Worksheet Grade 10 Math
Ochreford Utility Staffing: Operator Shifts, Licenses, and Pay
A grade 10 worksheet where students staff a fictional water plant around the clock, then compare paying overtime with hiring using national operator wage data.
Objectives
- Students will calculate how many full-time operators a round-the-clock plant needs from available work hours.
- Students will compare overtime cost with the cost of an additional hire using stated wage and benefit rates.
- Students will interpret published wage and job-opening figures as rates rather than as totals.
Vocabulary
Key words: median, percentile, shift coverage, overtime, benefit rate
Teacher overview
The Ochreford Water District is fictional, and its pay scale and staffing figures are set for this worksheet, while the national wage and job-opening figures come from the Bureau of Labor Statistics. Students work out how many operators a plant needs when one licensed person must be on duty at every hour of the year, then price two ways of covering the gap. The misconception this worksheet targets is reading a median wage as an amount every operator earns; the median is the middle of a wide range, and item 5 makes that range visible. A second common slip is dividing 8,760 hours by 2,080 paid hours instead of by the 1,840 hours an operator is actually available.
Student Worksheet
Ochreford is a fictional town of 18,000 people, and its water district is used here as a planning example. Its treatment plant must have one licensed operator on duty at all times. Each full-time operator is paid for 2,080 hours a year, and 240 of those hours go to training and leave, so 1,840 hours remain for shift coverage. The district pays a Class I operator $46,400 a year, pays overtime at $42.00 an hour, and adds benefits worth 25 percent of any salary.
National figures for this worksheet: water and wastewater treatment plant and system operators earned a median of $60,020 a year in May 2025, with about $39,110 at the 10th percentile and about $91,060 at the 90th percentile. About 10,000 openings for these operators are projected each year from 2025 to 2035, and about 131,000 people held these jobs in 2025. EPA estimates that roughly one-third of the water sector workforce is eligible to retire in the next 10 years.
The plant needs one operator on duty every hour of the year. How many operator-hours of coverage does a 365-day year require?
Each operator covers 1,840 hours a year. How many full-time operators does the district need? Round up to a whole person and explain the rounding in one phrase.
Suppose the board budgets five operator positions at the national median of $60,020 each. Find the total annual salary cost.
Ochreford pays a Class I operator $46,400. By what percent is that below the national median of $60,020? Round to the nearest tenth of a percent.
Find the dollar spread between the 90th percentile wage of $91,060 and the 10th percentile wage of $39,110.
There are about 10,000 openings each year among about 131,000 operator jobs. How many openings is that per 100 jobs? Round to the nearest tenth.
Across its treatment, wastewater, and distribution crews, the Ochreford district employs 12 operators. If its staff matched EPA's estimate that roughly one-third of water sector workers are eligible to retire in the next 10 years, how many of the 12 would be eligible to retire?
An operator-in-training must log 1,800 hours of documented plant experience before taking the Class II exam. At 40 hours a week, how many weeks does that take?
Suppose the district keeps only four operators. They cover 4 × 1,840 hours, and the rest of the 8,760 hours must be paid as overtime at $42.00 an hour. Find the overtime cost.
Now suppose the district hires a fifth operator at $46,400 plus benefits worth 25 percent of salary. Find the total first-year cost of that position.
Compare your answers to items 9 and 10. By how many dollars is the cheaper option less expensive?
Using the five-position budget from item 3, find the cost per hour of covered plant time. Round to the nearest cent.
The board must choose between the two options in items 9 and 10. Explain in two or three sentences which quantity supports that choice better, total annual cost or cost per covered hour, and why.
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: 8,760 hours. 24 hours per day × 365 days = 8,760 operator-hours of coverage.
Answer: 5 operators. 8,760 ÷ 1,840 = 4.76 operators, and the district cannot hire a partial person for a licensed shift, so it rounds up to 5.
Answer: $300,100. 5 positions × $60,020 = $300,100 in salary before benefits.
Answer: 22.7 percent. The gap is $60,020 − $46,400 = $13,620, and $13,620 ÷ $60,020 = 0.2269, or 22.7 percent below the median.
Answer: $51,950. $91,060 − $39,110 = $51,950 between the two percentile wages.
Answer: 7.6 openings per 100 jobs. 10,000 ÷ 131,000 = 0.0763, and 0.0763 × 100 = 7.6 openings for every 100 jobs.
Answer: About 4 operators. One-third of 12 is 12 ÷ 3 = 4 of the 12 operators.
Answer: 45 weeks. 1,800 hours ÷ 40 hours per week = 45 weeks of full-time work.
Answer: $58,800. Four operators cover 4 × 1,840 = 7,360 hours, leaving 8,760 − 7,360 = 1,400 hours. Then 1,400 × $42.00 = $58,800 in overtime.
Answer: $58,000. Benefits add 25 percent, so the cost is $46,400 × 1.25 = $58,000 for the first year.
Answer: $800. Hiring the fifth operator costs $58,000 against $58,800 in overtime, so hiring is $800 less expensive.
Answer: $34.26 per hour. $300,100 ÷ 8,760 hours = $34.2580, which rounds to $34.26 per covered hour.
Answer: Either quantity can be defended with a correct reason. Because both options must cover the same 1,400 hours, the annual totals compare them directly: $58,000 for the hire against $58,800 for overtime. Cost per covered hour gives the same ranking ($58,000 ÷ 1,400 = about $41.43 against $42.00) and stays useful if the board later changes how many hours the plant must staff. A strong answer also notes that the fifth operator is available for 1,840 hours, which leaves 440 spare hours for vacations and emergencies.
Differentiation
Support
Give students a filled-in first row of a two-column table labeled "overtime plan" and "fifth operator plan," with the hours line completed for both, so items 9 through 11 become arithmetic rather than setup. Provide the percent-change formula written with the item 4 numbers already substituted.
Extension
Ask students to find the overtime rate, in dollars per hour, at which the four-operator plan and the five-operator plan would cost exactly the same, then state whether the district's actual rate is above or below that break-even value. A further challenge is to recompute item 2 if training and leave rose from 240 hours to 400 hours per operator.
ELL supports
Provide a short glossary card defining median, percentile, overtime, and benefits, each with one plain-language sentence and a small number line showing where the median sits between the two percentile wages. Allow students to answer item 13 with a labeled two-column comparison instead of a paragraph.
Extensions
Invite a local utility manager to describe how their system covers nights, weekends, and holidays, and have students compare that staffing pattern with the five-operator plan they built for the fictional Ochreford district. Students can then revise item 2 using the visitor's stated hours of training and leave.