What make you of this?

Thanks again, Tina!

I think the temptation I have is to call this a “careless” mistake and urge more practice. Let’s probe deeper.

1. What does this kid know and understand about exponents?

2. What’s the fastest way to help?

3. What makes this mistake so tempting?

Thanks to Sadie Estrella for the awesome addition to our ever-mounting pile of exponents mistakes.

You grade these tests on Sunday, and you see these kids on Monday. What does the lesson plan look like?

For more context and analysis, go check out the blog from whence these came.

Marshall Thompson is offering a substantial bounty for the correct explanation for this mistake. (He knows the truth from talking to the student.)

Who’s got it?

What’s the quickest way to help this student?

Thanks to Triangleman for another excellent submission.

(Also, did I get the categorization right on this one?)

Bob Lochel writes:

“I used this question as part of a benchmark assessment given to over 1,100 students at our high school, as preparation for the state test. Only 14% of students gave the correct answer B, while 66% of students chose A as their response. I’m not surprised that students would perform weakly on a domain/range question, but I am surprised that so many chose A. I featured this problem as a set-up for a domain and range activity on my blog: http://mathcoachblog.wordpress.com/2013/01/22/home-on-the-range-and-the-domain/, but feel free to share it with the mathmistakes crowd.”

So, what do we think about choosing A? Any theories?

Thanks to John Burk for the submission. He writes, “I know this student wouldn’t simplify (6+2x)/(3-x) this way.”

So: if the student wouldn’t simplify (6+2x)/(3-x) this way, then how did the student end up messing it up for (6+2i)/(3-i)?