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Math problem set Grade 7 Engineering & Design

Copperline Lead Service Line Replacement: A Percent and Budget Set

Students plan a fictional town's lead service line replacement, finding yearly pace, program cost, grant share, and how a test result compares to the action level.

Objectives

  1. Students will calculate a yearly replacement pace and program cost from a stated number of service lines.
  2. Students will use percent reasoning to compare test results to the lead action level and to size a grant.

Vocabulary

Service line
A service line is the small pipe that connects the water main under the street to the plumbing inside one home or building. It is the last leg of the trip water makes to your tap.
Action level
A trigger number in lead and copper testing. If too many homes test above this level, the utility must take steps like improving treatment and telling the public.

Also: constraint, grant

Teacher overview

Older water systems across the country still carry drinking water through lead pipes, and EPA's most recent estimate (November 2025) is that about 4 million of these lead service lines remain in use. Federal rules now push utilities to replace nearly all of them within ten years, and the lead action level, which is 15 parts per billion (ppb) today, drops to 10 ppb in 2027. This set follows the fictional town of Copperline as its water utility plans a replacement program with a real deadline and a fixed budget.

A common misconception in this math is mixing up "percent of the yearly target" with "percent of all the lines." A crew can hit a large share of one year's goal while still replacing only a small share of the whole town. Watch for students who divide by the wrong total.

Copperline Lead Service Line Replacement: A Percent and Budget Set — Grade 7 Engineering & Design
Name: ____________________________ Date: ______________

Problems

Use these values for the fictional Copperline program. The 15 ppb and 10 ppb action levels are real; the town totals and costs below are made up for this scenario.

  • Copperline has 1,200 lead service lines to replace.
  • The utility must finish within 10 years.
  • Each replacement costs 6,000 dollars.

  1. To replace all 1,200 lines in 10 years at a steady pace, how many lines must the crew replace each year?

  2. In year one the crew replaced 96 lines. What percent of that year's target from problem 1 did they complete? Round to the nearest whole percent.

  3. What percent of all 1,200 lines in town were replaced in year one (96 lines)? Round to the nearest whole percent.

  4. Each replacement costs 6,000 dollars. What is the total cost to replace all 1,200 lines?

  5. A state grant will pay 30 percent of the total cost from problem 4. How many dollars does the grant cover?

  6. After the grant, how many dollars must Copperline pay for the rest of the program?

  7. A home tested at 18 ppb of lead. By how many ppb does that reading exceed the 2027 action level of 10 ppb?

  8. By how many ppb does the same 18 ppb reading exceed today's action level of 15 ppb?

  9. Because only 96 lines were replaced in year one, the crew is behind. Over the remaining 9 years, how many lines must they average each year to still finish all 1,200 within the ten-year deadline? Round up to a whole line.

  10. In one or two sentences, explain how the ten-year deadline acts as a constraint that shapes how much the utility must budget each year.

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: 120 lines.
    1,200 lines ÷ 10 years = 120 lines per year.

  2. Answer: 80%.
    96 ÷ 120 = 0.80, which is 80% of the yearly target.

  3. Answer: 8%.
    96 ÷ 1,200 = 0.08, which is 8% of all the lines in town.

  4. Answer: 7,200,000 dollars.
    1,200 lines × 6,000 dollars per line = 7,200,000 dollars.

  5. Answer: 2,160,000 dollars.
    30 percent of 7,200,000 = 0.30 × 7,200,000 = 2,160,000 dollars.

  6. Answer: 5,040,000 dollars.
    7,200,000 − 2,160,000 = 5,040,000 dollars remaining for the town to pay.

  7. Answer: 8 ppb.
    18 ppb − 10 ppb = 8 ppb above the 2027 action level.

  8. Answer: 3 ppb.
    18 ppb − 15 ppb = 3 ppb above today's action level.

  9. Answer: 123 lines.
    Lines left = 1,200 − 96 = 1,104. Over 9 years: 1,104 ÷ 9 = 122.67, which rounds up to 123 lines per year to finish on time.

  10. Answer: The deadline forces a steady yearly pace and budget.
    Accept any answer explaining that the fixed ten-year limit means the utility cannot spread the work out slowly. It must replace a set number of lines and spend a set amount every year, so the deadline drives the annual budget rather than the other way around.

Differentiation

Support

Provide problem 1 already framed as "1,200 ÷ 10 = ___" and give a printed note reminding students that "percent of the target" divides by 120 while "percent of all lines" divides by 1,200. Allow a calculator throughout.

Extension

Ask students to figure out how many years the program would take if the town could only afford to replace 80 lines per year, and to explain why that pace would miss the ten-year deadline.

ELL supports

Pre-teach "service line," "action level," and "grant" with a simple picture: a pipe running from the street main to a house, a number line showing 15 and 10 ppb, and a coin labeled "grant." Provide a sentence frame for problem 10: "The deadline is a constraint because the town must ___ each year."