A seventh grade student came to the math center to prepare for
a test on fractions. She brought in a review sheet with various
practice problems which she completed with time to spare. The student,
somewhat anxious about the test, asked if I could make up problems on
the whiteboard. I complied and wrote out the following problem:

My student proceeded to simplify by canceling common factors.

And then declared this was all she could do.

Me: I think you can simplify this further.

The student tested adjacent numerator-denominator pairs: 24 and 7, 5 and 8, 8 and 27

Student: No, that's it. I can't simplify this.

Me: Have you tried 24 and 27?

Student: (spins around) I wanted to but aren't they

*?*

**too far apart**Me: Nah, I think the limit is around 3 feet.

*(I couldn't resist.)*

After 45 minutes of rather predictable practice problems, we finally had a teachable moment.

It
makes me wonder what other misconceptions our students have that we
never uncover. And it reminds me to never stop pushing past the surface.

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