Worksheet Grade 6 Engineering & Design
Elmridge Water Main Pipe Material Trade-off Worksheet
Ten items comparing three fictional pipe materials by total cost, cost per year of service, and a scored decision matrix for a water main replacement.
Objectives
- Students will calculate total material costs for three pipe options across a fixed pipe run length.
- Students will calculate a cost-per-year-of-lifespan figure for each pipe material.
- Students will complete a decision matrix scoring three materials against cost, lifespan, and corrosion resistance.
Vocabulary
Key words: trade-off, corrosion, lifespan, decision matrix
Teacher overview
Elmridge's public works department (a fictional town used for this worksheet) is replacing an old water main and must choose among three pipe materials before construction begins. This worksheet walks students through comparing PVC, ductile iron, and HDPE (polyethylene) pipe by total cost, cost per year of expected service life, and a scored decision matrix that also accounts for corrosion resistance, the kind of systematic comparison real infrastructure engineers use before recommending a material.
Student Worksheet
All figures on this worksheet are fictional, invented for the Elmridge scenario, and the ratings are simplified for the exercise. Elmridge needs 500 feet of new water main and is comparing three pipe materials:
| Material | Cost per foot | Expected lifespan (years) | Corrosion resistance (1-5) |
|---|---|---|---|
| PVC | $8 | 50 | 4 |
| Ductile iron | $14 | 75 | 3 |
| HDPE | $22 | 60 | 5 |
Find the total material cost for 500 feet of PVC pipe.
Find the total material cost for 500 feet of ductile iron pipe.
Find the total material cost for 500 feet of HDPE pipe.
Based on problems 1 through 3, which material has the lowest total cost, and which has the highest?
Elmridge's project budget is $9,000. Which of the three materials fit within this budget?
For each material, find the cost per year of service life. Divide the total cost by the lifespan in years, and round to the nearest dollar.
Based on the cost-per-year figures from problem 6 alone, which material is the most cost-effective?
Complete the "Total score" column below. Each material is already scored from 1 (worst) to 5 (best) on cost, lifespan, and corrosion resistance. Find each row's total by adding its three scores.
Material Cost score Lifespan score Corrosion score Total score PVC 5 3 4 ? Ductile iron 3 5 3 ? HDPE 1 4 5 ? Based on the total scores from problem 8, which material scores highest overall?
The total-score method in problem 8 and the cost-per-year method in problem 7 can point to different materials. Explain one reason why, even though both happen to favor the same material here.
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: $4,000. 500 ft x $8 per ft = $4,000.
- Answer: $7,000. 500 ft x $14 per ft = $7,000.
- Answer: $11,000. 500 ft x $22 per ft = $11,000.
- Answer: PVC lowest, HDPE highest. PVC totals $4,000, the lowest of the three; HDPE totals $11,000, the highest.
- Answer: PVC and ductile iron. PVC ($4,000) and ductile iron ($7,000) both fit within the $9,000 budget; HDPE ($11,000) exceeds it.
- Answer: PVC about $80 per year, ductile iron about $93 per year, HDPE about $183 per year. PVC: $4,000 divided by 50 equals $80. Ductile iron: $7,000 divided by 75 equals $93.33, which rounds to $93. HDPE: $11,000 divided by 60 equals $183.33, which rounds to $183.
- Answer: PVC. At about $80 per year of expected service, PVC costs the least per year of the three materials.
- Answer: PVC 12, ductile iron 11, HDPE 10. PVC: 5 + 3 + 4 = 12. Ductile iron: 3 + 5 + 3 = 11. HDPE: 1 + 4 + 5 = 10.
- Answer: PVC. PVC's total score of 12 is higher than ductile iron's 11 and HDPE's 10.
- Answer: The two methods could disagree because they weigh different factors: cost-per-year (problem 7) considers only cost and lifespan and ignores corrosion resistance entirely, while the decision matrix (problem 8) gives cost, lifespan, and corrosion resistance equal weight; a material with weak corrosion resistance but a low cost-per-year figure could win by one method and lose by the other, even though both methods happen to favor PVC on this worksheet.
Differentiation
Support
Provide a worked example for a fourth practice material (not PVC, ductile iron, or HDPE) showing the full cost calculation and cost-per-year division before students begin problems 1 through 7 on their own.
Extension
Ask students to invent a fourth pipe material with its own fictional cost, lifespan, and corrosion score, calculate its total cost and cost-per-year figure, and determine whether it would outscore PVC on the decision matrix.
ELL supports
Provide the price table with a small icon next to each material (a pipe segment shaded a different color for PVC, ductile iron, and HDPE) to connect the vocabulary to the visual. Allow students to show their multiplication and division work as numbers in a simple table rather than in full sentences.
Extensions
Invite students to interview a family member or family friend who has done home plumbing work, asking which pipe material they have used and why, then compare that answer with the worksheet's decision-matrix result.