Water for Schools
Menu

Math problem set Grade 9 Math

Nethersby Water District: Operator Staffing and Wage Math

A grade 9 problem set on staffing a fictional utility's round-the-clock shifts, then comparing its starting wage with national operator pay and openings data.

Objectives

  1. Students will calculate the operator-hours and staff count required for round-the-clock coverage at a treatment plant.
  2. Students will compare a local starting wage with published national pay data using percent.
  3. Students will choose the quantity that best answers a stated staffing question and justify the choice.

Vocabulary

Key words: shift coverage, operator-hours, relief factor, state license

Teacher overview

A treatment plant runs every hour of every day, so a utility must staff it around the clock rather than for a single workday. Operators reach the job by several routes: a high school diploma with on-the-job training and a state license earned by exam, a certificate program at a community college, or a two-year or four-year degree in a related field. This set has students staff one fictional district, then compare its wage and its retirement outlook against published national figures. The error the set is designed to catch is counting three shifts as three operators, which ignores both the number of people needed on duty at once and the hours that vacation, training, and sick leave remove from the schedule.

Nethersby Water District: Operator Staffing and Wage Math — Grade 9 Math
Name: ____________________________ Date: ______________

Problems

The Nethersby Water District is a fictional utility. Its treatment plant runs 24 hours a day, seven days a week, in three 8-hour shifts, with two licensed operators on duty at all times. Use these values throughout.

  • A full-time operator works 40 hours per week and 2,080 hours per year.
  • The district's starting wage for a Class I operator is $26.40 per hour.
  • The district budgets an extra 15 percent of coverage hours for vacation, training, and sick leave.
  • Across its treatment plant, wells, and distribution system the district holds 24 operator positions, and 9 of them are held by operators who become retirement-eligible within 5 years.
  • Nationally, operators earned a median of $60,020 per year in May 2025, about 10,000 openings are projected each year from 2025 to 2035, and about 131,000 operators were employed in 2025.
  1. Find the operator-hours of coverage the plant needs each week with two operators on duty at all times.
  2. Find how many full-time operators that coverage alone would take, before any allowance for vacation, training, or sick leave. Round up to a whole operator.
  3. Add the district's 15 percent allowance to your item 1 answer to find the total operator-hours budgeted each week.
  4. Find how many full-time operators the budgeted hours require. Round up to a whole operator.
  5. Find the annual straight-time wage cost of staffing at your item 4 number, at $26.40 per hour and 2,080 hours per operator.
  6. Find the district's annual starting wage as a percent of the national median of $60,020. Round to the nearest tenth of a percent.
  7. Let n be the number of operators the district must license each year to replace its 9 retirement-eligible operators evenly over 5 years. Write an equation for n, solve it, and state the whole number of trainees the district should actually plan for each year.
  8. A trainee needs 1,800 hours of on-the-job experience before sitting for the Class I exam. At 40 hours per week, find how many weeks that takes.
  9. The district can describe its staffing need as operators per shift, operator-hours per week, or operators per million gallons treated per day. Choose the quantity that best answers the question "how many people do we hire this year," and explain why the other two answer different questions.
  10. Find the projected 10,000 annual national openings as a percent of the 131,000 operators employed in 2025. Round to the nearest tenth of a percent.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 336 operator-hours per week. Two operators on duty x 24 hours x 7 days = 2 x 168 = 336 operator-hours.
  2. Answer: 9 operators. 336 / 40 = 8.4, and a partial operator cannot cover a shift, so the district needs 9.
  3. Answer: 386.4 operator-hours per week. 336 x 1.15 = 386.4 operator-hours budgeted.
  4. Answer: 10 operators. 386.4 / 40 = 9.66, which rounds up to 10 full-time operators.
  5. Answer: $549,120. Each operator earns 26.40 x 2,080 = $54,912 per year, and 10 operators cost 10 x 54,912 = $549,120 in straight-time wages.
  6. Answer: 91.5 percent. The district's starting pay of $54,912 divided by the national median of $60,020 gives 0.9149, and 0.9149 x 100 = 91.49, which rounds to 91.5 percent. A starting wage sits below a median that includes experienced operators, so this result is what one would expect.
  7. Answer: 2 trainees per year. The equation is 5n = 9, so n = 1.8. The district cannot license 1.8 people, and licensing 1 per year would leave a gap, so it should plan on 2 trainees per year.
  8. Answer: 45 weeks. 1,800 hours / 40 hours per week = 45 weeks, which is a little over 10 months of full-time work.
  9. Answer: Operator-hours per week. Hiring is a question about total labor time, and only operator-hours per week captures both the number of people on duty and the number of hours the plant must cover. Operators per shift answers how to write the duty roster once the staff exists. Operators per million gallons treated per day is a benchmark for comparing this district with others of a different size, not a count of positions to fill.
  10. Answer: 7.6 percent. 10,000 / 131,000 = 0.0763, and 0.0763 x 100 = 7.63, which rounds to 7.6 percent of the current workforce each year.

Differentiation

Support

Give students a blank weekly grid for this fictional plant with the three shifts down the side and the seven days across the top, so they can count the staffed cells before computing item 1. Provide the multiplication 40 x 52 alongside the annual hours figure so the 2,080 hours is visible rather than assumed.

Extension

Ask students to recompute items 3 and 4 for the fictional district using relief allowances of 10 percent, 20 percent, and 25 percent, then describe how the required staff count changes and identify the allowance at which an eleventh operator becomes necessary.

ELL supports

Pre-teach "shift," "coverage," "relief," and "license" with a simple clock diagram divided into three shaded eight-hour blocks. Provide a sentence frame for problem 9: "The best quantity is ___, because the district is asking about ___ rather than ___."

Extensions

Have students find their own state's operator certification requirements, which are published by the state environmental or health agency, and list the license classes, the experience required for each, and the exam schedule. Ask them to write a short paragraph comparing that path with a four-year environmental engineering degree, naming one advantage of each for a student deciding after high school.