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# Unit #1.Lesson #3.The Commutative and Associative Properties

It is so unfortunate that the emphasis on the commutative and associative properties so often boils down to which property is being illustrated, versus what is being illustrated. That’s why I wanted to introduce this topic by having students add a string of integers that consisted of pairs that summed to 10. In that case, they naturally use both properties to rearrange the sum to make it easier.

## 6 thoughts on “Unit #1.Lesson #3.The Commutative and Associative Properties”

1. This lesson set off a spirited discussion in my department about associative versus distributive property. In example 6, associative property is given as the justification for removing the parentheses. I like this but many others justify this step as the distributive property w/ a multiplier of 1. I don’t think this would come up on an end of year test b/c there are two legitimate answers but I was arguing that associative property was a better choice (particularly b/c it matched w/ putting the parentheses back in later) but I was on the losing end of this battle. Any thoughts?

2. Meg

Well, obviously I agree with you. I think the distributive property with the number 1 is more or less the associative property. I’ll think more about this.

3. Typos? Homework Application question 3. “…Robert came up with the following expression: 4w+155”. Should it read 45w+155?

Answer key to same problem part (b) reads, at one point, 2704/25 + 45(42) + 155. Should it read 2704/25+45(52) + 155?

I like the “error analysis problem” 5. I think that it helps students focus on specific issues well.

4. Sorry! That last post should have gone in the lesson 2 thread!

5. One of the difficulties that I have coming into the Algebra year is the over reliance on two-signs (8+-4). From the very beginning I focus on using the definition of subtraction (a + b = a+-b) to not have to write that.I understand how it connects with the commutative +, but I have found that it can reinforce the “clutter” of two signs. Do you find this is an issue with your students? Do you deal with the double sign issue later on?

6. Scott,

Thanks for all of the comments. The 4w+155 was changed to 45w+155 in a later version and is correct in our workbook but not on the site yet. Sorry about that. Also, the answer key has a correct final answer, but you are completely correct in terms of that intermediate step being incorrect. Thanks for that catch!