Standards: 5.OA.1, 5.OA.2, 5.OA.3 · Expressions with parentheses, brackets, braces; numerical patterns and graphs

Part 1 — Two pattern machines (start + add/multiply rules) stamp terms in sync; each stamp forms an ordered pair that flies onto an auto-scaling first-quadrant grid, and once three pairs exist the sim detects and explains the relationship (B = k × A, B = A + c, or none). Expression Grammar Lab: a real tokenizer/validator renders ( ), [ ], { } as nested containers; “Compute one package” highlights the operation, performs it in grammar order, and pops a container open when a single number is left.
Part 2 — 8 lock-in rounds: five structure comparisons (3 × (sum) vs the sum, inside-vs-outside-the-container traps, 12 − 4 × 3 = 0), two words-to-expression rounds, one paired-pattern relationship round — each revealed with computed values or a term table.
Part 3 — Evaluate Machine (one operation per step with its grammar reason), Read-Without-Computing Machine (finds the last operation, names the package, writes the sentence, states the “k times as large” comparison before any value), Pattern Pair Machine (rules typed as “start 0, add 3” → patterns → pairs → relationship test on every pair → graph guidance).
Part 4 — Quiz, tiers: Master Mechanic / Senior Mechanic / Apprentice / First Day in the Shop.

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