Worksheet Grade 7 Engineering & Design

Foundry Row Water Main: Comparing Pipe Life-Cycle Costs

A grade 7 worksheet where students calculate cost per year of service for two pipe materials and use the results to recommend a water main replacement design.

Grade: Grade 7
Subject: Engineering & Design
Material: Worksheet
Time: 35 min
Prep: No prep
Materials: Calculator

Standards

7.NS.A.3 Common Core Math

Solve real-world and mathematical problems involving the four operations with rational numbers.

How this material aligns: Students divide, multiply, and subtract dollar amounts and years of service for two pipe materials, the four-operation rational-number work this standard requires in a real infrastructure decision.

All materials for 7.NS.A.3 →

MS-ETS1-2 NGSS

Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

How this material aligns: Students evaluate cast iron against PVC pipe using cost-per-year-of-service data, the systematic comparison process this standard requires before recommending one design solution over another.

All materials for MS-ETS1-2 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-16.

Objectives

Students will calculate cost per year of service for two competing pipe materials.
Students will compare total life-cycle costs over a fixed time period and justify a design recommendation with the data.

Vocabulary

Key words: life-cycle cost, service life, cast iron, PVC

Teacher overview

Foundry Row, a fictional neighborhood used in this worksheet, has an aging cast-iron water main that has reached the end of its useful life, and the city's engineers are comparing two replacement materials before recommending one to the city council. This worksheet has students calculate each material's cost per year of service, then project both options across a full century of use to see which one is the better long-term investment, the same life-cycle-cost comparison real utility engineers run before choosing a pipe material.

Foundry Row Water Main: Comparing Pipe Life-Cycle Costs — Grade 7 Engineering & Design

Name: ____________________________ Date: ______________

Student Worksheet

In this fictional scenario, Foundry Row's engineers are comparing two pipe materials for the replacement project. Use these facts for all items:

Cast iron main: costs $80,000 to install, with an expected service life of 40 years.
PVC main: costs $110,000 to install, with an expected service life of 75 years.

Find the cast iron main's cost per year of service.
Find the PVC main's cost per year of service, rounded to the nearest dollar.
Which material has the lower cost per year of service?
By how many dollars per year is that material's cost lower than the other's, rounded to the nearest dollar?
If the city plans to keep a working water main in place at this location for 100 years total, replacing it as each main reaches the end of its service life, how many full cast iron mains would need to be installed back-to-back to cover 100 years? (Round up to a whole number of mains.)
Using your answer from item 5, find the total installation cost of cast iron mains over the full 100 years.
How many full PVC mains would need to be installed back-to-back to cover the same 100 years? (Round up to a whole number of mains.)
Using your answer from item 7, find the total installation cost of PVC mains over the full 100 years.
Based on items 6 and 8, which material is the better long-term investment for Foundry Row, and by how many dollars over the full 100 years?
Explain your reasoning: even though PVC costs more per single installation, why might city engineers still recommend it after evaluating both options against the criteria of cost and service life?

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: $2,000 per year. $80,000 ÷ 40 years = $2,000/year.
Answer: $1,467 per year. $110,000 ÷ 75 years = $1,466.67, which rounds to $1,467/year.
Answer: PVC has the lower cost per year of service ($1,467 versus $2,000 for cast iron).
Answer: About $533 per year lower. $2,000 − $1,466.67 = $533.33, which rounds to about $533 per year.
Answer: 3 mains. 100 years ÷ 40 years per main = 2.5, which rounds up to 3 full mains, since a partial main cannot be installed.
Answer: $240,000. 3 mains × $80,000 per main = $240,000.
Answer: 2 mains. 100 years ÷ 75 years per main = 1.33, which rounds up to 2 full mains.
Answer: $220,000. 2 mains × $110,000 per main = $220,000.
Answer: PVC is the better long-term investment, cheaper by $20,000 over 100 years. $240,000 (cast iron) − $220,000 (PVC) = $20,000.
Answer: Accept any explanation noting that PVC's much longer service life (75 years versus 40 years) means fewer replacements are needed over a century, which lowers the total cost and reduces how often the street has to be dug up and traffic disrupted, even though each single PVC installation costs more upfront than a cast iron one.

Differentiation

Support

Provide the division for items 1 and 2 already set up as "$80,000 ÷ 40 = ___" and "$110,000 ÷ 75 = ___," and allow a calculator for every item.

Extension

Ask students to find the number of years at which cast iron and PVC would cost the exact same amount per year of service if the city could choose any service life for cast iron between 40 and 75 years, keeping the $80,000 installation cost fixed.

ELL supports

Provide a simple two-column reference card listing "Cast iron: $80,000, 40 years" and "PVC: $110,000, 75 years" for students to keep visible throughout the worksheet. Allow item 10's explanation to be written as one sentence using a provided frame: "PVC costs more at first, but it lasts ___ years longer, so the city replaces it ___ often."

Every figure in this scenario is fictional, chosen so students work with realistic engineering numbers.