You'll have to hold the project, the math, the code, the facilitation moves, and the instructional goals in your head at once. This page is just the math — so you know the destination before the journey starts. Read this first. The Toolkit Guide and the deep walkthroughs come after.
01Five mathematical relationships, one per stat.
Each of the four stats carries a different functional relationship — and the 20-point budget is itself an algebraic constraint. Together they cover proportional, linear, coordinate, quadratic, and equation-as-balance reasoning. The relationships aren't decorative; the program's whole job is to teach them through use.
Speed · Day 1
Proportional
Motor% = Speed × 5
Doubling input doubles output.
CCSS 7.RP.A.2 — Recognize and represent proportional relationships.
Endurance · Day 2
Linear decay
P(t) = 100 − (20−E) × 1.5 × t
Slope as negative rate of change.
CCSS 8.F.B.4 — Construct a function to model a linear relationship.
Turning · Day 3
Coordinate geometry
d = √((x₁−x₂)² + (y₁−y₂)²)
Position and distance on the plane.
CCSS 8.G.B.8 — Distance between two points in a coordinate system.
Power · Day 4
Quadratic
Charge% = Power²
Doubling input quadruples output.
CCSS 8.EE.A.1 — Properties of integer exponents.
Budget · Day 5
Equation as constraint
S + E + T + P = 20
"=" means balance, not arithmetic.
CCSS 6.EE.B.5 — Solving equations as a process of finding values that make the equation true.
02How proportional, linear, and quadratic emerge.
The five relationships are introduced one per day in Week 1, then layered: applied as predictions, derived from real data, compared via percent change, written as inequalities, finally translated to plain language. The same math reappears at each layer with more demanded of it.
D 01 → 05
Introduce
One stat per day. One relationship type per day. Students predict, calculate, compare, and program the formula into the bot.
D 06 → 10
Apply + Derive
Formulas become predictions before matches. From class scatter plots, students derive their own linear equation (y = mx + b) — formula from data, not from the teacher.
D 11 → 12
Compare + Constrain
Percent change surfaces linear vs. quadratic scaling. Students write CAP/FLOOR inequalities as Commissioner proposals — equations now as constraints on the system, not just predictions.
D 13 → 14
Revise
Residual = predicted − actual. A pattern in residuals implicates a specific model parameter — slope, intercept, or formula type — that students update with percent-change reasoning.
D 15 → 16
Translate
Students explain one formula in plain language — no jargon — and teach a stranger to complete three mini-challenges (unit rate, distance, scaling). Math leaves the arena.
The single sentence to remember: Days 1–5 introduce the relationships, Days 6–10 use them to predict, Days 11–12 use them to argue, Days 13–14 use them to revise, Days 15–16 use them to teach. Same math, harder demands at each layer.
03Four mathematical understandings — the destination.
These are what students should leave with on Day 16. They're stated in math terms here; the Toolkit Guide's Program Goals translate the same ideas into evidence statements.
1
Formulas are predictions, not procedures.
A formula gives you a number to test against reality. When the prediction is wrong, the formula's parameters — not the student — are what needs revision.
Goal 1 · Transfer
2
Models are authored, not received.
Students derive their own linear equation from their own scatter plot data and defend it against another team's equation by pointing at the math, not at the teacher.
Goal 2 · Ownership
3
Residuals name the gap.
Predicted − actual is a signed number with a hypothesis attached. A losing match doesn't mean "we're bad"; it means a specific parameter of the model needs updating.
Goal 3 · Failure
4
Math is teachable.
If a student can't explain the formula to a stranger using the field and the bot as concrete examples — first try, no jargon — they don't yet own it. The Exhibition is the summative.
Goal 4 · Teach
04Now go deeper.
Three parallel walkthroughs share the same five-phase arc. Each answers a different prep question. Open them after this primer.