1. Objective The student will be able to:
recognize and use the commutative and associative properties and the properties of equality.
SOL: A.4b
Designed by Skip Tyler, Varina High School

2. Commutative Property
Commutative means that the order does not make any difference.
a + b = b + a a • b = b • a
Examples
4 + 5 = 5 + 4
2 • 3 = 3 • 2
The commutative property does not work for subtraction or division.

3. Please select a Team. Boys Girls 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1516 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

4. Associative Property
Associative means that the grouping does not make any difference.
(a + b) + c = a + (b + c) (ab) c = a (bc)
Examples
(1 + 2) + 3 = 1 + (2 + 3)
(2 • 3) • 4 = 2 • (3 • 4)
The associative property does not work for subtraction or division.

5. Name the property 1) 5a + (6 + 2a) = 5a + (2a + 6)
commutative (switching order)
2) 5a + (2a + 6) = (5a + 2a) + 6
associative (switching groups)
3) 2(3 + a) = 6 + 2a
distributive

6. Which property would justify rewriting the following expression without parentheses? 3(2x + 5y)
Associative property of multiplication
Distributive property
Addition property of zero
Commutative property of multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

7. Which property would justify the following statement? 8x + 4 = 4 + 8x
Associative property of addition
Distributive property
Addition property of zero
Commutative property of addition 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

8. Which property would justify the following statement
Associative property of addition
Distributive property
Addition property of zero
Commutative property of addition 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

9. Team Scores
Team 1
Team 2
Team 3
Team 4
Team 5

10. Participant Scores Participant 1 Participant 11 Participant 2
Participant 1
Participant 11
Participant 2
Participant 12
Participant 3
Participant 13
Participant 4
Participant 14
Participant 5
Participant 15
Participant 6
Participant 16
Participant 7
Participant 17
Participant 8
Participant 18
Participant 9
Participant 19
Participant 10
Participant 20