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Lesson plan Grade 8 Careers & CTE

Staffing Aldermist's Recycled Water Program: A Careers Lesson

A 55-minute grade 8 careers lesson where students model a fictional recycled water program's growth with a linear function and decide when a second operator is needed.

Objectives

  1. Students will construct a linear function for the growth of a recycled water program.
  2. Students will solve linear equations to find the month a staffing threshold is reached.
  3. Students will explain why a utility hires staff before program revenue covers the cost.

Vocabulary

Recycled water
Wastewater that has been cleaned and used again, often to water parks, golf courses, and crops instead of being thrown away. Purple pipes usually carry it.

Also: connection, linear function, rate of change, staffing threshold

Teacher overview

Cities facing long droughts increasingly treat wastewater to a high standard and pipe it back out for irrigation, cooling, and industry, which creates jobs that did not exist in those utilities a decade ago. This lesson puts students in the workforce planner's seat for a fictional city starting such a program, where the open question is when to add each position rather than whether to add it. Students model the program's growth as a linear function and use it to find the month each staffing threshold arrives. The misconception the lesson addresses is that a growing program can hire whenever revenue catches up; students see that licensing rules tie staffing to the size of the system, so the utility must hire before revenue catches up.

Procedure

Framing the program (6 min). Explain that Aldermist, a fictional city, has spent three dry years under watering restrictions and is opening a recycled water program. Treated wastewater will be cleaned further, dyed-purple pipe will carry it to parks, a cemetery, a golf course, and two factories, and customers connect one at a time. Ask students which jobs the city has to fill before it can deliver any recycled water at all.

Role cards (12 min). Give each group four role cards to read and sort by the education route each requires. The four roles are the recycled water plant operator, who holds a state license and runs the treatment process; the cross-connection control specialist, who tests backflow devices so recycled water can never enter a drinking water pipe; the water quality laboratory technician, who runs the daily samples the permit requires; and the customer program coordinator, who signs up sites, trains their grounds crews, and handles complaints. Groups decide which roles could be filled by promoting from inside the utility and which usually require outside hiring.

Modeling the growth together (10 min). Put the connection counts for the first three months on the board and ask what stays the same from month to month. Establish that the count rises by a constant amount, which makes the relationship linear, and write one example of the function form together without solving the handout items for students.

Working the handout (20 min). Students complete the Student Handout individually or in pairs. Circulate and watch for two errors: writing the rate of change as the initial value, and stopping at the connection count in item 8 without carrying it back into the function in item 9.

Share and exit check (7 min). Ask three students to report their answers to items 4, 8, and 9. Use item 4 as the formative check: if fewer than three-quarters of the class found month 8, work that equation on the board before students leave. Close by asking whether the utility should hire the second operator early, late, or exactly on the threshold, and collect two reasons.

Staffing Aldermist's Recycled Water Program: A Careers Lesson — Grade 8 Careers & CTE
Name: ____________________________ Date: ______________

Student Handout

Suppose you are the workforce planner for Aldermist Water, a fictional city utility opening a recycled water program. Every figure below was invented for this lesson. The program opens with 30 connections already signed up, and the sales team expects to add 15 new connections each month. Let m stand for the number of months after opening and c stand for the number of connections.

  1. Write a linear function for c in terms of m. State the initial value and the rate of change, and say what each one means for the program.
  2. How many connections will the program have 8 months after opening?
  3. State rules in this scenario require one licensed operator for every 75 connections. Solve to find the month when the count reaches 75.
  4. A second operator is required when the count reaches 150. Solve to find the month when that happens.
  5. Each operator costs the utility $6,300 per month in wages and benefits. What is the total monthly staffing cost once the second operator is hired?
  6. Each connection brings the utility $40 per month in recycled water sales. What is the monthly revenue at 150 connections?
  7. At 150 connections, how much more is the monthly staffing cost than the monthly revenue?
  8. How many connections would the program need for monthly revenue to equal the two-operator staffing cost?
  9. Using your function from item 1, in which month does the program reach the number of connections you found in item 8?
  10. Explain why the utility hires the second operator in the month you found in item 4 rather than waiting until the month you found in item 9.

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

Answer Key

All figures below come from the fictional Aldermist scenario on the Student Handout.

  1. Answer: c = 30 + 15m.
    The initial value 30 is the number of connections on opening day, and the rate of change 15 is the number of new connections added each month.
  2. Answer: 150 connections. c = 30 + 15(8) = 30 + 120 = 150 connections.
  3. Answer: 3 months.
    Solve 30 + 15m = 75. Subtract 30 from both sides: 15m = 45. Divide by 15: m = 3.
  4. Answer: 8 months.
    Solve 30 + 15m = 150. Subtract 30 from both sides: 15m = 120. Divide by 15: m = 8. This agrees with item 2.
  5. Answer: $12,600.
    Two operators at $6,300 each: 2 x 6,300 = 12,600 per month.
  6. Answer: $6,000.
    150 connections x $40 per connection = $6,000 per month.
  7. Answer: $6,600.
    12,600 - 6,000 = 6,600, so staffing costs $6,600 more per month than the program earns at that point.
  8. Answer: 315 connections.
    Divide the staffing cost by the revenue per connection: 12,600 divided by 40 = 315 connections.
  9. Answer: 19 months.
    Solve 30 + 15m = 315. Subtract 30 from both sides: 15m = 285. Divide by 15: m = 19.
  10. Answer: The license rule ties staffing to the size of the system, not to revenue.
    Once the program reaches 150 connections in month 8, state rules in this scenario require a second licensed operator, so waiting until month 19 would put the utility out of compliance for eleven months. The utility covers the gap from its regular water budget, treating the early hire as part of the cost of starting the program.

Differentiation

Support

Give students a table of months 0 through 10 with the connection counts for the first three months filled in, so the constant increase is visible before they write the function. Provide the frame "c = (connections at opening) + (new connections each month)m" for item 1.

Extension

Ask students to write a second function for a version of this invented program that opens with 30 connections but adds 20 each month, then find how many months earlier the second operator would be needed.

ELL supports

Pre-teach "connection," "licensed operator," and "threshold" using a simple diagram of the plant, a purple pipe, and three customer sites. Allow item 10 to be answered with two short sentences, and post the frame "The utility must hire when ___ because ___."

Extensions

Have students draft a job posting for one of the four roles, listing the daily tasks, the education or license required, and one reason the job exists only because the city recycles water. Students can also find out whether any utility in their own state delivers recycled water and what it is used for there.