Power Stat Challenge · Day 4

Section 1 · The Formula

Charge Speed = Power²

Power controls your charge speed. Before you read the formula — answer this.

✋ Commit now — no backing out

If you double Power, what happens to charge speed?
You must choose A or B. You are not allowed to say "it depends."

B is correct — and the gap is bigger than most people expect. Doubling Power doesn't double charge speed. It quadruples it. Power 4 → 16%. Power 8 → 64%. That's 4×, not 2×. Most people pick A. Find out why below.

Find the Pattern Before You See the Formula

Power 1 gives charge speed 1. Power 4 gives 16. Power 8 gives 64.
What single operation takes you from Power to charge speed?

Power 1

1 + 1 = 2 ✗

1 × 2 = 2 ✗

1 × 1 = 1 ✓

Power 4

4 + 4 = 8 ✗

4 × 2 = 8 ✗

4 × 4 = 16 ✓

Power 8

8 + 8 = 16 ✗

8 × 2 = 16 ✗

8 × 8 = 64 ✓

✋ State the rule — then scroll

The operation is: Power _____ Power = charge speed. What fills the blank?

C. Multiply by itself. Power × Power. That's squaring. 4 × 4 = 16. 8 × 8 = 64. Adding and doubling both fail. Now look at the formula — you just discovered it.

The Rule

Charge Speed = Power²

If Power = 4 → chargePower = 4 × 4 = 16% | If Power = 8 → chargePower = 8 × 8 = 64%

📖

Squared (²) = multiply by itself. 4² = 4 × 4 = 16. Not the same as doubling (4 × 2 = 8). Squaring is bigger.

✋ One exact number — no ranges

Power 8 charge speed = ___%. Write the exact number before you touch the selector.
Not "around 60." Not "more than 50." One number.

%

The answer is 64%. Power 8 × Power 8 = 64. If you wrote 32 (double of 16), that's the squaring trap — doubling Power doesn't double charge speed, it quadruples it. Now move the selector to 8 and verify.

Check your prediction — pick a Power stat

The Square

4 × 4 units

→

Charge Speed

4 × 4 = 16

Motor speed

16%

✋ Watch the right chart only

Look at the Power chart. When Power doubles, that bar gets: 2× taller / 4× taller / same?

4× taller every time. That's what makes Power different from Speed — doubling the stat quadruples the output.

Speed (linear) vs Power (quadratic) — same numbers, totally different results

⚡

Double Power → charge speed ×4. Not ×2. Not ×3. Four times. That's squaring.

How the Cutebot Pro Knows When to Charge

In a match, the bot uses its ultrasonic sensor to detect the ball. Ball within 70 cm → charge fires automatically.

How the sensor triggers the charge

Cutebot Pro

Sensor active

≤ 70 cm → charge!

Ultrasonic distance pulse

⚽

The ball

Target

Distance > 70 cm

Driving

Navigating the arena. Sensor scanning continuously.

Distance ≤ 70 cm

Charging

Fires at chargePower% (= Power²). Then follow-through at base speed.

Two-phase charge (Part 2): Strike at chargePower%, then follow-through at motorPower% for 120 + (POWER × 35) ms. Power 4 → 260 ms. Power 8 → 400 ms. Speed = 0 → follow-through does nothing.

📡

Ultrasonic sensor — fires a sound pulse, times the echo. Shorter echo = closer object. Reads in centimeters.

Section 2 · Calculate

Fill the Table

Formula: Speed = Power × Power. Calculate each row.

✋ Predict before you calculate

Write both predictions before touching the table.
No formulas yet. One number each. Then check.

Power 4 charge speed

%

Power 8 charge speed

%

Power 4 → 16%. Power 8 → 64%. If you wrote 32 for Power 8 (double of 16), you're still thinking linearly. Double the Power = quadruple the charge speed. Now fill the full table and confirm the pattern for Power 1 and Power 2 too.

Part 1 — Power² Table

Power Points	Power × Power = ?	Charge Speed %
1
2
4
8

Part 2 — Find the Ratios

You doubled Power. Speed went 4% → 16%, then 16% → 64%. What's the ratio each time? Write "1 : ___"

Power 2 → Power 4

4% to 16%

Ratio: 1 :

Power 4 → Power 8

16% to 64%

Ratio: 1 :

The Hardest Question in This Lesson

⚡

Power 1 → Power 2: charge speed goes 1% → 4% (gain: +3 points)
Power 4 → Power 5: charge speed goes 16% → 25% (gain: +9 points)
Power 7 → Power 8: charge speed goes 49% → 64% (gain: +15 points)

✋ Pick A or B. You are not allowed to say "it depends."

Each extra Power point gives you the same charge speed boost?

B — and this is the entire concept. The boost is 3, then 9, then 15. It keeps growing because you're squaring. Adding 1 point at low Power gives you almost nothing. Adding 1 point at high Power gives you a massive jump. The rate of increase is not the same as the value increasing. If you said A, look at the three examples again — the gains are 3, 9, and 15.

Section 3 · Code & Test

Program Your Bot, Run the Test

You calculated. Now program and measure.

1 Floor Setup — Do This Before Every Run

Top-down view of your test lane

TAPE 1
Bot nose here

40 cm

TAPE 2
Ball starts here

⚽

Ball
Measure from here

Measure from TAPE 2 to where the ball stops. That is the number you record — not from TAPE 1.

🚫

Non-negotiable reset between runs. Bot nose back to TAPE 1. Ball back to TAPE 2. If the ball or bot shifts even a few centimeters, you are not testing Power — you are testing tape placement.

2 Open MakeCode — Set Your POWER Stat

Open MakeCode Program ↗

MakeCode · Cutebot Pro · micro:bit

🔴

Step 1

Update your
Stat variables

Your stats

→

⚡

Step 2

Set POWER
to 4

Run 1 first

→

⬇

Step 3

Click
Download

Then press A

Update your Stat variables

          set SPEED ▾ to your stat

          set ENDURANCE ▾ to your stat

          set TURNING ▾ to your stat

          set POWER ▾ to
          0
          →
          4
        

✋ Estimate first — no bot allowed yet

Charge speed goes from 16% (Power 4) to 64% (Power 8). The ball will travel ___ × farther.
Write one number. No ranges. Then run. If your estimate is off, you must explain why in Step 3.

× farther

Estimate locked. Now run both tests. When you record results below, calculate the actual multiplier (Power 8 distance ÷ Power 4 distance) and compare it to what you wrote. If they don't match — that gap is your reflection question. The bot can't give you this answer. Your brain had to go first.

Slider-scrubbing the bot until "it looks right" is not reasoning. Write the number first.

Run 1 — POWER = 4, SPEED = 0 → chargePower = 16%

📏

Expected: 8–15 cm. Under 3 cm or over 70 cm → check placement, one re-run.

Run 2 — POWER = 8, SPEED = 4 → chargePower = 84%

📏

Expected: 35–65 cm. Code says 5× more. Physical distance is 2–4× more. That gap is the point.

Troubleshooting — Bot not behaving?

Bot doesn't move at POWER = 4 (chargePower 16% stalls) Some Cutebot Pro units stall at very low motor speeds. Try POWER = 5 (chargePower = 25%) and note the adjustment. The ratio math still holds.

Sensor reads 0 or "no charge" on button A The sonar returns 0 when nothing is detected, or a large number when the ball is too far. Make sure the ball is on TAPE 2 (within 40 cm of the bot nose) before pressing A.

Ball rolls sideways instead of straight The bot's approach angle is off. Center the bot exactly on TAPE 1. Measure the straight-line distance from TAPE 2 rather than the ball's curved path.

Power 8 result is more than 4× Power 4 result Something shifted in your setup. Reset both tape marks, re-run once, and document what changed. You only get one re-run — imperfect data is still usable if you note it.

Finished both runs in under 8 minutes total? Extension: set POWER = 2 (chargePower = 4%). Does the ratio hold between Power 2 and Power 4 ball distances? You now have three data points.

3 Record Your Results

Power 4 Charge speed: 16% expected 5–12 cm

Ball traveled: cm

Power 8 Charge speed: 84% expected 35–65 cm

Ball traveled: cm

Section 4 · Reflect

Connect the Math to the Match

Formula said X. Bot did Y. What does the gap mean?

📋 Worksheet — Part 4: Reflect

Answer Questions 1–3 on your worksheet as you work through this section. Use the sentence starters below to get started.

The Key Question

Formula predicted one number. Bot did another.
That gap is: a problem — or information?

Think again → Did you follow the setup exactly — same tape marks, same reset every run? If yes, the gap didn't come from your error. It came from something the formula doesn't know about. What might the formula be missing?

Exactly right. The formula models the motor code — it says nothing about real-world physics. Friction, acceleration time, ball weight — those aren't in the formula. The gap is evidence. Engineers use gaps to find what their models don't account for yet.

Why doesn't the physical ratio match the code ratio?

Code says

16% → 64%

4× charge power

≠

Ball does

~2–4× farther

not 4×

🏎

16% ≠ 16% of top speed

The bot starts from rest. It's still accelerating when it hits the ball. Contact speed is much lower than the code % implies.

⚽

Harder hit ≠ proportionally farther roll

Friction absorbs more energy at higher speed. Twice the impact doesn't move the ball twice as far.

The gap between code and physics is the data. That's the point.

Question 1 of 3

Power doubled. Ball distance went: exactly 4× / roughly 4× / way less than 4×?
Circle one. Then explain.

Starter: "When I doubled Power, charge speed went from ___% to ___%. The ball moved ___ times farther, not 4×, because…"

Tap a starter to begin

0 / 15 min

Question 2 of 3

Your gap is: a problem / information. Pick one — then name ONE thing the formula missed.

Pick one: friction / acceleration / ball weight / floor surface. Then explain why it matters.

Tap a starter to begin

0 / 10 min

Question 3 of 3

Speed: double points = double output. Power: double points = 4× output.
More points into Speed or Power? Choose one. Then say why.

Your answer must include all three:
1. The stat you chose (Speed or Power)
2. The exact charge speed % your Power value gives
3. Why equal Power points give unequal charge speed boosts

⚠

Not accepted: "Power because it gives more charge speed." That's a conclusion with no reasoning. You need all three components above to get credit.

Tap a starter to begin

0 / 15 min

Stat Card — Record Your Power Choice

Power Points Chosen

Charge Speed

?%

Your name

Record this on your individual stat card before you leave the table.

Charge Speed = Power²

Fill the Table

Program Your Bot, Run the Test

Connect the Math to the Match

Stat Card — Record Your Power Choice

Challenge Complete! ⚡