Project Grade 12 Math
Fenwick County Water Utility: A Capital Plan and Rate Proposal Project
A grade 12 multi-session project where student teams build a capital improvement and rate plan for a fictional utility, constrained by an affordability limit.
Objectives
- Students will calculate a per-household monthly surcharge needed to fund a stated capital project over different financing timelines.
- Students will apply a real-world affordability benchmark and a board-adopted policy constraint to classify financing options as viable or non-viable.
- Students will design and present a rate-plan proposal that meets the stated financial and policy constraints to a fictional county water board.
Vocabulary
- Capital improvement plan
- A utility's long-term to-do list of big construction projects, such as replacing old pipes or building new tanks. It shows what will be built, when, and how it will be paid for.
Also: surcharge, affordability threshold, viable solution, financing timeline
Teacher overview
Fenwick County Water Utility (a fictional utility used for this project) serves 8,000 households through a distribution system old enough that engineers have identified $18 million in urgently needed pipe replacement. Nationally, EPA's needs assessment estimates $625 billion in drinking-water infrastructure investment is needed over the next 20 years, with distribution pipes accounting for about two-thirds of that total, so Fenwick County's situation mirrors a pattern playing out in utilities across the country. Student teams take on the role of the utility's rate-analysis staff, tasked with designing a financing and rate plan that pays for the pipe replacement without pushing the typical household's combined water and sewer bill past what the community can reasonably afford.
The final deliverable asks teams to meet two affordability limits at once. A widely used rule of thumb, built by adding two EPA benchmarks based on a community's median household income (2.5 percent for drinking water and 2 percent for wastewater), treats combined water and sewer costs above roughly 4.5 percent of household income as a high burden, although EPA has no single official cutoff. Fenwick County's own water board has additionally adopted a stricter internal policy: no financing plan may raise the average combined monthly bill above $90. Teams will discover that not every reasonable-looking financing timeline satisfies that board policy, even when it easily satisfies the broader 4.5 percent benchmark, which is the central modeling tension this project is built around.
Project Brief
Driving question: Fenwick County Water Utility (a fictional utility used for this project) needs $18 million for pipe replacement. How can the utility pay for this work while keeping the typical household's combined monthly bill at or below the county board's $90 policy ceiling?
Scenario: The Fenwick County water board has asked student rate-analysis teams to propose a financing plan. The utility serves 8,000 households. Its current typical combined monthly bill is $65. The service area's median household income is $52,000 per year.
Constraints:
- Capital need: $18,000,000 for pipe replacement. The utility will recover this cost through a monthly surcharge added to the current $65 bill.
- Financing timeline: the board will only consider whole-number timelines of 5, 10, or 20 years. Each timeline needs a different bond structure.
- Board policy ceiling: the combined monthly bill, the $65 base plus the new surcharge, must not exceed $90.
- Affordability reference point: teams must also calculate a second, broader ceiling. Use the $52,000 median income and the widely used 4.5 percent affordability benchmark to find this dollar-per-month reference point, then compare it to the board's stricter $90 ceiling.
Final deliverable: A one-page written proposal that recommends one financing timeline. The proposal must show the surcharge and combined bill for all three timelines, state which timelines are board-viable, and compare the recommended plan to the 4.5 percent reference point. Teams also build a short poster or chart to summarize their recommendation for the class presentation.
Milestones
Session 1 — Calculate the affordability reference point: Teams use the $52,000 median income and the 4.5 percent affordability benchmark to calculate the affordability ceiling in dollars per year and dollars per month. Teams also record the project's known facts: the $18,000,000 capital need, 8,000 households, the $65 current bill, and the board's $90 ceiling. Output: a constraint worksheet with the affordability ceiling and all known facts recorded.
Session 2 — Model three financing timelines: For each timeline (5, 10, and 20 years), teams calculate the monthly surcharge per household. They divide the capital need by the number of households, then by the number of months in the timeline. Teams add the surcharge to the $65 base bill to find the combined bill, then mark each timeline viable or non-viable against the $90 ceiling. Output: a comparison table showing the surcharge, combined bill, and viability call for each timeline.
Session 3 — Choose and justify a plan: Teams pick one board-viable timeline from Session 2. They write a short justification for their choice, weighing how fast the pipes get replaced against how low the monthly bill stays. Output: a one-page proposal stating the chosen timeline, the resulting bill, and the justification.
Session 4 — Present to the water board: Teams finish their poster or chart. They present their plan and calculations to the class, who role-play the Fenwick County water board. Each team answers at least one board question about its reasoning. Output: a finished poster or chart and a short 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 |
|---|---|---|---|---|
| Surcharge and bill calculations | Surcharge or combined-bill calculations contain errors for more than one timeline | Calculations are correct for at least two of the three timelines | Surcharge and combined-bill calculations are correct for all three financing timelines | Calculations are correct for all three timelines and are clearly organized so a reader can verify each step without asking |
| Constraint compliance | Proposal does not identify which timelines are viable or non-viable under the $90 board ceiling | Proposal identifies viability for most, but not all, timelines, or makes a viability error | Proposal correctly classifies all three timelines as viable or non-viable against the $90 ceiling | Proposal correctly classifies all three timelines and also compares the recommended plan against the calculated 4.5 percent affordability reference point |
| Use of real-world context | Proposal does not reference the 4.5 percent affordability benchmark or misstates it | Proposal mentions the 4.5 percent benchmark but does not calculate or apply the affordability ceiling correctly | Proposal correctly calculates and applies the 4.5 percent affordability benchmark as a reference point distinct from the board's policy ceiling | Proposal accurately explains why the board's $90 ceiling is a stricter, locally chosen standard than the broader 4.5 percent affordability benchmark |
| Presentation & proposal clarity | Presentation or written proposal is incomplete or difficult to follow | Presentation covers the recommendation but with limited reasoning | Presentation and proposal clearly explain the chosen plan and how it satisfies the board's constraint | Presentation and proposal clearly explain the plan, satisfy the constraint, and anticipate a likely question from the board |
Differentiation
Support (below grade level)
Provide the affordability-ceiling calculation from Session 1 already worked out, and give teams a partially completed comparison table for Session 2 with the formula for monthly surcharge already set up (capital need ÷ households ÷ months), so teams only need to substitute each timeline's number of months.
Extension (above grade level)
Ask teams to design a fourth financing option using a non-whole-number timeline (for example, 7.5 years) and calculate whether it produces a combined bill that falls strictly between two of the original three options, then explain what real-world factor (such as bond terms typically being sold in whole-year increments) might explain why the board restricted its consideration to whole-number timelines in the first place.
ELL supports
Pre-teach "capital need," "surcharge," and "viable" using a simple visual of a jar labeled with Fenwick's fictional $18,000,000 total being divided into smaller monthly pieces across many households. Provide a proposal template with sentence starters such as "We recommend the -year plan because the combined bill of $ stays ___ the board's $90 ceiling."
Extensions
Invite a local water utility's billing or finance staff member to review one or two teams' proposals, or share a real water/sewer rate study from a nearby utility (with names and figures the utility has already made public) for teams to compare against their own Fenwick County recommendation. Many utilities publish their rate studies or capital improvement plans online, and a short comparison discussion connects this project's fictional numbers to how a real utility actually communicates a rate increase to its board and customers.