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.