Module 6: Developing Multiplication and Division in All Grades

Approximately 5 hours

Introduction

This 5 hour module is designed to get you thinking about multiplication and division and how children can work with these concepts informally at very young ages. Many children have developed some intuitive understanding of working with equal sized groups before they begin kindergarten. This intuition needs to be developed in grades K to 2 so that they will be prepared to make connections to the more formal thinking in grade 3. Multiplication and division are also foundational for understanding place value. Children who explain that 50 means 5 groups of 10 are explaining that 50=5x10 but in a less formal way.

The first activity shows how number talks involving dot patterns can help students think multiplicatively. There are many ways that children can think about computing with equal sized groups that will help them develop multiplicative reasoning strategies. You will begin to look at how students describe seeing groups of dots and the relationship with the strategies of thinking multiplicatively.

The second activity is designed for you to begin looking at the different strategies that children use to solve multiplication problems and asks you to rank the problems based on sophistication levels. You will compare your thinking with the thinking of other teachers.

 You and a partner will plan and practice multiplication number talks involving dot patterns containing equal groups in the third activity. 

These number talks can be used with a wide range of children. One goal for this activity is for you to work on your recording of strategies using both the dot pattern as well as symbols. Your number talks will continue to get better with your actual students as you get better recording their thinking to make it public and use the recording strategies to highlight connections among their thinking.

You will learn how to write multiplication word problems as well as two different types of division word problems in the fourth activity. The difference between the two ways to think about division depends on the context of the problem. You will also learn about the different strategies that children think about multiplication. The strategy names are similar to the ones you learned in Session 3 but involve equal sized groups. You will be able to connect these strategies with the different ways that children describe how they see the number of dots during a number talk.

 The research presented in activity 5 suggests that children in kindergarten are very capable of thinking about multiplication and division in informal ways. You will be able to make connections between the results of this research and what you are learning in this training.

  Module 6 Goals

• Teachers will be able to carry out number talks focused on multiplication with whole numbers.
• Teachers will be able to identify the key features of multiplication and distinguish between two types of division.
• Teachers will be able to write multiplication, partitive division, and measurement division word problems.

As you navigate through the 6 activities in this session you will:

• Watch teachers conduct number talks relating to multiplication
• See example student work and comment on the sophistication of their thinking
• Experience conducting a number talk yourself with other members of your PLC.