Math problem set Grade 6 Careers & CTE

Hartsmoor Valve Crew: A Week of Unit Rates

A grade 6 careers problem set on a valve maintenance crew's week, covering valves-per-hour unit rates, percent of a program finished, and decimal multiplication.

Grade: Grade 6
Subject: Careers & CTE
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculators

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: Problems 1 through 3 express each day's work as a valves-per-hour unit rate so three unequal days can be compared fairly.

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: Problem 5 finds the percent of valves that would not turn, problem 7 finds the percent of the program finished, and problem 6 scales a weekly rate.

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: Problem 8 multiplies a multi-digit decimal, the 2.5 minutes each valve takes, by a whole number count of valves.

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 2026-09-23.

Objectives

Students will calculate a valves-per-hour unit rate for each day of a crew's week.
Students will find what percent of a maintenance program has been completed.
Students will multiply a decimal number of minutes by a count of valves.

Vocabulary

Valve: A valve is a device in a pipe that operators can open or close to control where water flows. Valves let crews shut off one street for repairs without turning off the whole town.
Distribution system: A distribution system is the network of pipes, pumps, valves, and storage tanks that carries treated water from a treatment plant to homes, schools, and businesses. Most of it is buried underground beneath streets.

Also: exercising a valve, unit rate, percent

Teacher overview

Every problem in this set comes from one week with the valve crew at the fictional Hartsmoor Water Department, and the problems follow the order the crew's own records are filled in. Students move from a single day's rate, to the week's total, to the share of a multi-year program that has been finished. One misconception runs through the whole set and is worth naming first. Students often compare the raw daily totals and decide that the day with the most valves was the crew's fastest day, which ignores the hours worked. Tuesday shows why that reading fails, because its 21 valves is close to Monday's 24 while the crew worked an extra hour to reach it.

Hartsmoor Valve Crew: A Week of Unit Rates — Grade 6 Careers & CTE

Name: ____________________________ Date: ______________

Problems

The Hartsmoor valve crew. You keep the records for the valve crew at the fictional Hartsmoor Water Department. A valve is a gate inside a buried water main that crews turn from the street with a long key to shut off one section of pipe. Crews exercise a valve by turning it closed and open again, which keeps rust and grit from locking it in place. A valve nobody has turned in twenty years may seize, and then a crew that only wanted to shut one block has to shut six. Valve crew members usually finish high school, train on the job, and earn a state distribution operator license by passing an exam, and some add a two-year degree in water technology later. Water and wastewater treatment plant operators, a related licensed job at the same utility, earned a median of $60,020 a year in May 2025, which describes operators specifically rather than every water job. Show every step of your work.

The crew's week

Day	Valves exercised	Hours worked
Monday	24	6
Tuesday	21	7
Wednesday	30	6
Thursday	18	6
Friday	27	6

On Monday the crew exercised 24 valves in 6 hours. How many valves per hour is that?
On Tuesday the crew exercised 21 valves in 7 hours. How many valves per hour is that?
On Wednesday the crew exercised 30 valves in 6 hours. How many valves per hour is that?
Add the five days in the table. How many valves did the crew exercise during the whole week?
Of the valves the crew exercised that week, 12 would not turn all the way and were written up for repair. Using your total from problem 4, what percent of that week's valves would not turn?
The fictional Hartsmoor distribution system has 1,200 valves in all. If the crew keeps exercising 120 valves a week, how many weeks would the whole system take?
The crew has now worked 3 weeks at 120 valves a week. What percent of the system's 1,200 valves have been exercised?
Turning one valve closed and open again takes an average of 2.5 minutes. How many minutes of turning was Wednesday's work, when the crew exercised 30 valves?
Three workers make up the crew, and together they exercised 120 valves during the week. How many valves is that for each worker?

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 valves per hour.
A unit rate divides the count by the time. 24 valves divided by 6 hours equals 4 valves per hour.
Answer: 3 valves per hour.
21 valves divided by 7 hours equals 3 valves per hour. Tuesday's total of 21 is close to Monday's 24, yet the crew needed an extra hour, so its rate is lower.
Answer: 5 valves per hour.
30 valves divided by 6 hours equals 5 valves per hour, the crew's best rate of the week.
Answer: 120 valves.
24 plus 21 equals 45. 45 plus 30 equals 75. 75 plus 18 equals 93. 93 plus 27 equals 120 valves.
Answer: 10 percent.
12 divided by 120 equals 0.1, and 0.1 written as a percent is 10 percent.
Answer: 10 weeks.
1,200 valves divided by 120 valves per week equals 10 weeks.
Answer: 30 percent.
3 weeks times 120 valves equals 360 valves. 360 divided by 1,200 equals 0.3, which is 30 percent.
Answer: 75 minutes.
30 valves times 2.5 minutes equals 75 minutes of turning.
Answer: 40 valves per worker.
120 valves divided by 3 workers equals 40 valves for each worker.

Differentiation

Support

Give these students the fictional Hartsmoor table with a third column headed "Valves per hour" so the division in problems 1 through 3 has a place to go, and print problem 5 with the fraction already written as 12 over 120. Assign problems 1 through 6 only, and allow a calculator throughout.

Extension

Ask students to find the crew's rate for Thursday and Friday, rank all five days from fastest to slowest, and write a short paragraph explaining why the fictional Hartsmoor supervisor should look at rates rather than daily totals when planning next week's route.

ELL supports

Pre-teach "valve," "exercise a valve," and "unit rate" with a simple drawing of a valve under a street beside a wrench. Provide the sentence frame "On ____ the crew did ____ valves in ____ hours, so the rate was ____ valves per hour." Allow students to say each answer aloud before writing it.

Extensions

Have students plan a two-year schedule for the fictional Hartsmoor system so that every one of the 1,200 valves is exercised twice, stating how many valves a week that takes and whether the current crew can reach it. Students then write two sentences explaining how many weeks of the two years that schedule would take the current crew and what the crew could do with the remaining time.