Water for Schools
Menu

Classroom activity Grade 8 Engineering & Design

Ottermill Bend Meter Test Bench: Modeling Three Meter Errors

A grade 8 station activity where teams pour known volumes through three rigged water meters, then write the linear function that describes each meter's error.

Objectives

  1. Students will collect paired true-volume and meter-reading data at three test stations.
  2. Students will write a linear function for each meter and name its rate of change and initial value.
  3. Students will recommend one meter for purchase, citing the rate of change and initial value they measured.

Vocabulary

Water meter
A device that measures how much water a home or business uses so the utility can bill fairly. Reading the meter can also reveal hidden leaks.

Also: registration, rate of change, initial value, calibration

Teacher overview

Utilities test water meters on a bench by running a measured volume of water through the meter and comparing what the meter registers against what actually went in. This activity rebuilds that bench with three bottles whose taped scales have been prepared to behave like three different meters: one accurate, one that registers too much at every volume, and one that misses a fixed amount on every pass. Teams of three or four rotate through the stations, pour known volumes, and record what each meter reads, then turn the pairs into a linear function. Because one meter's error grows with volume and the other's does not, the activity gives the rate of change and the initial value distinct physical meanings that students can point to.

Activity Directions

  1. Before class (20 min of prep). Cut the tops from three clear 2-liter bottles and run a strip of masking tape up the side of each. Label the bottles A, B, and C. On bottle A, pour in 100 mL of water and mark the tape at the water line as "100," then add 100 mL at a time and mark 200, 300, 400, and 500. Bottle A is the accurate meter.
  2. Prepare bottle B (the meter that registers too much). Empty it, pour in 80 mL, and mark that line "100." Add 80 mL at a time, marking the next lines 200, 300, 400, and 500. Every reading on bottle B will run high because each labeled step holds only 80 mL.
  3. Prepare bottle C (the meter that misses a fixed amount). Empty it, pour in 50 mL, and mark that line "0." Add 100 mL at a time from there, marking 100, 200, 300, and 400. Bottle C never registers the first 50 mL that enters it.
  4. Set up three stations (5 min). Place one prepared bottle, one funnel, one pitcher of water, and a towel at each station. Keep the graduated cylinders with the teams rather than at the stations, so every team measures its own true volumes. For more than three teams, prepare a second or third set of bottles A, B, and C so that no team waits for a station.
  5. Open the activity (5 min). Tell students that a utility bills customers from meter readings, so a meter that reads wrong sends the wrong bill. Explain that their job is to test three meters and report which one the town should buy. Do not tell them how the bottles were prepared.
  6. Round 1 (10 min). Each team goes to a station, empties the bottle, measures exactly 100 mL in the graduated cylinder, pours it through the funnel, and records the meter reading on the handout. They repeat with 200 mL and then 300 mL, emptying the bottle before each trial.
  7. Rounds 2 and 3 (20 min). Teams rotate to the next station and repeat the three trials, then rotate once more, so every team collects three data pairs from all three meters.
  8. Graph and model (10 min). Back at their seats, students plot each meter's three points on graph paper with true volume on the horizontal axis and meter reading on the vertical axis, then complete handout items 1 through 6.
  9. Debrief (5 min). Ask each team to report the rate of change they found for meter B and the initial value they found for meter C, then to name the meter they would recommend the town buy and the number behind that choice. Close by asking the two questions in handout items 7 and 9 aloud: which meter would overcharge a customer, and why testing at a single volume would have hidden one of the two errors. The activity ends when every team has reported both values and a recommendation.
Ottermill Bend Meter Test Bench: Modeling Three Meter Errors — Grade 8 Engineering & Design
Name: ____________________________ Date: ______________

Student Handout

Your team is testing three meters for the water department in the town of Ottermill Bend. Record the true volume you poured and the reading the meter showed.

Meter True volume poured (mL) Meter reading (mL)
A 100
A 200
A 300
B 100
B 200
B 300
C 100
C 200
C 300
  1. Using your three data pairs for Meter A, find the rate of change in meter reading for each milliliter of true volume.
  2. Write a function for r, Meter A's reading, in terms of t, the true volume poured.
  3. Using your three data pairs for Meter B, find its rate of change.
  4. Write a function for Meter B's reading in terms of the true volume poured.
  5. Look at your graph for Meter C. What reading does the line give when the true volume is 0 mL?
  6. Write a function for Meter C's reading in terms of the true volume poured.
  7. Which meter would charge a customer for more water than the customer actually used? Use your rate of change to explain.
  8. Which meter's error stays the same size no matter how much water passes through it?
  9. A utility tests every new meter at a low volume and again at a high volume. Using your results for Meters B and C, explain why one test volume is not enough.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: About 1 mL of reading for each 1 mL poured.
    Accept rates from about 0.95 to about 1.05. Meter A's marks were set with a graduated cylinder, so its readings should track the true volume closely. Small differences come from pouring loss and from reading the tape between marks.
  2. Answer: r = t.
    Accept any function with a rate of change near 1 and an initial value near 0, such as r = 1.02t.
  3. Answer: About 1.25 mL of reading for each 1 mL poured.
    Accept rates from about 1.15 to about 1.35. Meter B's labeled steps each hold only 80 mL, so 100 mL of water rises a quarter of the way from the 100 mark to the 200 mark, a reading of about 125, which is why the readings run high in proportion to the volume.
  4. Answer: r = 1.25t.
    Accept any function whose rate of change matches the value the team reported in item 3 and whose initial value is near 0.
  5. Answer: About -50 mL.
    Meter C's zero line sits 50 mL above the bottom of the bottle, so the graph crosses the vertical axis near -50. Accept values from about -40 to about -60.
  6. Answer: r = t - 50.
    Accept any function with a rate of change near 1 and an initial value near -50, matching the value the team reported in item 5.
  7. Answer: Meter B.
    Its rate of change is greater than 1, so every reading is larger than the volume that actually passed through. A customer billed from Meter B pays for water they never used, and the overcharge grows with the amount used.
  8. Answer: Meter C.
    Meter C misses the same 50 mL on every pass, whatever the volume. Its error is a constant, which is why it shows up as the initial value rather than in the rate of change.
  9. Answer: A single volume can hide one of the two errors.
    Strong answers explain that Meter C's fixed 50 mL loss looks large at a small test volume and nearly invisible at a large one, while Meter B's error grows with volume and is easy to miss at a small test volume. Testing at two volumes shows whether the error is a constant amount or a constant percentage.

Differentiation

Support

Give these students a partly completed data table with the true volumes already entered and the first Meter A trial filled in from a demonstration run. Provide a printed pair of axes with the scales already labeled, so plotting begins immediately.

Extension

Have students design a fourth meter that would read correctly at 200 mL but wrong at every other volume, describe how they would tape its scale, and write the function it would produce. Ask them to explain why a utility that tested only at 200 mL would approve it.

ELL supports

Demonstrate one full trial at the front of the room, naming each step aloud while pointing at the cylinder, the funnel, and the tape line. Provide a word bank with "pour," "reading," "true volume," "rate of change," and "initial value," each paired with a small sketch of the step where it applies.