Keeping the Meaning in Mathematics: The Craft of Word Problems

CONTENTS OF CURRICULUM UNIT 07.06.05

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Objectives
  4. Addition and Subtraction Categories
  5. Multiplication and Division Categories
  6. Multi-step
  7. Strategies for Teaching Students to Use the Singapore Bar Models
  8. Activity 1
  9. Activity 2
  10. Activity 3
  11. Appendix A: Collection of Problems
  12. Appendix B: Resources for Classroom Use
  13. Appendix C: Annotated Bibliography
  14. Appendix D: Implementing District Standards:

Dr. Word Problem - Solving Word Problems with the Four Operations Using Singapore Bar Models

Valerie J. Schwarz

Published September 2007

Tools for this Unit:

Activity 2

In the next activity I will teach the students to use the bar models to show multiplication and division. I will once again begin on the computer with the projection screen. I will use the Thinking Blocks website. This time I will model a multiplication problem. The Singapore bar models would be cumbersome to draw with a large multiplier, as 7 x 36. These examples come from the Primary Mathematics Workbook 3A (1992).

Roy had 3 times as many comic books as Samy. If Samy had 7 comic books, how many comic books did Roy have?

image 07.06.05.06

Roy had ____ comic books? The equation for this problem is 7x3=21. Once again by changing the unknown a new problem is created.

In this next problem the inverse relationship of division is represented. Roy has 21 comic books. Roy has 3 times as many comic books as Samy has. How many comic books does Samy have?

image 07.06.05.07

21 / 3 = 7

Much as I did with addition and subtraction, I am pairing up the inverse operations of multiplication and division to help the students to build a critical piece of understanding. By developing this understanding of the relationship between multiplication and division, the students will not only learn their division facts more easily, but also become better problem solvers. Carpenter, Franke, & Levi (2003) assert, "understanding the relation between multiplication and division is critical for learning division number facts and for dealing flexibly with problem situations involving multiplication and division."

Again, once the students learn how to use the model to represent division, the difficulty can increase to the level of their division skills. More difficult division problems can be solved later in the year, once long division has been taught.

Comments:

Kathryn Patrice Freeman

November 9, 2010 at 11:52 pm

Dr. Word Problem - Solving Word Problems with the Four Operations Using Singapore Bar Models by Valerie Schwarz

This unit gave me exactly the information I needed to confidently discuss word problems with our home-schooled daughter. We've done extensive work with bar modeling while using Singapore's curriculum over the last 5 years, but I still never felt completely versed in the method. We take an 'everyone around the table' approach to math, more so than any other subject, so that my daughter can benefit from seeing the very different ways I work problems as compared to her father, and although we can all three wiggle out the answers to word problems, none of us are really confident enough in our method to adequately explain it. This was incredibly helpful to me, and to my daughter. Thank you! Kathryn Freeman

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