Chapter 7 of Making Number Talks Matter is all about division strategies. What I love about this chapter is that many of the strategies can be applied to larger numbers. It’s all about number sense! If our students understand the meaning of division, they can develop strategies that are useful to them.
The authors also mention that this is the only number talk where students are allowed to use pencil and paper to help with the recording. However, in many cases, most of the work can still be done mentally.
The illustration below shows the four strategies highlighted in the chapter and is a quick overview of how students may articulate how they use each of the strategies, as titled in the text. I chose to use different problems than the ones in the book so that I could apply my own explanations to each strategy.
Note: The authors offer that all of the strategies are intuitive for students except for the “Make a Tower” strategy which involves making a tower of multiplication facts until students find one that will help them divide with the least number of steps. I think of it as estimating quotients, using the closest product to the value of the two largest place values without going over. See the example below.
In my area of the world, we tend to teach the “Chunk Out” strategy as a beginning division strategy. I call it partial quotients because students can keep taking out chunks until they reach the remainder. This strategy helps students understand the meaning of division and encourages them to find the most efficient chunks they can use. It’s actually my favorite way to help students understand the division process.
In the latter part of the chapter, the authors give a detailed explanation of how to develop the strategies above. This section includes a more in-depth description of the strategy, sample problems, and questions to probe when students use each strategy. In addition, throughout the chapter, the authors offer ways to use the same division strategies with decimals.
Note: In order to honor the authors’ work, I will only share my own personal experiences, thoughts, and reflections as related to the book’s content. If something really strikes me, I will share a quote from time to time with the appropriate citations.
Reference: Humphreys, C and Parker, R. (2016). Making Number Talks Matter. Portland, Maine: Stenhouse Publishers