By Chandra Mongroo, Ph.D, Full-time Faculty and Doctoral Lecturer, General Education

This page offers diverse problem-solving approaches in mathematics, recognizing that different methods suit different situations or learning preferences. Having a range of strategies fosters flexibility, enriches understanding, and cultivates resilience, preparing individuals to tackle complex problems effectively across various contexts.

A. Review of Problem Solving Process: Polya’s Problem Solving Techniques (Berkeley Math)

Q: I read the math question but do not know where to start. How do I proceed?

A: The key is to unlock the theme of the question. Here are some suggestions on how to begin: 

  1. Gather as much knowledge as possible from the problem. Highlight or underline key words. This is where you should return to the text and review the unit’s vocabulary.
  2. Re-visit worked out examples. Pay close attention to details in the problem solving process that are not clearly stated. Write out these steps with explanations in your notes. 
  3. Return to the question you were tasked with and approach it in a similar way as the text. 
  4. Analyze your solution. What did you solve? What does it mean in the context of the problem? Is it reasonable with the given constraints? 
  5. Report your results. Writing out a summary of your findings will help you reinforce the ideas that were developed in the problem solving process.

B. General Problem Solving Heuristics

A heuristic is a general strategy for solving a problem. Here you will find various examples of heuristics for problem solving (Ohio State University). 

Worked Examples (Lippman)

C. Estimating Solutions

When problem solving, it is suggested to have an idea of your solution when you attempt a problem. Estimating solutions isolates concept application from numerical accuracy. Below are some useful videos. 

  1. Estimating Whole Number Sum & Differences
  2. Estimating Decimal Addition
  3. Estimating Decimal Differences
  4. Estimating Whole Number Products
  5. Estimating Decimal Products

You may find the term “significant digits”, “significant figures”, or “sig figs” in a math or science related course. We say significant figures are specific digits in a number that are used to express precision.  

Useful resources:

  1. Practicing Sig Figs (Purdue University)
  2. A Short Guide to Sig Figs (Yale University)
  3. Worked Examples (Libre Texts)