When solving problems in Number Talks, the strategies, en route to the solution, are the focus of the discussion. However, not all problems posed during a Number Talk are created equal or solved the same way every time by every student. While I know the majority of students use a particular strategy for one reason or another, whether it be because of the numbers involved or maybe it is the only strategy they are comfortable using, I like to take time and make these choices explicit. I want the students to think about the numbers before just computing and become more metacognitive about their actions.

Last week, the 5th grade teachers and I planned for a card sort to get at just this. The students have been adding decimals and using some great strategies, but we really wanted to hear about the choices they were making. With the help of the *Making Number Talks Matter *book, we chose problem types for students to think relationally between whole number and decimal operations. While there are no right or wrong answers, these are the problems we chose with strategies we thought went along with each. The expectation was not to have the students solving it the way we had listed, but to hear, and have other students hear the choices being made.

We gave partners the cards, they sorted, and named the categories whatever they wanted:

While the card sort conversations were really interesting, the class discussion afterwards was amazing! There were so much questioning of one another about how one strategy is any different than another. For example, some groups used rounding for a problem that another group used compensation and another grouped called it using friendly numbers…so groups had the same problem in three differently-named categories. Again, the category was not important, but more the fact they were actually thinking about the numbers they were given.

The other 5th grade teacher and I are planning to do the same activity with multiplication when they get there! Excited!

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howardat58Doesn’t just get so complicated. When I was at primary school in the UK in 1950 (!) we learned a rule. “Write the numbers one of them above, one below, lining up the decimal points. Then add as with whole numbers. The decimal point in the answer is in the same place as in the numbers”. We had an even more useful rule for multiplication. It helps if the kids can see that 3 and 3.00 are representations of the same number. Doesn’t there ever become a point at which “explanations” and “understanding” don’t matter?

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LisaThanks for sharing this! I agree- this is a powerful way of getting students to become more metacognitive about their actions. I’m looking forward to trying it out with our fifth graders! Do you have the multiplication sort that the teacher was going to try out? Would love to see or hear about it!

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