F
Student Book
SERIES
Name _____________________________________
Multiplication and Division
Series F – Multiplication and Division
Contents
Date completed
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$" _______________________________________
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division ______________________________________________
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")$ ________________________________
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-$apply __________________________________
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'apply __________________________________
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puzzles – apply ________________________________________
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!
"#
%&'$!!(
*+,,"!#%!
Series Authors:
Rachel Flenley
Nicola Herringer
Copyright ©
Mental multiplication strategies – doubling strategy
0 )$
)
$$.
15 × 4 1%
13 × 8 double once = 26
)13
)14!
$1*
1
a
b
c
2
*
1
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4
6
3
4
D
#
4
2
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D
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7
6
%
12
D
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24
(
32 16
4
2
a 4
(
_________
16
__________
_________
64
__________
_________
b 3
_________
__________
_________
__________
#3
_________
c 4
_________
__________
*
_________
__________
_________
d !4
4
_________
__________
_________
__________
_________
e 7
_________
!(
__________
_________
__________
224
_________
f :4
_________
%
__________
_________
__________
_________
3
4
Two sets of twins turn 12. They decide to have a joint birthday party with 1 giant cake but they all want
Multiplication and Division
Copyright © 3P Learning
F
1
SERIES
TOPIC
1
Mental multiplication strategies – doubling strategy
5
6
7
8
!
×2
×4
a 13 × 4
26
__________
52
__________
b 16 × 4
__________
__________
c 24 × 4
__________
__________
d !4× 4
__________
__________
e 32 × 4
__________
__________
f 21 × 4
__________
__________
g %4× 4
__________
__________
,-/
,0/
!
×2
×4
;(
a !;(
24
____________
___________
96
___________
b *;(
____________
___________
112
___________
c !4;(
____________
___________
___________
d !;(
____________
84
___________
___________
e %;(
____________
___________
___________
f 3;(
32
____________
___________
___________
Work out the answers in your head using the appropriate doubling strategy. Use a table like the one
above if it helps.
a (;*1
b 16 × 4 =
c 26 × 4 =
d !*;(1
e 4;(1
f !!;(1
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2
F
1
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
Mental multiplication strategies – multiply by 10s, 100s and 1,000s
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Ten Thousands
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4
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T Th
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b
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a *;
1
b *; 1
c *;1
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1
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f #!; 1
g ;1
h ; 1
i ;
1
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,#
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Multiplication and Division
Copyright © 3P Learning
F
1
SERIES
TOPIC
3
Mental multiplication strategies – multiply by 10s, 100s and 1,000s
F$-)$) $!!$
4 ×!$)-*×!D
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__________
b !;#
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____________ !;#
__________
c 6 × $4 ____________ 3;<* ____________ 3;<* __________
d (;%
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e 3 × $7 ____________ %;<: ____________ %;<: __________
f !;(
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g %;#
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a J-4-)-H) $")-@
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4
a !
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4
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d *
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f !
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_________
g !
*
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__________
!
_________
F
1
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
Mental multiplication strategies – split strategy
KL)-)$$
B-3*×(
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1
2
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a 46 × 4
b :*;4
c *(;*
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OOOOOOONOOOOOOO
OOOOOOONOOOOOOO
=
=
=
OOO;OOONOOO;OOO
OOO;OOONOOO;OOO
d 37 × 7
e 3!;(
f #;4
OOO;OOONOOO;OOO
OOO;OOONOOO;OOO
OOO;OOONOOO;OOO
OOOOOOONOOOOOOO
OOOOOOONOOOOOOO
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=
=
=
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a *(;(1 OOOOOOOOOONOOOOOOOOOO1
It's a good thing I
know how to work
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b 4!;:1 OOOOOOOOOONOOOOOOOOOO1
c #;*%1 OOOOOOOOOONOOOOOOOOOO1
d (;!#1 OOOOOOOOOONOOOOOOOOOO1
e (3;:1 OOOOOOOOOONOOOOOOOOOO1
3
These problems have been worked out incorrectly. Circle where it all went wrong.
a 37 × 6
b :;4
c %!;#
%;3N:;3
;4N:;4
%;#N!;#
(N%
:N%4
!:N(
1#%
14
1
Multiplication and Division
Copyright © 3P Learning
*4
F
1
SERIES
TOPIC
5
Mental multiplication strategies – split strategy
4
H
+
!J
!
correctly. There are errors in the other two. Find and color the winning trail.
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:(
!#
114
%;#N%;#
;3N%;3
13 × 6
464
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42 × 7
%%;#
!#*
F
1
SERIES
TOPIC
3;#
4
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4(;(
<,AM,
6
;#N3;#
Multiplication and Division
Copyright © 3P Learning
%N!
17 × 3
Mental multiplication strategies – compensation strategy
&$)$P
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57
b (;!#1OOOOOOOO;OOOOOOOOOOOOOOOO1
c (;31OOOOOOOO;OOOOOOOOOOOOOOOO1
d :;%#1OOOOOOOO;OOOOOOOOOOOOOOOO1
e !(;41 ________ × ________ – ________ =
&PB-$))$)$3;3!D
3!3&3;3$)-)3;31%3
3;31%3
&$"$! 3D%3N!1%:!
6 × 62 = 372
2
(&,@&
40
3
3
a *;%1OOOOOOOO;OOOOOOOONOOOOOOOO1
123
L
strategy with numbers such as
'>0-
b (;*1OOOOOOOO;OOOOOOOONOOOOOOOO1
c !!;#1OOOOOOOO;OOOOOOOONOOOOOOOO1
d %!;#1OOOOOOOO;OOOOOOOONOOOOOOOO1
e 7 × 62 =OOOOOOOO;OOOOOOOONOOOOOOOO1
Multiplication and Division
Copyright © 3P Learning
F
1
SERIES
TOPIC
7
Mental multiplication strategies – compensation strategy
3
L
!
$#
:$
&
/
@
@
:
#
out the answers to the problems.
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Ones
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1
×
=
9
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2
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1
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9
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8
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2
×
=
1
×
=
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b ?
)$)$)$$$$)
8
F
1
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
copy
Mental multiplication strategies – factors and multiples
V$)$$D
×
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=
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1
2
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f 4
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h 42
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16
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c OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO$!*$
d OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO$%
e OOOOOOOOOO$4"
3
@&&Q0-
A factor divides into
a number evenly
with no remainder.
Multiplication and Division
Copyright © 3P Learning
F
1
SERIES
TOPIC
9
Mental multiplication strategies – factors and multiples
$)))$)! $-$%)$%) &$$ %@
3
×
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4
=
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a
5
b
8
c
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c
×
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=
×
=
d
×
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×
=
×
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F
1
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
48
Mental division strategies – use multiplication facts
X) $)$"$$" $$
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1
2
3
#&
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a 43Y:
8
_______
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b !Y
_______ × 11 = 121
!Y 1
c :!Y(
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1
d *#Y:
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1
e %3Y#
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f 3*Y(
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1
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b *Y41
c !Y%1
d 4*Y31
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f 3%Y#1
g %3Y*1
h *4Y#1
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Doing math
without knowing
facts is hard.
B
makes your life
much easier. It’s
worth persevering
EC
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b
36
24
3
42
c
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6
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72
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36
63 *4
Multiplication and Division
Copyright © 3P Learning
!(
44
*
Y*
24
32 (
F
2
SERIES
TOPIC
11
Mental division strategies – use multiplication facts
X) $ %;414
4;%14
4
a
:;( 143
b
(;# 1:!
c
:;# 13%
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a 6 × 7 = 42
b 4;#1*4
c #;314*
d :;(1%3
e !;(1#3
f 11 × 21 = 231
B#
!
&
+9S'V-
+9S-V'
L
$X
$
%
Y
Y
12
F
2
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
Mental division strategies – divide by 10s, 100s and 1,000s
&$)")"$"$$
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B-)$$*4)$)$D
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Thousands
Tens
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4
4
4
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4
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a
c
2
Ten Thousands
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Th
T
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4
4
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Th
T
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4
b
T Th
Th
T
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3
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d
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a
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b
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c
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d
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e
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f
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Multiplication and Division
Copyright © 3P Learning
#4
((
#4
((
%!
32
F
2
SERIES
TOPIC
13
Mental division strategies – halving strategy
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1
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a
32
16
43
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14
c
24
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halve
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2
b
72
4
4
halve
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halve
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56
7
OOOOOOOOYOOOOOOOO1
b **Y3
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c #3Y!
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d !!Y*
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e 3!Y(
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8
)
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for you.
a #Y(
3Y3
=
b 3*Y3
24 Y(
=
c !Y!
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=
d :Y*
*4Y#
=
e **Y!*
72 Y!
=
f *(Y3
32 Y(
=
F
2
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
5
Mental division strategies – halving strategy
K)-$")$" **Y%3 :!Y( %3Y#1*
4
]!
&#
L&
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a 216 Y%31 OOOOOOOOYOOOOOOOO1OOOOOOOOYOOOOOOOO1
b #3Y!(1 OOOOOOOOYOOOOOOOO1OOOOOOOOYOOOOOOOO1
c 224 Y%!1 OOOOOOOOYOOOOOOOO1OOOOOOOOYOOOOOOOO1
d 3(Y!*1 OOOOOOOOYOOOOOOOO1OOOOOOOOYOOOOOOOO1
e 144 Y%31 OOOOOOOOYOOOOOOOO1OOOOOOOOYOOOOOOOO1
f !((Y:!1 OOOOOOOOYOOOOOOOO1OOOOOOOOYOOOOOOOO1
5
Draw lines to connect numbers that could be doubled or halved to reach each other.
16
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32
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64
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3
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4
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6
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S$"A$P$$-$G$"
"$!((-'*(H)-')$@K$)$$"
Multiplication and Division
Copyright © 3P Learning
F
2
SERIES
TOPIC
15
Mental division strategies – split strategy
0" $", B-$**Y#
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1
f
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me here. What
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1
24
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d **Y(
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=
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16
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F
2
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
Mental division strategies – split strategy
3
Play this game with a partner. Use one copy of this page between you. Cut out the problems
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Multiplication and Division
Copyright © 3P Learning
copy
F
2
SERIES
TOPIC
17
Mental division strategies – divisibility rules
0" ""$$)$
1
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Divisible by
M
Test
2
M
"! L
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3
M
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Yes, because it ends in an even number.
F:!("%@
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Yes, because 18 is divisible by 3.
4
M
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18
F
2
SERIES
TOPIC
F"%@
F3%*4"#@
F43("@
Multiplication and Division
Copyright © 3P Learning
Mental division strategies – divisibility rules
2
,
!
#
@
can be used to divide them. Fill in the tables.
36
#
(*
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4
72
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Multiplication and Division
Copyright © 3P Learning
F
2
SERIES
TOPIC
19
Written methods – single-digit multiplication
1
1
1
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F
3
SERIES
TOPIC
T
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d
Multiplication and Division
Copyright © 3P Learning
f
×
T
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1
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4
4
Written methods – single-digit multiplication
3
~$#
!&'L&
#/
give them some feedback as to where they went wrong.
Jess
1
3
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1
7
2
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7
2
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7
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1
7
(
3
1
3
2
1
×
7
×
1
3
3
(
4
1
×
7
7
2
Multiplication and Division
Copyright © 3P Learning
(
7
F
3
SERIES
TOPIC
21
Written methods – multi-digit multiplication
2
1VD
4*!;31%!4!
×
2S$")
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6 in the ones place and
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$)$
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2 6
1
3 2 4 2
1 * # 2
Use a calculator to help you work out the values you could expect when
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a
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b
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c
$
d
e
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2 × 2 would give
me a one only. But
8 × 6 would give me
tens and ones. I’ll
#
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126 × 7
13 × 72
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a
6
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2
1
4 4 2
F
3
SERIES
TOPIC
7
2
3
4
b
(
×
#
3
1
7
Multiplication and Division
Copyright © 3P Learning
c
4
×
(
3
4
4
Written methods – multi-digit multiplication
3
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a
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d
4
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admission to the museum is
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Multiplication and Division
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c $ )
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F
3
SERIES
TOPIC
23
Written methods – division
F")-) $&#%3#N%N3
#"%%)%$$
3 1 2
%"%)$
3 # 3 6
3"%!)!$`Q>SQVQ*+
1
Z
!
c
b
a
4
(
4
4
4
4
#
#
#
4
4
(
4
3
#
#
#
2
4
6
2
6
6
6
3
6
#
3
Z
$
!
M
\
a
b
4
4
1
4
c
3
6
6
#
d
#
24
6
L/
&
are no tens in a number we
9
also to hold the place of
C
KL$Q&
#%3#N%3
#"%%)%$
$
3 1 2
%3"%!&$$
3 # 3 6
$!$
`Q>SQVQ*+
2
3
i
h
g
#
f
e
d
3
#
F
3
SERIES
TOPIC
2
7
e
4
(
4
Multiplication and Division
Copyright © 3P Learning
4
(
1
2
Written methods – division with remainders
KL""$A"$remainder
B-4!:"4
4"4
1 4 !
!:"44)$!A"$$
4 4 2 7
$)'!
'+?S'V*9'+
1
Divide these 2 digit numbers. Each problem will have a remainder.
a
#
7
4
d
2
4
6
3
7
4
c
6
3
(
f
4
#
6
6
2
Divide these 3 digit numbers. Each problem will have a remainder.
a
4
4
4
3
#
#
#
4
b
7
d
3
4
e
4
b
6
6
1
4
e
4
(
4
c
4
4
(
1
f
6
6
3
(
<!
"L$"$ $$$)
a ]
$*:$H)$$ $L$"@
H))$)$$@
__________________________________________________________________________
b S $"4#M$^$4M$H) -@
Multiplication and Division
Copyright © 3P Learning
F
3
SERIES
TOPIC
25
Written methods – division with remainders
$%) GH))
$))L)$$$)B-D
4
4
4
2
7
!
One way is to write r 2 as in the example above. We use this when we don’t care about being absolutely
precise and when the remainder can’t be easily broken up. An example would be sharing 527 jelly beans
'<!X
r.
a K$!3*
5
4
1
b K$!4:
X
&
X/*`#Q
>
<!X
&
a K$%,,*
6
3
1
1
3
9
b K$4)$
%
6
We express remainders as decimals when we must be absolutely precise.
<
X&
x
,
a K$!*
b K$!:)
!
4
26
1
F
3
SERIES
TOPIC
2
2
2
7
Multiplication and Division
Copyright © 3P Learning
27 divided by 2 is 13.
Now we have one dollar
x
&&
Written methods – problem solving
&"" FL
')$$)"$)$$$$
1
J}
&
@L$
&
&
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a
b
*\
„*`'
8 oz
Q\
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„0'9
ZOOOOOOOOOOOOOOOOOOOOOOOOOO
ZOOOOOOOOOOOOOOOOOOOOOOOOOO
c
d
-R0
„++`9
KR0
(`,
„+?'
ZOOOOOOOOOOOOOOOOOOOOOOOOOO
2
16 oz
%!`,
„+09
„*-9
ZOOOOOOOOOOOOOOOOOOOOOOOOOO
:
#&„'#„*?'
/%
&Q&„-'9
<
Multiplication and Division
Copyright © 3P Learning
F
3
SERIES
TOPIC
27
Written methods – problem solving
3
You’re planning a trip to the Wet and Wild theme park and
#&
&
E
Entry
Extras
„Q+
4$ „-+
! „-0
$ „?-
Annual pass „``
%$ „+9`
F" „*+
K „*+
„`'
B$ „++
j „'
Swim with the dolphins „?'
a F !)$$@
b H)$$$$)@
c F $$))"-
'$$!@
d &
$ $P$@H)$)" $$
$"@
e F -4$)$)$@
f &$ $$`$@&$)$@
g +L H)$)$@
28
F
3
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning
Crack the code
What
to do
apply
q$))-$$
__ __ __ __ __ __ __ __ __ __
2
1
3
6
A × A = A
4
4
3
(
7
__ __
#
(
A is _____
V1HNB
F = _____
;
1
N
M is _____
^1VY!
E = _____
T – M = A
T is _____
2 × L = I
I = _____
N1H
_____
!;BM1R C = _____
H
1B
B
_____
VNM1?
N = _____
3 × L = U
U is _____
3 × T = S
<V _____
What
to do
#
12
11
JL#@
/
C
$D
__ __ __ __ __ __ __ __ __ __
2
#
4
12
13
(
__ __ __ __ __ __
4
__ __ __
2
6
6
L&
/
them to get
the answer.
3
2
7
4
#
__ __
12
__ __ __
(
2
12
3
__ __ __ __ __
#
1
2
4
3
M;M1MNM A is _____ BN^1K
<
_____
MNM1
T is _____ ??1F
I is _____
;!1?
N is _____
U – A = C
C is _____
MBY1^
E is _____ K!;1+ P is _____
!;^1B
B
_____
2 × U – P = O
O is _____
^N1q
U is _____ KN^1~
M
_____
Multiplication and Division
Copyright © 3P Learning
F
4
SERIES
TOPIC
29
Smart buttons
‡ˆ
ready
What
to do
apply
F$"L-) "
>
qj?BS$!N;Y-
>)$%
VG-D
!!N!N!1!3Y!1%
~ ?)))$LH)$>@
R$$L@
&$L$@&$L$$@
What
to do
R$$-$)>or
$K)$>$
)-$4)$$
Bugs
investigate
‡ˆ
ready
What
to do
q-) $)-$)
$$)B$$
)$
]$"*$-$"#
M$$*(&-$)
$)$
What to
do next
Q9
F
4
SERIES
TOPIC
&$ $"($"3$!$@
H)Q)>@
Multiplication and Division
Copyright © 3P Learning
Puzzles
apply
What
to do
a
2
×
q-) )-$"D
(
b
3
7
×
(
d
e
×
#
g
4
2
(
7
c
2
#
2
6
(
(
6
(
×
4
h
6
4
2
1
2
6
6
(
4
i
3
4
What
to do
4
f
×
4
3
2
3
(
4
4
6
2
7
#
2
×
2
×
4
2
×
1
7
×
3
V$"
)-$$)$)
×
3
4
32
14
×
7
!
4
16
6
14
12
*
(
*4
#
12
24
3
36
3
×
12
24
×
#
6
14
%
27
4*
11
33
44
63
(
Multiplication and Division
Copyright © 3P Learning
64
F
4
SERIES
TOPIC
31
Puzzles
What
to do
apply
R$,,D
1
Across
2
Down
1 3Y4
1 11 × 11
2 !4;4
2 !;
3 7×6
3 7×7
4 4;3
5 33Y3
7 7×3
6 12 × 12
9 #;3
8 %#Y%
3
4
4
6
7
(
#
*9 3;4
What
to do
~$-$D
S0
What
to do
SQ
S?
43
#
21
16
6
7
64
(
14
(
12
:
32
24
*#
72
%
!(
24
27
42
(
33
%4
D
D
D
q$$-€"
$S
$ )$
If the decimals are confusing
/L
Q*9+`'
<% :-* Q
<!#4 *-: QH)$-@H)$
Q@
32
F
4
SERIES
TOPIC
Multiplication and Division
Copyright © 3P Learning