1 Now look at two more Circles of Evaluation to decide if the Commutative Property holds for problems involving addition.

(+ 20 5)

(+ 5 20)

20 + 5 = ?

5 + 20 = ?

What do you notice?

2 Now look at two more Circles of Evaluation to see how the Commutative Property holds for problems involving addition of three values. Can you fill in a third Circle so that the order changes, but not the groupings?

(+ (+ 9 2) 8)

(+ 8 (+ 9 2))

(+ (+        ) 8)

(9 + 2) + 8 = ?

8 + (2 + 9) = ?

What do you notice?

These Circles of Evaluation all represent the Commutative Property of Addition! Notice how, when we used three values, there were multiple ways of reconfiguring the numbers. (Do you think that is true, also, for the Commutative Property of Multiplication?)

3 Evaluate the Circles below to decide if the Commutative Property holds for problems involving subtraction.

(​- 50 4)

(​- 4 50)

50 - 4 = ?

4 - 50 = ?

Explain your response.

4 On a separate page, draw two additional examples - one pair of Circles that confirms what you observed about the Commutative Property and addition, and another pair of Circles that confirms what you observed about the Commutative Property and subtraction. Evaluate each Circle to verify your response.

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). CCbadge Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.