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Lesson plan Grade 9 Engineering & Design

Ledgewater Water Loss Audit: Non-Revenue Water and Payback

A grade 9 lesson where students run a water balance for a fictional utility, find non-revenue water, and test whether a leak-detection program pays for itself.

Objectives

  1. Students will run a water balance to find water losses and non-revenue water for a utility.
  2. Students will evaluate whether a leak-detection program pays for itself using cost and savings.

Vocabulary

Non-revenue water
Water that a utility treats and pumps but never gets paid for. Most of it escapes through leaks in old pipes, and some is lost to broken meters or theft.

Also: water balance, real losses, payback

Teacher overview

Ledgewater is a fictional utility with aging pipes that leak water it has already paid to pump and treat. Water that is produced but never billed is called non-revenue water, and reducing it is one of the clearest ways a utility saves money without building anything new. In this lesson students run a simple water balance for Ledgewater, find its non-revenue water, and decide whether a leak-detection program is worth its cost.

A common misconception is that all lost water is leaking from pipes. In fact, losses split into real losses, which are physical leaks, and apparent losses, which come from meter and billing errors. Only the real losses can be recovered by finding and fixing leaks, so students must separate the two before judging a repair program.

Procedure

Hook (5 min): Ask students where a town's tap water comes from and what it costs to make it. Then pose the question the lesson answers: if a utility loses one gallon out of every five it produces, is that a problem worth spending money to fix? Take a few quick answers without resolving them.

Direct instruction (12 min): Define the water balance for a fictional sample utility: water supplied minus water billed equals total losses. Model it with small numbers that are not the handout numbers. Suppose a sample utility supplies 500 million gallons and bills 430 million gallons. Total losses are 70 million gallons, and non-revenue water is 70 ÷ 500 × 100 = 14 percent. Then split losses into real losses (leaks) and apparent losses (meter and billing errors), and explain that only real losses respond to leak repair.

Guided practice (15 min): Work handout items 1 through 3 together as a class for the fictional Ledgewater system. Students find total losses, non-revenue water as a percent, and real losses. Pause after each item so pairs can compare answers before moving on.

Independent practice (15 min): Students complete handout items 4 through 6 on their own or in pairs. These items put a dollar value on the lost water and test whether a $90,000 leak-detection program pays for itself. Circulate and check that students multiply the real-loss volume by the production cost before comparing to the program cost.

Closure and exit ticket (8 min): Students answer one question on an index card: "Does Ledgewater's leak program pay for itself in its first year? Support your answer with the net benefit you found." Collect the cards and scan for the correct comparison of savings to program cost. If fewer than 80 percent compare the two numbers correctly, reteach the payback step next class.

Ledgewater Water Loss Audit: Non-Revenue Water and Payback — Grade 9 Engineering & Design
Name: ____________________________ Date: ______________

Student Handout

Use these facts about the fictional Ledgewater utility. All volumes are in millions of gallons per year (MG).

  • Water supplied: 1,150 MG. Water billed to customers: 920 MG.
  • Apparent losses (meter and billing errors): 35 MG.
  • Production cost: $1,300 per MG of water.
  • A leak-detection and repair program costs $90,000 per year and is expected to cut real losses by 40 percent.

  1. Find Ledgewater's total water losses in MG. (Supplied − billed.)

  2. Find the non-revenue water as a percent of water supplied. Round to the nearest tenth of a percent.

  3. Find the real losses in MG. (Total losses − apparent losses.)

  4. Find the yearly cost of the real losses. (Real losses × production cost per MG.)

  5. Find the yearly savings the program would produce. (40 percent of the real-loss cost.)

  6. Find the net yearly benefit of the program. (Savings − program cost.) Then state whether the program pays for itself in its first year.

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: 230 MG.
    Total losses = 1,150 − 920 = 230 MG.

  2. Answer: 20.0 percent.
    Non-revenue water = 230 ÷ 1,150 × 100 = 20.0%.

  3. Answer: 195 MG.
    Real losses = 230 − 35 = 195 MG.

  4. Answer: $253,500.
    Cost of real losses = 195 MG × $1,300/MG = $253,500 per year.

  5. Answer: $101,400.
    Savings = 0.40 × $253,500 = $101,400 per year.

  6. Answer: $11,400.
    Net benefit = $101,400 − $90,000 = $11,400. Because the savings exceed the program cost, the program pays for itself in its first year.

Differentiation

Support

Give students a partly filled water-balance diagram for the fictional Ledgewater system, with the supplied and billed boxes already placed, so they only compute the loss boxes. Provide the production-cost multiplication set up as $1,300 × 195 so item 4 becomes a single calculation.

Extension

Ask students to find the simple payback period in years if the program cost had to be paid once as equipment, using payback = program cost ÷ yearly savings. Then have them discuss what other costs a real utility would weigh before approving the program.

ELL supports

Pre-teach "supplied," "billed," "losses," and "savings" with a labeled flow diagram of water moving from a plant to homes, with a leak drawn along the way. Provide a sentence frame for the exit ticket: "The program pays for itself because ___ is greater than ___."