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SERIES

F

Name _____________________________________

Multiplication and Division

Copyright ©

Contents

          ______________________________________    _________________________      _________________________________________     _________________________________    ___________________________________ !   "  #     _________________________________  "  ___________________________  $"   _______________________________________      _________________________________________  "  _______________________________________ % &' $!!(     _______________________________     ________________________________  division ______________________________________________  ") $ ________________________________  " _______________________________________ * +,, "!#%!  - $  apply __________________________________   ' apply __________________________________   ƚ

Ʀźĭ ЊΑaź

_____________________________________  puzzles.-.apply ________________________________________

Date completed

............../............../ ............../............../ ............../............../ ............../............../ ............../............../ ............../............../ ............../............../ ............../............../ ............../............../ ............../............../ ............../............../ ............../............../ ............../............../ ............../............../ ............../............../ ............../............../ ............../............../ ............../............../ ............../............../

Series F ... Multiplication and Division

Series Authors:

Rachel Flenley

Nicola Herringer

SERIES TOPIC

1 C1

Multiplication and Division

ͧopyright © 39 Learning

5ƚǒĬƌźƓŭ źƭ ğ ǒƭĻŅǒƌ ƭƷƩğƷĻŭǤ Ʒƚ ǒƭĻ ǞŷĻƓ ƒǒƌƼƦƌǤźƓŭƷ͵

ƚ ƒǒƌƼƦƌǤ ğ ƓǒƒĬĻƩ ƷĬǤ ŅƚǒƩͲ ķƚǒĬƌĻ źƷ ƷǞźĭĻ͵ ƚ ƒǒƌƼƦƌǤ ğ ƓǒƒĬĻƩ ĬƷǤ ĻźŭŷƷͲ ķƚǒĬƌĻ źƷ ƷŷƩĻĻ ƼƒĻƭ.

15 × 4 ķƚǒĬƌĻ ƚƓĭĻ ў ЌЉ 13 × 8 double once = 26

ķƚǒĬƌĻ ƷǞźĭĻ ў ЏЉ ķƚǒĬƌĻ ƷǞźĭĻ ў ЎЋ

ķƚǒĬƌĻ ƷŷƩĻĻ ƼƒĻƭ ў ЊЉЍ wental multiplication strategies Y doubling strategy

1

    14 6 7 В

2Ў3DЊЉЋЉ

ЌЉ

ЎЉ

ЍЉ

ЌЎЋЎЊЎD

612
24
16 Б

32ВЏВD2

      a 4 _________ __________ _________ __________ _________ b 3 _________ __________ _________ __________ _________ c Ў _________ __________ _________ __________ _________ d ЋЎ _________ __________ _________ __________ _________ e 7 _________ __________ _________ __________ _________ f АЎ _________ __________ _________ __________ _________2            3Б16

ЎЉ4

ЍЉ

ЋБ

ЌЉЉ224ЍЉ64

ВЏ

T

wo sets of twins turn 12. They decide to have a joint birthday party with 1 giant cake but they all want

       4abc

SERIES TOPIC

F1 2

Multiplication and Division

Copyright © 3P Learning

Mental multiplication strategies - doubling strategy

...ƭĻ ƷŷĻ ķƚǒĬƌźƓŭ ƭƷƩğƷĻŭǤ Ʒƚ ƭƚƌǝĻ ƷŷĻƭĻʹ

a ЊЋ ќ Б ____________ ___________ ___________ b ЊЍ ќ Б ____________ ___________ ___________ c ЋЎ ќ Б ____________ ___________ ___________ d ЋЊ ќ Б ____________ ___________ ___________ e ЊЌ ќ Б ____________ ___________ ___________ f ЊЏ ќ Б ____________ ___________ ___________6 24

× 2× 4ќ Б

Work out the answers in your head using the appropriate doubling strategy. Use a table like the one above if it helps. 7 a

ЊБ ќ Ѝ ў

d ЋЍ ќ Б ў b 16 × 4 = e ЊЎ ќ Б ў c 26 × 4 =
f ЋЋ ќ Б ў 5

× 2× 4

bźĭƉ͸ƭ ķğķ ƚňĻƩĻķ ŷźƒ ƷǞƚ ƒĻƷŷƚķƭ ƚŅ ƦğǤƒĻƓƷ ŅƚƩ ŷĻƌƦźƓŭ ǞźƷŷ ğ Ў ǞĻĻƉ ƌğƓķƭĭğƦźƓŭ ƦƩƚƆĻĭƷ͵

aĻƷŷƚķ Њʹ υЋЍ ğ ǞĻĻƉ ŅƚƩ Ў ǞĻĻƉƭ͵

aĻƷŷƚķ Ћʹ υБ ŅƚƩ ƷŷĻ ŋƩƭƷ ǞĻĻƉͲ ƷŷĻƓ ķƚǒĬƌĻ ƷŷĻ ƦƷğǤƒĻƓƷ Ļğĭŷ ǞĻĻƉ͵

‘ŷźĭŷ ƒĻƷŷƚķ Ǟƚǒƌķ ĻğƩƓ bźĭƉ ƷŷĻ ƒƚƭƷƷ ƒƚƓĻǤͪ ‘ŷǤͪ

8 96
112
84
32

...ƭĻ ƷŷĻ ķƚǒĬƌźƓŭ ƭƷƩğƷĻŭǤ Ʒƚ ƭƚƌǝĻ ƷŷĻƭĻʹ

a 13 × 4 __________ __________ b 16 × 4 __________ __________ c 24
× 4 __________ __________ d ЋЎ × 4 __________ __________ e 32
× 4 __________ __________ f 21
× 4 __________ __________ g ЌЎ × 4 __________ __________2652 ƚ ƒǒƌƼƦƌǤ ĬǤ ЍͲ ķƚǒĬƌĻ ƷǞźĭĻ͵ ƚ ƒǒƌƼƦƌǤ ĬǤ БͲ ķƚǒĬƌĻ ƷŷƩĻĻ ƼƒĻƭ͵

SERIES TOPIC

3 C1

Multiplication and Division

ͧopyright © 39 Learning

a cbd

‘ŷĻƓ ǞĻ ƒǒƌƼƦƌǤ ĬǤ ЊЉ ǞĻ ƒƚǝĻ ƷŷĻ ƓǒƒĬĻƩ ƚƓĻ ƦƌğĭƷĻ ǝğƌǒĻ Ʒƚ ƷŷĻ ƌĻũ͵

‘ŷĻƓ ǞĻ ƒǒƌƼƦƌǤ ĬǤ ЊЉЉ ǞĻ ƒƚǝĻ ƷŷĻ ƓǒƒĬĻƩ ƷǞƚ ƦƌğĭĻ ǝğƌǒĻƭ Ʒƚ ƷŷĻ ƌĻũ͵

‘ŷĻƓ ǞĻ ƒǒƌƼƦƌǤ ĬǤ ЊͲЉЉЉ ƷǞĻ ƒƚǝĻ ƷŷĻ ƓǒƒĬĻƩ ƷŷƩĻĻ ƦƌğĭĻ ǝğƌǒĻƭ Ʒƚ ƷŷĻ ƌĻũ͵

[ƚƚƉ ğƷ ŷƚǞ Ʒŷźƭ ǞƚƩƉƭ ǞźƷŷ ƷŷĻ ƓǒƒĬĻƩ ЍЎʹ

Ten Thousands Thousands 

Tens Ones 4Ў

4ЎЉ

4ЎЉЉ

4ЎЉЉЉ

wental multiplication strategies Y multiply by 1Бs 1ББs and 1БББs

ќ ЊЉ

ќ ЊЉЉ

ќ ЊͲЉЉЉ

)&  *9/*99*/999 a ЊЍ ќ ЊЉ ў d ВЋ ќ ЊЉ ў g ЊЊ ќ ЊͲЉЉЉ ў b ЊЍ ќ ЊЉЉ ў e ВЋ ќ ЊͲЉЉЉ ў h ЊЊ ќ ЊЉЉ ў c ЊЍ ќ ЊͲЉЉЉ ў f ВЋ ќ ЊЉЉ ў i ЊЊ ќ ЊЉ ў 1 ,  2 :$ & ! ,#  !      ;< *99=>?0;,       !/       #  *9  & /@   '9    3

T Th Th  T O

17

ќ ЊЉ

ќ ЊЉЉ

ќ ЊͲЉЉЉ

T Th Th  T O

43

ќ ЊЉ

ќ ЊЉЉ

ќ ЊͲЉЉЉ

T Th Th  T O

БЎ

ќ ЊЉ

ќ ЊЉЉ

ќ ЊͲЉЉЉ

T Th Th  T O

ВВ

ќ ЊЉ

ќ ЊЉЉ

ќ ЊͲЉЉЉ

SERIES TOPIC

F1 4

Multiplication and Division

Copyright © 3P Learning

LƷ źƭ ğƌƭƚ ŷğƓķǤ Ʒƚ ƉƓƚǞ ŷƚǞ Ʒƚ ƒǒƌƼƦƌǤ ƒǒƌƼƦƌĻƭƷ ƚŅ ЊЉ ƭǒĭŷ ğƭ ЋЉ ƚƩ ƷЋЉЉ źƓ ƚǒƩ ŷĻğķƭ͵

4

× Ћ ŷĻƌƦƭ ǒƭ ǞƚƩƉ ƚǒƷ Ѝ × ЋЉʹ Ѝ × Ћ ў Б Ѝ × ЋЉ ў БЉ

‘Ļ ĭğƓ ĻǣƦƩĻƭƭ Ʒŷźƭ ğƭ Ѝ

× 2 × ЊЉ ў БЉ IƚǞ Ǟƚǒƌķ Ǥƚǒ ǞƚƩƉ ƚǒƷ Ѝ × ЋЉЉͪ

Mental multiplication strategies - multiply by 10s, 100s and 1,000s

...ƭĻ ƦğdžĻƩƓƭ Ʒƚ ŷĻƌƦ Ǥƚǒ ƭƚƌǝĻ ƷŷĻƭĻʹ4

a

Ў ќ Ћ ____________ Ў ќ ЋЉ ____________ Ў ќ ЋЉЉ __________

b

Ћ ќ В ____________ Ћ ќ ВЉ ____________ Ћ ќ ВЉЉ __________

c

6 × $4 ____________ Џ ќ υЍЉ ____________ Џ ќ υЍЉЉ __________

d

Б ќ Ќ ____________ Б ќ ЌЉ ____________ Б ќ ЌЉЉ __________

e

3 × $7 ____________ Ќ ќ υАЉ ____________ Ќ ќ υАЉЉ __________

f

Ћ ќ Б ____________ ЋЉ ќ Б ____________ ЋЉЉ ќ Б __________

g

Ќ ќ В ____________ ЌЉ ќ В ____________ ЌЉЉ ќ В __________

CźƓźƭŷ ƷŷĻƭĻ ĭƚǒƓƼƓŭ ƦğdžĻƩƓƭʹ

a ЊЉ ЋЉ _________ _________ __________ _________ b ЋЉ ЍЉ _________ _________ __________ _________ c ЌЉ ЏЉ _________ _________ __________ _________ d ЍЉ БЉ _________ _________ __________ _________ e ЎЉ ЊЉЉ _________ _________ __________ _________ f ЊЉЉ ЋЉЉ _________ _________ __________ _________ g ЋЉЉ ЍЉЉ _________ _________ __________ _________ 6

ЌЉ

БЉ

ЍЉЉ

ЊͲЋЉЉЋЍЉ

ЊЎЉ

ЊЎЉ!ƓƭǞĻƩ ƷŷĻƭĻ ƦƩƚĬƌĻƒƭʹ a

WğĭƉ ƩǒƓƭ ЎЉ Ɖƒ ƦĻƩ ǞĻĻƉ͵ IƚǞ ŅğƩ ķƚĻƭ ŷĻ ƩƷǒƓ ƚǝĻƩ ЊЉ ǞĻĻƉƭͪ

b

Iǒŭƚ ĻğƩƓƭ ğƓ ğƌƌƚǞğƓĭĻ ƚŅ υЋЉ ƦĻƩ ǞĻĻƉ͵ LŅ ŷĻ ƭğǝĻƭ ŷğƌŅ ƚŅ ƷŷźƭͲ ŷƚǞ ƒǒƷĭŷ

Ǟźƌƌ ŷĻ ŷğǝĻ ƭğǝĻķ ğƷ ƷŷĻ ĻƓķ ƚŅ Б ǞĻĻƉƭͪ

c

ŷĻ ƭǒƒ ƚŅ ƷǞƚ ƓǒƒĬĻƩƭ źƭ ЋБ͵ ‘ŷĻƓ Ǥƚǒ ƒǒƌƼƦƌǤ ƷŷĻƒ ƷƚŭĻƷŷĻƩͲ ƷŷĻ

ğƓƭǞĻƩ źƭ ЊЏЉ͵ ‘ŷğƷ ğƩĻ ƷŷĻ ƓǒƒĬĻƩƭͪ

5

ЏЉ

ЋЉЉ

If you"re struggling with

ǤƚǒƩ ƷğĬƌĻƭͲ ŭĻƷ ƚƓƷƚ [źǝĻ ağƷŷƌĻƼĭƭ ğƓķ ƦƩğĭƼĭĻͧ

SERIES TOPIC

5 C1

Multiplication and Division

ͧopyright © 39 Learning

{ƚƒĻƼƒĻƭ źƷ͸ƭ ĻğƭźĻƩ Ʒƚ ƭƦƌźƷ ğ ƓǒƒĬĻƩ źƓƷƚ ƦğƩƷƭ ğƓķ ǞƚƩƉ ǞźƷŷ ƷŷĻ ƦğƩƷƭ ƭĻƦğƷƩğƷĻƌǤ͵

[ƚƚƉ ğƷ ЏЍ

× Б

{ƦƌźƷ ƷŷĻ ƓǒƒĬĻƩ źƓƷƚ ЏЉ ğƓķ Ѝ

‘ƚƩƉ ƚǒƷ ΛЏЉ

× БΜ ğƓķ ƷŷĻƓ ΛЍ × БΜ

!ķķ ƷŷĻ ğƓƭǞĻƩƭ ƷƚŭĻƷŷĻƩ ЍБЉ њ ЌЋ ў ЎЊЋ

wental multiplication strategies Y split strategy      E  1      E  ,   & #   a

ЍБ ќ Б ў ΗΗΗΗΗΗΗΗΗΗ њ ΗΗΗΗΗΗΗΗΗΗ ў

b

ЎЋ ќ А ў ΗΗΗΗΗΗΗΗΗΗ њ ΗΗΗΗΗΗΗΗΗΗ ў

c

В ќ ЍЌ ў ΗΗΗΗΗΗΗΗΗΗ њ ΗΗΗΗΗΗΗΗΗΗ ў

d

Б ќ ЋВ ў ΗΗΗΗΗΗΗΗΗΗ њ ΗΗΗΗΗΗΗΗΗΗ ў

e

БЏ ќ А ў ΗΗΗΗΗΗΗΗΗΗ њ ΗΗΗΗΗΗΗΗΗΗ ў

2

3These problems have been worked out incorrectly. Fircle where it all went wrong.

a 46 × 4 ΛЍЉ ќ ЍΜ њ ΛЏ ќ ЍΜ ΗΗΗΗΗΗΗ њ ΗΗΗΗΗΗΗ = d 37 × 7 ΛΗΗΗ ќ ΗΗΗΜ њ ΛΗΗΗ ќ ƷΗΗΗΜ ΗΗΗΗΗΗΗ њ ΗΗΗΗΗΗΗ = b АЍ ќ Ў ΛΗΗΗ ќ ΗΗΗΜ њ ΛΗΗΗ ќ ƷΗΗΗΜ ΗΗΗΗΗΗΗ њ ΗΗΗΗΗΗΗ = e ЏЋ ќ Б ΛΗΗΗ ќ ΗΗΗΜ њ ΛΗΗΗ ќ ƷΗΗΗΜ ΗΗΗΗΗΗΗ њ ΗΗΗΗΗΗΗ = c ЍБ ќ Ѝ ΛΗΗΗ ќ ΗΗΗΜ њ ΛΗΗΗ ќ ƷΗΗΗΜ ΗΗΗΗΗΗΗ њ ΗΗΗΗΗΗΗ = f ВЊ ќ Ў ΛΗΗΗ ќ ΗΗΗΜ њ ΛΗΗΗ ќ ΗΗΗΜƷ ΗΗΗΗΗΗΗ њ ΗΗΗΗΗΗΗ =

ItGs a good thing I

know how to work   &  C a 37 × 6
ΛЌЉ ќ ЏΜ њ ΛА ќ ЏΜƷ ЊБЉ њ ЊЌ ў ЊВЌb ЊА ќ Ў ΛЊЉ ќ ЎΜ њ ΛА ќ ЎƷΜ АЉ њ ЌЎ ў ЊЉЎc ЌЋ ќ В ΛЌЉ ќ ВΜ њ ΛЋ ќ ВΜƷ ЋА њ ЊБ ў ЍЎ

SERIES TOPIC

F1 6

Multiplication and Division

Copyright © 3P Learning

Mental multiplication strategies - split strategy

49ğĭŷ ƷƩğźƌ ĭƚƓƷğźƓƭ Ћ ƒǒƌƼƦƌźĭğƼƚƓ ƦƩƚĬƌĻƒƭ ğƓķ ƭƷĻƦƭ Ʒƚ ƭƚƌǝĻ ƷŷĻƒ͵ hƓƌǤ ƚƓĻ ƷƩğźƌ ŷğƭ ĬĻĻƓ ƭƚƌǝĻķ

corr ectly. There are errors in the other two. Find and color the winning trail.

CLbL{I

АБ

42 × 7ЎБ ќ Б17 × 3

ΛЍЉ ќ АΜ њ ΛЋ ќ АΜЍЉЉ њ ЏЍЌЉ њ ЋЊ

ЌЌ ќ В13 × 6ЊЏ ќ В

ЎЊ464ЋВЍ

ΛЌЉ ќ ВΜ њ ΛЌ ќ ВΜΛЊЉ ќ ЏΜ њ ΛЌ ќ ЏΜΛЊЉ ќ ВΜ њ ΛЏ ќ ВΜ

ЋВЊ114

{!w

SERIES TOPIC

7 C1

Multiplication and Division

ͧopyright © 39 Learning

‘ŷĻƓ ƒǒƌƼƦƌǤźƓŭ ǞĻ ĭğƓ ƩƚǒƓķ Ʒƚ ğƓ ĻğƭźĻƩ ƓǒƒĬĻƩ ƷğƓķ ƷŷĻƓ ğķƆǒƭƷ͵

[ƚƚƉ ŷƚǞ ǞĻ ķƚ Ʒŷźƭ ǞźƷŷ Ѝ ќ ЋВʹ

ЋВ źƭ ĭƌƚƭĻ Ʒƚ ЌЉ͵ ‘Ļ ĭğƓ ķƚ Ѝ ќ ЌЉ źƓ ƚǒƩ ƷŷĻğķƭ ĬĻĭğǒƭĻ ǞĻ ƉƓƚǞ Ѝ ќ Ќ ў ЊЋ

Ѝ ќ ЌЉ ў ЊЋЉ

‘Ļ ŷğǝĻ Ʒƚ ƷğƉĻ ƚň Ѝ ĬĻĭğǒƭĻ ǞĻ ǒƭĻķ ƚƓĻ ŭƩƚǒƦ ƚŅ Ѝ Ʒƚƚ ƒğƓǤʹ ЊЋЉ Α ΛЊ ќ ЍΜ Ʒў ЊЊЏ

Ѝ ќ ЋВ ў ЊЊЏ

wental multiplication strategies Y compensation strategy     E  ,@   &

a ЊВ ќ Ќ ў ΗΗΗΗΗΗΗΗ ќ ΗΗΗΗΗΗΗΗ Ʒ Α ΗΗΗΗΗΗΗΗ ў

b Б ќ ЋВ ў ΗΗΗΗΗΗΗΗ ќ ΗΗΗΗΗΗΗΗ Ʒ Α ΗΗΗΗΗΗΗΗ ў

c ЊБ ќ Џ ў ΗΗΗΗΗΗΗΗ ќ ΗΗΗΗΗΗΗΗƷ Α ΗΗΗΗΗΗΗΗ ў

d

А ќ ЌВ ў ΗΗΗΗΗΗΗΗ ќ ΗΗΗΗΗΗΗΗ Ʒ Α ΗΗΗΗΗΗΗΗ ў

e ЋБ ќ Ў ў ________ × ________ - ________Ʒ = 1 2   ( & ,@  

&a ЍЊ ќ Ќ ў ΗΗΗΗΗΗΗΗ ќ ΗΗΗΗΗΗΗΗ Ʒ њ ΗΗΗΗΗΗΗΗ ў

b

БЊ ќ Ѝ ў ΗΗΗΗΗΗΗΗ ќ ΗΗΗΗΗΗΗΗƷ њ ΗΗΗΗΗΗΗΗ ў

c

ЋЋ ќ В ў ΗΗΗΗΗΗΗΗ ќ ΗΗΗΗΗΗΗΗ Ʒ њ ΗΗΗΗΗΗΗΗ ў

d

ЌЋ ќ В ў ΗΗΗΗΗΗΗΗ ќ ΗΗΗΗΗΗΗΗ Ʒ њ ΗΗΗΗΗΗΗΗ ў

e 7 × 62 = ΗΗΗΗΗΗΗΗ ќ ΗΗΗΗΗΗΗΗ њ ƷΗΗΗΗΗΗΗΗ ў

20 3357

40 3 3

123

‘Ļ ĭğƓ ğƌƭƚ ğķƆǒƭƷ ǒƦ͵ [ƚƚƉ ŷƚǞ ǞĻ ķƚ Ʒŷźƭ ǞźƷŷ Џ ќ ЏЋʹ

ЏЋ źƭ ĭƌƚƭĻ Ʒƚ ЏЉ͵ ‘Ļ ĭğƓ ķƚ Џ ќ ЏЉ źƓ ƚǒƩ ƷŷĻğķƭ ĬĻĭğǒƭĻ ǞĻ ƉƓƚǞ Џ ќ Џ ў ЌЏ

Џ ќ ЏЉ ў ЌЏЉ

‘Ļ ŷğǝĻ Ʒƚ ƷŷĻƓ ğķķ Ћ ƒƚƩĻ ƌƚƷƭ ƚŅ Џʹ ЌЏЉ њ ЊЋ Ʒ ў ЌАЋ

6 × 62 = 372

L   strategy with numbers such as '>0- 

SERIES TOPIC

F1 8

Multiplication and Division

Copyright © 3P Learning

Mental multiplication strategies - compensation strategy

LƓ Ʒŷźƭ ğĭƼǝźƷǤ Ǥƚǒ͸ƌƌ ǞƚƩƉ ğƌƚƓŭƭźķĻ ğ ƦğƩƷƓƭĻƩ͵ —ƚǒ͸ƌƌ Ļğĭŷ ƓĻĻķ ƷǞƚ ķźĭĻ ğƓķ ǤƚǒƩ ƚǞƓ ĭƚƦǤ

ƚŅ Ʒŷźƭ ƦğŭĻ͵ CƚƩ Ļğĭŷ ƌźƓĻͲ Ʃƚƌƌ ƷŷĻ ķźĭĻ Ʒƚ ŋƓķ ƷŷĻ ƷĻƓƭ ķźŭźƷ ğƓķ ƷŷĻƓ Ʃƭƚƌƌ źƷ ğŭğźƓ Ʒƚ ŋƓķ ƷŷĻ

ƒǒƌƼƦƌźĻƩ͵ —ƚǒƩ ƦğƩƷƓĻƩ Ǟźƌƌ ķƚ ƭƷŷĻ ƭğƒĻ͵ ...ƭĻ ƷŷĻ ĭƚƒƦĻƓƭğƼƚƓ ƭƷƩğƷĻŭǤ Ʒƚ ƒĻƓƷğƌƌǤ ǞƚƩƉ

out the answers to the problems. 3 a

/ŷĻĭƉ Ļğĭŷ ƚƷŷĻƩ ͸ƭ ĭğƌĭǒƌğƼƚƓƭ͵ —ƚǒ ƒğǤ ǞğƓƷ Ʒƚ ǒƭĻ ğ ĭğƌĭǒƌğƷƚƩ͵

b

bƚǞͲ ǒƭĻ ƷŷĻ ĭğƌĭǒƌğƷƚƩ Ʒƚ ğķķ ǤƚǒƩ ğƓƭǞĻƩƭ͵ ŷĻ ƦĻƩƭƚƓ ǞźƷŷ ƷŷĻ ŷźŭŷĻƭƷ ƭĭƚƩĻ ǞźƓƭ͵

TensOnesaǒƌƼƦƌźĻƩ!ƓƭǞĻƩ

1×=

9 ×= 2 ×= 1 ×= 8 ×= 1 ×= 9 ×= 8 ×= 2 ×= 1 ×= copy

SERIES TOPIC

P C1

Multiplication and Division

ͧopyright © 39 Learning

CğĭƷƚƩƭ ğƩĻ ƷŷĻ ƓǒƒĬĻƩƭ ǞĻ ƒǒƌƼƦƌǤ ƷƚŭĻƷŷĻƩ Ʒƚ ŭĻƷ Ʒƚ ğƓƚƷŷĻƩ ƓǒƒĬĻƩʹ

IƚǞ ƒğƓǤ ŅğĭƷƚƩƭ ķƚĻƭ ƷŷĻ ƓǒƒĬĻƩ ЊЋ ƷŷğǝĻͪ Ѝ ќ Ќ ў ЊЋͲ Џ ќ Ʒ Ћ ў ЊЋͲ Њ ќ ЊЋ ў ƷЊЋ

ЍͲ ЌͲ ЏͲ ЋͲ Њ ğƓķ ЊЋ ğƩĻ ğƌƌ ŅğĭƷƚƩƭ ƚŅ ЊЋ͵

wental multiplication strategies Y factors and multiples B & &  1       ,@   & a

ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƷƚƩ ΗΗΗΗΗ ƦĻƚƦƌĻ ĭğƓ ƭŷğƩĻ ЊЏ ƦźĻĭĻƭ ƚŅ ĭğƓķǤ ĻǝĻƓƌǤ͵

b

ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƷƚƩ ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƦĻƚƦƌĻ ĭƷğƓ ƭŷğƩĻ ЋЉ ƭƌźĭĻƭ ƚŅ Ʀźǩǩğ ĻǝĻƓƌǤ͵

c

ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƷƚƩ ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƚƩ ƷΗΗΗΗΗ ƦĻƚƦƌĻ ĭğƓ ƭŷğƩĻ ЋЍ ĭŷĻƩƩźĻƭ͵

d

ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƷƚƩ ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƚƩ ƷΗΗΗΗΗ ƦĻƚƦƌĻ ĭğƓ ƭŷğƩĻ ЌЉ ƦĻƓĭźƌƭ͵

e

ΗΗΗΗΗ ƚƩ ΗΗΗΗΗ ƦĻƚƦƌĻ ĭğƓ ƭŷğƩĻ Ў Ĭğƌƌƭ ĻǝĻƓƌǤ͵2

 @ & &Q0-  3 ŅğĭƷƚƩŅğĭƷƚƩǞŷƚƌĻ ƓǒƒĬĻƩ×=

124816

a c e gbdfhЊБ 14 16

ЌЉЋЎ

В

ЊЎ

42

R factor divides into

a number evenly with no remainder.

SERIES TOPIC

F1

ЊЉ

Multiplication and Division

Copyright © 3P Learning

abcd

aǒƌƼƦƌĻƭ ğƩĻ ƷŷĻ ğƓƭǞĻƩƭ ǞĻ ŭĻƷ ǞŷĻƓ ǞĻ ƒǒƌƼƦƌǤ Ћ ŅğĭƷƚƩƭ͵

ŷźƓƉ ğĬƚǒƷ ƷŷĻ Ќ ƼƒĻƭ ƷƷğĬƌĻƭ ǞŷĻƩĻ Ќ źƭ ğƌǞğǤƭ ğ ŅğĭƷƚƩ͵

‘ŷğƷ ğƩĻ ƷŷĻ ƒǒƌƼƦƌĻƭ ƚŅ Ќͪ

ЌͲ ЏͲ ВͲ ЊЋͲ ЊЎͲ ЊБͲ ЋЊͲ ƷЋЍͲ ЋАͲ ЌЉͲ ЌЌ ğƓķ ЌЏ Ͷ

bǒƒĬĻƩƭ ĭğƓ ĬĻ ĻźƷŷĻƩ ŅğĭƷƚƩƭ ƚƩ ƒǒƌƼƦƌĻƭ ķĻƦĻƷƓķźƓŭ ƚƓ ǞŷĻƩĻ ƷŷĻǤ ƭźƷ źƓ ƷŷĻ ƓǒƒĬĻƩ ƭƷĻƓƷĻƓĭĻ͵

Mental multiplication strategies - factors and multiples

Cźƌƌ źƓ ƷŷĻ ŭğƦƭ ƚƓ ƷŷĻƭĻ ƒǒƌƼƦƌĻ ĬƭƚğƩķƭʹ 4

5 4 8 16 5

ЊЉ

9 63
7 35

/ŷƚƚƭĻ Ћ ƓǒƒĬĻƩƭ ĬĻƷǞĻĻƓ Ћ ğƓķ Ў ğƓķ ƦǒƷ ƭƷŷĻƒ źƓ ƷŷĻ ŋƩƭƷ ŅƩğƒĻ ğƭ ŅğĭƷƚƩƭ͵ —ƚǒƩ ğƓƭǞĻƩ źƭ ƷŷĻ

ƒǒƌƼƦƌĻ͵ bƚǞ ƷğƉĻ ƷŷğƷ ƒǒƌƼƦƌĻ ğƓķ ƒğƉĻ źƷ ğ ŅğĭƷƚƩ źƓ ğƓƚƷŷĻƩ ƓǒƒĬĻƭƩ ƭĻƓƷĻƓĭĻ͵ ‘ƩźƷĻ źƓ ƷŷĻ ƚƷŷĻƩ

ŅğĭƷƚƩ ğƓķ ƭƚƌǝĻ ƷŷĻ ƦƩƚĬƌĻƒ͵ ŷĻƓ ƒğƉĻ ƷŷĻ ğƓƭǞĻƩ ğ ŅğĭƷƚƩ ğŭğźƓ͵ /ğƓ Ǥƚǒ ŋƌƌ ƷŷĻ ŭƩźķͪ ...ƭĻ ƭğ ĭğƌĭǒƌğƷƚƩ

ŅƚƩ ƷŷĻ ƌğƩŭĻƩ ƦƩƚĬƌĻƒƭ͵ ŷĻ ŋƩƭƷ ƚƓĻ ŷğƭ ĬĻĻƓ ķƚƓĻƭ ŅƚƩ Ǥƚǒ͵

a × = × = × = b × = × = × = c × = × = × = d × = × = × =

3ŅğĭƷƚƩƒǒƌƼƦƌĻ×=

31224422122448

SERIES TOPIC

11 C

Multiplication and Division

ͧopyright © 39 Learning

2 abc

YƓƚǞźƓŭ ƚǒƩ ƒǒƌƼƦƌźĭğƷƼƚƓ ŅğĭƷƭ ŷĻƌƦƭ ǒƭ ǞźƷƷŷ ķźǝźƭźƚƓ ğƭ ƷŷĻǤ ķƚƷ ƷŷĻ ƩĻǝĻƩƭĻ ƚŅ Ļğĭŷ ƚƷŷĻƩ͵

ŷĻǤ ğƩĻ źƓǝĻƩƭĻ ƚƦĻƩğƼƚƓƭ͵ Ќ ќ Ў ў ЊЎ Ʒ ЊЎ ѝ Ў ў ƷЌ wental division strategies Y use multiplication facts  # & &    ! E   a ЎЏ ѝ А _______ ќ А ў ЎЏ ЎЏ ѝ А ў b ЊЋЊ ѝ ЊЊ _______ × 11 = 121 ЊЋЊ ѝ ЊЊ ў c АЋ ѝ Б _______ ќ Б ў АЋ АЋ ѝ Б ў d ЍВ ѝ А _______ ќ А ў ЍВ ЍВ ѝ А ў e ЌЏ ѝ В _______ ќ В ў ЌЏ ЌЏ ѝ В ў f ЏЍ ѝ Б _______ ќ Б ў ЏЍ ЏЍ ѝ Б ў g

ЊЉБ ѝ ЊЋ _______ ќ ЊЋ ў ЊЉБ ЊЉБ ѝ ЊЋ ў

1 "   a

БЊ ѝ В ў

c ЋЊ ѝ Ќ ў e ЍЋ ѝ А ў g ЌЏ ѝ Ѝ ў i ЌВ ѝ Ќ ў b ЍЉ ѝ Ў ў d ЎЍ ѝ Џ ў f ЏЌ ѝ В ў h ЍЎ ѝ В ў j ЋЍ ѝ Џ ў 2 3   !      & 

БЊ В

ЎЍ

72
63

ЍЎ 36 ЊБ

ѝ В 3616

ЋБ

44
32
Б 24 ЍЉ

ѝ Ѝ36 24

ЏЉ

42

ЌЉ

ЊБЍБ6

ѝ Џ

8

Doing math

without knowing   facts is hard. B  makes your life much easier. Its worth persevering EC

SERIES TOPIC

F 12

Multiplication and Division

Copyright © 3P Learning

2

YƓƚǞźƓŭ ƚǒƩ ŅğĭƷ ŅğƒźƌźƷĻƭ źƭ ğƌƭƚ ŷĻƌƦŅǒƌ͵

Ќ ќ Ў ў ЊЎ Ў ќ Ќ ў ЊЎ ЊЎ ѝ Ў ў Ќ ЊЎ ѝ Ќ ў Ў

Mental division strategies - use multiplication facts a А ќ Б ў ЎЏ Б ќ А ў ЎЏ ѝ ў Б ѝ Б ў А b Б ќ В ў АЋ В ќ Б ў АЋ ѝ ў В ѝ В ў Бc А ќ В ў ЏЌ В ќ А ў ЏЌ ѝ ў В ѝ В ў А 4

5/ƚƒƦƌĻƷĻ ƷŷĻ ŅƚƌƌƚǞźƓŭ ƦğdžĻƩƓƭ͵ IƚǞ ƒğƓǤ ƒƚƩĻ ƒǒƌƼƦƌźĭğƼƚƓ ğƓķ ķźǝźƭźƚƓ ŅğĭƷƭ ĭğƓ Ǥƚǒ ŋƓķͲ ŭźǝĻƓ ƷŷĻ

ŋƩ

ƭƷ ŅğĭƷͪ

‘ƩźƷĻ ķƚǞƓ ğƓƚƷŷĻƩ ƒǒƌƼƭƦƌźĭğƼƚƓ ŅğĭƷ ğƓķ ƷǞƚ ķźǝźƭźƚƓ ŅğĭƷƭ ŅƚƩ Ļğĭŷ ƨǒĻƭƼƚƓ͵

6[ƚƚƉ ğƷ ƷŷĻƭĻ ƷǞƚ ķźǝźƭźƚƓ ŅğĭƷƭʹ ЋЉ ѝ Ў ў Ѝ ğƓķ ЋЉ ѝ Ѝ ў Ў

LƒğŭźƓĻ Ǥ

ƚǒ͸ƩĻ ĻǣƦƌğźƓźƓŭ Ʒƚ ğ ǤƚǒƓŭĻƩ ĭŷźƌķ ŷƚǞ ƷŷĻǤ͸ƩĻ ƩĻƌğƷĻķ ǤĻƷ ķźňĻƩĻƓƷ͵ IƚǞ Ǟƚǒƌķ Ǥƚǒ ķƚ źƷͪ

‘ŷğƷ Ǟƚǒƌķ Ǥƚǒ ƭğǤΉǞƩźƷĻΉķƩğǞͪ

a 6 × 7 = 42 d ЊА ќ Б ў ЊЌЏb Ў ќ В ў ЍЎ e ЊЋ ќ Б ў ВЏc В ќ Џ ў ЎЍ f 11 × 21 = 231

SERIES TOPIC

13 C

Multiplication and Division

ͧopyright © 39 Learning

2

‘ŷĻƓ ǞĻ ķźǝźķĻ ĬǤ ЊЉ ǞĻ ƒƚǝĻ ƷŷĻ ƓǒƒĬĻƩ ƚƓĻ ƦƌğĭƷĻ ǝğƌǒĻ Ʒƚ ƷŷĻ ƩźŭŷƷ͵

‘ŷĻƓ ǞĻ ķźǝźķĻ ĬǤ ЊЉЉ ǞĻ ƒƚǝĻ ƷŷĻ ƓǒƒĬĻƩ ƷǞƚ ƦƌğĭĻ ǝğƌǒĻƭ Ʒƚ ƷŷĻ ƩźŭŷƷ͵

‘ŷĻƓ ǞĻ ķźǝźķĻ ĬǤ ЊͲЉЉЉ ǞĻ ƒƚǝĻ ƷŷĻ ƓǒƒĬĻƩ ƷŷƩĻĻ ƦƌğĭĻ ǝğƌǒĻƭ Ʒƚ ƷŷĻ ƩźŭŷƷ͵

[ƚƚƉ ǞŷğƷ ŷğƦƦĻƓƭ Ʒƚ ЍЎͲЉЉЉ ǞŷĻƓ ǞĻ ğƦƦƌǤ ƷŷĻƭĻ ƩǒƌĻƭʹƷ

Ten Thousands Thousands 

Tens Ones

4ЎЉЉЉ

4ЎЉЉ

4ЎЉ

4Ў wental division strategies Y divide by 1Бs 1ББs and 1БББs

ѝ ЊЉ

ѝ ЊЉЉ

ѝ ЊͲЉЉЉ

Z 

    E   a

‘ŷğƷ ƓǒƒĬĻƩ źƭ ƚƓĻ ƷŷƚǒƭƷğƓķ ƼƒĻƭ ƭƒğƌƌĻƩ ƷŷğƷƓ ЌЋͲЉЉЉͪ

b ‘ŷğƷ ƓǒƒĬĻƩ źƭ ƚƓĻ ŷǒƓķƩƷĻķ ƼƒĻƭ ƭƒğƌƌĻƩ ƷŷğƓƷ ЌЋͲЉЉЉͪ

c ‘ŷğƷ ƓǒƒĬĻƩ źƭ ƚƓĻ ŷǒƓķƩƷĻķ ƼƒĻƭ ƭƒğƌƌĻƩ ƷŷğƓƷ ВЎͲЉЉЉͪ

d ‘ŷğƷ ƓǒƒĬĻƩ źƭ ƷĻƓ ƼƒĻƭ ƭƒğƌƌĻƩ ƷŷğƓ ƷВЎͲЉЉЉͪ

e ‘ŷğƷ ƓǒƒĬĻƩ źƭ ƚƓĻ ŷǒƓķƩƷĻķ ƼƒĻƭ ƭƒğƌƌĻƩ ƷŷğƓƷ БͲБЉЉͪ

f ‘ŷğƷ ƓǒƒĬĻƩ źƭ ƷĻƓ ƼƒĻƭ ƭƒğƌƌĻƩ ƷŷğƓ ƷБͲБЉЉͪ

1 2Z ! &  *9/*99*/999 a cbd

T Th Th  T O

4ЎЉЉЉ

ѝ ЊЉ

ѝ ЊЉЉ

ѝ ЊͲЉЉЉ

T Th Th  T O

43ЉЉЉ

ѝ ЊЉ

ѝ ЊЉЉ

ѝ ЊͲЉЉЉ

T Th Th  T O

БЎЉЉЉ

ѝ ЊЉ

ѝ ЊЉЉ

ѝ ЊͲЉЉЉ

T Th Th  T O

ББЉЉЉ

ѝ ЊЉ

ѝ ЊЉЉ

ѝ ЊͲЉЉЉ

ВͲЎЉЉ

ББ

ВЎЉ

ББЉ

ЌЋЉ

32

SERIES TOPIC

F 14

Multiplication and Division

Copyright © 3P Learning

2 halvehalvehalve

‘ŷĻƓ ƷŷĻ ƷǞƚ ƓǒƒĬĻƩƭ ƭĻĻƒ Ʒƚƚ ƌğƩŭĻ Ʒƚ ǞƚƩƉ ǞźƷŷ źƓ ƚǒƩ ŷĻğķƭͲƷ ǞĻ ĭğƓ ŷğƌǝĻ ƷŷĻƒ ǒƓƼƌ ǞĻ ŭĻƷ

Ʒƚ ğ ķźǝźƭźƚƓ ŅğĭƷ ǞĻ ƩĻĭƚŭƓźǩĻ͵ .ƚƷŷ ƓǒƒĬĻƩƭ ƒǒƭƷ ĬĻ ĻǝĻƓ ŅƚƩ Ʒŷźƭ Ʒƚ ǞƚƩƉ͵

ЊЋЏ ѝ ЊЍ

ΛŷğƌŅ ЊЋЏΜ ѝ ΛŷğƌŅ ЊЍΜ Ʒ ЏЌ ѝ А ў ƷВ

Mental division strategies - halving strategy

tƩğĭƼƭĻ ǤƚǒƩ ŷğƌǝźƓŭ͵ ŷĻ ŋƩƭƷ ƚƓĻ ŷğƭ ĬĻĻƓ ķƚƓĻƭ ŅƚƩ Ǥƚǒ͵1

2IğƌǝĻ Ļğĭŷ ƓǒƒĬĻƩ Ʒƚ ŭĻƷ Ʒƚ ğ ƩĻĭƚŭƓźǩğĬƌĻ ķźǝźƭźƚƓ ŅğĭƷ͵ ŷĻ ŋƩƭƷ ƚƓĻ ŷğƭ ĬĻĻƓ ķƚƓĻƭ ŅƚƩ Ǥƚǒ͵

a

ЊЊЋ ѝ ЊЍ ΗΗΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗΗΗ ў

b

ЊЍЍ ѝ ЊЏ ΗΗΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗΗΗ ў

c

ВЏ ѝ ЊЋ ΗΗΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗΗΗ ў

d

ЋЋЉ ѝ Ѝ ΗΗΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗΗΗ ў

e

ЊЏЋ ѝ ЊБ ΗΗΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗΗΗ ў

3ağƷĭŷ ƷŷĻ ƦƩƚĬƌĻƒƭ ǞźƷŷ ƷŷĻźƩ ŷğƌǝĻķ ĻƨǒźǝğƌĻƓƷƭ͵ ŷĻƓ ƭƚƌǝĻ ƷŷĻ ƦƩƚĬƌĻƒ͵ ŷĻ ŋƩƭƷ ƚƓĻ ŷğƭ ĬĻĻƓ ķƚƓĻƭ

f or you. a ВЉ ѝ ЊБ ЏЉ ѝ Џ = b ЏЍ ѝ ЊЏ 24 ѝ Б = c ЊЋЉ ѝ ЊЋ ЌЎ ѝ А = d АЉ ѝ ЊЍ ЍЎ ѝ В = e ЊЍЍ ѝ ЋЍ 72 ѝ ЊЋ = f ЍБ ѝ ЊЏ 32 ѝ Б = a 32 16

ЎЏ

36

БЍ

ВЏ

b 24

ЍБ

72
144

ЊВЋ

c ЎЉ

ЎЉЉ

ЊͲЉЉЉ

ЋЎЉ

ЊЉЉ

856 7
5

SERIES TOPIC

15 C

Multiplication and Division

ͧopyright © 39 Learning

2

{ƚƒĻƼƒĻƭ ǞĻ ƓĻĻķ Ʒƚ ƉĻĻƦ ŷğƌǝźƓŭ ǒƓƼƌ ǞĻ ƩĻğĭŷ ğƓ ĻğƭǤ ķźǝźƭźƚƓ ŅğĭƷ͵

ЊЍЍ ѝ ЌЏ

АЋ ѝ ЊБ ЌЏ ѝ В ў Ѝ wental division strategies Y halving strategy ]! & # L&  /( @   XJ /    a

216 ѝ ЌЏ ў ΗΗΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗΗΗ ў ΗΗΗΗΗΗΗΗ ѝ ƷΗΗΗΗΗΗΗΗ ў

b

ЊВЏ ѝ ЋБ ў ΗΗΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗΗΗ ў ΗΗΗΗΗΗΗΗ ѝ ƷΗΗΗΗΗΗΗΗ ў

c

224 ѝ ЌЋ ў ΗΗΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗΗΗ ў ΗΗΗΗΗΗΗΗ ѝ ƷΗΗΗΗΗΗΗΗ ў

d

ЊЏБ ѝ ЋЍ ў ΗΗΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗΗΗ ў ΗΗΗΗΗΗΗΗ ѝ ƷΗΗΗΗΗΗΗΗ ў

e

144 ѝ ЌЏ ў ΗΗΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗΗΗ ў ΗΗΗΗΗΗΗΗ ѝ ƷΗΗΗΗΗΗΗΗ ў

f

ЋББ ѝ АЋ ў ΗΗΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗΗΗ ў ΗΗΗΗΗΗΗΗ ѝ ƷΗΗΗΗΗΗΗΗ ў

4 Draw lines to connect numbers that could be doubled or halved to reach each other. 5

ЍБ

ЊЋБ

ЌЉ

64

ЍЉ

ВЏ

ЊЋЎ

16

ЏЉ

ЊЉ

ЋЉ

ЊЋЉ

ЊВЋ

32

ЋЎЏ

ЊЉЉ

ЎЉ

БЉ

ЋЎЉ

ЋЎ

#  !  ! 

—ƚǒ ŷğǝĻ ğƓ ğũĻƩ ƭĭŷƚƚƌ ƆƚĬ ğƷ ƷŷĻ ƌƚĭğƌ ĭğƓķǤ ƭŷƚƦͲ ƒğƉźƓŭ ǒƦ ƷƷŷĻ ƒźǣĻķ ĭğƓķǤ Ĭğŭƭ͵ ƚķğǤͲ Ǥƚǒ ŷğǝĻ Ʒƚ

ĻǝĻƓƌǤ ƭŷğƩĻ ЋББ ƭƉźdžƌĻƭ ğƒƚƓŭ ЍБ ƷĬğŭƭ͵ IƚǞ ƒğƓǤ ƭƉźdžƌĻƭ Ǟźƌƌ Ǥƚǒ ƦǒƷ źƓ Ļğĭŷ Ĭğŭͪ {ŷƷƚǞ Ļğĭŷ ŷğƌǝĻķ

ƭǒƒ͵

6

SERIES TOPIC

F 16

Multiplication and Division

Copyright © 3P Learning

2 bƚǞ ƷƩǤ ƷŷĻƭĻʹ a ВЉ ѝ Џ ў b ЊЉЎ ѝ А ў c АЋ ѝ Ѝ ў d ЊЍЍ ѝ Б = ΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗ ΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗ ΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗ ΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗ ΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗ ΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗ ΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗ ΗΗΗΗΗΗ ѝ ΗΗΗΗΗΗ a ЊЊЋ ѝ Б _____ _____ ѝ Б ѝ Б ΗΗΗΗΗ њ ΗΗΗΗΗ ў d ЏЍ ѝ Ѝ _____ _____ ѝ Ѝ ѝ Ѝ ΗΗΗΗΗ њ ΗΗΗΗΗ ў b БЎ ѝ Ў _____ _____ ѝ Ў ѝ Ў ΗΗΗΗΗ њ ΗΗΗΗΗ ў e ВЊ ѝ А _____ _____ ѝ А ѝ А ΗΗΗΗΗ њ ΗΗΗΗΗ ў c АБ ѝ Џ _____ _____ ѝ Џ ѝ Џ ΗΗΗΗΗ њ ΗΗΗΗΗ ў f ЊЍЍ ѝ Б _____ _____ ѝ Б ѝ Б ΗΗΗΗΗ њ ΗΗΗΗΗ ў

5źǝźƭźƚƓ ƦƩƚĬƌĻƒƭ ğƌƭƚ ĬĻĭƚƒĻ ĻğƭźĻƩ źŅ Ǥƚǒ ƭƦƌźƷ ƷŷĻ ƓǒƒĬĻƩ ƷƷƚ ĬĻ ķźǝźķĻķ źƓƷƚ ƩĻĭƚŭƓźǩğĬƌĻ ŅğĭƷƭ͵

[ƚƚƉ ğƷ ƷŷĻ ƦƩƚĬƌĻƒ ЊЍЍ ѝ В

/ğƓ ǞĻ ķźǝźķĻ ЊЍЍ źƓƷƚ Ћ ƒǒƌƼƦƌĻƭ ƚŅ Вͪ

‘Ļ ĭğƓ ķźǝźķĻ źƷ źƓƷƚ ЎЍ ğƓķ ВЉ͵ ŷĻƭĻ ğƩĻ ĬƚƷŷ ĻğƭźƌǤ

ķźǝźķĻķ ĬǤ В͵ ŷĻƓ ǞĻ ğķķ ƷŷĻ ƷǞƚ ğƓƭǞĻƩƭ ƷƚŭĻƷŷĻƩ͵

Mental division strategies - split strategy

...ƭĻ ƷŷĻ ƭƦƌźƷ ƭƷƩğƷĻŭǤ Ʒƚ ķźǝźķĻ ƷŷĻƭĻ ƓǒƒĬĻƩƭƭ͵ ...ƭĻ ƷŷĻ ĭƌǒĻƭ Ʒƚ ŭǒźķĻ Ǥƚǒʹ1

2 80 32

АЉЌЉ 6ЏЉ 6

24

ВЏ

50
718
10 24

216480

ЊЍЍ ѝ В ВЉ ЎЍ ѝ В ѝ В ЊЉ њ Џ Ʒў ЊЏ

Iƒƒƒ Ͷ ВЊ ѝ А͵

The ones digit helps

me here. What ƒǒƌƼƦƌĻ ƚŅ А ĻƓķƭ źƓ Њͪ L ƉƓƚǞͲ ЋЊ͵ {ƚ ƷŷğƷ ƒğƉĻƭ ƷŷĻ ƚƷŷĻƩ ƓǒƒĬĻƩ АЉͧ

SERIES TOPIC

17 C

Multiplication and Division

ͧopyright © 39 Learning

2 wental division strategies Y split strategy qlay this game with a partner. Use one copy of this page between you. Fut out the problems x #&   &# z{@   !  ! & J    /  X/ &   ?>S-/Q>-93 copy

ЍЎ ВЉ

ЋЎ 21

ЏЉ ЎЉ

БЉ АЉ

ЎЎ 36

ЌЉ ЏЉ

ЏЉ ЏЉ

27 32

24 ЍЉ

ЋБ ЊБ

ВЏ ѝ Ѝ

АЎ ѝ Ў

БА ѝ Ќ

ВБ ѝ А

ЊЌЎ ѝ В

АБ ѝ Џ

ЊЊЋ ѝ Б

ЎЊ ѝ Ќ

ВЎ ѝ Ў

БЍ ѝ Џ

SERIES TOPIC

F 18

Multiplication and Division

Copyright © 3P Learning

2

5źǝźƭźĬźƌźƷǤ ƩǒƌĻƭ ƷĻƌƌ ǒƭ źŅ ğ ƓǒƒĬĻƩ ĭƷğƓ ĬĻ ķźǝźķĻķ ĻǝĻƓƌǤ ĬǤ ğƓƚƷŷĻƩ ΛƷŷğƷ źƭ ǞźƷŷ Ɠƚ ƩĻƒğźƓķĻƩƭΜ͵

Mental division strategies - divisibility rules

Divisible by wǒƌĻTest

2 ! ƓǒƒĬĻƩ źƭ ķźǝźƭźĬƌĻ ĬǤ Ћ źŅ źƷ͸ƭ ĻǝĻƓ ΛĻƓķƭ źƓ ЉͲ ЋͲ

ЍͲ Џ ƚƩ БΜ͵Lƭ ЍЎБ ķźǝźƭźĬƌĻ ĬǤ ЋͪYes, because it ends in an even number.

3! ƓǒƒĬĻƩ źƭ ķźǝźƭźĬƌĻ ĬǤ Ќ źŅ the sum of its ķźŭźƷƭ źƭ ķźǝźƭźĬƌĻ ƷĬǤ Ќ͵Lƭ АͲЋБЊ ķźǝźƭźĬƌĻ ĬǤ ƷЌͪ

А њ Ћ њ Б њ Њ ў ƷЊБ

Yes, because 18 is divisible by 3.

4! ƓǒƒĬĻƩ źƭ

ķźǝźƭźĬƌĻ ĬǤ Ѝ źŅ ƷŷĻ ƓǒƒĬĻƩ ƒğķĻ ĬǤ ƷŷĻ ƌğƭƷ Ћ ķźŭźƷƭ

źƭ ķźǝźƭźĬƌĻ ĬǤ Ѝ͵Lƭ ЌͲВЊЋ ķźǝźƭźĬƌĻ ĬǤ ЍƷͪ

5 ! ƓǒƒĬĻƩ źƭ ķźǝźƭźĬƌĻ ĬǤ Ў źŅ ƷŷĻƩĻ͸ƭ ğ Љ ƚƩ Ў źƓ

ƷŷĻ ƚƓĻƭ ƦƌğĭĻ͵Lƭ ЍЎЎ ķźǝźƭźĬƌĻ ĬǤ Ўͪ

6 ! ƓǒƒĬĻƩ źƭ ķźǝźƭźĬƌĻ ĬǤ Џ źŅ źƷ Ʒ źƭ ķźǝźƭźĬƌĻ ĬǤ Ћ

!b5 Ќ͵Lƭ АЍͲЊЏЉ ķźǝźƭźĬƌĻ ĬǤ ƷЏͪ Lƭ źƷ ķźǝźƭźĬƌĻ ĬǤ ƷЋͪ

Lƭ źƷ ğƌƭƚ ķźǝźƭźĬƌĻƷ ĬǤ Ќͪ 9 ! ƓǒƒĬĻƩ źƭ ķźǝźƭźĬƌĻ ĬǤ В źŅ the sum of its ķźŭźƷƭ źƭ ķźǝźƭźĬƌĻ Ʒ

ĬǤ В͵Lƭ ЏͲЌЍЎ ķźǝźƭźĬƌĻ ĬǤ ВͪƷ

ЊЉ

! ƓǒƒĬĻƩ źƭ ķźǝźƭźĬƌĻ ĬǤ ЊЉ źŅ ƷŷĻƩĻ źƭ ğ ǩĻƩƚ źƓ

ƷŷĻ ƚƓĻƭ ƦƌğĭĻ͵Lƭ ЎͲЏБЉ ķźǝźƭźĬƌĻ ĬǤ ƷЊЉͪ...ƭĻ ƷŷĻ ƩǒƌĻƭ Ʒƚ ƷĻƭƷ ƚǒƷ ƷŷĻ ƓǒƒĬĻƩƭ źƓ ƷŷĻ ƌğƭƷ ĭƚƌǒƒƓ͵ ŷĻ ŋƩƭƷ ƷǞƚ ŷğǝĻ ĬĻĻƓ ķƚƓĻ ŅƚƩ Ǥƚǒʹ

1

SERIES TOPIC

1P C

Multiplication and Division

ͧopyright © 39 Learning

2 wental division strategies Y divisibility rules ,   !    # @   can be used to divide them. Kill in the tables.

36ВЉБЍВВЎЉ72

ЍЎЏЌЌЉБББЊЋЉВБЊЎЍБ

ЊͲЉЋЎ ЌͲЍБЏ ЏͲВВЌ ЊͲЋЎЏ ВͲЉЎЉ ЊЉͲЉАЋ

2 |umbers may go onto *C SQ S`

S'S-S>

SERIES TOPIC

F

ЋЉ

Multiplication and Division

Copyright © 3P Learning

3

{źƓŭƌĻΏķźŭźƷ ƒǒƌƼƦƌźƷĭğƼƚƓ źƭ ƚƓĻ ǞğǤ Ʒƚ ƭƚƌǝĻ ğ ƒǒƌƼƦƌźĭğƼƚƓ ƦƩƚĬƌĻƒ͵

CźƩƭƷ ǞĻ ǒƭĻ ƚǒƩ ƒĻƓƷğƌ ƭƷƩğƷĻŭźĻƭ Ʒƚ ĻƭƼƒğƷĻ ğƓ ĻğƭźĻƩ ƦƩƚĬƌĻƒʹ

Ќ ќ ЊЎЉ ў ЍЎЉ͵ ŷĻ ğƓƭǞĻƩ Ǟźƌƌ ĬĻ ğƩƚǒƓķ ЍЎЉ͵

‘Ļ ƭƷğƩƷ ǞźƷŷ ƷŷĻ ƚƓĻƭ͵ Ќ ќ Џ Ʒźƭ ЊБ ƚƓĻƭ͵ ‘Ļ ƩĻƓğƒĻ Ʒŷźƭ ğƭ Њ ƷĻƓ ğƓķ Б ƚƓĻƭ͵

‘Ļ ƦǒƷ Б źƓ ƷŷĻ ƚƓĻƭ ĭƚƌǒƒƓ ğƓķ ĭğƩƩǤ ƷŷĻ Њ Ʒƚ ƷŷĻ ƷĻƓƭ ĭƚƌǒƒƓ͵

Ќ ќ Ў Ʀƌǒƭ ƷŷĻ ĭğƩƩźĻķ Њ źƭ ЊЏ ƷĻƓƭ͵ ‘Ļ ƩĻƓğƒĻ Ʒŷźƭ ğƭ Њ ŷǒƓķƩĻķ ğƓķ Џ ƷĻƓƭ͵

‘Ļ ƦǒƷ Џ źƓ ƷŷĻ ƷĻƓƭ ĭƚƌǒƒƓ ğƓķ ĭğƩƩǤ ƷŷĻ Њ Ʒƚ ƷŷĻ ŷǒƓķƩĻķƭ ĭƚƌǒƒƓ͵

Ќ ќ Њ Ʀƌǒƭ ƷŷĻ ĭğƩƩźĻķ Њ źƭ Ѝ ŷǒƓķƩĻķƭ͵ ‘Ļ ƦǒƷ Ѝ źƓ ƷŷĻ ŷǒƓķƩĻķƭ ĭƚƌǒƒƓ͵

Written methods - single-digit multiplication

{ƚƌǝĻ ƷŷĻƭĻ ƦƩƚĬƌĻƒƭ ǒƭźƓŭ ƭźƓŭƌĻΏķźƭŭźƷ ƒǒƌƼƦƌźĭğƼƚƓ͵ 9ƭƼƒğƷĻ ŋƩƭƷʹ1

{ƚƌǝĻ ƷŷĻƭĻ ǞƚƩķ ƦƩƚĬƌĻƒƭ͵ {ŷƚǞ ŷƚǞ Ǥƚǒ ǞƚƩƉĻķ ƷŷĻƒ ƚǒƷʹ

a

5ğƓ͸ƭ ķğķ ŷğƭ ƭƷƚƚƦĻķ Ʒƚ ĬƩźĬĻƩǤ Ʒƚ ĭǒƩĬ 5ğƓ͸ƭ

tƌğǤ{ƷğƼƚƓ ğķķźĭƼƚƓ͵ CƚƩ ĻǝĻƩǤ ĻǝĻƓźƓŭͲ 5ğƓ

ƭƦĻƓķƭ ğǞğǤ ŅƩƚƒ ƷŷĻ tƌğǤ{ƷğƼƚƓͲ ŷźƭ ķğķ ƦğǤƭ

ŷźƒ υЌ͵ {ƚ ŅğƩͲ 5ğƓ ŷğƭ ƩğĭƉĻķ ǒƦ ğƓ źƒƦƩĻƭƭźǝĻ ЋА

ƓźŭŷƷƭ ΛƷŷƚǒŭŷ ŷĻ ƌƚƚƉƭ ƌźƉĻ ŷĻ ƒğǤ ŭźǝĻ ǒƦ ğƓǤ ķğǤ

ƓƚǞΜ͵ IƚǞ ƒǒĭŷ ƒƚƓĻǤ ķƚĻƭ Ʒŷźƭ ĻƨǒğƷĻ Ʒƚͪ

b

5ğƓ͸ƭ ƒƚƒ ƷŷźƓƉƭ ƭŷĻ ƒźŭŷƷ ŭĻƷ źƓ ƚƓ ƷŷĻ ğĭƼƚƓ

Ʒƚƚ ğƓķ ƦğǤƭ 5ğƓ υЍ ŅƚƩ ĻǝĻƩǤ ǞĻĻƉ ƷŷğƷ ŷĻ ƦǒƷƭ

ŷźƭ ķźƭŷĻƭ źƓ ƷŷĻ ķźƭŷƷǞğƭŷĻƩ ğƓķ ŷźƭ ķźƩƷǤ ĭƷƌƚƷŷĻƭ

źƓ ƷŷĻ ĬğƭƉĻƷ͵ 5ğƓ źƭ ƌĻƭƭ ĻǣĭźƷĻķ ğĬƚǒƷ Ʒŷźƭ ƦƌğƓ

ĬǒƷ ķƚĻƭ ƒğƓğŭĻ ЌЌ ǞĻĻƉƭ źƓ Њ ǤĻğƩ͵ IƚǞ ƒǒĭŷ

ŷğƭ ŷĻ ƒğķĻ ƚǒƷ ƚŅ ƷŷźƷƭ ƭĭŷĻƒĻͪ2

ITO

1Ў6

× 3

46Б

11

ĻʹĻʹĻʹ

a IT O b ITO c ITO

327 247 1Ў4

×3 ×4 ×Ў

ĻʹĻʹĻʹ

d IT O e ITO f ITO

31Ў 2Б6 1В4

×3 ×2 ×Ў

SERIES TOPIC

21
C

Multiplication and Division

ͧopyright © 39 Learning

3

Written methods Y singleЍdigit multiplication

~  $   # !&'L& # / give them some feedback as to where they went wrong.3

€ess

3Б7

×2 774

11В

×7 773

2Љ3

×3

6ЉВ

436
×3

12ЉБ

4Љ1

×7

2БЉ7

1 11

3Б7

×2 774

11В

×7

Б33

2Љ3

×3 6В 436
×3

13ЉБ

4Љ1

×7

2Б7

 1 6 111
1

SERIES TOPIC

F 22

Multiplication and Division

Copyright © 3P Learning

a672bБВ3c4Б3

×34 ×17 ×44

3

Written methods - multi-digit multiplication

Use a calculator to help you work out the values you could expect when

ƒǒƌƼƦƌǤźƓŭ ƷŷĻ ŅƚƌƌƚǞźƓŭ͵ źĭƉ ƷŷĻ ĭƚƌƭǒƒƓƭʹ

 I I I T O

ağ ƚƓĻ ĬǤ ğ ƚƓĻ В ќ А bğ ƷĻƓ ĬǤ ğ ƚƓĻ ЍЌ ќ Ў cğ ŷǒƓķƩĻķ ĬǤ ğ ƚƓĻ 126 × 7
dğ ƷĻƓ ĬǤ ğ ƷĻƓ 13 × 72 eğ ƷĻƓ ĬǤ ğ ŷǒƓķƩĻķ ЎЎ ќ ЊЋЉ 1

2 × 2 would give

me a one only. But 8 × 6 would give me tens and ones. I"ll ƼĭƉ ĬƚƷŷ ĭƚƌǒƒƓƭ͵

aǒƌƼƦƌǤźƓŭ ƌğƩŭĻƩ ƓǒƒĬĻƩƭ źƭ ğ ƦƩƚĭĻƭƭ ƚŅ ƒǒƌƼƦƌĻ ƭƷĻƦƭ͵

2 —ƚǒ ŷğǝĻ ƓƚǞ ǒƭĻķ ǒƦ ğƌƌ ǤƚǒƩ ƚƓĻƭ͵ /Ʃƚƭƭ ƚǒƷ ƷŷĻ

6 in the ones place and

ƦƌğĭĻ ğ ǩĻƩƚ źƓ ƷŷĻ ƓĻǣƷ ĭƚƌǒƒƓ Ʒƚ ƭŷƚǞ Ʒŷźƭ͵ bƚǞ Ǥƚǒ ƒǒƌƼƦƌǤʹ ЎЍЋ ќ ЋЉ ў ЊЉͲБЍЉ 1 CźƩƭƷͲ Ǥƚǒ ƒǒƌƼƦƌǤʹ ЎЍЋ ќ Џ ў ЌͲЋЎЋ 3 !ķķ ǒƦ ǤƚǒƩ ǞƚƩƉʹ ЌͲЋЎЋ њ ЊЉͲБЍЉ ў ЊЍͲЉВЋƷ

Ў42

× 26

32Ў2

њ

1ЉБ4Љ

1ЍͲЉВ2

1 12

tƩğĭƼĭĻ ƒǒƌƼƦƌǤźƓŭ ƒǒƭƌƼΏķźŭźƷ ƓǒƒĬĻƩƭ͵ 9ƭƼƒğƷĻ ŋƩƭƷʹ2

ĻʹĻʹĻʹ

SERIES TOPIC

23
C

Multiplication and Division

ͧopyright © 39 Learning

3 aБВ2bВ4Вc6Б3

×Ў3 ×2Б ×1Ў

d443e7В4fВВВ

×61 ×27 ×66

Written methods Y multiЍdigit multiplication

)   }   3    !   4

a ŷĻ ƭźǣƷŷ ŭƩğķĻ ƷĻğĭŷĻƩƭ ğƩĻ

ƷğƉźƓŭ ƷŷĻźƩ ĭƌğƭƭĻƭ ƷƷƚ ƷŷĻ

aǒƭĻǒƒ ƚŅ bğƷǒƩğƌ IźƭƷƚƩǤ͵ ŷĻƩĻ źƭ ğ ƷƚƷğƌ ƚŅ ЊЋЎ ƭƷǒķĻƓƷƭ źƓ ƭźǣƷŷ ŭƩğķĻ ğƓķ admission to the museum is υЊЌ ƦĻƩ ƭƷǒķĻƓƷ͵ ‘ŷğƷ źƭ ƷŷĻ

ƷƚƷğƌ ĭƚƭƷ ŅƚƩ ğƌƌ ƭźǣƷŷ ŭƩğķĻƩƭͪb !ƌƌźƭƚƓ ŷğƭ ğ ƭƷĻğķǤ ĬğĬǤƭźLjƓŭ ƆƚĬ ğƓķ ƒğƉĻƭ υЊЉЉ ğ ƒƚƓƷŷ͵ {ŷĻ ŷğƭ ĬĻĻƓ ƚƓ ƷŷĻ ƆƚĬ ŅƚƩ ЊБ ƒƚƓƷŷƭ͵ IƚǞ ƒǒĭŷ ƒƚƓĻǤ ŷğƭ ƭŷĻ ĻğƩƓĻķͪc ƚƒƒǤ ğƓķ ŷźƭ ŅğƒźƌǤ ǞğƓƷ Ʒƚ ƒƚǝĻ Ʒƚ .Ʃğǩźƌ ğƓķ ƭƷğǤ ǞźƷŷ ƷŷĻźƩ ŭƩğƓķƦğƩĻƓƷƭ ŅƚƩ ЊЏ ƒƚƓƷŷƭ͵ ŷĻǤ ğƩĻƓ͸Ʒ ƭǒƩĻ źŅ ƷŷĻ ǝźƭźƷ Ǟźƌƌ ǞƚƩƉ ǞźƷŷ ƷŷĻźƩ ĬǒķŭĻƷ͵ ŷĻǤ ĭğƌĭǒƌğƷĻ źƷ Ǟźƌƌ ĭƚƭƷ υЎЏА ƦĻƩ ƒƚƓƷŷ͵ IƚǞ ƒǒĭŷ Ǟźƌƌ ƷŷĻ ǞŷƚƌĻƷ ƷƩźƦ ĭƚƭƷͪ

SERIES TOPIC

F 24

Multiplication and Division

Copyright © 3P Learning

3 a d gbehcfi a c b de

LƓ ķźǝźƭźƚƓͲ ǞĻ ǒƭĻ ƚǒƩ ƉƓƚǞƌĻķŭĻ ƚŅ ƒǒƌƼƦƌźĭğƼƚƓ Ʒƚ ŷĻƌƦ ǒƭ͵ ‘Ļ ĭğƓ ƭƦƌźƷ ВЌЏ źƓƷƚ ВЉЉ њ ЌЉ њ Џ͵

ВЉЉ ķźǝźķĻķ ĬǤ Ќ źƭ ЌƷЉЉͲ ƭƚ ǞĻ ƦǒƷ ğ Ќ źƓ ƷŷĻ ŷǒƓķƩĻķƭ ƦƌğĭĻ͵

ЌЉ ķźǝźķĻķ ĬǤ Ќ źƭ ЊЉƷͲ ƭƚ ǞĻ ƦǒƷ ğ Њ źƓ ƷŷĻ ƷĻƓƭ ƦƌğĭĻ͵

Џ ķźǝźķĻķ ĬǤ Ќ źƭ ЋͲ Ʒƭƚ ǞĻ ƦǒƷ ğ Ћ źƓ ƷŷĻ ƚƓĻƭ ƷƦƌğĭĻ͵ Ʒ ВЌЏ ѝ Ќ ў ЌЊЋ

{ƚƒĻƼƒĻƭ źƷ͸ƭ ĻğƭźĻƩ Ʒƚ ƭƦƌźƷ ƷŷĻ ƓǒƒĬĻƩƭ ķźňĻƩĻƓƷƌǤ͵ ‘Ļ ĭğƓ ğƌƭƚ

ƭƦƌźƷ ВЌЏ źƓƷƚ ВЉЉ њ ЌЏ͵

ВЉЉ ķźǝźķĻķ ĬǤ Ќ źƭ ЌƷЉЉ ƭƚ ǞĻ ƦǒƷ ğ Ќ źƓ ƷŷĻ

ŷǒƓķƩĻķƭ ƦƌğĭĻ

ЌЏ ķźǝźķĻķ ĬǤ Ќ źƭ ЊЋ͵ Ʒ‘Ļ ƦǒƷ ƷŷĻ Њ źƓ ƷŷĻ ƷĻƓƭ

ƦƌğĭĻ ğƓķ ƷŷĻ Ћ źƓ ƷŷĻ ƷƚƓĻƭ ƦƌğĭĻ͵

ВЌЏ ѝ Ќ ў ЌЊЋ

Written methods - division

5źǝźķĻ ƷŷĻƭĻ ƓǒƒĬĻƩƭʹ1

25ĻĭźķĻ ŷƚǞ Ǥƚǒ͸ƌƌ ƭƦƌźƷ ƷŷĻƭĻ ƓǒƒĬƭĻƩƭ ğƓķ ƷŷĻƓ ķźǝźķĻ͵ wĻƒĻƒĬĻƩ

Ʒ ƚ ƦǒƷ źƓ ǩĻƩƚƭ ğƭ ƓĻĻķĻķ͵ 312

3В36

ВВВЉ

ЎЎ1Ў

44Б4

366В

6666

3ВВВ

ВВ27

2462

4Б12

36В3

4Б4ЎЎЎ3В3

LƓ ƷŷĻƭĻ ƦƩƚĬƌĻƒƭͲ źŅ ƷŷĻƩĻ are no tens in a number we ƦǒƷ ğ Љ źƓ Ʒƚ ƭŷƚǞ Ʒŷźƭ ğƓķ also to hold the place of ƷŷĻ ƚƷŷĻƩ ƓǒƒĬĻƩƭͧ 312

3В36

4БЉ4

SERIES TOPIC

25
C

Multiplication and Division

ͧopyright © 39 Learning

a dbecf 3

{ƚƒĻƼƒĻƭ ƓǒƒĬĻƩƭ ķƚƓ͸Ʒ ķźǝźķĻ ĻǝĻƓƌǤ͵ ŷĻ ğƒƚǒƓƷ ƌĻũ ƚǝĻƩ źƭ ĭğƌƌĻķ ƷŷĻ remainder͵

[ƚƚƉ ğƷ ЎЋА ķźǝźķĻķ ĬǤ Ў͵ ЎЉЉ ķźǝźķĻķ ĬǤ Ў źƭ ЊƷЉЉ͵

ЋА ķźǝźķĻķ ĬǤ Ў źƭ Ў ǞźƷƷŷ Ћ ƌĻũ ƚǝĻƩ ΛƷŷźƭ źƭ ƷŷĻ ƩĻƒğźƓķĻƩΜ͵

ŷźƭ ĭğƓ ĬĻ ǞƩźdžĻƓ ğƭ Ʃ Ћ͵ '+?S'V*9'+

Written methods Y division with remainders

Divide these 3 digit numbers. ƒach problem will have a remainder.Divide these 2 digit numbers. ƒach problem will have a remainder.

1 2 <!   a

DźƚǝğƓƓź͸ƭ ŭƩğƓķƒğ ŷğƭ ŭźǝĻƓ ŷźƒ ğ Ĭğŭ ƚŅ ŭƚƌķ ĭƚźƓƭ Ʒƚ ƭŷğƩĻ ğƒƚƓŭ ŷźƒ ğƓķ ŷźƭ ƷƷǞƚ ƭźƭƷĻƩƭ͵

ŷĻƩĻ ğƩĻ ЍА ŭƚƌķ ĭƚźƓƭ ğƌƷƚŭĻƷŷĻƩ͵ IƚǞ ƒğƓǤ ķƚĻƭ Ļğĭŷ ĭŷźƌķ ŭĻƷ źŅ ƷŷĻǤ͸ƩĻ ƭŷğƩĻķ ĻǝĻƓƌǤͪ

IƚǞ Ǟƚǒƌķ Ǥƚǒ ƭǒŭŭĻƭƷ ƷŷĻǤ ķĻğƌ ǞźƷŷ ƷŷĻ ƩĻƒğźƓķĻƩͪ

________________________________________________________________________Ʒ__ b

—ƚǒ ŷğǝĻ ЎВ !źƩŷĻğķƭ Ʒƚ ğķķ Ʒƚ ƦğƩƷǤ Ĭğŭƭ͵ 9ğĭŷ Ĭğŭ ŭĻƷƭ Ў !źƩŷĻğķƭ͵ IƚǞ ƒğƓǤ Ņǒƌƌ ƦğƩƷǤ

Ĭğŭƭ ĭğƓ Ǥƚǒ ƒğƉĻͪ3a dbecf Ʃ

В7Ў

Ʃ

ЎЎЎ7Ʃ

3661Ʃ

44Б1

Ʃ

ВВВ4Ʃ

4Б4ЎƩ

663Б

Ʃ

447Ʃ

63Б

Ʃ

44ВƩ

662

1ЉЎƩ Ћ

ЎЎ27

Ʃ

Ў63

SERIES TOPIC

F 26

Multiplication and Division

Copyright © 3P Learning

3

ŷĻƩĻ ğƩĻ Ќ ǞğǤƭ ƚŅ ĻǣƦƩĻƭƭźƓŭ ƩĻƒğźƓķĻƩƭ͵ IƚǞ ǞĻ ķƚ źƷ ķĻƦĻƓķƭ

ƚƓ ŷƚǞ ǞĻ͸ķ ķĻğƌ ǞźƷŷ ƷŷĻ ƦƩƚĬƌĻƒ źƓ ƷŷĻ ƩĻğƌ ǞƚƩƌķ͵ [ƚƚƉ ğƷʹ

Written methods - division with remainders

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

ğƒƚƓŭ Ў ƦĻƚƦƌĻ͵ {ƚƌǝĻ ƷŷĻƭĻ ƦƩƚĬƌĻƒƭ ĻǣƦƩĻƭƭźƓŭ ƷŷĻ ƩĻƒğźƓķĻƩƭ ğƭ

r .4 5 We express remainders as decimals when we must be absolutely precise. {ŷğƩźƓŭ ķƚƌƌğƩ ğƒƚǒƓƭ

Ʒƭ źƭ ğ ŭƚƚķ ĻǣğƒƦƌĻ ƚŅ Ʒŷźƭ͵ ‘Ļ ğķķ ƷŷĻ ĭĻƓƷƭ ğũĻƩ

ƷŷĻ ķĻĭźƒğƌ ƦƚźƓƷ Ʒƚ ŷĻƌƦ ǒƭ͵ ƩǤ ƷŷĻƭĻʹ6

‘Ļ ĭğƓ ğƌƭƚ ĻǣƦƩĻƭƭ ğ ƩĻƒğźƓķĻƩ ğƭ ğ ŅƩğĭƼƚƓ͵ ‘Ļ ķƚ Ʒŷźƭ ǞŷĻƓ ǞĻ ĭğƓ

ĻğƭźƌǤ ƭŷğƩĻ ƷŷĻ ƩĻƒğźƓķĻƩ͵ CƚƩ ĻǣğƒƦƌĻͲ ЊВ ĭğƉĻƭ ƭŷğƩĻķ ğƒƚƓŭ Ќ ƦĻƚƦƌĻ

źƭ Џ ğƓķ ƚƓĻ ƷŷźƩķ Ļğĭŷ͵ {ƚƌǝĻ ƷŷĻƭĻ ƦƩƚĬƌĻƒƭ ĻǣƦƩĻƭƭźƓŭ ƷŷĻ ƩĻƒğźƓķĻƩ

ğƭ ğ ŅƩğĭƼƚƓʹ

1ЉЎƩ Ћ

ЎЎ27

a {ŷğƩĻ ЊЋЏ ĬƌǒĻ ƦĻƓĭźƌƭ ğƒƷƚƓŭ Ѝ ƦĻƚƦƌĻ͵b {ŷğƩĻ ЋЊЎ ƦğƦĻƩ ĭƌźƦƭ ğƒƷƚƓŭ А ƦĻƚƦƌĻ͵

a {ŷğƩĻ ЊЌ Ʀźǩǩğƭ ğƒƚƓŭ Ѝ ƦĻƚƦƌĻ͵b {ŷğƩĻ ЎЉ ƭğƓķǞźĭŷĻƭ ğƒƚƓŭƷ Ќ ƦĻƚƦƌĻ͵

a {ŷğƩĻ ЊЋ ķƚƌƌğƩƭ ğƒƚƓŭ Ѝ ƦĻƚƦƌĻ͵b {ŷğƩĻ ЋА ķƚƌƌğƩƭ ĬĻƷǞĻĻƓ Ћ ƦĻƚƦƌĻ͵

6 319
1 3

27 divided by 2 is 13.

Now we have one dollar

ƌĻũ͵ IƚǞ ŷƚǞ ƒğƓǤ ĭĻƓƷƭ źƭ ŷğƌŅ ƚŅ ƚƓĻ ķƚƌƌğƩƭͪ

412ЉЉ227ЉЉ

SERIES TOPIC

27
C

Multiplication and Division

ͧopyright © 39 Learning

3 c

.ĻƭƷ ķĻğƌ źƭ ΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗd .ĻƭƷ ķĻğƌ źƭ ΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗa .ĻƭƷ ķĻğƌ źƭ ΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗ

b

.ĻƭƷ ķĻğƌ źƭ ΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗΗ

‘Ļ ƩĻŭǒƌğƩƌǤ ĭƚƒĻ ğĭƩƚƭƭ ƒǒƌƼƦƌźĭğƼƚƓ ğƓķ ķźǝźƭźƚƓ ƦƩƚĬƌĻƒƭ źƓ ƚǒƩ ĻǝĻƩǤķğǤ ƌźŅĻ͵ LƷ ķƚĻƭƓ͸Ʒ

ƒğdžĻƩ Ǟŷźĭŷ ƭƷƩğƷĻŭǤ ǞĻ ǒƭĻ Ʒƚ ƭƚƌǝĻ ƷŷĻƒͲ ǞĻ ĭğƓ ĭŷƚƚƭĻ ƷŷĻ ƚƓĻ ƷŷğƷ ƭǒźƷƭ ǒƭ ƚƩ ƷŷĻ ƦƩƚĬƌĻƒ ĬĻƭƷ͵

Written methods Y problem solving

1J}

&    @ L$   &        &  %  @   :    # &"'#"*?' /%  &Q  &"-'9   <  

2Б Ť ƚǩ

ЊЉ ƦğĭƉ /5{źƓŭƌĻ /5ЌЋ Ť ƚǩ "Q`'"0'9 8 oz 16 oz *\Q\ "*`'"'-Q "*-9"++`9"+09"+?'

SERIES TOPIC

F 28

Multiplication and Division

Copyright © 3P Learning

3

Written methods - problem solving

3You"re planning a trip to the Wet and Wild theme park and

ƷŷĻƩ

Ļ ğƩĻ ƒğƓǤ ƼĭƉĻƷ ƚƦƼƚƓƭ͵ ...ƭĻ ğ ƭƷƩğƷĻŭǤ ƚŅ ǤƚǒƩ ĭŷƚźĭĻ

ğƓķ ƷŷĻ ƦƩźĭĻ ƌźƭƷ ĬĻƌƚǞ Ʒƚ ğƓƭǞĻƩ ƷŷĻ ŅƚƌƌƚǞźƓŭ ƨǒĻƭƼƚƓƭʹ

a

LŅ Ǥƚǒ ĬǒǤ ğ ЋΏķğǤ ƦğƭƭͲ ǞŷğƷ źƭ ƷŷĻ ĭƚƭƷ ƦĻƩ ķğǤͪ

b

IƚǞ ƒǒĭŷ ĭŷĻğƦĻƩ źƭ ƷŷƷźƭ ƚƦƼƚƓ ƷŷğƓ ĬǒǤźƓŭ ƷƷǞƚ ЊΏķğǤ ƦğƭƭĻƭͪ

c

LŅ Ǥƚǒ ĬƚǒŭŷƷ ğƓ ğƓƓǒğƌ ƦğƭƭͲ ŷƚǞ ƷƒğƓǤ ƼƒĻƭ Ǟƚǒƌķ Ǥƚǒ ƓĻĻķ Ʒƚ ǝźƭźƷ Ʒƚ ƒğƉĻ źƷ

ğ ĬĻdžĻƩ ƚƦƼƚƓ ƷŷğƓ ĬǒǤźƓŭ ƷĻźƷŷĻƩ ğ ЊΏķğǤ ƚƩ ЋΏķğǤ Ʀğƭƭͪ

d

‘ŷğƷ źŅ Ǥƚǒ ĭŷƚƚƭĻ ƆǒƭƷ ƷŷĻ ƩźķĻƭͪ IƚǞ ƒǒĭŷ ǞƷƚǒƌķ Ǥƚǒ ƭğǝĻ źŅ Ǥƚǒ ĬƚǒŭŷƷ ƷŷĻ

ЊЉΏƩźķĻ Ʀğƭƭ źƓƭƷĻğķ ƚŅ ƷŷĻ źƓķźǝźķǒğƌ ƷƩźķĻƭͪ

e

LŅ Ǥƚǒ ƷƚƚƉ ğ ЎΏƒźƓǒƷĻ ŷĻƌźĭƚƦƷĻƩ ƩźķĻͲ ǞŷğƷ Ǟƚǒƌķ ĬĻ ƷŷĻ ĭƚƭƷ ƦĻƩ ƒźƓǒƷĻͪ

f

‘ŷğƷ ğĬƚǒƷ źŅ Ǥƚǒ ĭŷƚƭĻ ƷŷĻ ЊЉΏƒźƓǒƷĻ ŤźŭŷƷ ƚƦƼƚƓͪ ‘ŷğƷ Ǟƚǒƌķ ĬĻ ƷŷĻ ĭƚƭƷ ƦĻƩ ƒźƓǒƷĻͪ

g

tƌğƓ ğ ķğǤ͸ƭ źƼƓĻƩğƩǤ ŅƚƩ Ǥƚǒ ğƓķ ğ ƦğƩƷƓĻƩ͵ IƚǞ ƒǒĭŷ Ǟźƌƌ Ʒŷźƭ ĭƷƚƭƷͪ

Entry ЊΏķğǤ Ʀğƭƭ υЌЋ ЋΏķğǤ Ʀğƭƭ υЍБ Annual pass υВВ LƓķźǝźķǒğƌ ƩźķĻƭ υЊЋ ЊЉΏƩźķĻ Ʀğƭƭ υВЎ hƩķĻƩ ƚƓƌźƓĻ υЎ ķźƭĭƚǒƓƷ

Extras

ЎΏƒźƓǒƷĻ ŷĻƌźĭƚƦƷĻƩ ƩźķĻ υЍЋ

ЊЉΏƒźƓǒƷĻ ŷĻƌźĭƚƦƷĻƩ ƩźķĻ υАЍ

ЌЉΏƒźƓǒƷĻ ŷĻƌźĭƚƦƷĻƩ ƩźķĻ υЋЉВ

{ǒƓƭĻƷ ĭƩǒźƭĻ υЊЋ [ǒƓĭŷ ĭƩǒźƭĻ υЋЋ Swim with the dolphins υАЎ

SERIES TOPIC

2P C

Multiplication and Division

ͧopyright © 39 Learning

4

What to do

What to do

ͧrack the code apply

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __

21364Ў3Б7В БВ ЊЉ1211

...ƭĻ ƷŷĻ ĭƚķĻ ĬĻƌƚǞ Ʒƚ ǞƚƩƉ ƚǒƷ ƷŷĻ ŷźķķĻƓ ƒĻƭƷƭğŭĻ͵

A × A = A R is _____ C ў I њ [ K N _____ a ќ a ў a њ a † is _____ 9 ў C ѝ Ћ ƒ N _____ T - M = A T is _____ 2 × L = I I N _____

 њ  ў I 

_____ ΛЋ ќ [Μ Α ! ў / F N _____

I Α a ў [ B

_____ C њ ! ў b | N _____

3 × L = U U is _____ 3 × T = S <V _____

ƩǤ Ʒŷźƭ ƚƓĻʹ

__ __ __ __ __ __ __ __ __ __ __ __ __

4266312 ЉБ В12Ў3

! ќ ! ў ! њ ! R is _____ [ њ 9 ў { < _____ ! њ ! ў  T is _____ b Α b ў L I is _____  ќ Ћ ў b | is _____ U - A = C F is _____ ![ ѝ  ў 9 ƒ is _____ { Α ΛЋ ќ Μ ў t q is _____

Ћ ќ 9 ў [ B

_____ 2 × U - P = O O is _____

9 њ  ў ... U is _____ { њ 9 ў w M

_____

JL #@

 /  C

L& 

 /   them to get the answer. __ __ __ __ __ __ __ __ __ __ __ __ __

2В41213Б274В 2123

SERIES TOPIC

F

ЌЉ

Multiplication and Division

Copyright © 3P Learning

4

What to do next

What to do What to do What to do

DĻLjƓŭ

ready

DĻLjƓŭ

ready

Smart buttons apply

Bugs investigate

LƓ Ʒŷźƭ ğĭƼǝźƷǤͲ Ǥƚǒ͸ƌƌ ǒƭĻ ǤƚǒƩ ƉƓƚǞƌĻķŭĻ ƚŅ ƒǒƌƼƦƌźĭğƼƚƓͲ ķźǝźƭźƚƓͲ ƭǒĬƷƩğĭƼƚƓ ğƓķ

ğķķźƼƚƓ Ʒƚ ŋƓķ ğƭ ƒğƓǤ ƓǒƒĬĻƩ ƭƷğƷĻƒĻƓƷƭ Ǥƚǒ ĭğƓ Ʒƚ ĭƩĻğƷĻ ƚƓĻ ƓǒƒĬĻƩ͵

...ƭźƓŭ hb[— ƷŷĻ ƓǒƒĬĻƩ ЋͲ њͲ ќͲ Α ƷğƓķ ѝ ƉĻǤƭ ƚƓ ǤƚǒƩ ĭğƌĭǒƌğƷƚƩͲ

ŋƓķ ğƭ ƒğƓǤ ǞğǤƭ ğƭ Ǥƚǒ ĭğƓ Ʒƚ ĭƩĻğƷĻ ƷŷĻ ƓǒƒĬĻƩ ЊЌ͵

CƚƩ ĻǣğƒƦƌĻͲ Ǥƚǒ ĭƚǒƌķ ƒğƉĻʹ ЋЋ њ Ћ њ Ћ ў ЋЏ ѝ ƷЋ ў ЊЌ

wĻĭƚƩķ ǤƚǒƩ ƭƷğƷĻƒĻƓƷƭ ƚƓ ğ ƦźĻĭĻ ƚŅ ƦğƦƷĻƩ͵

bƚǞͲ ĭƚƒƦğƩĻ ǤƚǒƩ ğƓƭǞĻƩƭ ǞźƷŷ ğ ƦğƩƷƓĻƩ͸ƭ͵ IƚǞ ƒğƓǤ ķźķ ƷŷĻǤ ŋƓķͪ

/ğƓ Ǥƚǒ ğķķ Ʒƚ Ļğĭŷ ƚƷŷĻƩ͸ƭ ƌźƭƷƭͪ

‘ŷğƷ͸ƭ ƷŷĻ ƌƚƓŭĻƭƷ ƭƷğƷĻƒĻƓƷͪ ‘ŷğƷ͸ƭ ƷŷĻ ƭŷƚƩƷĻƭƷͪ

/ŷƚƚƭĻ ğƓƚƷŷĻƩ ƓǒƒĬĻƩ ƷƷƚ ƒğƉĻ ğƓķ ƭĻĻ ŷƚǞ ƒğƓǤ ƭƷğƷĻƒĻƓƷƭ Ǥƚǒ ĭğƓ ŋƓķ or

ĭŷğƌƌĻƓŭĻ ğ ƦğƩƷƓĻƩ Ʒƚ ğ ĭƚƒƦĻƼƼƚƓ͵ {ĻƷ ğ ƼƒĻ ƷƌźƒźƷ ğƓķ ƭĻĻ Ǟŷƚ ĭğƓ ŋƓķ ƷŷĻ ƒƚƭƷ

ǞğǤƭ Ʒƚ ƒğƉĻ ƷŷĻ ƓǒƒĬĻƩ ЊЎ ǞźƷŷźƓ ƷƷŷĻ ƼƒĻ ƭƦğƓ͵

...ƭĻ ǤƚǒƩ ƉƓƚǞƌĻķŭĻ ƚŅ ƒǒƌƼƦƌĻƭ Ʒƚ ŷĻƌƦ Ǥƚǒ ǞƚƩƉ ƚǒƷ ŷƚǞ ƒğƓǤ ĬƚǤ Ĭǒŭƭ ğƓķ

ŭźƩƌ Ĭǒŭƭ ƷŷĻƩĻ ğƩĻ źƓ ƷŷĻ ƦƩƚĬƌĻƒ ĬĻƌƚǞ͵ [źƭƼƓŭ ğƌƌ ƷŷĻ ƒǒƌƼƦƌĻƭƷ źƭ ğ ƭƷƩğƷĻŭǤ ƷŷğƷ

Ǟƚǒƌķ ŷĻƌƦ͵

DźƩƌ Ĭǒŭƭ ŷğǝĻ Ѝ ķƚƷƭ ƚƓ ƷŷĻźƩ ĬğĭƷƉƭͲ ĬƚǤ Ĭǒŭƭ ŷğǝĻ В͵

!ƌƷƚŭĻƷŷĻƩ ƷŷĻƩĻ ğƩĻ ЍБ ķƚƷƭ͵ ‘ƚƩƉ ƚǒƷ ŷƚǞ ƒğƓǤ ŭźƩƌ

Ĭǒŭƭ ğƓķ ŷƚǞ ƒğƓǤ ĬƚǤ Ĭǒŭƭ ƷŷĻƩĻ ğƩĻ͵

‘ŷğƷ źŅ ŭźƩƌ Ĭǒŭƭ ŷğǝĻ Б ķƚƷƭ ğƓķ ĬƚǤ ĬǒŭƷƭ ŷğǝĻ Џ ğƓķ ƷŷĻƩĻ ğƩĻ ЊЋЉ ķƚƷƭ ğƌƷƚŭĻƷŷĻƩͪ

IƚǞ ƒğƓǤ ķźňĻƩĻƓƷ ğƓƭǞĻƩƭ ĭğƓ Ǥƚǒ ŋƓķͪ

SERIES TOPIC

31
C

Multiplication and Division

ͧopyright © 39 Learning

4

What to do

What to do

9uΛΛles apply

...ƭĻ ǤƚǒƩ ƉƓƚǞƌĻķŭĻ ƚŅ ƒǒƌƼƦƌźĭğƼƚƓ Ʒƚ ǞƚƩƉ ƚǒƷ ƷŷĻ ƒźƭƭźƓŭ ǝğƌǒĻƭʹ

×В

6

11 33 44

63

Б64

×3 432
14

ЍЎ 27

12 24Cźƌƌ źƓ ƷŷĻ ƒǒƌƼƦƌźĭğƷƼƚƓ ğƓķ ķźǝźƭźƚƓ ƷğĬƌĻƭ ĬǤ

ǞƚƩƉźƓŭ ƚǒƷ ƷŷĻ ƒźƭƭźƓŭƷ ķźŭźƷƭ͵ ŷĻ ğƩƩƚǞƭ ƭŷƚǞ

Ǥƚǒ ƭƚƒĻ ŭƚƚķ ƭƷğƩƼƓŭ ƦƌğĭĻƭ͵

×76

ЋЉ 16 14

ЎЍЉ

36

3ЌЉ×БВ

12 24 312
14

ЎЍ

a2Бb7c7

×3 ×4 ×Ў

Б 2ББ 23Ў

g261h42iЎ6

× × 3×27

44 126 3В2

6БЉ

dБe6Бf23

×В × ×

72В 2Љ4 6ЎБ4

SERIES TOPIC

F 32

Multiplication and Division

Copyright © 3P Learning

4

...ƭĻ ƷŷĻ ͻŭǒĻƭƭ ğƓķ ĭŷĻĭƉͼ ƭƷƩğƷĻŭǤ Ʒƚ ƭƚƌǝĻ

Ʒŷźƭ ƦƩƚĬƌĻƒ͵ —ƚǒ ĭƚǒƌķ ǒƭĻ ğ ĭğƌĭǒƌğƷƚƩ

Ʒƚ ŷĻƌƦ źŅ Ǥƚǒ Ǟźƭŷ͵

ƩğĭĻǤ Ʀğźķ υЌ͵ЊЉ ŅƚƩ А ŭǒƒƷƒǤ ƭƓğƉĻƭ ğƓķ Ѝ ƦźĻĭĻƭ ƚŅ ƷğňǤ͵

ağķźƭƚƓ Ʀğźķ υЋ͵ВЎ ŅƚƩ ƷЍ ŭǒƒƒǤ ƭƓğƉĻƭ ğƓķ А ƦźĻĭĻƭ ƚŅ

ƷğňǤ͵ IƚǞ ƒǒĭŷ ķƚĻƭ ƚƓĻ ŭƷǒƒƒǤ ƭƓğƉĻ ĭƚƭƷͪ IƚǞ ƒǒĭŷ

ķƚĻƭ ƚƓĻ ƦźĻĭĻ ƚŅ ƷğňǤ ĭƚƭƷͪ

What to do

What to do What to do

Puzzles apply

12 3 4Ў 67
Б

ВЊЉ

Across

1 ЏЉ ѝ Ў 2 ЋЎ ќ Ў 3 7 × 6 4 ЊЎ ќ Џ 7 7 × 3 9 В ќ Џ ЊЉ Џ ќ ЎЉDown1 11 × 11 2 ЊЋ ќ ЊЉ 3 7 × 7 5 ЏЏ ѝ Џ 6 12 × 12 8

ЌВ ѝ Ќ/ƚƒƦƌĻƷĻ Ʒŷźƭ ĭƩƚƭƭƓǒƒĬĻƩ ƦǒǩǩƌĻʹ

ĻƭƷ ǤƚǒƩ ƭƦĻĻķ ğƓķ ğĭĭǒƩƷğĭǤ͵ wğĭĻ ğŭğźƓƭƷ ğ ƦğƩƷƓĻƩ ƚƩ ƷŷĻ ĭƌƷƚĭƉ Ʒƚ ĭƚƒƦƌĻƷĻ Ļğĭŷ ƷğĬƌĻʹ

ѝ Б

ЎЏ

16 64

БЉ

32
72
24

Бѝ Ќ

В 6

ЊБ

12 24

ЌЉ

27

33ѝ А

21
7 14

АЉ

ЍВ

ЋБ

42

ЌЎ

źƒĻʹźƒĻʹźƒĻʹ

If the decimals are confusing

ƒĻͲ L ĭğƓ ĭŷğƓŭĻ ƷŷĻ ğƒƚǒƓƷƭ Ʒƚ ЌЊЉ ĭĻƓƷƭ ğƓķ ЋВЎ ĭĻƓƷƭ͵

Multiplication Documents PDF, PPT , Doc

[PDF] about multiplication algorithms

1. Math

2. Basic Math

3. Multiplication

[PDF] about multiplication of decimals

[PDF] about multiplication of matrices

[PDF] about multiplication principle

[PDF] about multiplication rule

[PDF] about multiplication tables

[PDF] about multiplication word problem

[PDF] act against multiplication

[PDF] after multiplication the germ cells divide by

[PDF] anti multiplication

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