The Commutative and Associative Properties
Commutative property refers to switching around numbers without changing the outcome. For example, it does not matter what order the numbers are in when adding two numbers together. The answer will be the same. The multiplication and addition properties are commutative (Billstein, Libeskind & Lott, 2013). The sum of two numbers is the same regardless of the order in which they are added. So, if a = b, then a + c = b + c. I would use the method to teach this to my students by having them use physical objects, such as linking cubes, to model the problem. As they build the models, I would have them verbalize what they are doing. For example, “I am adding these two numbers together, and it doesn’t matter what order I put them in, I will still get the same answer.” I will also use number line diagrams to help them visualize the concept. I would have the students put two numbers on the number line side by side and then count up from one of the numbers to get the answer.
The associative property refers to regrouping numbers without changing the outcome. The multiplication of three numbers is associative, which means that the order of the numbers does not affect the answer (Billstein, Libeskind & Lott, 2013). For example, if a = b and b = c, then a x (b x c) = (a x b) x c. I would use to teach this to my students by using an array. I would create a display with three rows and three columns. I would then have the students fill in the numbers, changing the order each time. As they are doing this, I would have them verbalize what they are doing. For example, “I am multiplying these three numbers and it doesn’t matter what order I put them in, I will still get the same answer.” I will also use number line diagrams to help them visualize the concept.
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References
Billstein, R., Libeskind, S., & Lott, J. (2013). Problem Solving Approach to Mathematics for Elementary School Teachers, A: Pearson New International Edition PDF eBook. Pearson Higher Ed.
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Question 
The Commutative and Associative Properties
Discuss various methods you might use to teach the commutative property and the associative property of addition. Explain how these properties are used in everyday life and why they are essential to understand.