Parallel rewrite strips
Rewrite every old symbol once into a separate new row, preserving simultaneous-step boundaries.
Adult planning suggestion: about 9–12 · Logic & rule checking · Language & storytelling · Cooperation & communication
- Players
- Teams of three
- Time
- 12–18 minutes
- Materials and quantities
- Per team: two rule cards A→AB and B→A, old/new row mats, eight large A cards, five B cards and one log.
30 pupils: ten teams of three, old-symbol reader, new-row builder and boundary checker; rotate each round.
Prepare
Rules stay fixed: A becomes AB; B becomes A. Begin at round 0 with A. Place an OLD row and a separate NEW row, both read left to right. Symbols are abstract labels, not words requiring a dictionary.
Play
For each symbol in OLD, copy its replacement to the end of NEW in the same order. Mark that old symbol processed once. Never process a symbol newly written in this same pass. Only after every OLD symbol is processed, make the whole NEW row the next OLD row.
Example
Round 0 A → round 1 AB. Rewriting both old symbols gives round 2 AB+A=ABA. Round 3 comes from A,B,A as AB+A+AB=ABAAB. Replacing a newly created B immediately in round 1 would give AA and is the wrong sequential procedure.
Finish
Stop after round 3, record strings A,AB,ABA,ABAAB and lengths 1,2,3,5. Explain which old symbol created a chosen piece of the new row. Optional round 4 is ABAABABA, length 8, but only after checking the same simultaneous rule.
Adapt
Use two colours to distinguish old from new, not to change the meaning of A/B. Work with an adult reading one rule at a time and partners copying. This finite string exercise does not claim to model a child’s development or every natural growth process.
Aim: Rewrite every old symbol once into a separate new row, preserving simultaneous-step boundaries.
Practice within this activity: Preserving order, applying consistent substitutions and distinguishing old state from newly created state.
Adult observation: Ask whether a B created this round may be processed before the next round; look for the old/new boundary explanation.
Mechanism and adaptation: Our version uses simultaneous string production rules. Examples and print materials are separately written; the earliest inventor is not established here.
Reference checked 24 October 2026: University of Cambridge NRICH · Stringing It Out — Mathematical background for repeated string transformations. Source is marked ages 14–16; it does not validate our 9–12 suggestion. Our two rules, role split and cards are separately written.
Goals describe observable activity choices, not measured long-term gains or institutional endorsement.
Free alternatives: Write A and B on large recycled cards and draw two separate rows.
Buying recommendations reserved; no purchase required.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Player rewrite rules and symbol cards
A→AB; B→A. Copy OLD symbols once into a separate NEW row. Never process newly created symbols in the same pass.
Player old/new round log
| Round | OLD | NEW | NEW length |
|---|---|---|---|
| 1 | A | ________ | ____ |
| 2 | ________ | ________ | ____ |
| 3 | ________ | ________ | ____ |
| Optional 4 | ________ | ________ | ____ |
Teacher instructions and checked example · separate
30 pupils: ten teams of three, old-symbol reader, new-row builder and boundary checker; rotate each round.
Per team: two rule cards A→AB and B→A, old/new row mats, eight large A cards, five B cards and one log.
Write A and B on large recycled cards and draw two separate rows.
Print only the relevant player pages; keep this teacher page separate. Read the full web rules before leading. A helper may write or move pieces, and anyone may pause or pass. No classroom or physical-printer trial is claimed.
| Round | Result | Length |
|---|---|---|
| 0 | A | 1 |
| 1 | AB | 2 |
| 2 | ABA | 3 |
| 3 | ABAAB | 5 |
| 4 | ABAABABA | 8 |
Round 3 = AB + A + AB. AA after round 1 would be incorrect because it processed the newly created B too early.