Chapter 5 begins with a discussion about the importance of decreasing our focus on memorizing fact memorization and increasing students’ experiences looking for “relationships between quantities” and understanding the meaning of multiplication (Humphreys and Parker, 2015, p. 62). Opportunities to explore the properties of numbers “will support their understanding of algebra later” (Humphreys and Parker, 2015, p. 62).
The multiplication strategies in this chapter increase students’ abilities to work with numbers mentally and decrease their reliance on the traditional algorithm– a reliance the authors state results from limited experience “thinking with numbers” (Humphreys and Parker, 2015, p. 62). The multiplication strategies highlighted in the chapter are detailed in the illustration below.
The authors offer the following big ideas in relation to the multiplication strategies used during number talks:
* Use of the distributive property gives students the flexibility to make problems that seem hard much easier to solve.
* It is not necessary for students to break apart numbers into tens and ones. Students can also break factors into other addends.
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. At the end of the chapter, the authors illustrate how the strategies apply to fractions and decimals, as well as, a discussion on connecting algebra and arithmetic.
A note about Algebra: Using these strategies during number talks provides students with experiences using the distributive, associative, and commutative properties. These are the very strategies that are essential to help students understand important algebra concepts. In addition, using multiplication problems during number talks gives us the opportunity to make connections between the actions students are using to solve the problems and the names of the properties.
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