Worksheet Grade 7 Math

Harrowden's Water Meter Bench Tests: Percent Error

A grade 7 worksheet where students compute percent error for five meters tested at a fictional town's bench and decide which ones must be replaced.

Grade: Grade 7
Subject: Math
Material: Worksheet
Time: 35 min
Prep: No prep
Materials: None

Standards

7.RP.A.3 Common Core Math

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

How this material aligns: Items 2 through 6 have students divide each meter's error by the true volume and express it as a percent, the percent error calculation this standard names.

All materials for 7.RP.A.3 →

7.NS.A.3 Common Core Math

Solve real-world and mathematical problems involving the four operations with rational numbers.

How this material aligns: Items 8 and 9 multiply a yearly usage by a decimal accuracy factor and then subtract to find the unbilled gallons, operating on rational numbers in a real-world setting.

All materials for 7.NS.A.3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-09-03.

Objectives

Students will compute the percent error of a water meter from its reading and the true volume.
Students will compare percent errors against a replacement threshold.
Students will find the unbilled gallons caused by a meter that reads low.

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: test bench, percent error, unbilled water

Teacher overview

Water meters wear out slowly, and a worn meter almost always reads low, so the utility delivers water it never bills for. Utilities check old meters on a test bench, running a known volume through each one and comparing the meter's reading with that known volume. This worksheet uses five meters pulled from homes in a fictional town, and every item works from the same test results. The error to watch for is students dividing the difference by the meter's reading rather than by the true volume, which is the value percent error is always measured against.

Harrowden's Water Meter Bench Tests: Percent Error — Grade 7 Math

Name: ____________________________ Date: ______________

Student Worksheet

Suppose the fictional town of Harrowden pulled five old meters and tested each one on a bench. The table shows the true volume sent through each meter and what the meter recorded.

Meter	True volume (gallons)	Meter reading (gallons)
A	100.0	96.0
B	100.0	103.5
C	50.0	47.5
D	200.0	194.0
E	80.0	80.8

How many gallons less than the true volume did Meter A record?
What is the percent error of Meter A?
What is the percent error of Meter B?
What is the percent error of Meter C?
What is the percent error of Meter D?
What is the percent error of Meter E?
Harrowden replaces any meter whose percent error is greater than 3 percent. How many of the five meters must be replaced?
Meter A serves a home that truly used 6,400 gallons last year. How many gallons did Meter A record for that year?
How many gallons of that home's water went unbilled?
Explain why a meter that reads low costs the utility money while a meter that reads high costs the customer money.

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

Answer Key

Answer: 4 gallons. Subtract the reading from the true volume: 100.0 minus 96.0 equals 4.0 gallons.
Answer: 4 percent. Divide the error by the true volume: 4.0 divided by 100.0 equals 0.04, and Meter A reads low.
Answer: 3.5 percent. The error is 103.5 minus 100.0, or 3.5 gallons, and 3.5 divided by 100.0 equals 0.035, reading high.
Answer: 5 percent. The error is 50.0 minus 47.5, or 2.5 gallons, and 2.5 divided by 50.0 equals 0.05, reading low.
Answer: 3 percent. The error is 200.0 minus 194.0, or 6.0 gallons, and 6.0 divided by 200.0 equals 0.03, reading low.
Answer: 1 percent. The error is 80.8 minus 80.0, or 0.8 gallons, and 0.8 divided by 80.0 equals 0.01, reading high.
Answer: 3 meters. Meters A at 4 percent, B at 3.5 percent, and C at 5 percent are above the limit. Meter D is exactly 3 percent, which is not greater than 3, and Meter E is 1 percent.
Answer: 6,144 gallons. Meter A reads 4 percent low, so it records 96 percent of the true volume: 0.96 times 6,400 equals 6,144 gallons.
Answer: 256 gallons. Subtract the recorded amount from the true amount: 6,400 minus 6,144 equals 256 gallons.
Answer: The utility loses revenue on a low meter. Water that passes through but is not counted is treated, pumped, and delivered without being billed, while a meter that reads high charges a customer for water that never reached the house.

Differentiation

Support

Give these students the error column already filled in for all five meters so they only divide and convert to a percent. Provide a printed reminder reading "percent error equals error divided by true volume," and allow calculators throughout.

Extension

Ask students to find the percent error of a sixth meter from the fictional town that recorded 118.75 gallons when 125.0 gallons passed through, then rank all six meters from most accurate to least accurate and explain what the ranking would cost the utility.

ELL supports

Pre-teach "true volume," "reading," "low," and "high" using a drawing of a tank of known size beside a meter dial. Provide the frame "The meter was off by ___ gallons out of ___ gallons, so the percent error is ___" for items 2 through 6.