Math problem set Grade 7 Science

The Okonkwo Home Water Audit: Meter Tests, Leaks, and Wastewater

A grade 7 science problem set in which students use meter tests and a dye test to find a home leak, then trace where indoor and outdoor water goes.

Grade: Grade 7
Subject: Science
Material: Math problem set
Time: 50 min
Prep: No prep
Materials: Calculator

Standards

MS-ESS3-3 NGSS

Apply scientific principles to design a method for monitoring and minimizing a human impact on the environment.

How this material aligns: Problems 3 through 5 apply a controlled overnight meter test and a dye test to monitor a household leak, problem 10 has students design the follow-up test that confirms the repair, and problems 7 through 9 trace how the leak and the lawn water affect the river and the treatment plant.

All materials for MS-ESS3-3 →

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: Problems 2, 6, and 7 are multistep percent problems that find the outdoor share of July use, the leak's share of indoor use, and the share of July use that reaches the treatment plant.

All materials for 7.RP.A.3 →

7.RP.A.2 Common Core Math

Recognize and represent proportional relationships between quantities, including identifying the constant of proportionality and representing proportional relationships by equations.

How this material aligns: Problem 3 treats the leak as a constant rate, finding the constant of proportionality, 2 gallons per hour, from an 8-hour meter reading and scaling it to a day, and problem 6 scales that daily rate to a week.

All materials for 7.RP.A.2 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-10-12.

Objectives

Students will use controlled meter tests and a dye test to measure a household leak and identify its source.
Students will separate indoor from outdoor water use and explain where each goes after use.
Students will explain why removing clean leak water raises the concentration of waste in a home's wastewater.

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.
Wastewater: Wastewater is used water from sinks, showers, toilets, and businesses that goes down the drain. It travels through sewer pipes to a treatment plant to be cleaned before returning to nature.
Biochemical oxygen demand (BOD): Biochemical oxygen demand, or BOD, measures how much oxygen tiny microbes will use up as they eat the waste in water. Dirtier water has a higher BOD.
Transpiration: Transpiration is how plants release water into the air through tiny holes in their leaves. A tree pulls water up from the soil through its roots and lets it escape from its leaves as vapor.

Also: leak rate, controlled test, concentration

Teacher overview

A home water audit is a monitoring method: a family reads its water meter under controlled conditions to find out how much water it uses, where that water goes, and whether any is escaping through a leak. This set follows the fictional Okonkwo family of Amberside through the usual sequence of audit steps, using the audit records printed with the problems: two water bills, two overnight meter tests, and a toilet dye test. Students separate indoor from outdoor use, measure and locate a silent toilet leak, and then follow the water past the drain, where indoor water travels through the sewer to the treatment plant while lawn water returns to the air through evaporation and transpiration. A common misconception this set corrects is that fixing a leak makes a home's wastewater cleaner; leak water is clean tap water, so removing it leaves the same amount of waste in less water and raises its concentration, which problem 8 asks students to calculate and problem 9 asks them to explain.

The Okonkwo Home Water Audit: Meter Tests, Leaks, and Wastewater — Grade 7 Science

Name: ____________________________ Date: ______________

Problems

The Okonkwo family is fictional. They live in Amberside, a town where the sanitary sewer is separate from the storm drains. Everything that goes down a sink, shower, or toilet drain travels through the sanitary sewer to the Amberside wastewater treatment plant. Water that falls on lawns and streets does not go to the plant. Use the audit records below for every problem.

Audit records

Record A: Two water bills. In January the ground in Amberside is frozen, and the family does no outdoor watering. In July the family waters its lawn and vegetable garden.

Billing month	Days in the bill	Gallons used
January	31	7,440
July	31	12,400

Record B: Overnight meter test 1. The family turned off every faucet, shower, toilet flush, and water-using appliance, including the dishwasher, washing machine, and ice maker. No one used water between the two readings.

Reading	Time	Meter (gallons)
Start	Tuesday, 10:00 p.m.	48,215
End	Wednesday, 6:00 a.m.	48,231

Record C: Toilet dye test. On Wednesday afternoon, the family put 10 drops of food coloring into the tank of each toilet and waited 15 minutes without flushing. Water leaking past a worn flapper carries the color from the tank into the bowl.

Toilet	What the bowl looked like after 15 minutes
Upstairs	Blue water in the bowl
Downstairs	Clear water in the bowl

Record D: Overnight meter test 2. The family repeated test 1 with everything turned off in the same way. This time they also closed the shutoff valve behind the upstairs toilet, so no water could enter that toilet's tank.

Reading	Time	Meter (gallons)
Start	Wednesday, 10:00 p.m.	48,402
End	Thursday, 6:00 a.m.	48,402

Record E: Wastewater note. Biochemical oxygen demand (BOD) measures how much organic waste is in water, based on how much oxygen bacteria use to break it down. Raw household sewage usually has a BOD between about 100 and 300 mg/L. Suppose the wastewater leaving the Okonkwo house in January had a BOD of 160 mg/L. The water from the toilet leak is clean tap water, so it adds water to the sewer but adds no organic waste.

Questions

Use Record A. What was the family's average water use per day in January? What was it in July?
Because no water went outdoors in January, January's daily use measures the family's indoor use. Assume indoor use was the same in July. How many gallons per day went outdoors in July, and what percent of July's daily use is that?
Use Record B. How many gallons did the meter record during test 1? How many hours did the test last? Find the leak rate in gallons per hour. If the leak runs at that steady rate all day, how many gallons does it waste in 24 hours?
In test 1, the family turned off every fixture and appliance and ran the test overnight. Explain why each of those two choices makes the test a fair measure of a leak.
Use Records C and D. Which fixture is leaking? What does test 2 show that the dye test alone could not show?
The leak was present in January. What percent of the family's January indoor use was water lost to the leak? EPA WaterSense reports that household leaks waste about 180 gallons per week on average. How many gallons per week does the Okonkwo leak waste, and about how many times the national average is that, to the nearest tenth?
In July, the indoor water and the outdoor water take different paths after the family uses them. How many gallons per day from the Okonkwo house reached the treatment plant in July, and what percent of July's daily use is that? Describe where the outdoor water goes and where the indoor water goes after the plant treats it.
The family replaces the worn flapper, and the leak stops. Use Record E. How many gallons of wastewater per day will the house now send to the sewer in a winter month? The house sends the same amount of organic waste as before. What will the BOD of its wastewater be now?
Your answer to problem 8 shows that the wastewater became more concentrated after the repair. Explain why the repair still helps the treatment plant and the river or aquifer the town's water comes from.
Design a follow-up meter test that would show whether the new flapper fixed the leak. Describe the conditions of the test and the meter readings you would expect if the repair worked.

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: 240 gallons per day in January; 400 gallons per day in July.
January: 7,440 gallons divided by 31 days equals 240 gallons per day. July: 12,400 gallons divided by 31 days equals 400 gallons per day.
Answer: 160 gallons per day, which is 40 percent of July's daily use.
Indoor use is 240 gallons per day in both months, so outdoor use in July is 400 minus 240, which equals 160 gallons per day. Then 160 divided by 400 equals 0.40, or 40 percent.
Answer: 16 gallons in 8 hours, a leak rate of 2 gallons per hour, or 48 gallons per day.
The meter rose from 48,215 to 48,231, and 48,231 minus 48,215 equals 16 gallons. From 10:00 p.m. to 6:00 a.m. is 8 hours. The rate is 16 divided by 8, which equals 2 gallons per hour. Over 24 hours, 2 times 24 equals 48 gallons per day.
Answer: Turning everything off leaves a leak as the only thing that can move the meter, and the long overnight test makes a slow leak large enough to measure.
With every fixture and appliance off, no planned water use can pass through the meter, so any change in the reading must come from water escaping somewhere. This is a controlled test because the one possible cause left is a leak. Running the test overnight lets it last 8 hours without anyone needing water, and the longer time lets a leak of a couple of gallons per hour add up to a reading large enough to measure.
Answer: The upstairs toilet is leaking, and test 2 shows it is the only leak, accounting for all 48 gallons per day.
The dye moved from the tank into the bowl only in the upstairs toilet, so its flapper is leaking. The dye test cannot show how much water that toilet loses or whether there are other leaks. In test 2, closing only the upstairs toilet's valve stopped the meter completely (48,402 minus 48,402 equals 0 gallons), so the upstairs toilet caused the full 16 gallons in test 1 and no other leak in the house was found.
Answer: 20 percent of January indoor use; 336 gallons per week, about 1.9 times the national average.
The leak wastes 48 gallons per day out of 240 gallons per day of indoor use, and 48 divided by 240 equals 0.20, or 20 percent. In a week, 48 times 7 equals 336 gallons. Then 336 divided by 180 equals about 1.87, which rounds to 1.9 times the EPA average.
Answer: 240 gallons per day, which is 60 percent of July's daily use.
Only the indoor water goes down the drains to the sanitary sewer, so 240 gallons per day reached the plant, and 240 divided by 400 equals 0.60, or 60 percent. The 160 gallons per day of lawn and garden water soaks into the soil or lands on leaves. Some evaporates from the soil and leaves, and plant roots take up much of the rest and release it from their leaves as water vapor through transpiration, so most of it returns to the atmosphere. A smaller part may soak deep enough to reach groundwater, and any that runs off the lawn flows into the storm drains, which lead to a stream instead of the plant. The indoor water is cleaned at the treatment plant and then released to a river or stream, where it rejoins surface water downstream.
Answer: 192 gallons of wastewater per day, with a BOD of 200 mg/L.
Before the repair, the house sent 240 gallons per day, including the 48-gallon leak. After the repair it sends 240 minus 48, which equals 192 gallons per day. The amount of organic waste equals the BOD times the volume, and that amount stays the same, so 160 times 240 must equal the new BOD times 192. Then 160 times 240 equals 38,400, and 38,400 divided by 192 equals 200 mg/L. Another way to see it: 192 divided by 240 equals 0.8, so the same waste is now in 0.8 times as much water, and 160 divided by 0.8 equals 200 mg/L. This value is still inside the usual range of about 100 to 300 mg/L for household sewage.
Answer: The plant no longer has to pump and treat 48 gallons per day of clean water, and the town no longer has to take that water from its source.
The leak water was already treated to drinking-water standards and pumped to the house, and then it flowed down the sewer, where the plant had to pump and treat it again even though it carried no waste. Every gallon that reaches the plant uses pumping energy and treatment capacity, so removing clean water saves energy and leaves room in the plant for wastewater that needs treatment. The plant removes the same amount of organic waste either way. The repair also means 48 fewer gallons per day are drawn from the town's river or aquifer.
Answer: Repeat test 1 with the upstairs toilet's valve open; if the repair worked, the meter should move 0 gallons in 8 hours.
The follow-up test must match test 1 so the results can be compared: the same overnight hours, every fixture and appliance off, and the upstairs toilet's valve open so the new flapper is being tested. If the meter reads the same number at the start and the end, the leak is fixed. If it rises, students should find the new leak rate, as in problem 3, and repeat the dye test to find out whether the flapper or something else is still leaking. A strong answer also suggests repeating the test after a few weeks, since a flapper can wear out again.

Differentiation

Support

Give students a flow diagram before they begin, with arrows from the meter to the indoor fixtures, from the drains to the sanitary sewer and treatment plant, and from the hose to the lawn and then up into the air. Provide a worked model of problem 1 and a reminder that a leak rate is the gallons divided by the hours. For problem 8, show the same scoop of drink mix stirred into a full cup of water and into a smaller amount of water, and ask which drink is stronger before students do the calculation.

Extension

Amberside, like some real towns, sets each home's sewer charge from its January water use, because January use is almost all indoor water that reaches the plant. Ask students to explain why a leaking toilet raises a family's sewer charge while a leaking outdoor sprinkler line would not, and to find how many fewer gallons the Okonkwo family will be charged for in a 31-day January after the repair (48 times 31 equals 1,488 gallons).

ELL supports

Pre-teach "meter," "leak," "valve," "wastewater," "concentration," "evaporate," and "transpiration" with a labeled picture of a house, its water meter, and its sewer line. Provide sentence frames for problems 4 and 5: "The family turned everything off so that the only thing that could move the meter was ___." and "Test 2 shows that ___ because the meter ___."

Extensions

With a parent or guardian's permission, students can run the toilet dye test at home and, if the family can find its water meter, an overnight meter test like test 1. Students record their start and end readings, calculate a leak rate if the meter moved, and compare their results with the Okonkwo family's records.