“Every four-sided shape is a square.” A learner draws a rectangle with unequal adjacent sides. That one drawing is enough to disprove the claim, even though it does not tell us everything about four-sided shapes.
A counterexample is useful because it tests the word “every.” If a statement says that all members of a group have a property, one genuine member without that property shows the statement is false.
Check that the example belongs
The rectangle works because it has four sides and is not a square. A triangle would not work: it fails the entry condition of the claim. Ask learners to explain both parts rather than accepting any different-looking picture as a counterexample.
Try a number claim next: “Every even whole number is a multiple of four.” Six is even, but it is not divisible by four without a remainder. The example disproves the universal claim. It does not prove that no even number is a multiple of four; eight immediately shows why that replacement would also be wrong.
Revise without overcorrecting
Invite the learner to write a more precise statement. For the number example, “Some even whole numbers are multiples of four” is different from the original claim. Discuss which words changed and what evidence the new wording requires.
A classroom routine can have three short steps:
- Underline the condition and the promised property.
- Test a proposed example against both.
- State exactly what the example establishes.
Do not turn a run of successful examples into a proof of an unrestricted rule. Trying ten even numbers may suggest a pattern, but a claim about every even number needs reasoning that covers the whole set.
For feedback, praise the precision of the explanation rather than the speed of spotting an exception. A learner who can say why an example qualifies is practising a skill that transfers to reading arguments, checking assumptions and correcting their own work without replacing one overstatement with another.