Function Factory

What it is

Each factory machine follows a secret rule. Learners feed it numbers to fill an input–output table, predict outputs for new inputs, run it backwards, and pick the rule — from add 3 and multiply by 4 up to two-step rules, negative slopes and square rules in grade 8. Rules are fixed, reviewed data; every prediction is checked exactly.

What children learn

Functional thinking: input–output patterns, finding a rule from examples (and testing it on every example), two-step rules, inverse reasoning, linear rules with negative values, and telling linear from nonlinear rules.

What it teaches

• Input–output patterns
• Find function rules
• Linear and nonlinear functions