Number Talks: Two Perspectives

The new school year is coming, and I’m getting deep into planning expectations and routines for my students this year.

One of those routines is number talks. I first tried them in April last year and absolutely loved doing a number talk every day, wishing I’d started them from day one. By the end of the year, I was very comfortable with them, had tried a number of structures, and was pretty well settled on what they would look like the next year. My ideas came from Fawn Nguyen, Jo Boaler’s How to Learn Math course and other resources at her site Youcubed, and several sessions I attended at NCTM last year.

My routine: I put one question up on the board, and give students time to solve in their heads. No pencil and paper. Some are arithmetic, some are word problems, some are visual. Then, I take every answer and record them without judgment. I pick three students randomly (will introduce popsicle sticks this year) to share their methods — whether they found a precise answer, or estimated — and record these. If there is time, I take more students methods. I ask clarifying questions along the way to push students reasoning and articulation. Finally, students pick up their pencils and write down which of the methods that they’ve seen they like the best, and why.

Here are some sample questions:

All are meant to be questions with multiple solution paths, that lend themselves to estimation and strategies that reflect mathematical structure. I like this structure a lot: it pushes every student to participate, encourages flexible thinking and estimation, and doesn’t take too much time away from class.

Then, I read a great post from Graham Fletcher on his approach to number talks.

The key to Number Talks is in the number string.  It is not a single problem that is put on the board and discussed.  […] Using 3-4 expressions that are similarly related allow students to connect and immediately employ invented strategies repeatedly.  The repeated use of strategies is what builds automaticity.

This echoes ideas from a great book on number sense,

that number sense is best developed by teaching specific strategies through a string of similar problems, leading to a specific, pre-planned conclusion.

I’m torn: I really like my current plan because it’s important to me that number talks are a daily routine, and I’m uneasy giving up more classtime. I’m also torn about whether students can develop flexible understanding and fluency through one-shot daily number talks. I think there’s definitely benefits of both perspectives. As a compromise, I think I may have a weekly “theme” that number talks center on — fractions, or dot patterns, or percents. Students will have one piece of paper they use to write their explanations on, with space for each day of the week. Then, at the end of the week, we sum up the ideas that have been presented and talk about conclusions.

I’ll keep pondering. In the meantime, two more nuggets — Graham:

Number Talks in isolation does not work.  Students must be encouraged to use their “Number Talks Strategies” outside the 10-15 minute block.

Right on.

And, for a much bolder and more comprehensive approach to building number sense in a daily warm-up, Lisa Bejarano shares a weekly plan incorporating counting circles, talking points, estimation, visual patterns, and number talks.