# Properties of Multiplication

Contributed by:
Commutative Property
Associative Property
Identity Property
Zero Property
Distributive Property
1.
Properties  of  Multiplication  –  Grades  3  and  4    (Standard  3AF1.5  &  4AF1.0)

Preparation:    Place  five  poster  sheets  with  each  property  and  an  example  of  the
property  in  different  areas  of  the  classroom.    (Posters  included  if  needed)

Commutative  Property   Associative  Property  of
of  Multiplication:   Multiplication:

When  multiplying,  the   The  way  in  which  the
order   of  t he  factors  does   factors  are  grouped  does
not  change  the  product.   not  change  the  product.

4 ! 2 = 8 (2 ! 3) ! 5 = 30

2!4 =8 2 ! (3 ! 5) = 30

Identity  Property  of   Zero  Property  of

Multiplication:   Multiplication:

When  any  number  is   When  any  number  is

multiplied  by  1,  the   multiplied  by  0,  the

product  is  that  number.   product  is  0.

6 ! 1 = 6   8 ! 0 = 0

Distributive  Property  of
Multiplication:

One  factor  in  a
multiplication  problem
can  be  broken  apart  to
find  partial  products.    He
sum  of  the  partial
products  is  the  product
of  the  two  factors.

6 ! 7 = (6 ! 5) + (6 ! 2)

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2.
Introduction:    Review  each  poster  as  a  whole  class.  (This  is  not  a  time  to  take  notes)
Tell  the  students  you  will  be  giving  them  a  sheet  of  paper  that  has  an  example  of  one
of  the  properties.    It  is  their  job  to  decide  which  property  their  example  represents.

Example  1:    The  teacher  models  turning  the  property  card  over  (i.e.  6  X  0),  decide
which  property  the  problem  is  an  example  of  (zero  property),  and  walking  to  the
poster  of  the  property  and  stand  holding  the  card  so  all  students  can  see  the
example.

The  whole  class  should  choral  respond  by  reading  6  X  0  =  0  is  an  example  of  the
zero  property  of  multiplication  because  any  number  times  zero  equals  zero.

(Teacher  should  model  at  least  two  cards)

Example  2:    Give  each  student  a  card  face  down  on  their  desk.    On  the  signal
students  turn  their  card  over  and  decide  which  property  their  example  represents.

The  students  will  then  walk  to  the  property  and  display  their  card  for  everyone  to
see.

The  teacher  walks  to  each  property  and  asks  the  class  if  they  agree  everyone
belongs  to  the  property  where  the  teacher  is  standing.    Have  a  group  discussion
about  similarities  and  difference  in  the  examples.

Students  return  to  their  desks  and  the  cards  are  all  collected.

You-­‐Try  1:    Have  each  group  make  their  own  example  of  every  property  to  share
with  the  whole  class.    Students  should  be  creative  in  writing  their  examples  of  the
properties  and  not  use  the  same  examples  they  just  saw.

The  teacher  will  post  the  posters  around  the  room  and  each  group  will  take  a
“gallery  walk”  reviewing  other  students’  examples.    (The  assumption  is  the  class
knows  how  to  do  a  gallery  walk  otherwise  the  teacher  needs  to  take  a  few  minutes
to  review  the  expectations  of  a  GW).

You-­‐Try  2:    Have  each  student  write  in  their  own  notebook  the  definition  of  each
property  and  their  own  example  of  each  property.    The  can  share  it  with  a  partner  to
check  their  work  and  reinforce  the  concepts.  (TPS)

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3.
Date
Warm-­‐Up

CST    #12  N.S.  1.5   Review:
Which number means Which number makes
1000 + 600 + 8 ? this sentence true?
A. 168 7 +   = 10
B. 1068
A. 0
C. 1608 B. 3
C. 7
D. 1680
D. 17
Current:   Other:
Use the Commutative Kim had \$19.23 in her wallet.
Property to solve the She spent \$5.72 to rent a
following multiplication movie. How much money does
problems. she have left?
3! 5 =
5! 3 = A. \$13.51
B. \$14.41
C. \$14.61
8 !10 =
2) D. \$24.95
10 ! 8 =
Today’s  Objective/Standards:  Recognize  and  use  the
Properties  of  Multiplication  (3AF1.5  &  4AF1.0)
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4.
COMMUTATIVE  PROPERTY:
2  FACTORS  CAN  BE  MULTIPLIED
IN  ANY  ORDER  AND  THE
PRODUCT  WILL  BE  THE  SAME.

EXAMPLE:                     2 ! 5 = 10
5 ! 2 = 10

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5.
ZERO  PROPERTY:

ANY  FACTOR  MULTIPLIED  BY
ZERO  WILL  EQUAL  ZERO.

0!5= 0
EXAMPLE:

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6.
IDENTITY  PROPERTY:

ANY  FACTOR  MULTIPLIED  BY
ONE  WILL  EQUAL  THAT  FACTOR.

5 !1 = 5
EXAMPLE:

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7.
DISTRIBUTIVE    PROPERTY:
A  PROBLEM  CAN  BE  BROKEN
APART  INTO  SIMPLE  PROBLEMS.

EXAMPLE:      6 ! 7 = (6 ! 5) + (6 ! 2)

6 ! 5 = 30

6 ! 2 = 12

6 ! 7 = (6 ! 5) + (6 ! 2)
= 30+ 12
= 42

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8.
ASSOCIATIVE    PROPERTY:

THE  WAY  IN  WHICH  THE
FACTORS  ARE  GROUPED  DOES
NOT  CHANGE  THE  PRODUCT.

(2×3)  ×  4  =  2  ×  (3×4)
6    ×  4    =    2  ×  12
24  =  24
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9.

0×5=0
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10.

0×7=0
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11.

0×19=0
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12.

0×8=0
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13.

50×0=0
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14.

14×0=0
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15.

50×1=50
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16.

13×1=13
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17.

23×1=23
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18.

1×134=134

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19.

1×22=22
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20.

1×1=1

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21.

9×6=54
6×9=54
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22.

8×7=56
7×8=56
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23.

2×12=24
12×2=24
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24.

10×5=50
5×10=50
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25.

3×9=27
9×3=27
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26.

7×3=21
3×7=21
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27.

10×13=(10×5)+(10×8)

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28.

7×4=(7×2)+(7×2)

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29.

6×7=(6×5)+(6×2)

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30.

6×7=(6×4)+(6×3)

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31.

12×13=(12×10)+(12×3)

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32.

11×9=(11×5)+(11×4)

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33.

(3×4)×7=3×(4×7)

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34.

4×(4×5)=(4×4)×5

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35.

(8×4)×2=8×(4×2)

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36.

(9×2)×4  =9×(2×4)

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37.

(3×6)×5=3×(6×5)

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38.

2×(5×4)=(2×5)×  4

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39.

1×67=67
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40.

74×0=0
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41.

(9×9)×3=9×(9×3)

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42.

7×9=63

9×7=63
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