Download File - Brighten Academy​Middle School

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:

6 = 11
,,,
1. 9  8 
2. 15  4  3 = 3
3. (2  5)  3 = 21


Careful… the last one is tricky!



2
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
3
.5
90
2nd method
2 .9 .5
. .
10
.9
90
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
Explore: Marvin the Magician’s Cards
In your groups:
1st : Determine which cards are true and false.
Be sure to support your reasoning.
2nd: For the true cards only, complete
the worksheet provided.
5
Summary: Definitions
Click on a card.
13  8  8 13

12 5  5 12

4 0  4
(4  2)  8 
4  (2  8)

15 0  0



6
9 1  9

2(5 3)  (2 5)3
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.
Commutative Property of Addition
Click to Return
7
Summary: Definitions
Let’s discuss
the card:
12 5  5 12
Algebraically
a b  b a

Changing the order of the
numbers does not
change the PRODUCT.
Commutative Property of Multiplication
Click to Return
8
Summary: Definitions
Let’s discuss
the card:
9 1  9
Algebraically
a 1  a
a number by 1
Multiplying
leaves it unchanged.
Identity Property of Multiplication
Click to Return
9
Summary: Definitions
Let’s discuss
the card:
4 0  4
Algebraically
a0  a

Adding a number by 0 leaves
 it unchanged.
Identity Property of Addition
Click to Return
10
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
11
Summary: Definitions
Let’s discuss
the card:
(4  2)  8 
4  (2  8)
Algebraically
(a  b)  c  a  (b  c)

When ADDING
more than 2 numbers, the way we
group them does 
not change the SUM.
Associative Property of Addition
Click to Return
12
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
13
Summary: Definitions
Let’s discuss
the card:
(4  2)  8 
4  (2  8)
Algebraically
(a  b)  c  a  (b  c)

When ADDING
more than 2 numbers, the way we
group them does 
not change the SUM.
Associative Property of Addition
Click to Return
14
Summary: Definitions
Let’s discuss
the card:
4 0  4
Algebraically
a0  a

Adding a number by 0 leaves
 it unchanged.
Identity Property of Addition
Click to Return
15
Summary: Definitions
Let’s discuss
the card:
12 5  5 12
Algebraically
a b  b a

Changing the order of the
numbers does not
change the PRODUCT.
Commutative Property of Multiplication
Click to Return
16
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
17
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.
Commutative Property of Addition
Click to Return
18
Summary: Definitions
Let’s discuss
the card:
9 1  9
Algebraically
a 1  a
a number by 1
Multiplying
leaves it unchanged.
Identity Property of Multiplication
Click to Return
19
Practice
PART I
Using the Properties of Mathematics, match Column A to Column B. Write the expression
from Column B that matches the expression in Column A in the blank provided. State the
property that proves the equation true. You can choose from Commutative Property of
Addition, Commutative Property of Multiplication, Associative Property of Addition,
Associative Property of Multiplication. You may use a property more than once.
Column A
Column B
Commutative of
Multiplication
5 14 
5(14x) 
5  (14  x) 
5x 14 
5  (x 14) 
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Associative of Multiplication
Associative of Addition
Commutative of Addition
Commutative of
Multiplication
Practice
PART II Evaluate the following expressions quickly. State the property you used
to help make the computation faster.
1. 15 + 15 + 7 + 8
2. 5  9  4
5  4  9 Commutative
15 + 15 +15
of
20  9
45
Multiplication
180
Associative of Addition
3. 11 + 3 + 9 + 17
4. 13  2  5
13  10
11 + 9 + 3 + 17
130
20 + 20
Associative of Multiplication
Commutative of Addition
5. Tharzan’s grades for his last four quizzes are stated below. He wants to find
the average of his grades. Show Tharzan how he can add his scores quickly
using the properties you learned in class before he divides. Explain.
Quiz Grades: 81 + 0 + 88 + 82
Possible answer: add the 88 and 82 to get 172 using the Associative of Addition.
Then add 81 and 172 to get 253, using the Commutative of Addition, and adding 0
will not change the sum because of the Identity of Addition.
21
Practice
Click here for PART IV
PART III
1. Is the following equation 12 – 9 = 9 – 12 true? Explain.
No, because 12 – 9 is 3 and 9 – 12 is less than 0.
2. Do you think the Commutative Property works for subtraction? Why or why
not?
No. Changing the order in subtraction does not give you the same answer.
3. Is the following equation (15 – 9) – 6 = 15 – (9 – 6) true? Explain.
No. The left side of the equation equals 6 – 6, which equals 0. The left side of the
equation equals 15 – 3, which equals 12.
4. Do you think the Associative Property works for subtraction? Why or why
not?
No. Regrouping the numbers in subtraction does not give you the same answer.
22
Practice
PART IV
Make 24! Using the numbers provided, and the four basic
operations, +, - , , ÷ , make the number 24.
1. 1, 5, 4, 3
2.
5 4  3 1

3, 12, 4, 1
3 4 12 1
3. 10, 9, 7, 2
(9  7) (2 10)

Agenda
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