Project Grade 9 Math

Sundale Reservoir Supply and Demand: A 20-Year Modeling Project

A multi-session grade 9 project where teams model Sundale's reservoir supply and city demand over 20 years, then propose a conservation plan to close the gap.

Grade: Grade 9
Subject: Math
Material: Project
Time: 4 sessions, ~300 min total
Prep: Moderate prep
Materials: Graph paper, Calculators, Spreadsheet (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: Teams write and graph the two-variable demand equation D = 3.6 + 0.09y and the flat supply line in Milestone 2, labeling axes to find the gap year.

All materials for HSA-CED.A.2 →

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 Milestone 3 teams construct a linear population function and a 3 percent exponential function and compare their long-run behavior.

All materials for HSF-LE.A.2 →

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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 linear equations for a city's population and water demand.
Students will find the year demand outgrows a fixed reservoir supply.
Students will construct and compare linear and exponential growth models.

Vocabulary

Key words: supply, demand, yield, linear model, exponential model

Teacher overview

The fictional city of Sundale draws its water from one reservoir with a fixed yield. The city is growing, so demand rises each year while the supply stays flat. Over four sessions, teams model both supply and demand across 20 years, find the year demand outgrows supply, and propose a conservation plan to close the gap. Teams present a written proposal and a graph to the fictional Sundale Water Board.

Sundale Reservoir Supply and Demand: A 20-Year Modeling Project — Grade 9 Math

Name: ____________________________ Date: ______________

Project Brief

Driving question: Will Sundale's reservoir meet the city's water demand for the next 20 years, and if not, what conservation plan closes the gap?

Scenario: The fictional Sundale Water Board has asked student teams to study whether the city's one reservoir can keep up with growth, and to recommend a plan.

Constraints (all describe the fictional city of Sundale):

The reservoir yields a fixed 4 MGD.
The population starts at 40,000 and grows by 1,000 people per year.
Per-person water use is 90 gallons per person per day (gpcd). Per-person use in the US is commonly cited at 80 to 100 gpcd.
The planning horizon is 20 years.

Final deliverable: A written proposal and a labeled graph, presented to the fictional Sundale Water Board. The proposal recommends whether to set a conservation target, add new supply, or both, with the math that supports the choice.

Milestones

Session 1 (build the demand model): Teams write the population equation P = 40,000 + 1,000y, where y is years from now. They then show that demand is D = 3.6 + 0.09y in MGD, because 40,000 people times 90 gpcd is 3.6 MGD and each 1,000 new people add 0.09 MGD. Output: the labeled equations and a demand table for years 0, 5, 10, and 20.
Session 2 (find the gap year): Teams graph the demand line and the flat 4 MGD supply line on labeled axes, then solve 3.6 + 0.09y = 4 to find when demand passes supply. Output: a graph with the crossing point marked and the solved gap year (about year 4.4).
Session 3 (test a conservation plan): Teams model cutting per-person use to 80 gpcd, giving D = 3.2 + 0.08y, and find the new gap year. They also build an exponential population model P = 40,000 x 1.03^y for 3 percent yearly growth and compare it with the linear model. Output: a second graph and a short written comparison of linear versus exponential growth.
Session 4 (write and present): Teams write the proposal to the fictional Sundale Water Board, recommending a conservation target, new supply, or both, backed by their equations and graphs. Output: the written 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
Modeling accuracy	Equations or the demand table contain major errors	Equations are set up but the demand conversion or table has errors	Population and demand equations are correct and the table matches them	Equations and table are correct, and the team explains how each number was derived
Gap analysis and constraints	The graph or gap year is missing or wrong	The graph is drawn but the crossing point is not correctly found	The graph is labeled and the gap year is solved correctly against the 4 MGD supply	The gap year is solved correctly and the conservation case is graphed and compared clearly
Proposal and presentation	The proposal states no clear recommendation	The proposal gives a recommendation but little supporting math	The proposal recommends a plan supported by the team's equations and graphs	The proposal is well supported and anticipates a likely question from the Water Board

Differentiation

Support

Provide the population equation P = 40,000 + 1,000y already written, and a demand table with the year-0 value filled in, so teams can focus on finding the gap year. Give a pre-labeled graph grid with the axes scaled.

Extension

Ask teams to combine a conservation target with a small new supply, find the latest year Sundale could still meet demand, and defend the trade-offs in cost and feasibility to the Water Board.

ELL supports

Pre-teach "supply," "demand," "yield," and "gap" with a picture of a flat reservoir line and a rising demand line that crosses it. Provide sentence frames for the written proposal.