Multifaceted Number Concepts 195Commutative and Associative Properties
CONCEPT:
What are the Commutative and Associative
Properties?
The commutative property involves changing the order of
the operations of numbers without changing the result.
Students work with foundational ideas of the commutative
property, also called the order property, when they work with
fact families. They learn that 3 + 5 = 5 + 3 and 6 x 8 = 8 x 6.
It is important for students to understand that addition
and multiplication have the commutative property, while
subtraction and division do not. Similarly, the associative
property involves changing the grouping of the numbers
without changing the result. (2 + 7) + 3 = 2 + (7 + 3) and
(4 x 5) x 2 = 4 x (5 x 2). Students must understand that
addition and multiplication have the associative property,
while subtraction and division do not.CCSS
Operations and Algebraic ThinkingFormative Assessment
To fi nd out if a student understands the commutative and
associative properties ask the students to identify which
property (commutative or associative), if any, the following
equations represent:
8 + 7 = 7 + 8
2 + (5 + 3) = (2 + 5) + 3
(5 x 2) x 3 = 5 x (2 x 3)
(5 x 2) x 7 = 7 x 3
(6 + 8) + 9 = (8 + 6) + 9