exponents Expressions Expressions and Equations

Combining like terms…

john weisenfeld

…is probably looking like an unfortunate name for adding monomials when you see a mistake like this one. Right?

Or wrong? Speak up in the comments. And more thanks to John Weisenfeld for the mistake.


Expressions and Equations Simplifying expressions Solving Linear Equations

Solving the Expression

Clearly the kid doesn’t have a deep conceptual understanding of how to solve equations or simplify expressions. True, the kid probably learned some stuff proceduraly as opposed to conceptually. (Though, I can confirm, that in this classroom nobody ever said anything, like, “When you have an equation you need to add something to each side to isolate the x.” The balanced-scale model was used at first.)

There’s still two interesting, deeper questions, to consider. (Possibly more: bring it up in the comments.)

a) Would this kiddo always make this mistake, when presented with an expression to simplify?

b) If not, then what exactly is it about this problem that prompts the kid to employ a basic move from equations?

Expressions and Equations Solving Linear Equations

Solving Simple Equations

Say something smart about this in the comments.

Thank you to John Weisenfeld for the submission.

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?


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

exponents Expressions and Equations Feedback

What do powers mean, again?

Would the student have made this mistake if she were just given a^2 to evaluate? If yes, then what’s the misconception. If no, then what’s going on?

Oh, and go check out Chris Robinson’s stuff, and go follow him on twitter.

Expressions and Equations Solving Linear Equations

Solving equations

Where did this kid go wrong? What does it reveal about his understanding of solving equations? What is your next step for him?

Distributive Property Expressions and Equations Simplifying expressions

Combining like terms

The mistake is clear. Why is this mistake so damned tempting, and how would you help?

Conditional Probability and the Rules of Probability Expressions and Equations Limits

Khan Academy Potpourri

I’m sitting on a bunch of Khan Academy questions from users that I marked as very interesting. I never posted them, and I feel a little cheap giving them all their own posts. So I figured I’d just dump the whole lot on you all. These questions reveal interesting things about the way these students are thinking. If you think that you’ve got something interesting to add, either on the diagnosis or prescription side of things, dig into the comments below.

The first is a nice probability puzzler. How did this student get 3/8?

I love this conceptual question.

Not sure exactly why I clipped the first question here, but the second question is great. “Why do they call it a limit?”

A good reminder: some vocab is tricky. Why are these two vocabulary words the one that this student confused?

This is a great point from a kid about variable use.

A little bit of context for this next one: we’re talking about protractors here.

8.EE.7 Solving Linear Equations


What does the student understand, and what does she not? How would you help?

8.EE.1 8.EE.4 exponents Feedback Scientific Notation

Scienfitic Notation


What does the student know? What are the student’s misconceptions? How would you help?