Success criteria
- I can show how grouping changes the order of work.
- I can use one rule consistently across a table.
- I can describe what changes and what stays constant.
Explain
(18 + 7) × 4 and 18 + (7 × 4) use the same numbers but not the same instructions. Explain what the brackets tell the reader to do first.
Independent practice
Evaluate (18 + 7) × 4.
Evaluate 18 + (7 × 4).
A machine multiplies by 4, then adds 7. What is the output for input 4?
The outputs are 7, 11, 15, 19. What is their constant difference?
Each input rises by 1, so multiplying by 4 makes each output rise by 4.
Start at 9, multiply by 5, then subtract 8.
Transfer
Invent a two-step function machine whose first four outputs form an increasing pattern. Give only the input-output table to someone else. They must infer and test your rule.
Delayed check
After one week, explain the difference between 3 × (12 + 5) and (3 × 12) + 5, then make a table for “multiply by 6, subtract 2.”
Evidence and next step
Save the invented machine, another person’s guess, and your correction at jeremy/portfolio/math/unit-2/function-machine.md.
- Rule inferred, explained, and retained → Unit 2 review; unlock stretch only through the full gate.
- Table correct but rule description vague → revise using “for every input…” language.
- Bracket error → act out each instruction in order before retrying.