Gotham Tech · Plan v3 · Mon Jul 27 – Thu Jul 30

The whole arc in four days

Four weeks of Velocity Arena is really one loop run many times: predict → run → measure the gap → change one thing → predict again. The calendar was never the point; the number of times through the loop is. Gotham's bots drive fine but can't score with untuned stats, so matches keep coming out 0–0 and a 0–0 teaches nothing. So this plan runs the loop on distance instead — measure how far the bot drives — which can never come out 0–0 because it needs no opponent and no goal. It runs that loop about ten times in four days and attaches one piece of evidence to each project goal.

Running the room on Monday? Use the short version. This sheet carries the reasoning, which is for planning. For the table during the day, print “What To Do, Monday to Thursday” — numbered steps, clock times, the exact words to say, and nothing else.

The single principle behind this plan. Do not try to re-teach four weeks of math. Pick one model — a linear equation for how far the bot drives, built from the team's own measurements — and put it through the loop enough times that students can point to a change they made and the improvement it caused. More cycles through one model teach more than one pass through many topics — and cycles are what all four goals actually ask for.

Each goal, the moment that produces it, and the paper that proves it

If a goal has no scheduled moment, it will not happen on its own. This is the map — every goal gets one block on the calendar and one artifact.

Goal	The moment on the calendar	The artifact (evidence)
Goal 1 Transfer of Mathematical Reasoning	Mon build an equation from their own trials → hit taped targets in the Precision Final → Tue quantify how much their model improved with Percent Change.	Percent-change result on the poster: a change they made and the measured improvement. "Our 1-second guess was ___ cm/sec, corrected to ___ cm/sec — a ___% correction. That's why our first predictions were off."
Goal 2 Genuine Intellectual Ownership	Tue 10:15 — Model Swap. Teams post equations, study another team's, decide what to keep and what to change.	Model Swap slip: the other team's equation, what we kept, what we changed, and why — citing a number.
Goal 3 Productive Relationship with Failure	Every trial, Monday and Tuesday. Gap sentence after each run; the named failure modes (too far/short, not straight, different every run) turn a wrong result into the next thing to fix.	Gap-sentence log + the worksheet's gap column, showing each team's miss shrinking (or not) trial by trial.
Goal 4 The Ability to Teach	Wed PM teach-back rehearsal against another team playing "confused visitor" → Thu Exhibition, where visitors try each team's Target Challenge for real.	Visitor Completion Tracker — did the visitor hit the target after one explanation? — plus the line they rewrote after rehearsal.

Three moves that make the goals provable

The Mon-collect / Tue-analyze / Wed-assess+prep / Thu-present shape is right and this plan keeps it. But two of the four goals will not happen on their own, so three blocks carry them:

1 · The Target Challenge (the important one). Goal 1 asks students to point to a change that reduced the gap on a later attempt. Matches used to provide those attempts; without them, the Target Challenge does — predict the drive time to stop on a taped line, test it, refine. Run hard Monday afternoon against distances they have never driven. Hitting a distance you never measured is what turns a guess into a model, and it cannot come out 0–0.

2 · Tuesday morning: Model Swap. Goal 2 requires a documented comparison to another team's model and a specific keep/change decision. Students will not do this spontaneously — they will assume the other team is either right or irrelevant. It needs a scheduled half hour, a divergence step so the models actually differ, and a slip of paper.

3 · Wednesday afternoon: teach-back rehearsal. Goal 4's bar is high — a visitor completes the challenge after one explanation. No team clears that bar on the first attempt. They need one rehearsal against a genuinely confused human, and a chance to rewrite the sentence that failed.

Also moved: the Post-Task Diagnostic and Post-Reflection now run first thing Wednesday rather than late in the day. They are the pilot's before/after research measurement and the one thing that cannot be recovered later. Doing them at 10:00 on fresh minds guarantees they happen; anything scheduled after the day's activity is at the mercy of the clock.

Monday The Distance Lab Mon · Jul 27

Goal of the day: every team leaves with five measured trials and a written equation, and has run the Precision Final. That is the raw material for everything Tuesday.

Time	Block	What happens
10:00 – 10:15	Launch the Distance Lab	No warm-up video — the bot driving is the hook. Frame the day, then teach the two rituals that run all day: Prediction — one number in centimeters, written before the bot moves, signed. Gap sentence — after every run: "We predicted ___, we got ___, the gap was ___, because ___." Lock stats to sum 20; they don't change all week.
10:15 – 12:00	★ DISTANCE LAB worksheet	Drive 1 second → measure cm → the bot's speed in cm/sec. Predict-and-measure at longer times to five trials, then subtract two runs to fix the speed, find the start-up, and write `distance = speed × time + start-up` (start-up is negative, so it reads as −; speed = cm/sec, not the 1–17 stat). Worksheet → · protocol + code → Failure modes on the board: too far/short (model off), not straight (motors), different every run (batteries/start line).
12:00 – 1:00	Lunch	Protected.
1:00 – 1:55	★ TARGET CHALLENGE — Precision Final	Run the equation backwards to hit a taped line: `time = (target − start-up) / speed`, turn it into ms (× 1000), set the ★ line of the Target Challenge code, download, drive. A few practice targets, then a surprise target — best of 2, closest wins, crown a champion. Everyone programs the exact time, so it is fair; one neutral ref measures. Target Challenge worksheet →
1:55 – 2:40	Make the equation poster (Canva)	The equation and the graph of the five dots (poster how-to · worksheet). Also write the equation big on a sheet of paper and tape it to the wall, so all four are visible for tomorrow's Model Swap.
2:40 – 3:00	Close + preview Tuesday	Each team names what they were most wrong about today. Preview: "Tomorrow you compare equations, build a launch, and measure how much you improved." "Name the one thing about your bot you were most wrong about today. You have 3 minutes."
Materials	Distance Lab worksheet → · Protocol + code → · Target Challenge worksheet → · Target code →

How you know Monday worked: every team completes five measured trials and writes an equation. Three trials is the honest minimum; five is the target. Don't rush the measuring to reach five.

Bots driving crooked? Skills Arena Challenge 1 (Dead Straight) first — only if they need it.

Why distance, not matches

The bots drive fine — they just can't score. Scoring on a moving ball needs stats tuned for it, and that is not where this group is, so matches keep coming out 0–0. A 0–0 tells you nothing: no gap to close, no data to model. Running matches "just to try" burns a day for nothing.

Distance solves this exactly. How far a bot drives needs no opponent and no goal — just a tape measure — so it can never come out 0–0. Every bot produces a real number every single run.

Why this is better, not a downgrade

Distance is better raw material than goals would have been. Goals are noisy, small-numbered and depend on the opponent. Distance is a clean linear function of time, measurable to the centimeter, and its parameters are numbers the students control in their own code:

distance = speed × time + start-up ⟷ y = m x + b

Start-up is negative, so + start-up reads as a subtraction (e.g. 38 × time + (−7) = 38t − 7). "Speed" here is the bot's cm/sec from Trial 1 — not the 1–17 Speed stat.

The slope m is the bot's speed in cm/sec — a number they measured themselves, different for every team. The intercept b comes out negative, because the bot loses ground while it accelerates. A student who can say "our intercept is negative because our bot takes a moment to get going" has done exactly what Goal 1 describes.

“When your measurement stops telling you anything, you change the measurement.”

That sentence is the lesson. Choosing what to measure is mathematical modeling — Goal 2, not a consolation prize. Say it plainly; do not apologize for it:

"Matches keep coming out 0–0 because our stats aren't tuned to score. So we predict distance instead — it can't come out 0–0. The number we're predicting changed. The math didn't."

The Target Challenge is the scoring skill, without the 0–0. Stopping the bot on a taped line is precision to a spot — the same aiming a goal needs — but it needs no opponent and no goal, so it always produces a number. It uses the equation backwards: time = (target − start-up) / speed. That is where the predict-then-test loop lives all week.

Tuesday Compare, launch, measure Tue · Jul 28

Morning: compare models and build a launch. Afternoon: quantify the improvement. Goals 1 and 2 both land today.

Time	Block	What happens
10:00 – 10:15	Hook — read the equations on the wall	Look at the paper equations from yesterday. "Whose bot is fastest? How can you tell just from the equation?" (The speed is the number in front of the time.) Every team's is different — that's correct.
10:15 – 10:45	★ MODEL SWAP (Goal 2)	Every team's equation is already different — different bots, different speeds. Each team picks one other team and uses the equation tool's Compare panel (type the other team's speed and start-up to see both lines), then writes what they'd keep and what they'd re-check in their own — citing a number.
10:45 – 12:00	★ LAUNCH SEQUENCE (distance + a 2nd stat)	A two-leg launch: corner → midline → ball. Turn out to the midline and drive; turn to face the ball head-on and drive to it; then the locked code kicks (strength = Power²). Each drive time is ms from their equation, done twice. Angles are 45° or protractor-measured — no trig (pre-algebra). Worksheet · Launch Test. Test the kick first (wide goal, short distance); get it landing reliably — the competition is the after-lunch block.
12:00 – 1:00	Lunch
1:00 – 1:45	★ LAUNCH-AND-SCORE (competition)	Put the launch up against the other teams. Same field for everyone (corner, ball spot, goal). Five launches, no re-tuning between (numbers locked in warm-up), most goals of 5 wins; tie = closest to center. Can't come out 0–0. Rules + scoreboard →
1:45 – 2:30	★ PERCENT CHANGE (Goal 1)	How much did fixing your method change your speed? The tool teaches percent change, gives eight practice problems (mixed rise/fall + a same-raw-gain comparison), then teams compute their own: first-guess speed (1-second run) → corrected speed (from two runs). Both numbers are on their Distance Lab sheet. It is always there and always meaningful (~+20%), so it never assumes their targets improved — it measures the model correction. Trap: divide by the FIRST number.
2:30 – 2:55	Finish the poster	In Canva, add the percent-change result — a change they made and the measured improvement. This is the story they teach Thursday.
2:55 – 3:00	ENDS	"Finish the sentence: 'We changed ___ and cut our prediction error by ___%.' You have 3 minutes."
Materials	Equation tool (Model Swap) → · Launch Sequence worksheet → · Launch Test → · Percent Change tool →

If Monday's data is thin, pool the class's runs, or rebuild the equation on the worked bot in the Distance Lab answer key (distance = 38t − 7) first, then run Tuesday on whatever real numbers they got.

Wednesday Get ready to teach, then measure the growth Wed · Jul 29

Time	Block	What happens
10:00 – 10:25	Teach it in 30 seconds	Turn to the next team: in 30 seconds, no notes, explain what your speed and start-up numbers mean — not the numbers themselves. Then swap. A warm-up that surfaces the confusing spots before a real visitor hits them.
10:25 – 11:25	Teach the Math	In the Teach the Math tool, each student picks Linear Equation (or Percent Change) and explains it with their real numbers. "The 38 means our bot goes 38 cm every second; the −7 means it loses 7 cm getting started." After each, ask "how did you get that specific number?"
11:25 – 12:00	★ TEACH-BACK REHEARSAL (Goal 4)	Team A plays the confused visitor and attempts Team B's challenge after one explanation — no rescuing. Note exactly where they got stuck, rewrite that one sentence, then swap.
12:00 – 1:00	Lunch
1:00 – 1:15	★ Post-Task Diagnostic	Individual, 12-minute timer. Read the "we are comparing you to yourself four weeks ago" framing so it isn't heard as a test. The only formal assessment of the day.
1:15 – 1:25	★ Post-Reflection Survey	Same sitting. Confirm site + name spelling so it matches the Day 1 pre-reflection, or the pair is unusable.
1:25 – 2:15	Reflection Time — finish the station	Poster up, bot loaded, target line down, staged exactly as a visitor will meet it. One last rehearsal of the sentence rewritten in the teach-back.
2:15 – 3:00	Open Lab — finish posters + free build	Buffer and polish: finish posters, help another team, keep tuning launches — make sure every station is exhibition-ready. If the diagnostic or a rehearsal ran long, borrow from here. "What will you tell someone tomorrow at the Exhibition about what you learned? You have 5 minutes."
Materials	Teach the Math tool → · Post-Task Diagnostic → · Post-Reflection Survey → · Visitor Challenge Cards →

Protect the diagnostic and the reflection. They're the pilot's before/after measurement and the one thing that can't be recovered later. If Wednesday runs long, cut the Reflection-Time station polish — never the diagnostic, the reflection, or the teach-back.

Thursday Teach it for real, then celebrate Thu · Jul 30

Time	Block	What happens
10:00 – 10:45	Expert setup + last rehearsal	Stations: poster, bot, target line, the sentence they rewrote yesterday.
10:45 – 12:00	★ COMMUNITY EXHIBITION (Goal 4)	Visitors try each team's challenge — the team teaches them to use the equation to hit the line — plus the three printed mini-challenge cards (unit rate, coordinate plotting, proportional scaling, from weeks 1–3). Teams fill the Visitor Completion Tracker: not "did they enjoy it" but "did they succeed after one explanation?" Stay out of it — the students teach. Optional: teams that pass a morning go/no-go check (3 launches, 2 must score) may run a Demo Your Launch station — a demonstration, not a contest, so it fits the no-awards close.
12:00 – 1:00	Lunch
1:00 – 1:45	★ CELEBRATION — Victory Laps + Sign the Wall	The fun send-off, not a silent gallery. Victory laps: team by team, the room counts 3-2-1 and each bot takes one last run (launch or target) just for fun — everyone cheers, no scoring, every team the same. Sign the wall: music on, markers out; everyone signs each other's equations/posters and a class banner with one thing they're proud of. Group photo at the wall.
1:45 – 2:30	Closing circle + final journal	No competitive awards. Each student names one specific moment this week they solved something they thought they could not, with a number attached. Then the final journal. The point is the room hearing each other.
2:30 – 3:00	Open Lab — pack up + send-off	Strike the stations, take posters and notebooks home, last photos and goodbyes. "What did you learn about yourself as a problem solver? Name one specific moment from this program where you solved something you thought you could not. You have 5 minutes."
Materials	Visitor Challenge Cards + Completion Tracker → · NY Submission Checklist →

If a bot will not drive decide by 12:00 Monday

The Distance Lab only needs a bot whose wheels turn, so this is rarer than the match version — but if a bot is dead, do not spend the day troubleshooting it:

Triage in order: LEDs showing a number? (if not, re-flash) → batteries + the Cutebot's own power switch → the Cutebot Pro extension in the project.
Share working bots. If only one or two drive, teams rotate through them. Each team still writes its own prediction and measures its own trial, so every team keeps its own data and its own equation. Sharing hardware is not sharing an equation.
If almost nothing drives, teach Tuesday's method on the worked bot in the Distance Lab answer key (distance = 38t − 7) so the modeling still lands, then have teams rebuild the equation on whatever real numbers they get.

What we are deliberately not doing

Four days cannot hold four weeks. These are cut on purpose, so nobody spends Tuesday morning trying to squeeze them in:

Matches, the championship, and awards. The bots can't score, so head-to-head play stays 0–0. The Target Challenge carries the predict-then-test loop instead; the closing is a circle, not a competition.
Proportional scaling, decay equations, percent change as standalone lessons. The one model this week is the linear distance equation; that is where the depth goes.
Season 2, the Commissioner's Meeting, Rule Proposals, the Underdog Mechanic. Mark Rule Proposals as N/A for Gotham on the submission checklist so it is not chased at the end.
Breadth of topics generally. One model, run through the loop about ten times, taught to a stranger. That is the whole plan.

Velocity Arena · NYC FIRST — Gotham Tech, plan v3 (Mon Jul 27 – Thu Jul 30). Companion sheets: What To Do, Mon–Thu (the short version) · Distance Lab (protocol + code) · student worksheet.