FunctionForge

The four-condition adoption test (from `GUIDE_DISTRIBUTED_NARRATIVE_METHODOLOGY.md` § 2):

Level 1

Guess My Rule

The machine hides its rule. Feed numbers in, read what comes out, and deduce the rule that fits every pair — real function-detective work.

Crack a hidden machine →

Function Machine

Feed a number in, run it through the gears, see it drop out the chute. Predict outputs, work backwards to find inputs, and chain two machines together.

Apply the ruleGiven the rule, what comes out? Work backwardsGiven the output, what went in? Chain two machinesSend one machine's output into the next.

Graph Plotter

Draw functions on a coordinate grid. Build y = mx + b to match a target line, read slope and intercept off a plotted line, and use the vertical line test.

Build y = mx + bNudge slope & intercept to match the target line. Read the lineName the equation from the graph. Vertical line testIs this relation a function?

Concepts — choose a kit

Each kit is a short round of questions with hints when you need them. Your progress stays on this device.

Kit 1: Input-Output Machines: Understanding Functions Function machines · grades gr4-5 · 25 questions Kit 2: Function Tables and Growing Patterns Tables & patterns · grades gr4-5 · 25 questions Kit 3: Variables, Expressions, and Simple Equations Expressions & equations · grades gr5-6 · 25 questions Kit 4: Graphing Functions on the Coordinate Plane Graphing · grades gr5-6 · 25 questions Kit 5: Linear Functions and Rate of Change Linear functions · grades gr6-7 · 25 questions Kit 6: Non-Linear Functions: Quadratics and Exponentials Nonlinear functions · grades gr6-7 · 25 questions Kit 7: Function Analysis: Domain, Range, and Transformations Function analysis · grades gr7-8 · 25 questions Kit 8: Capstone: Real-World Modeling and Function Fluency Real-world modeling · grades gr7-8 · 25 questions Kit 9: Foundational Concepts Review Function machines · grades · 25 questions Kit 10: Applied Problem Solving Function machines · grades · 25 questions Kit 11: Critical Analysis & Evaluation Function analysis · grades · 25 questions Kit 12: Advanced Integration & Synthesis Real-world modeling · grades · 25 questions Kit 13: Cross-Topic Connections Real-world modeling · grades 5-6 · 25 questions Kit 14: Real-World Applications Real-world modeling · grades 6-7 · 25 questions Kit 15: Misconceptions & Reasoning Function analysis · grades 6-7 · 25 questions Kit 16: Advanced Synthesis Real-world modeling · grades 7-8 · 25 questions
FunctionForge mascot

Meet the cast — the characters who teach this

Each one stands for an idea you’ll practice. Tap a character to read their illustrated story and hear their audio drama.

Explore all the stories →

Privacy & how it works