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Worksheet Grade 8 Social Studies & Civics

Pipe Age and Main Breaks in Fairholt: A Scatter Plot Study

A grade 8 worksheet in which students plot pipe age against water main breaks for ten neighborhoods, find the outlier, and weigh two pipe replacement strategies.

Objectives

  1. Students will construct a scatter plot from a table of neighborhood infrastructure data.
  2. Students will describe the association between pipe age and break frequency and identify an outlier.
  3. Students will compare two replacement strategies using both the plotted data and a stated budget.

Vocabulary

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: outlier, association, trend line, capital budget

Teacher overview

The ASCE 2025 Infrastructure Report Card gave US drinking water a C- and wastewater a D+, and one reason is that buried pipe is replaced far more slowly than it wears out. Utilities decide which mains to replace using break records, and this worksheet gives students a fictional city's records for ten neighborhoods. Students plot the data, describe the association, and notice the one neighborhood that breaks far more often than its pipe age predicts. The misconception the outlier is there to correct is the belief that age alone determines condition; soil chemistry, pipe material, and pressure all matter, which is why utilities track break history rather than pipe age alone. The last items add the city's replacement budget, so students weigh two replacement strategies against what the city can afford to rebuild in a year.

Pipe Age and Main Breaks in Fairholt: A Scatter Plot Study — Grade 8 Social Studies & Civics
Name: ____________________________ Date: ______________

Student Worksheet

Fairholt is a fictional city with 240 miles of water main. Crews record every main break. The table shows each neighborhood's average pipe age and its break rate, measured as breaks per 10 miles of main each year.

Neighborhood Average age of mains (years) Breaks per 10 miles each year
A 20 4
B 25 5
C 30 7
D 35 8
E 40 24
F 45 12
G 50 13
H 55 17
I 65 20
J 75 26

Fairholt's council has set aside $8.4 million each year to replace pipe. Replacing one mile of main costs about $1.4 million in this city.

  1. Construct a scatter plot of the data. Put average pipe age on the horizontal axis and breaks per 10 miles on the vertical axis.
  2. Describe the association between pipe age and break rate.
  3. Which neighborhood does not fit the pattern the other nine follow?
  4. Give one reason a main only 40 years old might break far more often than its age predicts.
  5. Draw a trend line through the nine neighborhoods that follow the pattern. Use it to estimate the break rate for a neighborhood with 60-year-old mains.
  6. Use the same trend line to estimate the pipe age at which a neighborhood reaches 10 breaks per 10 miles each year.
  7. How many miles of main can Fairholt replace in one year with its budget?
  8. At that pace, how many years would replacing all 240 miles take?
  9. Plan A replaces the oldest mains first. Plan B replaces the neighborhoods with the highest break rates first. Under which plan would Neighborhood E be replaced sooner?
  10. Explain one limitation of deciding replacement order from pipe age alone.
  11. Write two sentences recommending Plan A or Plan B to the council. Use one number from the table or from your answers as evidence.

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: A correctly scaled plot with ten points.
    Accept any plot with pipe age on the horizontal axis, break rate on the vertical axis, evenly spaced scales, and all ten neighborhoods plotted. Neighborhood E should sit well above the others.
  2. Answer: A positive linear association.
    As pipe age increases, the break rate increases, and the nine points other than E fall close to a straight line.
  3. Answer: Neighborhood E.
    At 40 years, E records 24 breaks per 10 miles, more than Neighborhood I, whose mains are 25 years older, and nearly as many as 75-year-old Neighborhood J. It is the clear outlier.
  4. Answer: Accept any reasonable cause other than age.
    Corrosive or shifting soil, a pipe material that fails early, high or fluctuating pressure, heavy truck traffic overhead, and poor installation are all acceptable. Accept any answer naming a physical cause rather than restating the age.
  5. Answer: about 19 breaks per 10 miles each year.
    A reasonable trend line through the nine points is close to y = 0.4x - 5, which gives 0.4(60) - 5 = 19. Accept any estimate from 17 to 21, since hand-drawn lines vary.
  6. Answer: about 38 years.
    Setting 0.4x - 5 = 10 gives 0.4x = 15 and x = 37.5, which rounds to about 38 years. Accept any estimate from 34 to 42.
  7. Answer: 6 miles.
    8.4 million divided by 1.4 million per mile = 6 miles of main each year.
  8. Answer: 40 years.
    240 miles divided by 6 miles each year = 40 years to replace the whole system once.
  9. Answer: Plan B.
    Neighborhood E has the second-highest break rate in the city but only mid-range pipe age, so a plan that ranks by break rate reaches it second while a plan that ranks by age would replace five older neighborhoods before it.
  10. Answer: Age does not capture the conditions that make a pipe fail.
    Neighborhood E shows that two mains of the same age can be in very different condition. A utility that sorts only by age would replace sound pipe in one neighborhood while leaving failing pipe in another. Accept any answer that uses E as evidence.
  11. Answer: Accept either plan when supported by a number.
    A strong response cites evidence, such as recommending Plan B because Neighborhood E records 24 breaks per 10 miles while 75-year-old Neighborhood J records 26, or recommending Plan A because replacing the whole system takes 40 years and the oldest pipe will fail during that wait anyway. Reject responses with no supporting figure.

Differentiation

Support

Provide a printed grid with the axes already labeled and scaled and with neighborhoods A, B, and C plotted, so students continue an established pattern. Give these students items 1, 2, 3, 7, 8, and 11 only, and allow a calculator for items 7 and 8.

Extension

Ask students to calculate what yearly budget the fictional city would need to replace all 240 miles within 30 years, and to explain in writing why a utility might still not spend that amount even if it could.

ELL supports

Pre-teach "main," "break rate," "outlier," and "trend line" by pointing to each one on a completed sample plot with three points. Provide sentence frames for items 2 and 10, such as "As pipe age increases, the break rate ___" and "Age alone is not enough because ___."

Extensions

Some utilities publish a map or dashboard of recent main breaks. Students can look for one covering their region, count the breaks reported in a single month, and write a short paragraph comparing that record with the pattern in the fictional Fairholt data.