Flopped today. Did

I was excited about it because there are so many different representations of fractions (see Hung-Hsi Wu for a discussion of fractions in the elementary grades), and my students lean pretty hard on procedures and calculators. I think this failed because the answer was instantly clear to everyone, and there was no value in representing it a different way.

Leads me to my first productive rule for conducting number talks:

The purpose of number talks is to give students opportunities to look for and make use of structure and think flexibly about relatively simple problems. However, if the problem presents a trivial solution using a traditional algorithm, the problem is unlikely to be successful in getting students to find structure and alternative approaches.

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AshliHow would you change the above for the future? Different divisor? Different dividend? something like 6 divided by 3/4?

dkane47Post authorGood question. I think the goal is to bring out ways that the structure of dividing fractions is consistent with the structure of dividing whole numbers by finding questions where alternate representations and techniques are valuable over the “standard algorithm”. Like your example — jumping off of that, I would like to do something like 10 divided by 2/3 — give kids an opportunity to break down numbers, to see that 2/3 goes into 2, the same way that 6 divided by 3/4 gives kids an opportunity to see that 3/4 goes into 3, then double it. A few other ideas:

8.5 divided by 1/2

15 divided by 1 1/2

1/2 divided by 1/16

70 divided by 1.25

I think I’m hitting a bunch of similar structures here though. I wonder what other ways of thinking about fractions would be helpful for students?