Lesson plan Grade 9 Engineering & Design
Ranking Water Main Replacements with a Decision Matrix
A 50-minute grade 9 engineering lesson where students build a weighted decision matrix to rank three aging water mains for replacement under a limited budget.
Objectives
- Students will build a weighted decision matrix from stated criteria and weights.
- Students will score three water mains, rank them, and justify a replacement priority under a budget constraint.
Vocabulary
Key words: decision matrix, criteria, weight, constraint, trade-off
Teacher overview
A water utility can never replace every aging pipe at once, so engineers must decide which segments to fix first. A weighted decision matrix turns that judgment into a clear, defensible process: list the criteria that matter, assign each a weight, score every option, and compare the totals. This lesson has students build such a matrix for a fictional utility choosing among three aging water mains, a task that mirrors how asset managers set replacement priorities under a fixed budget.
Procedure
Hook (5 min): Share two facts to frame the problem. The ASCE 2025 Infrastructure Report Card gave US drinking water a grade of C-, and a water main breaks somewhere in the US roughly every two minutes. Ask students how a utility with money to replace only one pipe this year should decide which one.
Direct instruction (12 min): Introduce the weighted decision matrix. Name four criteria and their weights: break history (weight 0.40), pipe age (0.25), material risk (0.15), and customer criticality (0.20), which add to 1.00. Explain that each option is scored 1 to 5 on each criterion, where 5 means the highest replacement priority, and that the weighted score is the sum of weight times score. Connect this to specifying criteria and constraints before choosing a solution.
Model the method (10 min): Present the fictional Fairmont Water District's Segment A: cast iron installed in 1958, 6 breaks in the last 5 years, and it serves a hospital. With the class, assign scores (break history 5, age 5, material 4, criticality 5) and compute the weighted score: 0.40 x 5 + 0.25 x 5 + 0.15 x 4 + 0.20 x 5 = 2.0 + 1.25 + 0.6 + 1.0 = 4.85.
Guided practice (13 min): In pairs, students use the district's scores for Segment B (ductile iron, installed 1992, 1 break in 5 years, serves a residential street) and Segment C (cast iron, installed 1965, 3 breaks in 5 years, serves downtown businesses) listed on the handout, compute each weighted score with the same rubric, then rank all three. Segment B totals 2.2 and Segment C totals 3.6, so the order is A, then C, then B.
Discuss trade-offs (5 min): Ask which pipe to replace first if the budget covers only one, and why criticality (a hospital versus a quiet street) can outweigh raw break counts. Point out that a matrix makes the trade-off visible rather than hidden.
Exit ticket (5 min): Students recompute Segment C's weighted score (question 5 on the handout) if the district raised the criticality weight to 0.30 and lowered break history to 0.30 (keeping age 0.25 and material 0.15). Collect the handouts before dismissal.
Student Handout
The Fairmont Water District's engineering staff scored its three aging water mains from 1 to 5 on each of the four criteria, where 5 means the highest replacement priority. The weights are the same for every segment: break history 0.40, pipe age 0.25, material risk 0.15, and customer criticality 0.20. A segment's weighted score is the sum of weight times score across the four rows. Use the scores in the table to answer the questions.
| Criterion (weight) | Segment A | Segment B | Segment C |
|---|---|---|---|
| Break history (0.40) | 5 | 2 | 3 |
| Pipe age (0.25) | 5 | 2 | 4 |
| Material risk (0.15) | 4 | 2 | 4 |
| Customer criticality (0.20) | 5 | 3 | 4 |
- Compute the weighted score for Segment A.
- Compute the weighted score for Segment B.
- Compute the weighted score for Segment C.
- Rank the three segments from highest weighted score to lowest, and name the segment the district should replace first.
- The district revises its weights, raising customer criticality to 0.30 and lowering break history to 0.30, while pipe age stays 0.25 and material risk stays 0.15. Recompute Segment C's weighted score using its scores from the table.
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: 4.85.
Segment A weighted score = 0.40 x 5 + 0.25 x 5 + 0.15 x 4 + 0.20 x 5 = 2.0 + 1.25 + 0.6 + 1.0 = 4.85.Answer: 2.2.
Segment B weighted score = 0.40 x 2 + 0.25 x 2 + 0.15 x 2 + 0.20 x 3 = 0.8 + 0.5 + 0.3 + 0.6 = 2.2.Answer: 3.6.
Segment C weighted score = 0.40 x 3 + 0.25 x 4 + 0.15 x 4 + 0.20 x 4 = 1.2 + 1.0 + 0.6 + 0.8 = 3.6.Answer: Replace Segment A first.
The ranking by weighted score is A (4.85), then C (3.6), then B (2.2), so Segment A is the top replacement priority.Answer: 3.7.
With the revised weights, Segment C = 0.30 x 3 + 0.25 x 4 + 0.15 x 4 + 0.30 x 4 = 0.9 + 1.0 + 0.6 + 1.2 = 3.7. Raising the weight on criticality lifts Segment C's score slightly, which shows how the chosen weights shape the ranking.
Differentiation
Support
Provide the matrix with Segment A already scored and computed as a worked model, and give students a filled-in weight column so they only enter scores and multiply. Allow a calculator for every weighted total.
Extension
Ask students to propose and defend a fifth criterion (for example, whether a pipe sits under a busy road that is costly to dig up), assign it a weight by reducing the others so the weights still sum to 1.00, and recompute all three segment scores to see whether the ranking changes.
ELL supports
Pre-teach "criteria," "weight," "score," and "trade-off" with a simple two-option matrix example unrelated to pipes. Provide a sentence frame for the trade-off discussion, such as "I would replace ___ first because its weighted score is ___."