Math practice · Unit #04 · both grades · Measurement & graphing

Honest Numbers

The math base camp. Statistics on the Time Trial Board, percent error on your own measurements, conversions until they're reflexes, and one Fermi problem to remind you that estimation is a superpower.

skills: mean / median / range percent error unit conversion estimation ≈ 40 min
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Name Period Date
PART A

The Time Trial Board

Five teams timed the same beetle crossing 30 cm of tile. One stopwatch caught the beetle's mid-trial snack break.

Times to cross 30 cm (seconds)
Team 1Team 2Team 3Team 4Team 5
4.24.54.34.48.9

  1. Mean of all five times:

  2. Median of all five times:

  3. Range (max − min):

  4. Drop the outlier (Team 5) and recompute the mean of the four honest times. Which statistic — mean or median — barely moved when the outlier was included? That's the robust one.

  5. Whose number was "right"? Use your statistics to argue which single time best represents the beetle — one sentence, cite a number.

PART B

Percent-error leaderboard

% error = |your value − official| ÷ official × 100
The official tile length is 30.0 cm. Three teams measured it. Rank them — lowest % error takes the board.

Leaderboard (compute % error, then rank)
TeamMeasurement (cm)Error (cm)% errorRank
Amber29.1
Iris30.6
Sage28.4

  1. Iris's measurement was the highest, but she won. Explain: why does percent error care about distance from the truth and not about being high or low?

PART C

Conversion reflexes

One system, ten at a time. No calculator — move the decimal like you mean it.

  1. 3.2 km → ___ m

  2. 450 mL → ___ L

  3. 90 cm → ___ mm

  4. 2.5 kg → ___ g

  5. 150 cm → ___ m

  6. Two-step: a beetle walks 0.04 km. How many cm is that?

PART D

The estimated digit

Your ruler is marked in centimeters only. The desk edge lands between 78 and 79 cm — closer to 78.4. You may record one estimated digit beyond the marks, but exactly one.

  1. Recorded: 78.4 cm. Circle the digits you're certain of; underline the one you estimated. Why is writing 78.42 cm with this ruler actually dishonest?

  2. Fermi break — estimate, showing your factors: the height in cm of a stack of every textbook in this classroom. (Books × thickness of one.)

Answer key — teachers

Part A

  1. Mean = 26.3 ÷ 5 = 5.26 s
  2. Median = 4.4 s
  3. Range = 8.9 − 4.2 = 4.7 s
  4. Without outlier: 17.4 ÷ 4 = 4.35 s. The median barely moved (4.4 both ways) — median is robust.
  5. Best single representative: the median 4.4 s (or Team 4's time) — it sits with the pack and ignores the snack break.

Part B

Amber: 0.9 cm → 3.0% (rank 2) · Iris: 0.6 cm → 2.0% (rank 1) · Sage: 1.6 cm → ≈5.3% (rank 3).

  1. Percent error measures closeness to the true value in either direction — accuracy is about distance from truth, not direction.

Part C

  1. 3,200 m
  2. 0.45 L
  3. 900 mm
  4. 2,500 g
  5. 1.5 m
  6. 0.04 km = 40 m = 4,000 cm

Part D

  1. Certain: 7 and 8; estimated: the 4. A second decimal (78.42) claims precision the tool can't deliver — an invented digit is a small lie.
  2. Accept reasonable factors, e.g., 30 books × 2.5 cm ≈ 75 cm. Credit the setup, not the exact answer.