Project Grade 12 Math

Dorwyn Water District: A 20-Year Drought Supply Plan

A grade 12 project where teams forecast a fictional city's water demand with an exponential model and design a supply portfolio that closes the drought gap on budget.

Grade: Grade 12
Subject: Math
Material: Project
Time: 5 sessions, ~300 min total
Prep: Moderate prep
Materials: Calculators, Spreadsheet or graphing tool, Printed option-and-cost sheet, Presentation supplies

Standards

HSF-LE.A.2 Common Core Math

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs.

How this material aligns: In Session 1 teams construct the exponential population function and use it to project 20-year demand, building an exponential model from a growth rate and starting value exactly as this standard requires.

All materials for HSF-LE.A.2 →

HSA-CED.A.3 Common Core Math

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

How this material aligns: In Sessions 3 and 4 teams represent the budget and gap-closing requirements as constraints and mark which portfolio combinations are viable, the viable-versus-non-viable interpretation this standard names.

All materials for HSA-CED.A.3 →

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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 build an exponential model of population growth and project future water demand.
Students will find the drought-year supply-demand gap in MGD.
Students will design a supply-and-conservation portfolio that closes the gap within a fixed budget.

Vocabulary

Key words: exponential growth, per-capita demand, supply-demand gap, portfolio, constraint, budget cap

Teacher overview

The fictional city of Dorwyn is growing, and its reservoir shrinks in dry years, so its water district must plan two decades ahead. Over five sessions, teams forecast Dorwyn's demand with an exponential population model, measure the gap between drought-year supply and future demand, and assemble a portfolio of conservation and new-supply options that closes the gap without breaking a fixed budget. The final deliverable is a written 20-year supply plan and a short presentation to a fictional water district board.

Dorwyn Water District: A 20-Year Drought Supply Plan — Grade 12 Math

Name: ____________________________ Date: ______________

Project Brief

Driving question: How can Dorwyn keep its water supply ahead of demand through 20 years of growth and drought, without spending beyond its capital budget?

Scenario: The board of the fictional Dorwyn Water District has asked each team to prepare a 20-year supply plan. Dorwyn's current population is 40,000, growing about 2 percent per year. Average demand runs about 90 gallons per person per day. The district's normal reliable supply is 4.5 MGD, but in a drought the reservoir-based portion drops, cutting reliable supply by 30 percent.

Constraints:

The plan must keep supply at or above projected demand in a drought year 20 years out.
Total capital spending must stay at or under a $25 million budget cap (a figure set for this project).
Teams choose from this fictional option-and-cost menu:
- Conservation program: cuts per-capita demand by 10 percent; costs $2 million.
- Recycled-water reuse for irrigation: adds 1.5 MGD of reliable supply; costs $12 million.
- New well field: adds 1.0 MGD normally, but only 0.8 MGD in a drought; costs $6 million.
- Brackish desalination: adds 2.0 MGD of drought-reliable supply; costs $20 million.
- Leak-reduction program: recovers 0.4 MGD; costs $3 million.

Final deliverable: A written 20-year supply plan showing the demand forecast, the drought-year gap, the chosen portfolio with its total cost, and the math proving supply meets demand within budget, plus a 5-minute presentation to the board.

Milestones

Session 1 — Forecast demand: Teams write the exponential population function P(t) = 40,000 × 1.02^t and use it to project Dorwyn's population and average daily demand now and in 20 years. Output: a demand table and the function, with year-20 demand stated in MGD.
Session 2 — Inventory supply and size the gap: Teams compute the drought-year reliable supply by applying the 30 percent reduction, then subtract it from the year-20 demand to find the supply-demand gap in MGD. Output: a one-page gap analysis naming the gap the plan must close.
Session 3 — Screen options against constraints: Teams cost each option and model how it changes demand or supply, then test several combinations against both the gap and the $25 million budget cap, marking each combination viable or non-viable. Output: a constraint table with at least four combinations judged against both limits.
Session 4 — Choose and justify a portfolio: Teams select one portfolio that closes the gap within budget, then draft the written plan showing the supply-meets-demand math and the total cost. Output: a complete draft plan with the chosen portfolio.
Session 5 — Present to the board: Teams present the plan to classmates role-playing the fictional Dorwyn Water District Board, who ask one question each about cost or reliability. Output: the final written plan and the delivered 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
Demand forecast (exponential model)	No working exponential model; demand is guessed or held flat	Model is set up but the growth factor or projection is misapplied	Correct P(t) = 40,000 × 1.02^t used to project year-20 demand in MGD	Correct model, plus demand shown for both normal and drought conditions with clear units throughout
Gap analysis (quantities and units)	Gap is not quantified	Gap is attempted but supply or demand carries wrong units or the 30 percent cut is omitted	Drought-year gap is computed correctly in MGD from supply and demand	Gap computed correctly and sensitivity to a different growth rate or per-capita figure is briefly examined
Portfolio meets constraints	Portfolio ignores the gap or the budget	Portfolio meets one of the two limits but not both	Portfolio closes the gap and stays at or under the $25 million cap, shown with totals	Portfolio meets both limits and the team explains a tradeoff it made among competing options
Presentation and justification	Plan is incomplete or hard to follow	Plan states a choice but the reasoning is thin	Plan clearly justifies the portfolio against gap and budget for the board	Plan justifies the choice and anticipates a board question about reliability or cost

Differentiation

Support

Provide the year-20 population already computed so teams can move straight to demand and the gap, and give a worked example of one option's effect on supply. Supply a spreadsheet template with the option-and-cost menu pre-entered so teams focus on the combinations rather than data entry.

Extension

Ask teams to test how their portfolio holds up if growth runs at three percent per year instead of two, recomputing the year-20 demand and stating whether their plan still closes the gap within budget. Have them recommend one adjustment that would make the plan more drought-resilient without raising total cost.

ELL supports

Pre-teach "demand," "supply," "gap," "portfolio," and "budget cap" with a simple picture of a supply bar needing to reach a demand line. Provide sentence frames for the written plan, such as "Our forecast shows demand of ___ million gallons per day, and our portfolio adds ___ to close the gap for ___ dollars."