10 =
h 6 000 ÷ 100=
i 55 000 ÷ 1 000=
2
Show how you would use the halving strategy to
solve 96 ÷ 24:
3
Use a strategy of your choice to solve these division problems. Show how you arrived at your answer.
aThe 4 Herringer kids want to buy a Karaoke
machine costing $192 for their mother’s
birthday. Show how they could mentally
work out each kid’s share of the cost.
Finish this split strategy problem to solve 98 ÷ 7:
b85 swimmers are divided into 5 equal
teams. How many swimmers in each team?
Skills
Not yet
Kind of
Got it
• Uses knowledge of multiplication facts to solve division problems
• Solves division problems using strategy of choice
• Divides by tens, hundreds, thousands
• Recognises and uses a range of mental division strategies
halving
split
other
• Applies strategies to real life problems
Series F Topic 2 Assessment
Copyright © 3P Learning
41
Mental division strategies
1
Solve these division problems:
a 40 ÷ 5
=
8
b 36 ÷ 6
=
6
c 21 ÷ 3
=
7
d 54 ÷ 6
=
9
e 49 ÷ 7
=
7
f 48 ÷ 8
=
6
g 500 ÷ 10 =
2
Name______________________
h 6 000 ÷ 100=
50
Show how you would use the halving strategy to
solve 96 ÷ 24:
i 55 000 ÷ 1 000=
60
55
Finish this split strategy problem to solve 98 ÷ 7:
35 ÷ 7= 5
98 ÷ 7
96 ÷ 24= 48 ÷ 12
=4
63 ÷ 7= 9
3
= 14
Use a strategy of your choice to solve these division problems. Show how you arrived at your answer.
aThe 4 Herringer kids want to buy a Karaoke
machine costing $192 for their mother’s
birthday. Show how they could mentally
work out each kid’s share of the cost.
b85 swimmers are divided into 5 equal
teams. How many swimmers in each team?
$192 ÷ 4
85 ÷ 5 = 17
192 ÷ 2 = 96
Working out will vary.
96 ÷ 2
= 48
Working out will vary.
Skills
Not yet
Kind of
Got it
• Uses knowledge of multiplication facts to solve division problems
• Solves division problems using strategy of choice
• Divides by tens, hundreds, thousands
• Recognises and uses a range of mental division strategies
halving
split
other
• Applies strategies to real life problems
42
Series F Topic 2 Assessment
Copyright © 3P Learning
Written methods
1
Solve these written multiplication problems using a strategy of your choice:
a
1
3
×
b
2
2
×
4
2
×
3
6
c
5
4
e
6
3
×
0
×
5
f
8
4
1
8
×
3
7
Solve these written division problems:
c
b
a
4
8
4
5
5
0
5
6
6
5
4
4
8
5
6
3
8
2
9
2
7
5
5
0
6
8
8
9
1
i
h
g
3
f
e
d
3
4
3
d
2
Name______________________
9
9
2
You buy 7 train tickets at $65 each. How much
have you spent?
3
Five DVDs cost $27. What is the cost of 1 DVD?
Skills
Not yet
Kind of
Got it
• Solves 1 digit × 2 or 3 digit written multiplication problems
• Solves written division problems with:
no trading or remainders
with remainders
with trading and remainders
• Chooses and uses correct process for solving real life problems
Series F Topic 3 Assessment
Copyright © 3P Learning
43
Written methods
1
Solve these written multiplication problems using a strategy of your choice:
a
1
3
×
b
2
2
×
e
6
5
Methods will vary.
c
5
4
1
4
2
2
×
9
d
6
8
8
3
6
3
×
×
1
4
5
1
5
2
5
0
5
8
8
3
f
4
2
0
×
7
2
6
1
8
3
0
9
9
2
7
1
0
1
5
0
6
1
1
1
8
9
1
Solve these written division problems:
a
4
d
6
2
1
8
4
1
0
6
5
g
b
5
3
8
e
r5
4
6
6
3
4
3
3
2
Name______________________
3
2
h
r4
2
9
1
0
1
5
0
5
1
2
1
4
8
5
1
0
2
9
2
3
You buy 7 train tickets at $65 each. How much
have you spent?
3
$
6
×
4
5
3
f
r1
5
i
r5
8
1
r1
r3
1
Five DVDs cost $27. What is the cost of 1 DVD?
5
$
7
$
c
5
5
Skills
5
2
Not yet
7
4
2
0
0
0
Kind of
Got it
• Solves 1 digit × 2 or 3 digit written multiplication problems
• Solves written division problems with:
no trading or remainders
with remainders
with trading and remainders
• Chooses and uses correct process for solving real life problems
44
Series F Topic 3 Assessment
Copyright © 3P Learning
Series F – Multiplication and Division
Region
Topic 1
Mental multiplication
strategies
Topic 2
Mental division
strategies
Topic 3
Written methods
NS3.3 – selects and applies appropriate strategies for multiplication and division
NSW
• apply appropriate mental, written or calculator strategies to solve multiplication and
division problems
• recognise and use different notations to indicate division
• record remainders as fractions and decimals when appropriate
• multiply 3 digit numbers by one digit numbers using mental or written strategies
• divide a number with 3 or more digits by a single digit divisor using mental or written strategies
• use mental strategies to multiply or divide a number by multiples of ten
• estimate answers to problems and check to justify solutions (WM)
• select an appropriate operation and strategy for the solution of multiplication and
division problems
• question the meaning of packaging statements in best buy situations
VELS Number – Level 4
VIC
•
•
•
•
•
•
•
e xplain and use mental and written algorithms for multiplication and division of whole numbers
develop automatic recall of tables and understand factors and multiples
establish equivalence relationships between mathematical expressions
explain reasoning and procedures and interpret solutions
understand factors and multiples
use the mathematical structure of problems to choose strategies for solutions (WM)
use estimates for computations and apply criteria to determine if estimates are reasonable or
not (WM)
• use inverse relations to validate calculations
• identify calculation errors resulting in unreasonable results (WM)
Level 4
QLD
• w
ork out multiplication and related division, applying number properties and mental
computation strategies to larger numbers
• use mental and written strategies to estimate and calculate a single operation
• multiply and divide numbers by 10 and 100 mentally
• know what factors and multiples are for 2 and 3 digit numbers
• read and interpret practical problems, identify which operation/s to use, express it
mathematically and then solve it, making sure their answer makes sense in the context
• use a variety of methods including estimating and technology, to check for reasonableness of
results (WM)
Series F Outcomes
Copyright © 3P Learning
45
Series F – Multiplication and Division
Region
Topic 1
Mental multiplication
strategies
Topic 2
Mental division
strategies
Topic 3
Written methods
3.8
SA
• use a variety of estimation and calculating strategies including memorising multiplication and
division facts
Standards 3 - 4
TAS
• r ecall automatically basic multiplication and division facts
• use knowledge of place value and number properties to increase the range of problems that
can be carried out mentally
• use estimation to check the results of written calculations
• analyse a problem that may involve different operations and choose the appropriate
computational methods to solve it
Level 4
WA/NT
ACT
46
• understand the meaning, use and connections between operations and use this to choose and
apply the correct operation
• construct and completes statements
• calculate with whole numbers (with multipliers and divisors to 10) drawing mainly on
mental strategies
• recognise, identify and use patterns involving operations
16.LC.16recall or use suitable strategies to work out multiplication and related division facts and
apply facts to calculate mentally with larger numbers
16.LC.17use calculators to explore, develop and refine strategies for multiplication and division
and for calculations using numbers beyond their mental scope
16.LC.18explain the calculation approaches they use, compare them with other approaches and
check the reasonableness of their answers
16.LC.19apply number properties to modify calculations so that they can more easily be carried
out (e.g. doubling, halving and bridging to the nearest decade number) and use inverse
operations to solve relevant problems
16.LC.20choose when to use mental computation, written or electronic methods to calculate
with numbers and form quick mental estimates to check calculations
Series F Outcomes
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