Today, asked this question, from Fawn Nguyen

Got some really awesome answers. A bunch of estimates, including several who chose to estimate by finding 4 times 30, which coincidentally gives the exact answer of 120.

Had a tough time representing student ideas as they explained. For instance, in two classes a student presented an approach that I scribed like this:

3 x 32 = 96

1/2 x 32 = 16

1/4 x 32 = 8

= 120

Which was fine for representing the process, but what I want to get at ,and what is explicit in the Common Core definition of Look for and make use of structure (MP.7), is visualizing the distributive property, the idea that (3 + 1/2 + 1/4) = 3.75 — and maybe even representing the fraction-to-decimal conversion as well.

Beyond that, I’m curious what ways I can find to get other students to engage with that thinking. One student coming up with it and explaining it is one thing, and representing the mathematical structure helps as well, but it’s made me think more about having students write along with me to push them to engage with the ideas in the number talks. One big idea might just be to slow down and spend more time on fewer approaches.

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AshliI really want to ask the kiddos “32/___ = 120?”

I’m also wondering if writing or trying to make pictures of the arithmetic here would prove useful. I feel like I would trip on the language, but creating a visual (like the ones over at Fawn’s:http://fawnnguyen.com/2013/05/21/20130518.aspx) and then explaining verbally would be doable. But that’s me 🙂