Math problem set Grade 7 Science

Corbray Reservoir in a Dry Year: Acre-Feet and Days of Supply

Ten problems in which students convert acre-feet to gallons, compute days of supply for a fictional town, and test how growth and evaporation shorten it.

Grade: Grade 7
Subject: Science
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculator

Standards

MS-ESS3-4 NGSS

Construct an argument supported by evidence for how increases in human population and per-capita consumption of natural resources impact Earth's systems.

How this material aligns: Problems 6, 7, and 10 have students use their own computed days of supply to argue how added population at the same per-person use draws the reservoir down faster.

All materials for MS-ESS3-4 →

7.RP.A.3 Common Core Math

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

How this material aligns: Problem 1 finds 40 percent of the reservoir's capacity, and problem 5 applies a 20 percent reduction to the daily use from problem 3 before recomputing the days of supply.

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7.EE.B.3 Common Core Math

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically, and assess the reasonableness of answers using mental computation and estimation strategies.

How this material aligns: Problems 4, 8, and 9 are multi-step problems with large rational numbers, combining the acre-foot conversion from problem 2 with daily use and with an evaporation loss computed from surface area and depth.

All materials for 7.EE.B.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 convert acre-feet of reservoir storage into gallons.
Students will compute days of supply from a stored volume and a daily use.
Students will explain how population growth and evaporation shorten a reservoir's supply.

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.
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.
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.

Also: days of supply, per-person use

Teacher overview

Western utilities measure stored water in acre-feet, where one acre-foot equals 325,851 gallons, while household use is counted in gallons per day. This set follows the fictional town of Corbray through a dry summer, starting with a reservoir at 40 percent of capacity and asking how long that water lasts under several conditions. Per-person use at home in the United States is commonly cited at 80 to 100 gallons per day, and Corbray sits at the low end of that range. Teaching note: students often divide acre-feet directly by a daily use written in gallons, which makes the days of supply come out hundreds of thousands of times too small. Requiring the conversion in problem 2 before any division catches that error early.

Corbray Reservoir in a Dry Year: Acre-Feet and Days of Supply — Grade 7 Science

Name: ____________________________ Date: ______________

Problems

The town of Corbray draws its water from one reservoir. The reservoir holds 2,400 acre-feet when full, and one acre-foot equals 325,851 gallons. Corbray has 12,000 residents, and each uses about 80 gallons per day.

After a dry winter, the reservoir sits at 40 percent of capacity. How many acre-feet of water does it hold?
Convert your answer from problem 1 into gallons.
How many gallons does the whole town use in one day?
Ignoring evaporation and any inflow, how many days would the water in problem 2 last at the daily use in problem 3? Round to the nearest whole day.
The town council asks residents to cut use by 20 percent from the amount in problem 3. At that reduced daily use, how many days would the water in problem 2 last? Round to the nearest whole day.
Suppose 1,000 new residents move to Corbray, and every resident still uses 80 gallons per day. What is the town's new daily use?
At the daily use from problem 6, how many days would the water in problem 2 last? Round to the nearest whole day.
The reservoir's surface covers 60 acres, and in the summer heat it loses 0.2 inch of depth to evaporation each day. How many gallons does evaporation remove each day? Start by converting 0.2 inch to feet.
Combine the original daily use from problem 3 with the evaporation loss from problem 8. How many days would the water in problem 2 last then? Round to the nearest whole day.
Write a claim about how population growth and per-person use affect this reservoir. Support it with two numbers you calculated in this set.

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: 960 acre-feet.
40 percent of 2,400 acre-feet is 0.40 times 2,400, which equals 960 acre-feet.
Answer: 312,816,960 gallons.
960 acre-feet times 325,851 gallons per acre-foot equals 312,816,960 gallons.
Answer: 960,000 gallons per day.
12,000 residents times 80 gallons per person per day equals 960,000 gallons per day.
Answer: 326 days.
312,816,960 gallons divided by 960,000 gallons per day equals 325.85 days, which rounds to 326 days.
Answer: 407 days.
A 20 percent cut leaves 80 percent of 960,000, which is 768,000 gallons per day. Then 312,816,960 divided by 768,000 equals 407.3 days, which rounds to 407 days.
Answer: 1,040,000 gallons per day.
12,000 plus 1,000 equals 13,000 residents, and 13,000 times 80 gallons per day equals 1,040,000 gallons per day.
Answer: 301 days.
312,816,960 divided by 1,040,000 equals 300.8 days, which rounds to 301 days.
Answer: 325,851 gallons per day.
0.2 inch divided by 12 inches per foot equals 0.0167 foot. Then 60 acres times 0.0167 foot equals 1 acre-foot per day, and 1 acre-foot equals 325,851 gallons.
Answer: 243 days.
The combined daily loss is 960,000 plus 325,851, which equals 1,285,851 gallons per day. Then 312,816,960 divided by 1,285,851 equals 243.3 days, which rounds to 243 days.
Answer: Accept any claim supported by two computed values.
A strong claim states that adding residents shortens the supply even when nobody changes personal habits, citing the drop from 326 days to 301 days when 1,000 people arrive. A second strong claim states that cutting per-person use stretches the supply, citing the rise from 326 days to 407 days after a 20 percent reduction.

Differentiation

Support

Give these students a conversion card showing that one acre-foot equals 325,851 gallons, with problem 1 worked out for the town of Corbray. Let them use the printed value of 312,816,960 gallons in later problems so an early arithmetic slip does not spread through the set.

Extension

Ask students to find the per-person daily use that would stretch the Corbray reservoir to a full year of supply at the original population, then compare that figure with the 80 to 100 gallons per day commonly cited for home use in the United States.

ELL supports

Provide a labeled picture of one acre-foot as a field one acre in area covered by one foot of water, alongside the gallons figure. Give a sentence frame for problem 10: "When the population grows from ___ to ___, the days of supply change from ___ to ___."

Extensions

Students can look up the current storage in a real reservoir published by a state water agency, express it as a percent of capacity, and repeat the Corbray days-of-supply calculation using their own community's population.