Build examples and counterexamples for a new term

Separate what must be true from any illustrative feature in the textbook. Make an example satisfying every condition and explain how each condition is met.

Use the terms rectangle and square to build cases that have some conditions in common. Attach the feedback to a specific output rather than to a general judgement of performance. Record which part the learner could repair immediately and which part depended on a fresh explanation. The distinction helps you plan practice that addresses a real gap without unnecessarily rehearsing everything around it.

A rectangle with unequal adjacent sides can test the difference between the definitions. Observe how the activity works the first time somebody encounters it. A learner who has already seen the worked answer can use hints available only through memory. Replace one illustration with a new example of the same relationship and see where the method still works without the original image, phrasing or order.

Keep the example mostly intact and remove one required property. Explain why this new case falls outside the definition even though it still looks familiar.

Changing a right angle as well as a side length obscures which property mattered. Give the activity a clear output, such as a sentence, a worked step or a marked drawing. That output supplies a record you can compare with the material. A vague feeling of confidence can be hard to assess after a delay, particularly when the subject begins to look familiar through repetition alone.

Draw a four-sided comparison in which only one chosen condition changes. Use one very short follow-up after enough time has passed for the wording to feel less familiar. Ask for the same kind of reasoning on a similar problem and keep the two attempts together. Notice whether the repair changed the behaviour you originally set out to improve and give that change a concrete example.

Ask a learner to justify the classification without relying on the angle of the drawing. Let one practice attempt continue without intervention while you record where a question arises. When it finishes, point to the exact decision that caused hesitation. Brief feedback tied to the place of confusion is easier to use than a general correction that has to be interpreted across an entire exercise.

The second activity should feel recognisably related without calling for the same response. Keep the essential concept and replace the example, order or wording. If a method works only with the original arrangement, the new result gives you a direct clue about the understanding still to develop. Let the learner mark the place where they changed course and write one reason for it. Give them time to find their own words before supplying the expected language. A correct final answer is useful, but the explanation helps show whether they can take the same kind of decision in a fresh example under ordinary conditions. Give both examples names and check one unfamiliar example after discussing them. A learner may remember the two drawings while missing the actual rule. Give space in the written record for a correction beyond the final answer. Show the starting point, the change and the part of the original work you still trust. A short labelled correction can prompt better review than a clean page that hides both the earlier difficulty and the reason it was repaired.

Keep the two cases side by side and ask someone which change they notice first. Write one expected explanation and one common incomplete version before the review begins. This helps you spot when a learner gives a correct short answer without the connection that matters. Ask for one additional sentence that shows how they reached it, then use that sentence to shape the next practice item.