Cross-Topic Connections
📋 What it is
The reasoning tools connect: a conjecture from a pattern gets settled by a proof or killed by a counterexample.
🗣️ Coach says
None of these tools live alone. You spot a pattern (induction), guess a rule (conjecture), then either prove it (deduction) or break it (counterexample). Real thinking flows between them.
🧠 Memory hook
Spot → guess → prove-or-disprove. The tools hand off to each other like a relay.
😂 Giggle
Why was the axiom so confident?
Because everyone just accepted it as true — no proof needed!
😲 Whoa!
Most real discoveries loop through all four: notice a pattern, conjecture a rule, attempt a proof, and let a counterexample redirect you when the proof stalls.
✅ Quick check: You conjecture a rule from 6 examples, then find one case where it fails. Which two tools did you just use?
Say your answer out loud first — then reveal.
Induction (spotting the pattern to conjecture) and counterexample (the one failing case that disproves it).
Reasoning chains tools together: a conjecture from induction is tested by seeking a counterexample.
🧪 Try it! (2 minutes)
Take any pattern you noticed this week, conjecture the rule, then actively hunt for a counterexample before you trust it.