Day 18 · Final Block

You Did Real Data Science.

The matches are done. Answer 2 prompts. Every answer must include the formula written out with your actual numbers and your result.

Step 1

15 min

Written Reflection

Two prompts. Every answer needs the formula written out with your actual numbers.

Step 2

10 min

Math Patterns

Explore the 6 math concepts behind your bot's formulas — graphs, sliders, and questions.

This Tool Covers

0:00 – 5:00

Transition In

Open this tool. Enter your name at the top of the Reflect screen.

5:00 – 20:00

Individual Reflection

Work alone. Answer both prompts. Every answer needs a formula written out with your numbers and your result.

20:00 – 30:00

Math Patterns

Explore the 6 math concepts — unit rate, linear, decay, nonlinear, scaling, and ratio — with interactive graphs and questions.

Step 1 · Individual Reflection

Your Reflection

Work alone. Answer both prompts. Every answer must include the formula written out — with your actual stat numbers and your result.

Write the formula. Plug in your number. Show your result.

✗ "I used the Speed formula."

✓ "I used the formula motorPower% = S × 100 ÷ 20, and my S was 8, so my result was 40%."

The formula I used most in this camp was ___.

Tap a formula below — it will be written into your answer automatically. Then fill in your stat number and result. Describe one specific moment you used it.

WRITE THE FORMULA WITH YOUR NUMBERS

Tap a formula card — the formula will appear in your answer box, pre-written. You only need to fill in your stat number and your result. Then describe the moment.

Tap the formula you used most

Speed

motorPower% = (S × 100) ÷ 20

Endurance

P(t) = 100 − (20−E) × 1.5 × t

Turning

ratio = 0.2 + T × 0.02

Power

charge = P² · followThrough = 120 + P × 35 ms

Budget

S + E + T + P = 20

% Change

(New − Old) ÷ Old × 100

Formula written into your answer. Fill in your stat number and result, then describe the moment.

Your answer:

Fill in the blanks. Change anything you need. Add the moment when you used it.

The hardest moment was ___. Here is what I did:

Be specific. Name the exact moment. Describe what you actually did. Include at least one number — a stat, a round, a result.

INCLUDE A NUMBER

Tap a moment type below to identify your hardest moment. Then use a sentence starter to begin writing. Include a specific number.

What type of hard moment was it?

Our formula gave a wrong or unexpected answer

A match didn't go the way I predicted

I had to fix a calculation mistake

I didn't understand a formula or concept

My team disagreed on a strategy or number

Sentence Starters — Tap one to use it

Write your answer:

Describe a specific moment, what you did, and include a number.

Fill in both prompts above before moving on. Remember — every answer needs a formula written out with your numbers.

Math Patterns

How the Math Works

Six math patterns power your bot. See each one with a graph and a question.

Unit Rate

Speed → Motor Power

A unit rate means one input always produces the same fixed output — in this case, every +1 Speed gives exactly +5% motor power. The rate is constant: 5% per Speed point.

Speed (S): 5

Speed (S)

×5 =

Motor Power %

25%

Speed goes from 4 → 8. Motor power goes from 20% to ___?

8 × 5 = ?

Linear Function

A Straight Line on a Graph

When you plot Speed vs. Motor Power, you get a straight line. That's the definition of a linear function — constant slope, no curves. Every point on the line follows the same rule: y = 5x.

Move point (S): 5

Slope

Point on line

(5, 25%)

The slope of motorPower% = S × 5 is ___. That means for every +1 Speed, motor power increases by ___.

Think: rise ÷ run from (1,5) to (2,10).

Linear Decay

Endurance → Power Over Time

Linear decay is a straight line going down. P(t) = 100 − (20 − E) × 1.5 × t. Low Endurance makes the slope steeper — the bot loses power faster. High Endurance means a shallower drop.

Endurance (E): 10

Endurance (E)

Drop per round

−15%

Power at t=3

55%

A bot with E = 20 (max endurance) loses ___ % power per round.

Plug E=20 into (20 − E) × 1.5.

Nonlinear Function

Power → Charge (P²)

The Power formula is nonlinear: charge = P². Doubling P doesn't double charge — it quadruples it. The graph curves upward. Compare it to the straight Speed line.

Stat value: 5

Speed × 5 (linear)

Power² (nonlinear)

Power doubles: P goes from 3 → 6. Charge goes from 9 to ___?

6² = ?

Proportional Scaling

Does Doubling the Input Double the Output?

Proportional means input × k → output × k. Speed is proportional — double it, double motor power. Power is not proportional — double P, and charge quadruples.

Set stat value: 4

Speed → Motor Power
motorPower% = S × 5

20%

S=4 → 4×5=20%

Power → Charge
charge = P²

P=4 → 4²÷2=8

Speed goes from 5 → 10 (doubled). Motor power goes from 25% → ___. Is this proportional?

10 × 5 = ? Does it double from 25%?

Ratio

Comparing Stats to Each Other

A ratio compares two numbers. S:E = 8:4 = 2:1 — your bot is twice as fast as it has endurance. Ratios reveal how you built your robot and what its strengths are.

Your stat spread — drag to adjust

S 8

E 4

T 4

P 4

Budget total

20 ÷ 20

S:E = 8:4 = 2:1 | S:P = 8:4 = 2:1

A bot has S = 12, E = 4. The S:E ratio in simplest form is ___.

Divide both by GCD: 12÷4 = 3, 4÷4 = 1.

Reflection Complete

Save or print your answers before you leave.

Save Your Work

Print it, save as a PDF, or copy the text to email to yourself.

To email yourself: tap "Copy Answers" → open your email → paste → send to yourself.