What are these kids struggling with? What are they getting right? Are there interesting differences between the three different students whose work is shown?

Thanks again to Ms Miles (twitter / blog)  for the submission!

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

What’s the mistake? Why did the student make this mistake, in particular?

Thanks again to the tweeting and blogging Kate Nowak for this submission.

Assignment: reconstruct what was going through the student’s mind as she solved this problem and, apparently, answered the problem with confidence.

This mistake has been brought to you by Kate Nowak, who blogs and tweets and stuff.

Here’s the work:

Can you make sense of it? What’s the cause of this mistake? How could you help?

What’s the nature of this student’s mistake? Is it the sort of mistake that the kid would make given a linear equation to solve, or is the mistake particular to the trig context? How might you help the kiddo?

In case you’re having trouble reading the kid’s work, and because the top of the question is cut off, I’m going to reproduce the problem in text below the image:

Question: What is the product of $\frac{x^2-1}{x+1}$ and $\frac{x+3}{3x+3}$?

Answer: $\frac{3x^2-3}{3x+3}*\frac{x+3}{3x-3}$

$\frac{3x^2+9}{9x+9} \rightarrow \frac{1x^2+3}{3x+3}$

The usual: What does he know, what doesn’t he know, and what would you do next?