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:

Multiplication and Division One-Step Problem Taxonomy

The Common Core State Standards for Mathematics (CCSS- M) courses emphasizes computational fluency with the four basic operations using whole and rational numbers beginning in the late elementary grade levels and throughout middle school. An expectation of students entering the high school CCSS Integrated Math 1 (CCIM-I) course is a level of computational fluency with whole numbers and fractions using the four basic operations, exponents, and radicals. However, my past experience included classes where a majority of students did not have positive experiences and prior success in their previous middle school math courses. This unit begins by reinforcing the computational skills while utilizing the Royals Rise Up! personalized scenario to frame the problems. By starting the unit with a focus on multiplication and division one-step problems, more students should be able to meet the entry threshold,

The taxonomy of the common multiplication and division situations sorts problems into nine different classifications, as outlined from the Mathematics Glossary, Table 2, from the Common Core State Standards for Mathematics.11 There are three major categories: problems with equal groups, arrays and area, and multiplicative comparison. Each of these categories is broken down based on the unknown quantity that the problem is seeking to find.

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