Lesson plan Grade 11 Engineering & Design
Prioritizing Water-Main Replacement: A Dunmore Decision-Matrix Lesson
A grade 11 engineering lesson where students use a weighted decision matrix to rank which aging water mains the fictional city of Dunmore should replace first.
Objectives
- Students will build a weighted decision matrix that combines several criteria into a single priority score.
- Students will rank three replacement options and defend the ranking using the weighted scores.
Vocabulary
Key words: decision matrix, weighted criteria, trade-off, criticality, prioritization
Teacher overview
No utility can replace every aging pipe at once, so engineers rank the work using explicit criteria rather than gut feeling. This lesson gives students a real engineering tool for that ranking, the weighted decision matrix, and a fictional city, Dunmore, with three failing main segments competing for one replacement budget. The national backdrop is genuine: a water main breaks somewhere in the country about every two minutes, the ASCE 2025 report card graded US drinking water a C-, and EPA estimates $625 billion is needed for drinking-water infrastructure over 20 years, roughly two-thirds of it for distribution pipes. Students learn that the matrix still depends on judgment, which it records openly in the choice of weights.
Procedure
Hook (5 min): Ask students how a city should decide which old pipe to fix first when it can only afford one this year. Take two or three answers, then note that "the one that breaks most" and "the one serving the hospital" can point to different pipes, which is the problem a decision matrix is built to handle.
Background (10 min): Share the national figures above and explain that every utility faces more failing pipe than it can fund in any one year. Introduce four criteria a utility weighs: break history, pipe age, service criticality (what the pipe serves), and replacement cost. Explain that criteria are not equal, so each gets a weight.
Model the matrix (12 min): On the board, build a matrix for Dunmore's three segments using weights of 4 for break history, 3 for pipe age, 2 for service criticality, and 1 for replacement cost, with each segment scored 1 to 5 on each criterion (5 means highest priority to replace). Work the weighted total for one segment fully, multiplying each score by its weight and summing, so students see how the weights pull the result.
Team scoring (15 min): In teams, students complete questions 1 through 4 on their handout, using the given scores to compute the weighted total for all three segments. Each team then ranks the segments and identifies which one Dunmore should replace first. Circulate and confirm teams multiply before adding.
Share and rank (8 min): Two teams post their weighted totals and rankings. As a class, compare results and discuss how changing one weight, for example raising service criticality from 2 to 4, could change the ranking, illustrating that the weights encode the city's priorities.
Exit ticket (5 min): Students turn in a card stating which segment Dunmore should replace first and one sentence explaining how the weights, not just the raw scores, produced that answer.
Student Handout
The city of Dunmore can fund one water-main replacement this year and must choose among three failing segments: the Old Mill Line, the Harbor Main, and Vale Street. Each criterion carries a fixed weight: break history counts 4, pipe age counts 3, service criticality counts 2, and replacement cost counts 1. Every segment has already been scored from 1 to 5 on each criterion, where 5 marks the strongest case for replacing that segment first. The scores are given in the table below.
| Segment | Break history (weight 4) | Pipe age (weight 3) | Service criticality (weight 2) | Replacement cost (weight 1) |
|---|---|---|---|---|
| Old Mill Line | 5 | 5 | 3 | 2 |
| Harbor Main | 2 | 3 | 5 | 3 |
| Vale Street | 4 | 4 | 2 | 4 |
To find a segment's weighted total, multiply each of its four scores by that criterion's weight, then add the four products. Answer each question below.
- Find the weighted total for the Old Mill Line.
- Find the weighted total for the Harbor Main.
- Find the weighted total for Vale Street.
- Rank the three segments from highest to lowest weighted total, and state which segment Dunmore should replace first.
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: 43 points (Old Mill Line). Weighted total = (5 × 4) + (5 × 3) + (3 × 2) + (2 × 1) = 20 + 15 + 6 + 2 = 43 points.
- Answer: 30 points (Harbor Main). Weighted total = (2 × 4) + (3 × 3) + (5 × 2) + (3 × 1) = 8 + 9 + 10 + 3 = 30 points.
- Answer: 36 points (Vale Street). Weighted total = (4 × 4) + (4 × 3) + (2 × 2) + (4 × 1) = 16 + 12 + 4 + 4 = 36 points.
- Answer: Old Mill Line first. Its weighted total of 43 is the highest, ahead of Vale Street at 36 and Harbor Main at 30, so it is the first replacement. Accept an alternate ranking only if a student re-weights a criterion and shows the recalculated totals that justify it.
Differentiation
Support
Provide the matrix with one segment's weighted total already computed as a model, and give a row-by-row checklist reminding students to multiply each score by its weight before summing so the two-step calculation stays in order.
Extension
Ask students to choose one weight they think is too low, raise it, recompute all three weighted totals, and write a short paragraph explaining how the ranking changed and why they believe the new weighting better reflects a city's real priorities.
ELL supports
Pre-teach "criteria," "weight," "criticality," and "priority" with a simple two-column example unrelated to pipes, such as choosing a phone by price and battery life. Provide a sentence frame for the exit ticket: "Dunmore should replace ___ first because the weight on ___ made its score highest."