Module 5: Expanding Benchmarks and Picturing Subtraction
Approximately 5 hours
Module 5 Goals
- Teachers will be able to carry out number talks (with symbols, number lines, open number lines, and Rekenreks) focused on operations with whole numbers.
- Teachers will be able to use recording strategies that highlight connections and differences among student strategies.
- Teachers will be able to distinguish among three different ways that students use to think about subtraction.
Introduction
This 5 hour module will help you develop your number talk routines using the Rekenrek and then focus on the different ways that children think of subtraction. You will learn three different ways to view subtraction and how to record their thinking using symbols and an open number line.
The first activity will focus on looking at student work and ranking the sophistication levels of each one. The purpose of this exercise is for you to make sense of the different strategies that children use and then assess the level of thinking that this strategy demonstrates. The goal is for teachers to help students become more sophisticated in their thinking when they are ready.
The second activity is designed to help you develop your number talk routines using a Rekenrek. You learned one routine in a previous session and now will plan and practice one more routine. Most teachers that use the Rekenrek for number talks select among five different routines. You can help students visualize numbers around important benchmarks with consistent use of number talks involving Rekenreks.
In the third activity you will connect word problems and student strategies. The goal is to notice how different contexts encourage students to think of addition and subtraction in different ways and how the strategies used to solve these problems match these different views.
Subtraction can be viewed in three different but overlapping ways. In the fourth activity you will be able to name and describe each view. Understanding these different views will help you understand the different ways that your students will solve problems involving subtraction and make you better at drawing these strategies out during whole class discussions. We have found that teachers who internalize these three different strategies are more flexible in thinking about subtraction themselves.
In the fifth activity, you will plan and practice a number talk involving subtraction. You will learn how to record the various strategies that students use as they solve subtraction problems. You will learn how to use symbols and an open number line to record their thinking. The open number line is a tool for you to make student thinking visible during whole class discussions.