Teach the Cast
Some of FunctionForge’s cast are still learning. When you teach them, YOU learn it best — catch what they get wrong, then quiz them.
Teach Stride the Pattern-Walker
Teach the connections
Show how the function ideas connect
Stride the Pattern-Walker (linear functions (constant rate of change)) × Echo the Sameness-Keeper (constant functions (zero rate of change))
How is Echo's flat, unchanging output related to Stride's straight line?
Stride the Pattern-Walker then says: “Echo's output "5, 5, 5, 5" can't be linear — linear functions always go UP.” — is that right?
Now they see it: "no change" is a rate of change too — just zero.
Stride the Pattern-Walker (linear functions (constant FIRST difference)) × Arc the Curve-Catcher (quadratic functions (constant SECOND difference))
Arc's steps grow (+3, +5, +7…). What's constant about a quadratic, if the steps aren't?
Stride the Pattern-Walker then says: “Arc's outputs jump +3, +5, +7 — the steps grow by 2 each time, so it's linear with slope 2.” — is that right?
Now they see it: a curve is a line's idea, one level deeper — constant change in the change.
Stride the Pattern-Walker (linear growth (constant ADDITIVE rate — +k each step)) × Burst the Doubler (exponential growth (constant MULTIPLICATIVE rate — ×k each step))
Stride and Burst both have a "constant rate". What's the difference in what stays constant?
Stride the Pattern-Walker then says: “Burst goes 2, 4, 6, 8 — it adds 2 each time, so exponential is just linear with step 2.” — is that right?
Now they see it: adding keeps you on a line; multiplying launches you off it.
Capstone — model five real situations
Match each real situation to the function type that models it. Each part below needs ONE of the cast's ideas — bring in the right person for each.
A flat-fee locker costs $5 no matter how many hours you use it.
A car travels a steady 60 km every hour — distance over time.
A ball thrown up rises, slows, and falls — its height over time.
A rumor doubles the number of people who've heard it every day.
Parking is free for the first hour, then a flat rate after — one rule, then another.
The whole cast, working together — because you taught each one and saw how they fit.
Your concept map