Worksheet Grade 6 Math

Thornbury's Aging Water Mains: Break Rates and Percent

A grade 6 worksheet where students turn water-main break and pipe-replacement data for the fictional town of Thornbury into unit rates, ratios, and percents.

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

Standards

6.RP.A.2 Common Core Math

Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship.

How this material aligns: Items 1, 4, 5, and 7 ask students to state a unit rate, such as breaks per hour, years per full replacement, and breaks per mile, which is exactly the per-one reasoning this standard defines.

All materials for 6.RP.A.2 →

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 3 and 6 use ratio and percent reasoning to describe how much pipe Thornbury replaces each year, the real-world ratio problem solving this standard requires.

All materials for 6.RP.A.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 convert a break-every-two-minutes rate into breaks per hour and per day.
Students will use unit rates and percent to compare two pipe-replacement plans.

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: unit rate, percent, ratio

Teacher overview

Much of the country's buried water pipe is old, and engineers who graded US drinking water gave it a C- in 2025. Across the country, a water main breaks about every two minutes. This worksheet uses the fictional town of Thornbury, which tracks its own pipe and breaks, to turn those ideas into unit rates, ratios, and percents. Teaching note: watch for students who read "only 5 percent replaced" as good news; the follow-up items show that this pace means a very long wait to renew the whole system.

Thornbury's Aging Water Mains: Break Rates and Percent — Grade 6 Math

Name: ____________________________ Date: ______________

Student Worksheet

Across the US, a water main breaks about every 2 minutes. The fictional town of Thornbury has 60 miles of water main. Thornbury replaces 3 miles of old pipe each year, and it had 24 breaks last year.

A water main breaks about every 2 minutes. How many breaks is that in one hour?
At that same rate, how many breaks happen in one full day of 24 hours?
Thornbury replaces 3 of its 60 miles of main each year. What percent does it replace each year?
At 3 miles per year, how many years would it take to replace all 60 miles?
Thornbury had 24 breaks last year across its 60 miles. What is the break rate per mile?
Write the ratio of miles replaced (3) to total miles (60) in simplest form.
A council member suggests spreading the work out so all 60 miles are replaced over 30 years. How many miles per year is that?
Is the 30-year plan faster or slower than the current 3 miles per year? Explain.
Suppose breaks drop to 18 next year. What is the new break rate per mile?
Explain why replacing more miles of old pipe each year would likely lower the number of breaks.

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: 30 breaks.
One hour is 60 minutes. 60 ÷ 2 = 30 breaks each hour.
Answer: 720 breaks.
A day has 24 hours. 30 breaks/hour × 24 hours = 720 breaks in a day.
Answer: 5 percent.
3 ÷ 60 = 0.05, and 0.05 × 100 = 5 percent replaced each year.
Answer: 20 years.
60 miles ÷ 3 miles per year = 20 years to replace all of it.
Answer: 0.4 breaks per mile.
24 breaks ÷ 60 miles = 0.4 breaks per mile.
Answer: 1 to 20.
The ratio 3 to 60 divides by 3 on both sides to give 1 to 20.
Answer: 2 miles per year.
60 miles ÷ 30 years = 2 miles per year.
Answer: Slower.
The 30-year plan replaces 2 miles per year, which is fewer than the current 3 miles per year, so it is slower.
Answer: 0.3 breaks per mile.
18 breaks ÷ 60 miles = 0.3 breaks per mile, down from 0.4.
Answer: Fewer old pipes remain.
Old pipe breaks most often, so replacing more of it each year leaves fewer weak pipes in the ground, which lowers the number of breaks over time.

Differentiation

Support

Provide a filled-in first row for the rate items, showing "60 minutes ÷ 2 = 30 breaks per hour," so students can copy the method for items 2, 5, and 9. Allow a calculator for the division steps.

Extension

Ask students to figure out how many miles per year Thornbury would need to replace to renew all 60 miles in only 15 years, then compare that pace to the 3 miles it manages now and describe what the town would need to change.

ELL supports

Pre-teach "main," "break," and "replace" with a simple drawing of a pipe under a street with a crack in it. Give a sentence frame for the explanation items: "Replacing more pipe each year lowers breaks because ___."

Extensions

Invite students to write two sentences to a town council explaining, with their own numbers from this worksheet, why a faster replacement plan could be worth the cost.