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:

Reading Problems With Intention

Though the context is personalized to allow students more familiarity with the word problems, the ability to read and comprehend is a vital skill for mathematical word problem solving. Often, a large number of students in my classes were English Language Learners. One strategy I used to assist students with word problem comprehension in all of my math classes, from Algebra 1 through calculus, is to structure the reading of each problem to ensure students understand what is being asked.

When reading word problems or any text-heavy scenario, I would begin by having the problem read aloud in its entirety by either student volunteers or myself. Reading a problem aloud while following along will give the first opportunity for students to process the word problem. My students often need to have problem read through multiple times. I would often ask students to think about “What is going on in this problem?,” “What are we being asked to find?,” and “What do we know?.”

Often, I see my students look at word problems and read through it once, if at all. This would be followed by students taking any numbers given in the problem in order to perform haphazard computations. A necessary component in developing problem solving is understanding the problem, and this may require rereading the problem, perhaps several times. By rereading after prompting students with questions about what the problem is asking, there is an opportunity to read with the goal of identifying key features along the way. In my class, when we read a problem a second time through as a class, I will model how to analyze the word problem by highlighting key vocabulary, terms, and values in the problem while working under a document camera. I will also point out which key terms in a problem provide useful information when solving a problem. Once students understand what the problem is asking, I would then allow students time to work on finding solutions.

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