Checking Arguments and Counterexamples

Checking Arguments and Counterexamples

What students learn

Students learn that one counterexample can show a universal claim is false. Start with A Counterexample Can Disprove a Claim to see why one exception matters.

Why it matters

Strong reasoning needs more than confidence. Examples and Nonexamples Check Arguments shows how to test an argument instead of just repeating it.

Learn the idea

If a claim says something is true for every case, then one clear counterexample can break it. Simple Claims Still Need Careful Testing gives students practice deciding whether the evidence is enough.

Try it

Give the student a claim such as "All even numbers are divisible by 4." Ask them to test it with examples, then challenge them to find one counterexample if the claim is false.

Parent guide

Ask follow-up questions that force precision: "Does that prove it for every case?" and "Can you find one example that breaks it?" Encourage the student to show the exact number or example they used.