Water Main Break Trends and Capital Planning in Milbrook

Hook (5 min): Share the national statistic that a water main breaks somewhere in the US roughly every two minutes, and ask students to guess how many times that adds up to in a single day. Do not confirm or correct guesses yet.

Direct instruction (15 min): Present Milbrook's seven years of break data for its cast iron mains: 14, 16, 12, 18, 15, 20, and 17 breaks per year. Tell students that Milbrook has about the same length of cast iron, PVC, and ductile iron main in the ground, so yearly break counts can be compared directly; utilities with unequal lengths compare breaks per 100 miles of pipe instead. Model calculating the mean (sum the values and divide by 7: 14+16+12+18+15+20+17 = 112, so 112 / 7 = 16.0 breaks per year) and the population standard deviation, since this is Milbrook's complete break record for these years, not a sample: find each year's deviation from the mean, square each deviation, average the squares, and take the square root. Walk through the arithmetic on the board.

Guided practice (20 min): In pairs, students calculate the mean and standard deviation for Milbrook's seven years of PVC main break data: 3, 5, 4, 2, 6, 3, and 5 breaks per year. They should find a mean of 4.0 breaks per year and a standard deviation of about 1.31. Once all pairs finish, lead a class discussion comparing the two materials' means (16.0 versus 4.0) and standard deviations (about 2.45 versus about 1.31), and connect the comparison to national context: Milbrook's cast iron mains, like aging cast iron mains nationwide, break far more often and less predictably than newer PVC pipe, which is part of why EPA's $625 billion national estimate weights distribution-pipe replacement so heavily.

Independent practice (10 min): Students solve two practice problems on their own, numbered to match the answer key. Item 1: recalculate the cast iron mean if an eighth year of data, 22 breaks, is added to the original seven years. Item 2: calculate the mean for a third pipe material, ductile iron, using five years of data: 6, 8, 7, 5, and 9 breaks per year.

Closure / exit ticket (5 min): Item 3: students answer on an index card: based on the three means calculated in this lesson (cast iron 16.0, PVC 4.0, and ductile iron 7.0), rank the three materials from most to least reliable and justify the ranking in one sentence. Also note that combined water and sewer bills nationally have already risen about 24 percent from 2019 to 2024, so any capital plan Milbrook adopts has to weigh reliability against what ratepayers can absorb. Before collecting cards, reveal the hook answer: one break every two minutes is about 720 breaks a day (1,440 minutes / 2). Collect and scan responses before dismissal.