Day 14 — Percent Change: How Big Was the Correction?

Percent change tells you how big a change is compared to where you started. It turns a raw change into a fair "how much bigger (or smaller)" number.

Today: learn it, practice it, then use it on your own bot's speed.

Why not just the raw change?

Two changes can be the same size but mean totally different things.

Same +5, very different story

A bot speeding up from 10 → 15 cm/s gained 5 — that's a big deal. A bot going 100 → 105 also gained 5 — but that barely matters. Percent change captures the difference: 10 → 15 is a 50% jump; 100 → 105 is only 5%. Same raw +5, very different percent change.

The formula

percent change = new − oldold × 100

⚠ The one trap

You divide by the OLD number — where you started from. That's what the change is measured against.

Worked: 20 → 25
new − old = 25 − 20 = 5
5 ÷ old = 5 ÷ 20 = 0.25
0.25 × 100 = 25%

Practice — work through these

Do each on paper first, then type the percent. It checks as you go. Watch the sign — up is positive, down is negative, and you always divide by the old number.

1. A bot's speed went from 40 to 50 cm/s.

percent change = %

2. A bot's speed went from 30 to 36 cm/s.

percent change = %

3. A bot's speed went from 20 to 30 cm/s.

percent change = %

4. A team's 1-second guess was 25 cm/s; done properly it was 40 cm/s.

percent change = %

5. A team's prediction gap shrank from 16 cm to 4 cm. (It went down.)

percent change = %

6. A bot slowed from 50 to 45 cm/s as its battery drained.

percent change = %

A drop (5 and 6) is a negative percent change; a rise is positive. If your answer looks huge or tiny, check that you divided by the old number, not the new one.

Same raw gain — who improved more?

Two teams each made their bot 6 cm/s faster. Same raw gain. Find each team's percent change, then read the takeaway.

Team A: 30 → 36 cm/s.

percent change = %

Team B: 60 → 66 cm/s.

percent change = %

The whole point of percent change

Both gained +6, but Team A jumped 20% while Team B moved only 10%. Compared with where they started, Team A improved twice as much. The raw number (+6) hides that; percent change shows it.

Now your own bot

From your Distance Lab sheet: your first-guess speed (the 1-second run) and your corrected speed (from two runs). How much did fixing your method change your speed?

First-guess speed (cm/s)

Corrected speed (cm/s)

Fill in both speeds.

—

percent change from your first guess to your corrected speed

Say it on your poster

"Our 1-second guess was cm/s. Doing it properly gave cm/s — a % correction. That's why our first predictions were off."

That sentence is your Goal-1 evidence: a change you made to your model, and how much more accurate it made your speed.

★

Challenge — for fast finishers

Two-step problems. Try these only once you've finished the eight above.

A. Work backwards. A team's speed went up 25% and landed at 50 cm/s. What was the old speed?

old speed = cm/s

B. A percent of a percent. A bot sped up 20%, then sped up another 10% from there. What is the total percent change from the start?

total change = %

A: "up 25%" means the new speed is 1.25 × the old — so you divide, not multiply. B: the second 10% is taken on the bigger number, so the two percents don't simply add to 30% — start from 100 and step through.