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```The Properties of Mathematics
1
Warm Up
OBJECTIVE: Students will be able to identify the properties of operations.
Language Objective: Students will be able to recite the properties of operations.
Fill in the blanks with any operation:

= 11
, , ,
1. 9  8  6
2. 15  4  3 = 3
3. (2  5)  3 = 21



Careful…
the last one is tricky!


2
Agenda
Launch
Evaluate the following expressions in two
different ways.
. 9. 5
2. 218
1. 92+7+13
99
+13
112
2nd method
92+(7+13
(20) )
92+
112
.5
90
2nd method
2 .9 .5
. .
10
.9
90
Agenda
3
Explore: Marvin the Magician’s Cards
Marvin the Magician needs your help! He uses
a deck of math cards for one of his tricks.
However, only some cards are TRUE.
Help Marvin find the TRUE cards.
Examples
4  3  3 4
12  0  0
TRUE!
FALSE!

4
Agenda
Explore: Marvin the Magician’s Cards
1st : Determine which cards are true and false.
Be sure to support your reasoning.
2nd: For the true cards only, complete
the worksheet provided.
Agenda
5
Summary: Definitions
Click on a card.
13  8  8  13

12  5  5 12
9 1  9

40  4
(4  2)  8 
4  (2  8)

15  0  0
2(5 3)  (2 5)3



6

Agenda
Summary: Definitions
Let’s discuss
the card:
13  8  8  13
Algebraically
ab ba

Changing the order of the numbers does not

change the SUM.
Click to Return
Key Words
7
Agenda
Summary: Definitions
Let’s discuss
the card:
Algebraically
12  5  5 12
a b  b a

Changing the order of the
numbers
does
not

change the PRODUCT.
Commutative Property of Multiplication
Click to Return
Key Words
8
Agenda
Summary: Definitions
Let’s discuss
the card:
9 1  9
Algebraically
a 1  a
 a number by 1leaves it unchanged.
Multiplying
Identity Property of Multiplication
Click to Return
Key Words
9
Agenda
Summary: Definitions
Let’s discuss
the card:
40  4
Algebraically
a0  a

Adding a number by 0 leaves
it unchanged.

Click to Return
Key Words
10
Agenda
Summary: Definitions
Let’s discuss
the card:
2(5 3)  (2 5)3
Algebraically
a(bc )  ( ab )c

When MULTIPLYING more than 2 numbers, the
way we group them doesnot change the
PRODUCT.
Associative Property of Multiplication
Click to Return
Key Words
11
Agenda
Summary: Definitions
Let’s discuss
the card:
(4  2)  8 
4  (2  8)
Algebraically
(a  b)  c  a  (b  c )

more than 2 numbers, the way we
group them does 
not change the SUM.
Click to Return
Key Words
12
Agenda
Summary: Definitions
Let’s discuss
the card:
15  0  0
Algebraically
a 0  0

Multiplying
a number 
by 0 is always 0.
Zero Property of Multiplication
Click to Return
Agenda
13
Summary: Definitions
Let’s discuss
the card:
(4  2)  8 
4  (2  8)
Algebraically
(a  b)  c  a  (b  c )

more than 2 numbers, the way we
group them does 
not change the SUM.
Click to Return
Key Words
14
Agenda
Summary: Definitions
Let’s discuss
the card:
40  4
Algebraically
a0  a

Adding a number by 0 leaves
it unchanged.

Click to Return
Key Words
15
Agenda
Summary: Definitions
Let’s discuss
the card:
Algebraically
12  5  5 12
a b  b a

Changing the order of the
numbers
does
not

change the PRODUCT.
Commutative Property of Multiplication
Click to Return
Key Words
16
Agenda
Summary: Definitions
Let’s discuss
the card:
2(5 3)  (2 5)3
Algebraically
a(bc )  ( ab )c

When MULTIPLYING more than 2 numbers, the
way we group them doesnot change the
PRODUCT.
Associative Property of Multiplication
Click to Return
Key Words
17
Agenda
Summary: Definitions
Let’s discuss
the card:
13  8  8  13
Algebraically
ab ba

Changing the order of the numbers does not

change the SUM.
Click to Return
Key Words
18
Agenda
Summary: Definitions
Let’s discuss
the card:
9 1  9
Algebraically
a 1  a
 a number by 1leaves it unchanged.
Multiplying
Identity Property of Multiplication
Click to Return
Key Words
19
Agenda
Assessment- Exit Slip
1. Evaluate the expression
below. List the properties that
you used.
12  (8  46 )  80
(12  8)  46  80
20  80  46
100  46
146
Associative
Property
2. Which property of
multiplication is
shown? 3 1  3
A. Commutative
B. Associative
 C. Identity
Commutative
Property
Agenda
20
```