Math problem set Grade 11 Science

Tamsin Reservoir Drawdown: A Drought Water-Budget Set

A grade 11 problem set on a fictional reservoir's drought drawdown, converting MGD to acre-feet and solving a linear storage equation for the days to an emergency level.

Grade: Grade 11
Subject: Science
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculator

Standards

HS-ESS3-3 NGSS

Create a computational simulation to illustrate the relationships among the management of natural resources, the sustainability of human populations, and biodiversity.

How this material aligns: Problems 2, 3, 7, and 8 build a simplified storage model from demand and evaporation, then run it to compare how long the supply lasts with and without a conservation order, the resource-management calculation this standard allows.

All materials for HS-ESS3-3 →

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: Problems 1, 5, and 6 carry the town's demand from MGD to gallons to acre-feet per day, the consistent multi-step unit conversion this standard requires for a water budget.

All materials for HSN-Q.A.1 →

HSA-CED.A.1 Common Core Math

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

How this material aligns: Problems 3, 4, and 7 create the linear storage equation S = 3,200 minus 15d and solve it for the number of days until the reservoir reaches its emergency level.

All materials for HSA-CED.A.1 →

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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 convert a daily water demand from MGD to acre-feet per day.
Students will build and solve a linear equation for reservoir storage over time.
Students will quantify how a demand reduction extends the time to an emergency level.

Vocabulary

Water budget: A water budget is a way of tracking all the water coming into an area, like rain and snowmelt, against all the water leaving it, like evaporation and streamflow. Scientists use water budgets to see whether a watershed or aquifer is gaining or losing water over time.
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.
Drawdown: Drawdown is how far the water level in a well drops when a pump pulls water out. The harder and longer you pump, the bigger the drawdown gets.
Evaporation: Evaporation happens when liquid water, often warmed by the sun, turns into an invisible gas called water vapor that rises into the air. It is how water leaves oceans, lakes, and puddles.

Also: consumptive demand

Teacher overview

During a drought a reservoir behaves like a bank account with no deposits: water leaves for demand and evaporation while little or nothing flows in, so the storage falls in a straight line that a linear equation can model. This set follows the fictional Tamsin Reservoir, which supplies the town of Wickmoor, as planners project how long the supply will last and how much a conservation order buys them. A common student error is to convert MGD to acre-feet per day with the wrong constant, or to leave evaporation out of the daily loss entirely; both make the reservoir look like it will last far longer than it will. Students first find the daily loss in consistent units, then build and solve the storage equation.

Tamsin Reservoir Drawdown: A Drought Water-Budget Set — Grade 11 Science

Name: ____________________________ Date: ______________

Problems

The town of Wickmoor is a fictional town whose only supply is Tamsin Reservoir. At the start of a drought the reservoir holds 3,200 acre-feet of usable water and receives essentially no inflow. The town draws 4.5 MGD, and evaporation removes another 1.2 acre-feet per day from the surface. Use 1 acre-foot = 325,851 gallons.

Convert the town's demand of 4.5 MGD to acre-feet per day.
Add the 1.2 acre-feet per day of evaporation to find the total daily loss from the reservoir, in acre-feet per day. Round to the nearest tenth.
Using your total daily loss rounded to 15.0 acre-feet per day, write an equation for the storage S, in acre-feet, remaining after d days.
The utility declares an emergency when storage falls to 800 acre-feet. Solve your equation for the number of days until that level is reached.
Convert the reservoir's starting 3,200 acre-feet of usable water to gallons.
Suppose the town cuts demand by 20 percent through restrictions. Find the new demand in acre-feet per day. Round to the nearest hundredth.
With the reduced demand and the same 1.2 acre-feet per day of evaporation, find the number of days it now takes to fall from 3,200 acre-feet to the 800-acre-foot emergency level.
How many extra days did the 20 percent restriction buy, compared with your answer to problem 4?
Explain why, as demand falls, evaporation becomes a larger share of the reservoir's daily loss.
The reservoir surface covers about 210 acres. Using the 1.2 acre-feet per day of evaporation, find the average depth of water lost from the surface each day, in inches.

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

Answer Key

Answer: 13.81 acre-feet/day.
4.5 MGD = 4,500,000 gallons per day; 4,500,000 divided by 325,851 = 13.81 acre-feet per day.
Answer: 15.0 acre-feet/day.
13.81 + 1.2 = 15.01, which rounds to 15.0 acre-feet per day.
Answer: S = 3,200 minus 15.0d.
Storage starts at 3,200 acre-feet and drops 15.0 acre-feet each day, so S = 3,200 - 15.0d.
Answer: 160 days.
3,200 - 15d = 800; 15d = 2,400; d = 2,400 / 15 = 160 days.
Answer: about 1.04 billion gallons.
3,200 acre-feet x 325,851 gallons per acre-foot = 1,042,723,200 gallons, about 1.04 billion gallons.
Answer: 11.05 acre-feet/day.
New demand = 4.5 x 0.80 = 3.6 MGD = 3,600,000 gallons per day; 3,600,000 / 325,851 = 11.05 acre-feet per day.
Answer: 196 days.
New daily loss = 11.05 + 1.2 = 12.25 acre-feet per day; the drop from 3,200 to 800 is 2,400 acre-feet; 2,400 / 12.25 = 195.9, about 196 days.
Answer: 36 days.
196 - 160 = 36 additional days gained by the restriction.
Answer: Evaporation is fixed while demand shrinks.
Evaporation stays near 1.2 acre-feet per day regardless of use, so when demand drops the same evaporation makes up a larger fraction of the smaller total daily loss.
Answer: about 0.07 in/day.
1.2 acre-feet spread over 210 acres = 0.00571 feet of depth; 0.00571 x 12 = 0.069, about 0.07 inches per day.

Differentiation

Support

Provide the MGD-to-acre-feet conversion worked once as a labeled example, and give students the rounded daily loss (15.0 acre-feet per day) so they can focus on building and solving the equation in problems 3 and 4. Allow calculators throughout.

Extension

Ask students to write and solve a single equation for the day on which the restricted-demand reservoir (problem 7) and the unrestricted reservoir would differ in storage by 500 acre-feet, given they start at the same level.

ELL supports

Pre-teach "storage," "demand," "evaporation," and "drawdown" with a labeled picture of a reservoir showing water leaving for the town and rising off the surface as vapor. Provide the equation frame "S = ___ minus ___ times d" for problem 3.