Project Grade 11 Math
Wexford's Lost Water: A Non-Revenue Water Audit Project
A grade 11 multi-session project auditing a fictional utility's water loss, fitting a trend line to monthly leakage and weighing a repair program against lost revenue.
Objectives
- Students will compute monthly non-revenue water and express it as a percent of production.
- Students will fit a trend line to monthly loss data and check its fit with residuals.
- Students will compare the cost of a leak-detection program against the value of the water it recovers.
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.
- Water audit
- A careful check of where water goes, either in a home or across a whole water system. Audits find leaks and waste so they can be fixed.
Also: trend line, cost-benefit
Teacher overview
Over four sessions, student teams act as consultants auditing water loss for a fictional utility, Wexford Municipal Water, whose aging pipes leak treated water before it reaches customers. The driving question is whether the water Wexford loses is large enough to justify a leak-detection program. Teams analyze a year of monthly data, fit a trend line to the loss, and weigh the program's cost against the value of the recovered water. The final deliverable is a short data report and a presentation to a fictional utility board.
Project Brief
Driving question: How much treated water does Wexford lose to leaks each year, and is a 250,000-dollar leak-detection program worth funding?
Scenario and client: Wexford Municipal Water (a fictional utility) pumps treated water into its distribution system, but only bills customers for the water that actually reaches them. The gap between water produced and water billed is called non-revenue water, and much of it is leakage from old mains. The utility board has hired student consulting teams to size the loss and recommend whether to fund a leak-detection program.
Given data: Over the past 12 months, Wexford produced 1,825 million gallons of treated water and billed customers for 1,460 million gallons. Teams also receive the month-by-month table of production and billed water below to analyze the trend. Teams fill in the last column.
| Month | Water produced (million gallons) | Water billed (million gallons) | Non-revenue water (million gallons) |
|---|---|---|---|
| 1 (January) | 145 | 118 | |
| 2 (February) | 138 | 111 | |
| 3 (March) | 147 | 119 | |
| 4 (April) | 150 | 121 | |
| 5 (May) | 158 | 129 | |
| 6 (June) | 165 | 135 | |
| 7 (July) | 172 | 141 | |
| 8 (August) | 170 | 139 | |
| 9 (September) | 158 | 126 | |
| 10 (October) | 150 | 117 | |
| 11 (November) | 142 | 108 | |
| 12 (December) | 130 | 96 | |
| Total | 1,825 | 1,460 |
Constraints:
- Water sells at 4 dollars per 1,000 gallons (a fictional rate set for this project).
- The proposed leak-detection and repair program costs 250,000 dollars for the year.
- The utility's goal is to bring non-revenue water below 15 percent of production.
Final deliverable: A two-page data report plus a short presentation to the fictional Wexford utility board. The report must state the annual non-revenue water in million gallons and as a percent, show the fitted trend line and a residual check, give the value of the lost water in dollars, and make a funded-or-not recommendation with reasoning.
Milestones
- Session 1, quantify the loss: Using the annual totals, teams compute the year's non-revenue water in million gallons and as a percent of production, then fill in the monthly table with each month's loss. Output: a completed data table with the annual non-revenue water and percent shown.
- Session 2, model the trend: Teams make a scatter plot of monthly loss against month number, fit a trend line by least squares or by eye, and plot residuals to check whether a line is a reasonable model. Output: a labeled scatter plot with a fitted line and a short residual comment.
- Session 3, weigh cost against value: Teams convert the annual loss from million gallons to gallons, then to dollars of lost revenue at the stated rate, and compare that value to the 250,000-dollar program cost. Output: a cost-benefit calculation showing the recovered value and the payback reasoning.
- Session 4, report and present: Teams write the two-page report and present their recommendation to the class acting as the utility board, answering one board question. Output: the finished report and a team presentation.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Rubric
| Criterion | Emerging | Developing | Proficient | Advanced |
|---|---|---|---|---|
| Data analysis and accuracy | Non-revenue water is not correctly computed | Annual loss is found but the percent or monthly table has errors | Annual loss, percent, and monthly table are all correct | All values are correct and the team notes how the 20 percent loss compares to the 15 percent goal |
| Trend line and residuals | No trend line or an unlabeled plot | A line is drawn but residuals are not used to judge fit | A fitted line is shown and residuals are used to comment on fit | The fit is judged with residuals and the team explains what a pattern in the residuals would mean |
| Cost-benefit and recommendation | Lost value is not converted to dollars | Lost value is computed but not clearly compared to the program cost | Lost value is compared to the 250,000-dollar cost with a clear recommendation | The recommendation weighs cost, recovered value, and the goal, and anticipates a board objection |
Differentiation
Support
Provide the annual non-revenue water already computed so teams can start from the percent and the trend line, and give the monthly table pre-formatted with the production column filled in. Supply a worked unit chain converting million gallons to dollars for a sample month.
Extension
Ask teams to estimate how many years of recovered revenue would repay the program if it cut non-revenue water from 20 percent to 12 percent, and to state one assumption their estimate depends on.
ELL supports
Pre-teach "non-revenue water," "production," and "billed" with a simple diagram of water leaving the plant, some leaking from pipes, and the rest reaching homes. Provide sentence frames for the report's recommendation section.