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Reasoning Detective

Run the Reasoning Detective MicroSim Fullscreen

About This MicroSim

The Reasoning Detective is an interactive game that challenges students to practice three types of mathematical reasoning fundamental to geometry:

  1. Inductive Reasoning -- Observe patterns in examples and make generalizations
  2. Deductive Reasoning -- Apply given facts and logical rules to reach conclusions
  3. Counterexample Hunting -- Find specific numbers that disprove false conjectures

Each problem type has a distinct interaction style: multiple-choice for inductive and deductive challenges, and a number pad with a "Test It!" button for counterexample problems.

How to Play

  1. Read the problem displayed in the top section
  2. For Inductive and Deductive problems, click on the answer option you believe is correct
  3. For Counterexample problems, use the number pad (or keyboard) to enter a number, then click "Test It!"
  4. Use the Hint button if you need help
  5. Use Explain Answer to see the full reasoning after answering
  6. Click New Problem to get a random new challenge

Problem Types

Type Badge Color Description
Inductive Blue Pattern recognition from examples
Deductive Green Logical conclusions from given facts
Counterexample Orange Find numbers that disprove conjectures

Iframe Embed Code

You can include this MicroSim on your website using the following iframe:

<iframe src="https://dmccreary.github.io/geometry-course/sims/reasoning-detective/main.html"
        height="702px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

9-12 (High School Geometry)

Duration

20-30 minutes

Learning Objectives

After using this MicroSim, students will be able to:

  • Evaluate mathematical statements by applying inductive and deductive reasoning
  • Create counterexamples to disprove false conjectures
  • Distinguish between inductive reasoning (pattern-based) and deductive reasoning (logic-based)
  • Recognize that a single counterexample is sufficient to disprove a conjecture

Bloom's Taxonomy Levels

  • Evaluating -- Judging whether statements and conjectures are true or false
  • Creating -- Constructing counterexamples to disprove conjectures

Prerequisites

  • Basic understanding of geometric terms (angles, polygons, lines)
  • Familiarity with number properties (even, odd, prime, divisibility)

Activities

  1. Introduction (5 min): Discuss the differences between inductive and deductive reasoning with real-world examples
  2. Guided Practice (10 min): Work through 2-3 problems as a class, discussing the reasoning process for each type
  3. Independent Practice (10 min): Students work through problems individually, aiming for a high accuracy score
  4. Discussion (5 min): Share challenging problems and discuss strategies used to find counterexamples

Assessment

  • Can students correctly identify patterns using inductive reasoning?
  • Can students apply given facts to draw valid deductive conclusions?
  • Can students find counterexamples to disprove false conjectures?
  • Can students articulate the difference between inductive and deductive reasoning?

References

  1. Inductive and Deductive Reasoning - Khan Academy
  2. Counterexamples in Mathematics - Math is Fun
  3. Geometry Foundations: Reasoning - CK-12 Foundation

Note: Remember to take a screenshot and save it as reasoning-detective.png for social media previews.