Lesson plan Grade 11 Careers & CTE
Meddingham's Water Main Budget: Which Segments Get Replaced
A 55-minute grade 11 careers lesson in which students act as an asset management analyst, scoring five water main segments by risk and fitting them to a budget.
Objectives
- Students will calculate replacement cost and break rate for water main segments from length, break history, and unit cost.
- Students will combine break rate and consequence into a risk score and rank segments by that score.
- Students will identify which combinations of replacements are viable under a fixed budget and explain why the highest-risk-first ranking can fail.
Vocabulary
- Asset management
- The practice of keeping track of everything a utility owns, like pipes and pumps, and planning the smartest times to fix or replace each one. It helps spend repair money wisely.
Also: break rate, consequence of failure, risk score, capital budget
Teacher overview
Every water utility replaces a small fraction of its pipe each year and has to decide which fraction. The analyst who makes that recommendation works from break records, pipe attributes, and a construction estimate, and the recommendation always has to fit inside a capital budget that was set before the analysis began. This lesson puts students in that seat at the fictional Meddingham Water District, where five candidate segments compete for one year of funding. The misconception this lesson corrects is the belief that ranking by risk and working down the list always spends the budget best; a single expensive, high-risk segment can crowd out two cheaper segments that together score higher, and students discover that directly when the top three by risk come in over budget by a small margin.
Procedure
Hook (5 min): Project the Street, Length, and Breaks in 5 years columns of the handout table for the fictional Meddingham district, and ask students which street they would fix first. Take three or four answers and record the reasons on the board without evaluating them, noting whether students cited break counts, pipe length, or what sits above the pipe.
Direct instruction (12 min): Introduce the two halves of a risk score that asset management analysts use. Likelihood of failure is estimated here as a break rate, which is breaks divided by the segment's length in thousands of feet and then divided by the number of years of record. Consequence of failure is a 1 to 5 score the district assigns based on what the segment serves, with a hospital or a downtown block scoring high and a dead-end residential lane scoring low. Risk score is the product of the two. Model the break rate calculation once on the board using a sample segment that is not on the handout: 1,500 feet with 5 breaks over 5 years gives 5 divided by 1.5, then divided by 5, or 0.67 breaks per 1,000 feet per year.
Guided practice (13 min): Distribute the handout. Work items 1 through 4 together, pausing after item 3 to check that students divided by the segment's length in thousands of feet rather than in feet. Formative check: ask every student to hold up one finger for Segment A, two for Segment B, and so on, indicating the segment they believe has the highest break rate, and do not move on until at least three-quarters of the class shows four fingers for Segment D on Wren Lane. If fewer than three-quarters agree, rework Segment D's break rate on the board before continuing.
Independent work (18 min): Students complete items 5 through 10 on their own or in pairs. Circulate and watch for two errors in particular. The first is multiplying cost by risk instead of comparing them separately. The second is stopping after item 7 with the conclusion that nothing can be done, rather than searching other combinations in item 8.
Closure and exit ticket (7 min): Ask two students to state the combination they chose in item 8 and defend it in one sentence. Then collect a one-sentence exit response to this prompt: name one piece of information the district would want before committing to this list that is not in the table. Expect answers such as pipe material, soil corrosivity, the age of the pipe, whether a street repaving is already scheduled, or the cost of the water lost in each break.
Student Handout
The fictional Meddingham Water District has $1,000,000 available for water main replacement this year. Five segments are candidates. Break counts cover the past five years. The consequence score runs from 1 to 5 and reflects what each segment serves.
| Segment | Street | Length (ft) | Breaks in 5 years | Unit cost per foot | Consequence score |
|---|---|---|---|---|---|
| A | Harrow Street | 2,400 | 7 | $180 | 4 |
| B | Delling Avenue | 1,600 | 3 | $210 | 5 |
| C | Pell Road | 3,200 | 4 | $145 | 2 |
| D | Wren Lane | 900 | 6 | $260 | 3 |
| E | Callow Street | 2,000 | 2 | $170 | 5 |
Use these two definitions. Break rate equals breaks divided by length in thousands of feet, then divided by 5 years, reported to the nearest hundredth. Risk score equals break rate times consequence score, reported to the nearest hundredth.
- Find the replacement cost of Segment A.
- Find the replacement cost of Segment D.
- Find the break rate for Segment D, in breaks per 1,000 feet per year.
- Find the break rate for Segment A, in breaks per 1,000 feet per year.
- Find the risk score for Segment D.
- Find the risk score for Segment B.
- The district's first instinct is to rank segments by risk score and fund them in order. The three highest risk scores belong to Segments D, A, and B. Find the total cost of those three segments and state how much they exceed the $1,000,000 budget.
- Search the other combinations. Find the combination of segments with the highest total risk score whose total cost is at or below $1,000,000, and give that combination's total cost.
- Find the total risk score of the combination you chose in item 8.
- Explain in three or four sentences why funding segments in strict risk order did not produce the best result here, and describe the situation in which risk-order funding would work perfectly.
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: $432,000.
2,400 feet times $180 per foot equals $432,000. - Answer: $234,000.
900 feet times $260 per foot equals $234,000. - Answer: 1.33 breaks per 1,000 feet per year.
Segment D is 900 feet, or 0.9 thousand feet. Then 6 breaks divided by 0.9 equals 6.667 breaks per 1,000 feet over five years, and dividing by 5 years gives 1.3333, which rounds to 1.33. - Answer: 0.58 breaks per 1,000 feet per year.
Segment A is 2,400 feet, or 2.4 thousand feet. Then 7 divided by 2.4 equals 2.9167, and dividing by 5 years gives 0.58333, which rounds to 0.58. - Answer: 3.99.
Segment D's break rate of 1.33 times its consequence score of 3 equals 3.99. - Answer: 1.90.
Segment B is 1,600 feet, or 1.6 thousand feet. Then 3 divided by 1.6 equals 1.875, and dividing by 5 years gives 0.375, which rounds to 0.38. Multiplying 0.38 by the consequence score of 5 gives 1.90. - Answer: $2,000 over the budget.
Segment D costs $234,000, Segment A costs $432,000, and Segment B costs 1,600 times $210, or $336,000. The total is $1,002,000, which exceeds the $1,000,000 budget by $2,000. This combination is not viable. - Answer: $910,000 for Segments B, D, and E.
Segment E costs 2,000 times $170, or $340,000. Segments B, D, and E total $336,000 plus $234,000 plus $340,000, or $910,000, which fits the budget. Every other three-segment combination costs more than $1,000,000: A with B and C is $1,232,000, A with B and E is $1,108,000, A with C and D is $1,130,000, A with C and E is $1,236,000, A with D and E is $1,006,000, B with C and D is $1,034,000, B with C and E is $1,140,000, and C with D and E is $1,038,000. No four-segment combination fits, since the four cheapest total $1,342,000. - Answer: 6.89.
Segment B scores 1.90, Segment D scores 3.99, and Segment E's break rate is 2 divided by 2.0, or 1.0, divided by 5 years, which is 0.20; times its consequence score of 5 that gives 1.00. The three sum to 6.89. The best two-segment alternative, Segments A and D, reaches only 6.31, so 6.89 is the highest total available under the budget. - Answer: Risk order ignores cost, so a high-scoring but expensive segment can crowd out two cheaper segments that together score higher.
Segment A carries the second-highest risk score, yet it costs $432,000, which is more than Segment B or Segment E alone. Swapping Segment A out and Segment E in drops 2.32 risk points and adds 1.00, but it frees $92,000, which is what brings the package inside the budget. Ranking works only when the items cost the same, or when the budget happens to land exactly at the boundary of the ranked list, because in either case cost stops being a factor that distinguishes one choice from another.
Differentiation
Support
Give students a partially completed table for the fictional district with all five replacement costs and all five break rates already filled in, so the lesson's independent work focuses on the risk scores and the budget search. Provide a checklist of the ten possible three-segment combinations for item 8 so students test them systematically rather than guessing.
Extension
Ask students to redo the fictional district's search with the budget raised to $1,100,000 and report whether the best combination changes, then explain what that result says about how sensitive the recommendation is to a budget the analyst does not control.
ELL supports
Pre-teach "break rate," "consequence," "risk score," and "viable" with a labeled street cross-section showing a pipe beneath a road, a hospital, and a dead-end lane. Provide the sentence frame "Segment ___ has a higher risk score than Segment ___ because ___" for item 10, and allow students to answer item 10 in three short sentences rather than a paragraph.
Extensions
Have students look up how their own water utility describes its main replacement program, then write a one-page memo to a fictional board explaining what data the utility appears to use and what the Meddingham exercise suggests it should also weigh.