Arithmetic with Polynomials and Rational Expressions exponents Expressions Seeing Structure in Expressions Simplifying expressions

Combining Like Terms + Exponents

Here are 7 mistakes. There represent all of the variety of mistakes from a selection of 36 students. The first two mistakes were repeated by several students, but the last 5 were unique in the sample. Which of these mistakes would you predict? Which ones surprise you? Can you make sense of them all?

exponents Expressions & Equations Middle School

Exponents – Positive Integer Powers

Thoughts? (via Chris Robinson)

exponents The Number System

Zero and Exponents

This post is brought to you by David Wees. Thanks, David!

Distributive Property exponents Expressions and Equations

The Distributive Property of Exponents

Why is this mistake so enticing, and how might you help students avoid it? [Compare:] Thanks again to Anna Blinstein for the submission. Follow her! Virtually! Not literally!

Arithmetic with Polynomials and Rational Expressions Distributive Property exponents

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.

exponents N.RN.1

Classic: Zero exponents

What makes this idea so attractive to students? Why should it be true that ? How do you help them see the light?


Using Math Mistakes in Whole-Group Discussions

@mpershan I'm looking to understand how to use #mathmistakes in whole-class summary discussions. Any papers you like? Any insights to share? — Dan Meyer (@ddmeyer) October 7, 2015 This is such a good question. I don’t have a great answer, and I’d like to try articulating why that is. When people get in touch with […]

Area exponents Fractions Geometric Measurement and Dimension

5 and 1/2 x 2 and 1/4 = 7 and 3/4

I find this fascinating. This student clearly knows how that multiplying the base and the height of a rectangle gives you its area. She even knows how to multiply fraction. But when it comes to part (d), she adds the numbers instead of multiplying them. In earlier writing I hypothesized that, when put in unfamiliar situations, students […]

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Guest Post: Looking at Student Work with

Guest post by Justin Reich, cross-posted at Justin’s blog at Education Week (here). — In my Introduction to Education class, one of my goals is for students to get a sense of the value of looking at student work. Not just glancing at it, reading it, or grading it, but really trying to understand what we […]

Exponents Numbers & Operations in Base 10

“Two cubed is eight, but seven squared is fourteen.”

    Yes, yes, kids multiply the base and the power. Here’s what’s remarkable about this: They do know the definition of exponents. It’s written a line above. They did it a line above. They’re doing this with confidence. There aren’t erased numbers. This isn’t slow thinking. This is just what kids think seven squared ought to be. […]