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 3

The multi-step domain will be considerably more complicated to teach. I am focusing only on two-step problems. Mathematically there are 16 different combinations of the four operations since the order must be taken into account. Initially, I will group these problems together based on their types, or their similarities and differences. I will share examples of problems with the corresponding bar model. After taking the students through examples of each dimension, I will have the students work in cooperative groups to read word problems, look at the bar model and identify the two operations. They will also have to figure out the proper order in which to complete the operations. Once the students are proficient with this skill, I will move them into actually solving these two-step problems. This will begin as group work then it will progress to partner work and independent work.

Meihua saved $24. She saved 3 times as much as Weilin.

image 07.06.05.08

Write the missing numbers in the boxes as you answer each question below.

(a) How much did Weilin save?

(b) How much did they save together?

I will provide the students with many opportunities to solve the multi-step problems since these vary so much. The students will participate in discussions about the problems because my students can learn so much from each other. While practicing these problems it would be fun to give each student a word problem written on an index card. We could go outside and the students could draw the Singapore bar models and solve the problem on the blacktop using sidewalk chalk. The key to conquering the multi-step problems will be keeping it fun. This will be more frustrating for some students, but by mixing up the activities and keeping it fun the students will be more motivated.

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