Project Grade 12 Math
Quarryhill Water Works: Non-Revenue Water Audit and Plan
A grade 12 four-session project where teams audit a fictional utility's water losses, value them, and propose a loss-reduction plan within a fixed budget.
Objectives
- Students will compute a utility's non-revenue water volume and percentage from a water balance.
- Students will value water losses and build a loss-reduction plan that fits a fixed budget.
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: water balance, payback period
Teacher overview
Quarryhill Water Works is a fictional utility with aging mains that lose water before it ever reaches a customer's meter. Water lost this way, called non-revenue water, still costs money to pump and treat. Non-revenue water also includes water that reaches customers but is never billed, for example through meters that under-record, which is why meter replacement appears among the options. Because every lost gallon has a cost, utilities audit it, put a dollar value on it, and decide what to fix first. Across four sessions, teams build a water balance, value the loss, compare repair options against a fixed budget, and present a loss-reduction plan to a fictional water board. The driving question is how much of Quarryhill's treated water is lost and which repairs return the most for the money available.
Project Brief
Driving question: How much of Quarryhill's treated water is lost or never billed, and which loss-reduction plan gives the best return within a fixed budget?
Scenario: Quarryhill Water Works (a fictional utility) has asked your team, acting as its water-audit consultants, to review one year of records and recommend a plan to the utility's board. National context frames the work: aging pipes are a nationwide problem, a water main breaks somewhere in the US roughly every two minutes, and the ASCE 2025 report card graded US drinking water a C-.
The records (all figures fictional and provided for this project):
- Water produced and put into distribution: 900 million gallons for the year.
- Water billed to customers: 720 million gallons for the year.
- Value of water lost: 6.00 dollars per 1,000 gallons, the utility's own cost to pump and treat.
- Loss-reduction budget: 250,000 dollars for this year.
- Target: cut non-revenue water from its current level to 12 percent of water produced.
The options sheet (all figures fictional and provided for this project):
- Leak-detection survey and repair: costs 80,000 dollars and recovers 35 million gallons a year.
- Pressure management: costs 110,000 dollars and recovers 40 million gallons a year.
- Meter replacement: costs 140,000 dollars and recovers 30 million gallons a year.
Constraints:
- Every recommended repair must fit inside the 250,000-dollar budget.
- The plan must show a payback period for each option, using its cost and expected annual recovery.
- The final plan must state the projected non-revenue water percentage after the repairs and show it meets the 12 percent target.
Final deliverable: A written water-audit report and a short presentation to the fictional water board, including the water balance, the dollar value of the loss, a cost-benefit table of options, and the recommended plan with its payback and projected loss percentage.
Milestones
- Session 1 (build the water balance): Using the year's records, teams find the non-revenue water volume (water produced minus water billed) and express it as a percentage of water produced. Output: a completed water-balance sheet showing 180 million gallons of loss and a 20 percent non-revenue water rate.
- Session 2 (value the loss and set the target): Teams convert the loss volume to a yearly dollar value at 6.00 dollars per 1,000 gallons, then compute the volume that a 12 percent target allows and the volume that must be recovered. Output: a loss-valuation sheet showing the annual cost of the loss and the recovery needed to reach the target.
- Session 3 (compare options within budget): From the options sheet in the Project Brief, which lists a leak-detection survey, pressure management, and meter replacement, each with a cost and an expected annual recovery, teams build a cost-benefit table, compute each option's payback period, and choose a combination that fits the 250,000-dollar budget and reaches the target. Output: a cost-benefit table and a chosen plan totaling 250,000 dollars or less.
- Session 4 (write and present): Teams write the audit report and present it to the class acting as the fictional water board, defending their plan with the payback figures and the projected loss percentage. Output: the completed report and a short 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 |
|---|---|---|---|---|
| Water balance and loss valuation | The balance or the percentage is incorrect, or the loss is not valued in dollars | The balance is correct but the dollar valuation has errors or missing units | The balance, percentage, and dollar value of the loss are all correct with units shown | All figures are correct, clearly labeled, and the team explains what the numbers mean for the utility |
| Plan within budget and payback | The plan exceeds the budget or omits payback periods | The plan fits the budget but payback periods are incomplete or miscomputed | The plan fits the budget, reaches the target, and shows a correct payback for each option | The plan fits the budget, reaches the target, and justifies the option order using payback and recovery |
| Report and presentation to the board | The report is incomplete or hard to follow | The report covers the plan but reasoning is thin | The report clearly presents the balance, valuation, and recommended plan | The report is clear and anticipates a board member's likely question about cost or feasibility |
Differentiation
Support
Provide the water-balance formula and the loss-valuation steps already labeled, and give a partly completed options sheet with one payback period worked as a model. Let teams use a prepared spreadsheet that totals option costs automatically so they can focus on the reasoning.
Extension
Ask teams to model how the non-revenue water percentage would drift back upward over the next three years as mains keep aging, and to propose a recurring annual budget that would hold the loss at or below the target rather than fixing it once.
ELL supports
Provide a labeled diagram of a distribution system showing where water is produced, where it is billed, and where losses occur, glossing "non-revenue water," "water balance," "payback period," and "audit." Offer sentence frames for the board presentation, such as "Our plan recovers ___ each year and pays back its cost in ___."
Extensions
Have teams read the water-loss or non-revenue water section of a real utility's annual report or state water-audit filing, compare that utility's reported loss percentage with Quarryhill's, and note which repair strategies the real utility says it is pursuing.