Problem Solving and the Common Core

CONTENTS OF CURRICULUM UNIT 15.05.10

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Personalization of Problems
  4. Content Objectives
  5. Multiplication and Division One-Step Problem Taxonomy
  6. Equal Groups Problems
  7. Two-Step Multiplication and Division Problems
  8. Algebraic Representations of Word Problems
  9. Project Based Learning Activity
  10. Reading Problems With Intention
  11. Differentiation of Problem Sets
  12. Bibliography
  13. Appendix A: Royals Rise Up! Project Proposals
  14. Appendix B: Example Scenario
  15. Appendix C: Extensions of the Scenarios – Initial Cost
  16. Appendix D: Differentiation of Problems
  17. Appendix E
  18. Appendix F: Project Based Learning Activity Outline
  19. Appendix G: Academic Standards
  20. Notes

Personalizing Problem Solving

Lawrence Elliott Yee

Published September 2015

Tools for this Unit:

Appendix B: Example Scenario

One of the projects selected through the Royals Rise Up! public vote last year was “New Athlete Uniforms: New uniforms to better present and represent Overfelt,” which set aside $10,000 of the budget to be spent towards purchasing new uniforms for athletes from all sports. There are 15 teams at Overfelt that would like to update their uniforms. The athletic directors, Ms. Gonzalez and Mr. Delgado need your help to make decisions before they spend any money. They started looking and were given the following prices the uniform printing company.

Option A: Name Brand uniforms that cost $32 each.

Option B: Decent uniforms, good but not as fancy, that cost $24 each.

Option C: T-shirts with school logos for $8 each.

Underlined terms and numbers can be changed to create new problems of the same structure and allows for personalization of the problems.

One-step Multiplication/Division Word Problems

The following one-step word problems are examples based on the information presented in the new uniform story.

Equal Groups Problems

Unknown Product/Total

If there are 450 athletes that need new uniforms, how many Name brand uniforms can be purchased? Will we be within our budget? If 14 sports each get $700, how much money is spent? Do we have enough money?

Unknown Group size

If we spend $10,000, how many tee shirt uniforms can we purchase? If the 14 sports each got equal amounts of the $10,000, how much does each sport get?

Unknown Number of Groups

If we spend $9 for each tee shirt, how many new uniforms can we purchase with $10,000? If we give each sport $800, how many sports will get to spend the $10,000? Will we be able to cover all the sports?

Multiplication Comparison Problems

Unknown Smaller Quantity

T-shirts cost one fourth as much as the $32 Name Brand uniforms. How much do t-shirts cost?

Unknown Larger Quantity

If the Decent uniforms cost 3 times more than the $8 tee shirts, how much do the Decent Brand uniforms cost?

Unknown Ratio

If the tee shirts cost $8 each and the Name Brand uniforms cost $32 each, how many times as much do the Name Brand uniforms cost than tee shirts?

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