Math problem set Grade 7 Careers & CTE

Delvin's Leak Survey: Water-Loss Math for a Detection Crew

A grade 7 problem set following a leak detection crew through one fictional town's water audit, using percent of pumped water, unit rates, and percent change.

Grade: Grade 7
Subject: Careers & CTE
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculators

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: Problems 2, 3, and 8 require percent of a total, percent of a target, and percent increase computed from the crew's own survey records.

All materials for 7.RP.A.3 →

7.EE.B.3 Common Core Math

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically, and assess the reasonableness of answers using mental computation and estimation strategies.

How this material aligns: Problems 4 through 7 work with decimals and rates in several forms, and problems 5 and 7 each require two chained operations before an answer can be reported.

All materials for 7.EE.B.3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will compute unbilled water as a percent of the water a utility pumps.
Students will convert a leak rate in gallons per minute into daily and monthly totals.
Students will find the percent change in leaks found across two survey years.

Vocabulary

Leak detection: Finding hidden leaks in buried water pipes before they become big breaks. Crews listen for the sound of escaping water using sensitive equipment.
Water audit: A careful check of where water goes, either in a home or across a whole water system. Audits find leaks and waste so they can be fixed.
Water main: A big underground pipe that carries drinking water beneath the streets to a neighborhood. Smaller service lines branch off it to reach each building.

Also: unbilled water, unit rate

Teacher overview

A leak detection crew walks a water system at night with listening equipment, because buried leaks are easier to hear when traffic and household water use are quiet. Before the crew goes out, someone does the arithmetic that tells them where to start, and that arithmetic is a water audit comparing what the utility pumped with what it billed. Every problem here comes from one month at a utility in the fictional town of Delvin. A water main breaks somewhere in the United States roughly every two minutes, and aging pipe is the usual reason. Most leak detection technicians enter the work with a high school diploma and train on the equipment alongside an experienced crew, and many go on to earn a state water distribution operator license. The common error in this set is dividing the lost water by the billed water instead of by the water pumped, which overstates the loss and makes a system look leakier than it is.

Delvin's Leak Survey: Water-Loss Math for a Detection Crew — Grade 7 Careers & CTE

Name: ____________________________ Date: ______________

Problems

Suppose the town of Delvin runs the water system described in each problem. Show your work.

In March, Delvin pumped 84 million gallons into its water mains and billed customers for 71.4 million gallons. How many million gallons were not billed?
Delvin pumped 84 million gallons in March and did not bill 12.6 million gallons of it. What percent of the pumped water was not billed?
The crew's goal is to hold unbilled water to 9 percent of the water pumped. If Delvin pumps 84 million gallons in a month, how many million gallons would that goal allow?
In March, 12.6 million gallons went unbilled, and the crew's goal would allow 7.56 million gallons. How many million gallons of loss must the crew eliminate to reach the goal?
The crew finds a leak losing 12 gallons every minute. How many gallons does that leak lose in one full day?
A leak loses 17,280 gallons in one day. How many gallons does it lose in a 30-day month?
The crew surveys 6 miles of water main in 4 nights of listening. At that same rate, how many nights are needed to survey 51 miles?
On the same stretch of main, the crew found 18 leaks in the first year of the survey and 27 leaks in the second year. What was the percent increase in leaks found?

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: 12.6 million gallons. Subtract the billed amount from the pumped amount: 84 minus 71.4 equals 12.6.
Answer: 15 percent. Divide the unbilled 12.6 by the pumped 84, which gives 0.15, and 0.15 written as a percent is 15 percent. A student who divides 12.6 by the billed 71.4 instead gets about 17.6 percent, which is the common error named in the overview.
Answer: 7.56 million gallons. Multiply 84 by 0.09. Checking the size of the answer helps here, because 9 percent of 84 must be a little less than 8.4, which is 10 percent of 84.
Answer: 5.04 million gallons. Subtract the goal from the actual loss: 12.6 minus 7.56 equals 5.04.
Answer: 17,280 gallons. There are 60 minutes in an hour, so the leak loses 12 times 60, or 720 gallons per hour. There are 24 hours in a day, so 720 times 24 equals 17,280.
Answer: 518,400 gallons. Multiply 17,280 gallons per day by 30 days.
Answer: 34 nights. The crew covers 6 divided by 4, or 1.5 miles per night. Divide 51 miles by 1.5 miles per night to get 34.
Answer: 50 percent. The rise is 27 minus 18, which is 9. Divide 9 by the starting value of 18 to get 0.5, then multiply by 100. A student who divides by 27 has used the ending value.

Differentiation

Support

Provide problems 2 and 8 with the subtraction step already completed and the denominator labeled, so students practice choosing and carrying out the division. Reduce the set to problems 1, 2, 5, 6, and 8. Give students a place-value chart for the decimal subtraction in problems 1 and 4, lining up 12.6 and 7.56 by their decimal points.

Extension

Ask students to decide how many nights of surveying the crew should schedule if the town wants the whole system covered twice a year, using the rate in problem 7 and a system length the student chooses and states. Students must write the assumption they made, show the calculation, and name one reason the real schedule might differ.

ELL supports

Pre-teach "pumped," "billed," and "unbilled" with a simple two-bar drawing showing water going into the system and water paid for. Provide a labeled formula strip reading "part divided by whole, then times one hundred" beside the percent problems. Allow students to explain their reasoning for problem 2 orally before writing.

Extensions

Have students compare two ways of reducing loss on paper: sending the crew out more nights, or replacing the oldest section of main. Students list what each option costs the utility in staff time or construction, name who benefits first under each option, and write a short recommendation with one sentence acknowledging what their comparison leaves out.