Project Grade 11 Math

Amberly Landing's Drought Plan for Corvie Reservoir

A five-session grade 11 project building a monthly reservoir balance for a fictional district, then designing drought stages that hold a protected level.

Grade: Grade 11
Subject: Math
Material: Project
Time: 5 sessions, ~275 min total
Prep: Moderate prep
Materials: Spreadsheet software or graph paper, Calculator, Printed inflow and demand tables, Presentation slides or a poster

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: The session 1 model expresses end-of-month storage as an equation in inflow, demand, and evaporation, and in session 2 students graph storage against month with both quantities labeled and scaled.

All materials for HSA-CED.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: Sessions 3 and 4 treat the protected storage level and the purchased-water budget as constraints, and students must show their proposed stages produce a viable plan under both at once.

All materials for HSA-CED.A.3 →

HSF-IF.B.4 Common Core Math

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

How this material aligns: The session 2 graph requires students to identify the minimum of the storage function and the three-month window over which it decreases fastest, reading both against the protected level drawn as a horizontal line.

All materials for HSF-IF.B.4 →

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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 a month-by-month reservoir balance from inflow, demand, and evaporation data.
Students will design drought stages with storage triggers and demand reductions that keep storage above a protected level.
Students will evaluate a purchased-water option against a stated budget limit and defend the resulting plan to a board.

Vocabulary

Acre-foot: The amount of water it takes to cover one acre of land, about the size of a football field, one foot deep. Western states use acre-feet to measure large amounts of water.

Also: reservoir storage, drought stage, trigger level, demand reduction

Teacher overview

A drought plan is a set of rules written before the drought arrives, stating what storage level triggers which restrictions, so a utility is not improvising while a reservoir falls. In this project students act as staff analysts for the fictional Amberly Landing Water District, build a twelve-month storage model for the fictional Corvie Reservoir under a second consecutive dry year, and find that the reservoir crosses its protected level in late summer if nothing changes. They then design three drought stages and, if they choose, buy water through an interconnection within a fixed budget, and defend the resulting plan to a panel acting as the district board. The final deliverable is a written proposal of at most two pages, a storage graph, a stage table, and a six-minute presentation.

Amberly Landing's Drought Plan for Corvie Reservoir — Grade 11 Math

Name: ____________________________ Date: ______________

Project Brief

Driving question. What drought rules should Amberly Landing adopt so that Corvie Reservoir never falls below its protected level during a second dry year?

The client. You are staff analysts reporting to the board of the fictional Amberly Landing Water District. The board has asked for a plan it can adopt at its October meeting, before the water year begins.

The situation. Amberly Landing has just finished one dry year and starts this one with the reservoir about half full. The district's own forecast for the coming year is the driest sequence in its records. All of the following values are part of this fictional scenario.

Corvie Reservoir holds 4,200 acre-feet of usable storage.
Storage on October 1 is 2,100 acre-feet.
Storage must never fall below the protected level of 900 acre-feet, which covers the dead pool and a required release to the creek below the dam.
Average district demand is 1.9 MGD across the year.
The reservoir surface covers 210 acres.
Evaporation removes 0.32 ft of depth per month from June through September and 0.08 ft per month in each of the other eight months.
The district can buy water through an interconnection with a neighboring utility at $1,450 per acre-foot, and the board will commit at most $600,000 to those purchases.
Conversions: 1 acre-foot = 325,851 gallons; a year is 365 days.

Monthly inflow forecast, in acre-feet: October 40, November 70, December 110, January 150, February 140, March 160, April 95, May 55, June 25, July 15, August 12, September 28.

Monthly demand factors, to be multiplied by one-twelfth of the annual demand: October 0.85, November 0.75, December 0.70, January 0.70, February 0.70, March 0.80, April 0.95, May 1.15, June 1.35, July 1.50, August 1.45, September 1.10.

Rules your plan must follow.

Each drought stage names a storage trigger in acre-feet and a percent reduction in demand that takes effect while storage sits below that trigger.
Your plan must define exactly three stages, and the reductions must increase from stage to stage.
Storage may never fall below 900 acre-feet in any month of the model.
Purchased water counts against the budget cap, and your cost table must show the total.
A reduction larger than 35 percent in any month must be justified in writing, since restrictions that deep affect health and safety uses.

What you turn in. A completed twelve-month model in a spreadsheet or a table, a graph of end-of-month storage, a stage table, a cost table comparing at least two plans, a written proposal of at most two pages addressed to the board, and a six-minute presentation.

Milestones

Session 1, the baseline model. Compute annual demand in acre-feet from the 1.9 MGD average, distribute it across the months using the demand factors, convert the monthly evaporation depths into acre-feet, and build a twelve-row table with columns for inflow, demand, evaporation, net change, and end-of-month storage. The checkable output is a completed baseline table with no drought action, plus a written statement of the first month in which storage falls below the protected level.
Session 2, the graph and the diagnosis. Plot end-of-month storage against month with a labeled and scaled vertical axis, mark the protected level as a horizontal line, and identify the minimum storage and the steepest three-month decline. The checkable output is the labeled graph plus a one-paragraph diagnosis stating the shortfall in acre-feet and in gallons.
Session 3, the stage design. Choose the three triggers and the three reduction percentages, then rerun the model with the stages applied month by month, remembering that a reduction changes demand only in the months when the trigger is active. The checkable output is a revised twelve-row table in which storage stays at or above 900 acre-feet in every month, together with a short note explaining why each trigger sits where it does.
Session 4, cost and alternatives. Price any purchased water against the budget cap, then build a second plan that shifts the balance between restrictions and purchases, and compare the two in a cost table. The checkable output is the cost table plus a draft of the two-page proposal with a stated recommendation.
Session 5, the board presentation. Present for six minutes to a panel acting as the district board, showing the graph, the stage table, and the cost comparison, and answer at least two questions from the panel. The checkable output is the delivered presentation and the final proposal.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Rubric

Score each criterion at one of the four levels. The criteria map directly to the constraints in the brief, so a plan that violates a stated constraint cannot score above Developing on the second criterion.

Criterion	Exemplary	Proficient	Developing	Beginning
Model accuracy	Every month's inflow, demand, evaporation, and storage is computed correctly and units are labeled throughout; the annual demand conversion is shown in full.	The model is correct in structure with at most two arithmetic slips that do not change the conclusion; units are labeled in most columns.	The table is complete but a systematic error, such as omitting evaporation or misplacing the demand factors, shifts several months.	The table is incomplete, or storage is not carried forward from one month to the next.
Constraints met	Storage stays at or above the protected level in every month, purchases stay within the budget cap, and both are demonstrated in the table rather than asserted.	Both constraints are met and shown, though the demonstration requires the reader to recompute one figure.	One constraint is met and the other is missed, or the plan meets both only by an unstated assumption.	Neither constraint is met, or the plan does not address them.
Stage design and justification	Three increasing reductions with triggers placed at defensible storage levels, each justified by what the model shows about the month it activates.	Three increasing reductions with triggers that work, justified in general terms rather than from the model.	Stages are present but the reductions do not increase, or the triggers are chosen without reference to the model.	Fewer than three stages, or stages with no triggers attached.
Communication to the board	Proposal and presentation state the recommendation first, support it with the graph and the cost table, name the trade-off the board is accepting, and stay within the length and time limits.	The recommendation is clear and supported, with minor lapses in organization or a small overrun of the limits.	The material is presented but the recommendation must be inferred, or the visuals are not explained.	The presentation reports numbers without a recommendation, or key deliverables are missing.

Scoring the whole project: award 4 points for Exemplary, 3 for Proficient, 2 for Developing, and 1 for Beginning on each criterion, for 16 points total. Accept any plan that satisfies both constraints; there is no single correct set of triggers, and two groups with different reduction schedules can both earn Exemplary if each shows its plan holding the protected level.

Differentiation

Support

Give these students the annual demand already converted to acre-feet and the twelve monthly evaporation figures already computed, so session 1 begins at the table rather than at the conversions. Provide a spreadsheet with the column headings and the storage formula already entered in the first row, and allow the group to design two drought stages rather than three, scoring the stage-design criterion against two stages.

Extension

Ask students to add a third dry year to the model, carrying the ending storage forward as the new starting storage, and to state whether their stages still hold the protected level or whether a permanent supply project becomes unavoidable. A second extension is to add a rate impact, estimating what the demand reductions do to district revenue and whether the proposal should include a drought surcharge.

ELL supports

Pre-teach "storage," "inflow," "evaporation," "trigger," and "restriction" with a labeled cross-section of a reservoir showing full, protected, and empty levels. Provide a bilingual column-heading card for the model table and a proposal outline with headed sections, so the writing task is organized before the drafting begins. Allow the presentation to be delivered from a script the group has rehearsed.

Extensions

Have students find the drought plan their own water provider or state agency has published, identify how many stages it defines and what triggers each one, and compare those triggers against the ones their group chose. Many real plans use a percentage of full storage rather than an absolute volume, and asking students to convert their own triggers into that form is a short but genuine modeling exercise.