Math problem set Grade 6 Science

Ravensgate's Lead Service Lines: Sampling and Replacement Math

Ten grade 6 problems on lead sampling results, a ten-year replacement schedule, and yearly cost per account for the service lines under the town of Ravensgate.

Grade: Grade 6
Subject: Science
Material: Math problem set
Time: 45 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: Problem 10 has students explain how a corrosion control step lowers lead at the tap while the pipes stay in the ground, and problems 2 and 3 read the tap sampling results that show whether that step is holding.

All materials for MS-ESS3-3 →

6.RP.A.3 Common Core Math

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations, including finding a percent of a quantity and converting measurement units.

How this material aligns: Students find percents of a quantity in problems 1 through 3 and use unit rates for lines per year and cost per account in problems 5 and 8.

All materials for 6.RP.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 2026-07-23.

Objectives

Students will express sampling results as the percent of homes above a stated action level.
Students will calculate a yearly replacement rate needed to finish a ten-year pipe replacement program.
Students will explain how corrosion control lowers lead at the tap before pipes are replaced.

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.
Corrosion control: Treatment that keeps water from slowly eating away at the inside of pipes. It helps stop metals like lead from getting into drinking water.

Also: sampling, parts per billion

Teacher overview

Lead usually enters drinking water after it leaves the source, in the service line, which is the short pipe that runs from the water main in the street to the meter at a house, and in older solder and fixtures inside the building. This set walks students through the sampling results and the replacement schedule facing the town of Ravensgate, a fictional utility working under the federal requirement to replace nearly all lead service lines within ten years. The misconception to correct is that lead is a source water problem that treatment alone can fix, since students who believe that will look for a filter answer instead of a pipe replacement answer.

Ravensgate's Lead Service Lines: Sampling and Replacement Math — Grade 6 Science

Name: ____________________________ Date: ______________

Problems

The town of Ravensgate has 4,800 service lines in the ground, and records show that 1,200 of them are lead. The utility sampled tap water at 60 homes. Nine of those homes came back above 15 parts per billion, and 15 of them came back above 10 parts per billion. The federal action level is currently 15 parts per billion and drops to 10 parts per billion in 2027. Ravensgate must replace all of its lead lines within 10 years. The town bills 4,800 customer accounts.

The town has 4,800 service lines, and 1,200 of them are lead. What percent of the service lines are lead?
Of the 60 homes sampled, 9 came back above 15 parts per billion. What percent of the sampled homes is that?
Of the same 60 homes, 15 came back above 10 parts per billion. What percent of the sampled homes is that?
Nine homes were above 15 parts per billion and 15 homes were above 10 parts per billion. How many more homes exceeded the lower level than the higher one?
Ravensgate must replace 1,200 lead lines within 10 years, working at a steady pace. How many lines must the crew replace each year?
A crew replaces 3 lines on a working day. How many working days does the crew need to replace 120 lines?
Each replacement costs the town $6,000. What is the cost of replacing all 1,200 lead lines?
Suppose the town spreads a total cost of $7,200,000 evenly across 10 years and across its 4,800 accounts. What is the yearly cost per account?
Suppose Ravensgate speeds up and replaces 150 lines each year instead of 120. How many years would the 1,200 lines take at that faster pace?
Before any pipes are replaced, Ravensgate adds a corrosion control chemical that builds a thin coating on the inside of the old pipes. Explain how that coating lowers the lead measured at a kitchen tap even though the lead pipe is still in the ground.

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: 25 percent.
Divide the lead lines by all the lines, so 1,200 divided by 4,800 gives 0.25. Multiply by 100 to get 25 percent.
Answer: 15 percent.
Divide the homes above the level by the homes sampled, so 9 divided by 60 gives 0.15. Multiply by 100 to get 15 percent.
Answer: 25 percent.
Divide 15 by 60 to get 0.25, then multiply by 100 to get 25 percent. Point out that lowering the level from 15 to 10 parts per billion moves more homes above the line even though no home changed.
Answer: 6 homes.
Subtract the two counts: 15 - 9 = 6 homes.
Answer: 120 lines per year.
Divide the total lines by the years allowed: 1,200 divided by 10 is 120 lines per year.
Answer: 40 working days.
Divide the yearly target by the daily pace: 120 divided by 3 is 40 working days.
Answer: $7,200,000.
Multiply the number of lines by the cost of each: 1,200 x 6,000 = 7,200,000 dollars.
Answer: $150 per account per year.
First divide the total by the years, so 7,200,000 divided by 10 is 720,000 dollars each year. Then divide by the accounts, so 720,000 divided by 4,800 is 150 dollars per account per year.
Answer: 8 years.
Divide the total lines by the faster pace: 1,200 divided by 150 is 8 years.
Answer: The coating separates the lead pipe wall from the water flowing past it.
Look for the idea that lead reaches the tap by dissolving off the pipe wall, and that a coating formed by the corrosion control chemical puts a barrier between the metal and the water. Strong answers may also note that the treatment is a stopgap, because the lead pipe remains and the coating has to be maintained without interruption.

Differentiation

Support

Give students a percent frame for problems 1 through 3 showing the part over the whole with the denominators already entered. Provide the Ravensgate cost work in problem 8 as two labeled boxes, one for the yearly total and one for the cost per account, so the two-step structure is visible before students calculate.

Extension

Ask students to compare Ravensgate's replacement pace of 120 lines each year with a pace that finishes in 6 years, calculate the yearly cost per account at the faster pace, and write a short recommendation naming one advantage and one drawback of moving faster.

ELL supports

Pre-teach "service line," "action level," and "corrosion control" using a labeled drawing of a street with the water main, the service line, the meter, and the kitchen tap. Provide sentence frames for problem 10, such as "Lead gets into the water when ___," and "The coating helps because ___."

Extensions

Have students find whether your state publishes a lead service line inventory map, then write a paragraph comparing what that map shows about your area with the fictional Ravensgate figures. Students should state clearly which numbers came from the published inventory and which came from the problem set.