Worksheet Grade 6 Math

Elmridge's Aging Water Mains: Percent and Cost Worksheet

A grade 6 worksheet on a fictional town replacing old water pipes, using percent, unit rate, and decimals to plan the schedule and cost.

Grade: Grade 6
Subject: Math
Material: Worksheet
Time: 35 min
Prep: No prep
Materials: Calculator (optional)

Standards

6.RP.A.3 Common Core Math

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations, including finding a percent of a quantity and converting measurement units.

How this material aligns: Items 1 and 10 find a percent of a quantity, item 8 reads a cost from a ratio table of price per mile, and item 5 finds a per-customer unit cost, the ratio, rate, and percent reasoning this standard targets.

All materials for 6.RP.A.3 →

6.NS.B.3 Common Core Math

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

How this material aligns: Items 6 and 7 require fluent decimal subtraction and division of pipe mileage, such as 3 minus 2.4 and 2.4 divided by 6, the multi-digit decimal fluency this standard expects.

All materials for 6.NS.B.3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will find what percent of a town's water mains are old enough to replace.
Students will use unit rate and decimals to plan a pipe-replacement schedule and its cost.

Vocabulary

Water main: A big underground pipe that carries drinking water beneath the streets to a neighborhood. Smaller service lines branch off it to reach each building.

Also: percent, unit rate, infrastructure

Teacher overview

This worksheet follows the town of Elmridge, a fictional town whose underground water pipes are wearing out. Older pipes break more often, so the town has to replace them a few miles at a time over several years. Students use percent, unit rate, and decimals to plan how long the work takes and what it costs. As a teaching note, point out that the crew replaces only a small number of miles each year, yet the total cost is still large, which is the core idea of items 3 through 5.

Elmridge's Aging Water Mains: Percent and Cost Worksheet — Grade 6 Math

Name: ____________________________ Date: ______________

Student Worksheet

Use these numbers for every problem. The town of Elmridge has 60 miles of water main. Workers found that 15 miles are more than 90 years old and need to be replaced. A crew can replace 3 miles each year. Replacing pipe costs Elmridge $400,000 for each mile. Elmridge has 24,000 water customers.

What percent of Elmridge's 60 miles of water main are old and need replacing?
The crew replaces 3 miles each year. How many years will it take to replace all 15 old miles?
Replacing pipe costs $400,000 for each mile. What is the total cost to replace all 15 old miles?
In the first year the crew replaces 3 miles. What is the cost of the first year of work?
The town splits the total cost evenly among its 24,000 customers. How many dollars does each customer pay?
Last year the crew replaced only 2.4 miles instead of the planned 3 miles. How many miles short of the plan was that?
That crew worked 6 months to replace the 2.4 miles. How many miles did they replace each month?
At $400,000 for each mile, complete this cost table.

Miles of pipe Cost

0.5

1

2.5
Explain why replacing only a few miles of pipe each year can still add up to a very large total cost.
After 2 years at 3 miles each year, how many of the 15 old miles are done, and what percent of the old miles is that?

Miles of pipe	Cost
0.5
1
2.5

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: 25 percent. 15 old miles out of 60 total miles is 15 ÷ 60 = 0.25, which is 25 percent.
Answer: 5 years. 15 old miles ÷ 3 miles each year = 5 years.
Answer: $6,000,000. 15 miles × $400,000 for each mile = $6,000,000.
Answer: $1,200,000. 3 miles × $400,000 for each mile = $1,200,000.
Answer: $250. $6,000,000 ÷ 24,000 customers = $250 for each customer.
Answer: 0.6 mile. 3 planned miles − 2.4 miles done = 0.6 mile short.
Answer: 0.4 mile per month. 2.4 miles ÷ 6 months = 0.4 mile each month.
Answer: $200,000; $400,000; $1,000,000. 0.5 × $400,000 = $200,000; 1 × $400,000 = $400,000; 2.5 × $400,000 = $1,000,000.
Answer: Each mile is expensive, so even a few miles a year cost a lot; the small yearly amounts add up to a large total over the full 5 years of work.
Answer: 6 miles, which is 40 percent. 2 years × 3 miles = 6 miles done; 6 ÷ 15 = 0.4, or 40 percent of the old miles.

Differentiation

Support

Give students the total cost from item 3 already computed so they can focus on the division in item 5. Provide a printed strip that shows the two key steps: "percent = part ÷ whole" and "cost = miles × price for each mile." Allow a calculator for the decimal work in items 6 and 7.

Extension

Ask students to figure out how many years the work would take if the crew could replace 5 miles each year instead of 3, and how much the town would need to budget each year to finish in that time. Have them explain whether spending more each year saves money in the long run.

ELL supports

Pre-teach "water main," "replace," "percent," and "cost" with a simple labeled picture of a pipe under a street. Provide a sentence frame for item 9: "Replacing a few miles each year still costs a lot because ___." Allow students to answer with numbers and a short phrase rather than a full paragraph.