The Problem Solving and Communication Activity Series Use Logical Reasoning

Use Logical Reasoning

Logical reasoning is at the heart of so many math problems, so it can be hard to break it out as its own separate strategy. But we find that the guiding questions of, "what must be true? what might be true? what can't be true?" are useful for doing logical reasoning.

We also present some chains of questions for following deductions or searching for contradictions. Organizing and recording what depends on what or what contradicts what are really important parts of coming up with a good logical argument.

Activities to Learn this Strategy

Facilitation Questions

  • What must be true?
  • What might be true?
  • What can't be true?

Recommended Library Problems

The Strategy Examples documents linked from these problems contain examples of what students could do with the activities. You need a Class Membership or higher to access Library problems.


The Arm Wrestling Match
Winter is Coming

Math Fundamentals

Bobsled Sums
Dashing Through the Snow


The Oracle's Crowns
Movie Seating


Line Logic
Symbol Logic


Two Rectangles

Learn more about the different membership options.

© 2018 The Math Forum at NCTM. All Rights Reserved.