Project Grade 9 Math

Marrowfield's Water Loss: A Non-Revenue Water Reduction Project

A grade 9 project where teams audit a fictional utility's water loss, model savings with linear equations, and propose a repair plan within a fixed budget.

Grade: Grade 9
Subject: Math
Material: Project
Time: 4 sessions, ~240 min total
Prep: Moderate prep
Materials: Printed water-audit data sheet, Calculators, Grid paper or graphing tool, Spreadsheet access (optional)

Standards

HSA-CED.A.2 Common Core Math

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

How this material aligns: In Milestone 3 teams write and graph an equation relating cumulative water and dollar savings to the options funded, representing a relationship between two quantities with labeled, scaled axes.

All materials for HSA-CED.A.2 →

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Milestones 1 and 2 have teams carry MGD, gallons, and dollars through a multi-step water-audit and cost-per-MGD calculation, choosing and interpreting units consistently.

All materials for HSN-Q.A.1 →

Download Word file

This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will calculate a utility's non-revenue water volume, percent, and annual cost.
Students will model cumulative savings with a linear equation and recommend a plan within a 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: cost per MGD, budget constraint

Teacher overview

Every water utility produces more water than it sells. The gap, called non-revenue water, comes from leaks, from meters that under-count, and from water used but never billed. This project puts teams in the role of analysts for a fictional utility, asking them to measure that loss, price it, and propose a plan to cut it within a fixed budget. The final product is a written proposal and a short presentation to a fictional city council, backed by a simple linear model of savings.

Marrowfield's Water Loss: A Non-Revenue Water Reduction Project — Grade 9 Math

Name: ____________________________ Date: ______________

Project Brief

Driving question: How can Marrowfield's water utility cut its non-revenue water and recover revenue while spending no more than its repair budget?

Scenario: Marrowfield Municipal Water (a fictional utility) produces more water than it bills for, and the city council has asked your team to study the loss and recommend a one-year plan. You will present a written proposal and a short talk to the council.

Data provided (all figures are set for this fictional project):

Water produced: 5.0 MGD (million gallons per day).
Water billed to customers: 4.1 MGD.
Cost to produce and treat water: $2.50 per 1,000 gallons.
Repair budget for the year: $250,000.
Option A, leak survey and repair: costs $40,000 and recovers about 0.3 MGD.
Option B, replacing 1,000 old meters: costs $180,000 and recovers about 0.15 MGD of billed water.
Option C, pressure management: costs $30,000 and recovers about 0.05 MGD.
For this project, value all recovered water at the $2.50 production cost; real utilities value water recovered by meter replacement at the higher retail rate.

Constraints:

Your plan must spend $250,000 or less for the year.
Your plan must recover at least 0.4 MGD of the lost water.
Every recommended option must be justified with the water-audit math, not opinion.

Final deliverable: A one-page written proposal to the fictional city council and a short team presentation. The proposal must state the non-revenue water volume and percent, its annual cost, the options chosen with their costs and recovery, and a labeled graph of cumulative savings.

Milestones

Session 1, run the water audit: Using the produced and billed figures, teams find the non-revenue water in MGD, as a percent of production, and its cost per year (volume x days x the cost per 1,000 gallons). Output: a completed water-audit sheet with the yearly dollar loss.
Session 2, compare the options: Teams find the cost per MGD recovered for Options A, B, and C, and rank them from most to least efficient. Output: a comparison table with cost, recovery, and cost per MGD for each option.
Session 3, build the plan and model it: Teams pick a mix of options that meets both the budget and the 0.4 MGD recovery goal. They write a linear equation for cumulative dollars saved as a function of MGD recovered, then graph it with labeled, scaled axes. Output: a budget table and a labeled savings graph.
Session 4, write and present: Teams write the one-page proposal and present it to the class acting as the fictional council. Output: the finished proposal 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-audit math	Non-revenue water volume or percent is missing or wrong	Volume and percent are found but the yearly cost is incomplete	Volume, percent, and yearly cost are all correct and clearly shown	All audit figures are correct and the team explains what each number means for the utility
Budget constraint	Plan exceeds the budget or the recovery goal is not met	Plan meets one constraint but not both, or costs are not itemized	Plan meets both the budget and the 0.4 MGD goal with itemized costs	Plan meets both constraints, is itemized, and explains a tradeoff the team made among options
Savings model and graph	No equation, or the graph is missing or unlabeled	An equation is given but the graph lacks labels or a sensible scale	A correct linear equation is graphed with labeled, scaled axes	The model is correct, well labeled, and used to compare at least two possible plans
Proposal and presentation	Proposal is incomplete or hard to follow	Proposal covers the plan but reasoning is thin	Proposal clearly explains the audit, the plan, and the math behind it	Proposal is clear and anticipates a likely question from the council

Differentiation

Support

Provide the Session 1 audit partly worked: give teams the non-revenue water volume (produced minus billed) already found, so they focus on the percent and the yearly cost. Offer a template table for the Session 2 comparison with the column headings filled in.

Extension

Ask teams to find how many years of recovered-water value it takes for Option B's meter replacement to pay back its higher cost, and to fold that payback reasoning into their recommendation to the council.

ELL supports

Pre-teach "non-revenue water," "audit," and "budget" with a simple diagram of water produced, water billed, and the gap between them. Provide sentence frames for the proposal, such as "Our plan spends ___ and recovers ___ MGD, which meets the goal because ___."

Extensions

Invite a staff member from a local water utility to review the class proposals, or share a public water-loss audit summary from a nearby system so teams can compare their fictional Marrowfield figures with how a real utility reports non-revenue water.