Can you explain where each of the student’s responses came from? As in, how did he arrive at 8/24, 14/96, and what is either 24/72 or 14/72.

I saw this one in class last week:

Probability of flipping 10 heads when flipping 10 coins: (1/2)^10

Probability of flipping 9 heads when flipping 10 coins: (1/2)^9

At 1:30, a student says, “if you do that probability 3 times, you ought to get that probability at least once.”

How should I have responded to this student? (I actually have the footage, which we can analyze at some point if we think that’d be fun.)

Bob Lochel asks: “I am wondering if anyone can conjecture why “3” was featured in both answers, as I can’t wrap my head around it. Perhaps it was a counting of the number of cells in the row she needed?”

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.