Inductive reasoning, conjecture and counterexample
- One strip, and the twentieth item — 3 tasks
- Two students, one strip — 3 tasks
- A conjecture that dies at the sixth case — 6 tasks
- Both ticks, or it is not a counterexample — 4 tasks
- Not finding one is not the same as none — 6 tasks
- Practice — 24 tasks
- Summary — 2 tasks
- Cool-down — 6 tasks
Classroom activities
Things a class does rather than writes on. Each one is a finished PDF: print it, cut it up if it says so, and hand it round.
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Conjecture & Counterexample — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
Twelve pieces, each a claim and a case, sorted into three rows: a counterexample, a case that agrees, or a case the claim is not about. Every piece in the third row looks like a counterexample until check 1 is done.
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Conjecture & Counterexample — Answer Maze 10–15 minutes · 4 sheets
One page and nothing to prepare: eight claims, and at every box two answers. The wrong one skips check 1 or lets a pile of agreeing cases decide. The row of box numbers at the bottom shows where a student went wrong.
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Conjecture & Counterexample — Mystery Picture 25–35 minutes · 4 sheets
25 squares, five claims: is the case a counterexample? Fill it only when the case fits the if part and makes the then part false. Cases that only look like counterexamples stay white.