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## Mistake Analysis + Practice

Here’s an activity I just drafted for my Algebra 1 class. I’m trying to help them get very comfortable working with the distributive property and fractions. Thoughts?

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## What is the Distributive Property?

Here are a bunch of responses to the same question:

If this is your class (and this is the Spring!) then how do you respond?

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## “Prove the following conjecture: The sum of any 3 positive consecutive odd integers will be divisible by 3.”

First, I just love the question. Second: theorize! What happened to this student? What are some good signs in the student’s work?

Thanks to Bree  for the submission.

Also: I categorized this under “Standards for Mathematical Practice.” Does anyone have another CCSS standard that fits this problem and work?

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## Distributive Property, Again!

What task or problem would you have this student attempt? Or would you follow this up with an explanation?

Thanks to John Weisenfeld for the submission!

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## Another awesome Distributive Property mistake

We actually have an explanation from the student, and hopefully Alison Royster will be kind enough to jump in on the comments and provide it.

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## The Distributive Property of Fractions

See the title of the post.

What is the significance of this mistake? Say something smart about this piece of student work in the comments.

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## The Distributive Property of Absolute Value

Say something smart about the Distributive Property in the comments.

And thank Ms Miles (twitter / blog)  for the submission!

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## The Distributive Property of Exponents

Why is this mistake so enticing, and how might you help students avoid it?

[Compare: http://mathmistakes.org/?p=396]

Thanks again to Anna Blinstein for the submission. Follow her! Virtually! Not literally!

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## Distributive Property

What does the kid think the distributive property is?

It’s easy to say: “Well, I’d avoid this mistake in my class by teaching the distributive property correctly.” Well, what’s the wrong way to teach this thing, then? What’s the smartest possible way to teach this, and still end up with your kids making that mistake?

After you’re done writing an awesome comment to this post, go check out Josh Weisenfeld’s blog. He spotted and submitted this gem of a mistake.

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## Classic Mistakes with Exponents

Here are two classic mistakes:

Whenever I see a mistake that recurs at all different levels, and with all different students, I wonder: what makes this mistake so attractive? What’s the misconception? And what can we do about it?

Say something smart in the comments, and then go check out this post from Fawn Nguyen.