Patterns & Conjectures
📋 What it is
A conjecture is a smart guess about a pattern — believed but not yet proven.
🗣️ Coach says
When you spot a pattern (2, 4, 6, 8…) and guess the rule, that guess is a conjecture. It might be right — but a pattern that holds a few times isn’t proof. A conjecture is where proof STARTS, not where it ends.
🧠 Memory hook
Pattern spotted = conjecture made. It’s a promising guess, not a fact yet.
😂 Giggle
What did the conjecture say to the proof?
"I believe it's true — can you make it official?"
😲 Whoa!
Some conjectures stay unproven for centuries — the Goldbach conjecture (every even number > 2 is the sum of two primes) has been checked into the quintillions and STILL isn’t proven.
✅ Quick check: You see 1, 3, 5, 7 and conjecture “the next is 9.” Have you PROVEN the rule is +2?
Say your answer out loud first — then reveal.
No — you’ve made a strong conjecture, but four terms fit many rules; you’d need the rule stated and justified to prove it.
A finite run of examples supports a conjecture but never proves a general rule.
🧪 Try it! (2 minutes)
Write the sequence 1, 4, 9, 16 and conjecture the next number AND the rule. Then check: does your rule survive one more term?