Collatz Cricket: Track Every 3n+1 Chain Down to 1
Enter a two-digit start, then watch it split at each step—evens halve, odds jump to 3n+1—until the chain lands on 1. Three innings train you to reason about parity, sequence length, and unpredictable peaks.
A Larger Start Can Reach 1 Faster—Length Hides in the Parity Path
Students often assume a larger starting number must take more steps to reach 1, then get surprised when 27 outruns 96. The trap is that each step depends only on parity, not size: one wrong odd-even call sends the whole chain the wrong way. Because the game generates and displays every value as a scored run, you can trace exactly where a halving route stalls and where a 3n+1 jump makes the number soar. Comparing three innings side by side—casework across each starting value—turns an invisible rule into a chain you can point at, so the pattern becomes evidence rather than a guess.
From Sequence Rules to Function Thinking: A Grade 5–8 On-Ramp
Each output loops back as the next input—27 becomes 82, then 41, then 124—which is exactly the grade 4–5 skill of generating a sequence from a given rule (4.OA.C.5, 5.OA.B.3), applied one step at a time. Rapid odd-even sorting reinforces the division fluency of 6.NS.B.2, while tracking a conditional rule that feeds each output back as the next input previews the function idea of 8.F.A.1. The bridge is the same throughout: one input, one rule, one output, repeated until the pattern reveals itself.
Core Skills Practiced in Collatz Cricket
- rapid odd-even classification
- following a repeated number rule
- comparing starts, peaks, and chain length
Start in Three Steps
- Enter an unused two-digit number.
- Follow the generated odd-even chain to 1.
- Complete three innings and compare the total and longest chain.
Teacher and Parent Note
Ask students to predict which of two neighboring starts will last longer, then test the claim. Emphasize evidence without presenting an unproved conjecture as a theorem.