No math is taught yet. The work in Phase 1 is identifying the starting line for each of the eight concepts that the 16-day arc will move forward. Without this, "progression" is a feeling, not a measure.
The Pre-Task Diagnostic surfaces eight CCSS-aligned concepts the program will develop: proportional reasoning, unit rate, ratio, proportional scaling, coordinate geometry (distance), slope as rate of change, linear decay, and quadratic relationships. Each appears at a named day and is re-measured on the Day 15 Post-Task.
The post-task only measures growth if there is a matched pre-task taken without coaching. Day 1 is the only honest window: any later, students have already started absorbing the program's framing.
No legitimate growth claim. Goal 1 (transfer) has no baseline. Post-program percent-change reports become anecdote.
Use these in a pre-program planning meeting, after reviewing the diagnostic baseline.
- Of the eight concepts the program will develop, which two are you most worried about — for THIS cohort, based on the baseline? What's your contingency if they don't move?
- Pick a student whose baseline is much stronger or weaker than the group's. What's your plan for keeping their progression visible to you (and to them) across the 16 days?
Days 1 through 5 introduce one stat per day, and each stat carries a different mathematical relationship. The order isn't arbitrary — it walks from the most familiar (proportional) to the conceptual leap (quadratic) to the algebraic constraint that ties them together (budget).
A proportional relationship: doubling the input doubles the output. The shortcut Speed × 5 is mathematically equivalent to Speed × 100 ÷ 20 — students should discover the equivalence, not be told.
Proportional is the simplest functional relationship; it anchors the formula-as-predictor frame the entire program depends on. Doing this on Day 1 means every formula afterward inherits the same expectation: you predict, you run, you compare.
Students never form the formula-as-predictor frame. Every downstream formula collapses into "a recipe the teacher wants me to follow." Goal 1 evidence disappears from Day 1 onward.
Slope as rate of change, negative direction. The first formula with time as an input. The decay rate r = (20 − E) × 1.5 is itself a function of the stat — a meta-move that pays off in Week 3.
First non-trivial slope work. Sets up Day 7's slope-intercept conversion and Day 13's residual analysis — both depend on students seeing slope as a parameter that can be off, not as a number that's just right or wrong.
Residuals on Day 13 land without a foundation. Students can compute predicted − actual but have no concept of which parameter of the model the residual implicates.
Distance formula d = √((x₁−x₂)² + (y₁−y₂)²) on the arena grid. Turning ratio as the arc-shape parameter. Arcs as straight-line segment approximations of curves.
First multi-step quantitative reasoning. Sets up Day 6's launch-sequence planning (where students apply the distance formula to a real strategic decision) and Day 10's deep dive on efficiency ratio.
Day 6 launch sequences have no math behind them. Day 10's "movement vs. progress" insight vanishes. Distance, the most-tested CCSS concept on the post-diagnostic, has no in-program development.
A non-linear relationship: P=4 → 16%, P=8 → 64%. Doubling the input quadruples the output. The conceptual leap of the program.
Three days of proportional / linear work make the quadratic surprising in the way it needs to be. The Day 11 proportional-scaling discussion explicitly contrasts linear vs. quadratic — and that contrast only lands if students have lived both.
Students treat every formula as linear forever. The Day 11 percent-change-by-formula-type lesson has nothing to compare against. Power becomes a stat they manage by feel, not by math.
The budget equation: an equation as a balance, not as an arithmetic instruction. The equals sign means "both sides are the same" — and every point given to one stat is a point taken from another.
The equals-sign-as-arithmetic misconception is the most common math misconception at this age and the load-bearing one for Week 3's systems-of-inequalities work. Doing it on Day 5 makes the entire Commissioner's Week possible.
Week 3 breaks. Students can't reason about constraints they didn't experience as constraints. Commissioner proposals become opinion, not math. Goal 2 (Ownership) loses its biggest single artifact.
Use these at the end of Week 1, with student exit tickets and dashboard entries from Days 1–5 on the table.
- Walk Days 1 → 5 in your own words: name one specific student thought that shifted between two consecutive days. What facilitator move triggered it?
- If you could move Day 4 (Quadratic / Power²) earlier or later in the sequence, where would it go and what would break? Use the From → To statements to argue your position.
In Phase 2 the formula was the teacher's. In Phase 3 the formula becomes the student's — they derive it from their own match data. This is the inversion the program is built around, and it happens over five days.
Two-phase programming: a launch sequence runs once and ends at a handoff point, then the match loop takes over. Teams calculate distance from candidate handoff positions to the ball at (4, 2) and pick the position that wins on the math.
First application of Day 3's distance formula to a real strategic decision with consequences. The launch sequence becomes the team's first persistent artifact — a piece of code that says "this is our model of the field."
Day 7 predictions have no spatial reasoning behind them. The launch sequence becomes a vibe, not a math object. The week-1 math has nowhere to be applied before Day 7's matches arrive.
Plot every team's Match Day 1 Speed-stat vs. goals-scored on one class scatter. Pick two points, compute slope m, solve for b, write the equation y = mx + b. Interpret slope as "goals per Speed point" and intercept in context.
Inverts the formula-as-recipe relationship at the earliest point where students have real data of their own to fit. Sets up Day 13 residual work, where the same equation is used as a prediction tool and judged against new data.
Goal 2 (Ownership) evidence vanishes — there is no single moment in the program with more "I derived my own model" evidence than Day 8. The whole "your own model" frame becomes empty.
Day 9 Formula Relay runs all five formula types (proportional, linear decay, linear, quadratic, constraint) as a race — surfaces which types each team gets wrong by error sort. Day 10 returns to distance with the efficiency ratio: how much of the bot's movement actually shortened the gap to goal?
Synthesis before Season 2 reallocation. Cold Recall on Day 10 catches the students who can't yet recall Endurance decay from memory — without that diagnostic, Day 13's residual work will surprise the room.
Students arrive at Season 2 without fluency across the system. The "movement vs. progress" insight that drives Season 2 strategy is missing. Cold Recall miss-rate goes undetected and shows up as confusion in Week 3.
Use these between Season 1 and Season 2, with scatter plots and Formula Relay tallies in hand.
- Look at the Day 8 class scatter. Which team's equation is most different from the others — and is that difference math-defensible (picked different points) or math-error (computed slope wrong)?
- The Day 9 Formula Relay surfaces error patterns by formula type. Which type had the highest miss-rate across the class? What does that tell you about which Week 1 mini-block needs the most attention next cohort?
Commissioner's Week is the algebraic peak of the program. Students stop using equations to predict and start using inequalities to constrain — and they have to verify their own rule doesn't break their own allocation.
Percent change = (new − old) ÷ old × 100. Apply to Speed (50% Speed increase → 50% Motor% increase) and to Power (50% Power increase → 125% Charge% increase). Same input change, different output change, because the formula types are different.
Returns to Day 4's quadratic with a tool (percent change) that lets students measure the non-linearity instead of just feeling it. Required for the Day 12 Commissioner proposals — every proposal cites a percent change.
Commissioner proposals have no percent-change math; the "impact on last-place team" calculation is impossible. Goal 2 (Ownership) loses the artifact teachers most often point to as evidence of growth.
A CAP or FLOOR rule on a stat is an inequality constraint. Multiple passed rules form a system of inequalities. Verifying your own allocation still satisfies the system is solving the system informally — checking a point against multiple constraints.
Algebraic peak of the program. Builds on equation-as-balance (Day 5), percent change (Day 11), and the Goal-2 ownership artifacts from Days 7–8. Students arrive ready to use math as an argument, not just as an answer.
Students experience math as a thing teachers give them, never as a thing they author. Goal 2 (Ownership) has no climactic moment. Week 4 reallocation becomes "pick numbers and try them" with no constraint reasoning.
Use these after Day 12, with the actual proposals and the post-vote allocation revisions on the table.
- Pick a Commissioner proposal that passed and one that didn't. What was different about the math each cited — and was the failed proposal mathematically weak, or politically weak?
- Look at one team's post-vote allocation revision. Can they articulate which passed rule(s) forced which point shift? If not, what re-teach goes into Day 13's morning warm-up?
The final days close the modeling cycle (residual → revision) and shift the audience: students stop explaining their math to teammates and start explaining it to strangers.
Residual = predicted − actual. The sign matters. A pattern in the residuals across matches (always over-predicting; always under-predicting on Chaos mode) implicates a specific parameter of the model, not the whole model.
First explicit residual work, set up by all the prior prediction-vs-actual cycles. Days 13–14 are when Goal 3 (productive failure) becomes a math operation — a signed number with a hypothesis attached — instead of an emotional frame.
Students treat losses as personal failures rather than data. Goal 3 has no math operation behind it; "productive failure" stays a slogan. Season 2 reallocation becomes guesswork.
Apply Day 11's percent change to the Season 1 → Season 2 transition. Predict the percent change in performance from the percent change in the stat. Compare predicted to observed under Chaos mode (ping-pong ball) — a deliberate transfer test where the environment changed but the equation didn't.
Closes the modeling cycle that started Day 1: predict, run, residual, revise, predict again. Chaos mode introduces an environmental confound — useful evidence about whether students blame the model or the world (Goal 3 nuance).
Season 2 reallocation is guesswork. Day 13's residuals don't get applied. Goal 1 (transfer) loses the moment where percent change moves from worksheet topic to active decision tool.
Pick one formula. Calculate it with your own bot's numbers. Explain in plain terms — no "Motor%," no "Charge%," no jargon. Sentence starters built into the interactive lesson. Two errors to catch: "P squared equals P times 2" and "percent change divides by the new value."
Goal 4 rehearsal before the Day 16 visitor session. Students who can't explain plainly today will struggle tomorrow — and you want that surfaced one day before it counts.
Day 16 visitor explanations collapse. Goal 4 has no formative bridge. The jargon habit students built across four weeks doesn't get translated out.
Three mini-challenges, transferred to non-bot contexts: unit rate, coordinate distance, and proportional scaling. The math comes from Days 1, 3, and 11. The audience is visitors — strangers who have not seen the program.
Summative for Goal 4. Closes the program with explicit transfer to a non-bot context — the strongest single piece of evidence that the math, not the bot, was what students learned.
No summative for Goal 4. The program ends without external validation — students would never have to prove they can use the math outside the arena's framing.
Use these in the post-program debrief, after the Visitor Completion Tracker is filled in.
- Pick one student whose Day 16 visitor explanation worked. Walk backward: which earlier moments do you think built up to it — and is there a single Day 1–10 artifact you can point to that already hinted at this student's capacity?
- Look at the From → To shifts across all 14 cards on this page. Which shift do you think this cohort didn't quite make? What's the one change you'd build into next cohort's sequence to close it?
Each Program Goal has named developmental moments. Goal 1 (Transfer) accumulates across the whole arc; Goal 2 (Ownership) crests on Day 12; Goal 3 (Failure) becomes operational on Day 13; Goal 4 (Teach) emerges in the last two days and produces the summative.