Math problem set Grade 6 Science

Evaporation at Tarrant Reservoir: Depth, Volume, and Gallons

Ten grade 6 problems that turn a six-inch summer evaporation loss at Tarrant Reservoir into cubic feet, gallons, and a share of the reservoir's full pool.

Grade: Grade 6
Subject: Science
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculator

Standards

MS-ESS2-4 NGSS

Develop a model to describe the cycling of water through Earth's systems driven by energy from the sun and the force of gravity.

How this material aligns: Problem 10 asks students to trace the evaporated reservoir water through the water cycle and name the energy source that drives that change of state.

All materials for MS-ESS2-4 →

6.RP.A.3 Common Core Math

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations, including finding a percent of a quantity and converting measurement units.

How this material aligns: Students convert inches to feet and cubic feet to gallons in problems 2, 3, and 6, then find percents of a quantity in problems 7 and 9.

All materials for 6.RP.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 calculate the volume of water lost from a reservoir surface given an evaporation depth.
Students will convert a volume in cubic feet to gallons using a stated conversion factor.
Students will express an evaporation loss as a percent of a reservoir's full storage.

Vocabulary

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: surface area, cubic foot, full pool, conversion factor

Teacher overview

Tarrant Reservoir serves the town of Tarrant Flats, and in a hot July the lake loses several inches of depth to the air without a single gallon leaving through a pipe. These problems build one arc, moving from the lake surface area to the volume evaporated, then to gallons, and finally to the share of the full pool that disappears in two summer months. The misconception this set is designed to correct is that a deep reservoir evaporates more than a shallow one. Students commonly reach for the depth of the lake when the calculation actually depends on surface area and the depth of water lost from the top, which is why problem 1 establishes the surface first.

Evaporation at Tarrant Reservoir: Depth, Volume, and Gallons — Grade 6 Science

Name: ____________________________ Date: ______________

Problems

Tarrant Reservoir has a rectangular surface that measures 3,000 feet long by 1,200 feet wide. One cubic foot of water holds 7.48 gallons. The town of Tarrant Flats delivers 220,000 gallons of water to homes each day. When the reservoir is at full pool it holds 900,000,000 gallons.

The reservoir surface is 3,000 feet long and 1,200 feet wide. What is the surface area in square feet?
During July the reservoir loses 6 inches of depth to evaporation. Six inches is 0.5 feet. Using the surface area of 3,600,000 square feet, what volume of water is lost in cubic feet?
One cubic foot holds 7.48 gallons. Change the 1,800,000 cubic feet lost in July into gallons.
Treat July as a 30-day month. If 13,464,000 gallons evaporate over those 30 days, how many gallons evaporate on an average day?
The town of Tarrant Flats delivers 220,000 gallons to homes each day. Compare that with the 448,800 gallons lost each day to evaporation. How many times the town's daily delivery is the daily evaporation loss? Round to the nearest tenth.
In September the reservoir loses only 4.5 inches of depth. Using the same surface area of 3,600,000 square feet and the same factor of 7.48 gallons per cubic foot, how many gallons evaporate in September?
July lost 6 inches of depth and September lost 4.5 inches. By what percent did the depth lost decrease from July to September?
July lost 13,464,000 gallons and September lost 10,098,000 gallons. What is the total lost over the two months?
At full pool the reservoir holds 900,000,000 gallons. What percent of that full pool is the two-month evaporation total of 23,562,000 gallons? Round to the nearest tenth of a percent.
Evaporated water does not vanish. Describe where the water from Tarrant Reservoir goes after it evaporates, and name the energy source that drives the change from liquid to vapor.

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: 3,600,000 square feet.
Multiply length by width: 3,000 x 1,200 = 3,600,000 square feet.
Answer: 1,800,000 cubic feet.
Six inches is half of a foot, so the depth lost is 0.5 feet. Multiply the surface area by that depth: 3,600,000 x 0.5 = 1,800,000 cubic feet.
Answer: 13,464,000 gallons.
Multiply cubic feet by the conversion factor: 1,800,000 x 7.48. Break it up as 1,800,000 x 7 = 12,600,000 and 1,800,000 x 0.48 = 864,000, then add to get 13,464,000 gallons.
Answer: 448,800 gallons per day.
Divide the month total by the number of days: 13,464,000 divided by 30 is 448,800 gallons per day. Check by multiplying, since 448,800 x 30 = 13,464,000.
Answer: 2.0 times.
Divide the daily evaporation by the daily delivery: 448,800 divided by 220,000 is 2.04. Rounded to the nearest tenth that is 2.0 times as much.
Answer: 10,098,000 gallons.
Four and a half inches is 0.375 feet, since 4.5 divided by 12 is 0.375. Multiply by the surface area: 3,600,000 x 0.375 = 1,350,000 cubic feet. Then multiply by the conversion factor: 1,350,000 x 7.48 = 10,098,000 gallons.
Answer: 25 percent.
The depth lost fell by 6 - 4.5 = 1.5 inches. Divide that decrease by the July depth, so 1.5 divided by 6 gives 0.25, which is 25 percent.
Answer: 23,562,000 gallons.
Add the two months: 13,464,000 + 10,098,000 = 23,562,000 gallons.
Answer: 2.6 percent.
Divide the two-month loss by the full pool: 23,562,000 divided by 900,000,000 gives 0.02618. Multiply by 100 to get 2.618, which rounds to 2.6 percent.
Answer: It becomes water vapor in the air, and energy from the sun drives the change.
Look for two ideas: the liquid water changes to vapor and rises into the atmosphere, and sunlight supplies the energy for that change. Strong answers may also close the loop by noting that the vapor later condenses and falls as precipitation somewhere else.

Differentiation

Support

Give students a conversion ladder showing inches to feet on one rung and cubic feet to gallons on the next, with problem 2 already worked as an example. Allow the surface area from problem 1 to be provided directly for students who stall, so the first step does not block the rest of the problem sequence.

Extension

Ask students to calculate how many inches of depth the town of Tarrant Flats would need to save to offset one full month of home delivery, then explain in writing whether a floating shade cover over one quarter of the surface could reach that target.

ELL supports

Pre-teach "evaporation," "surface area," and "full pool" with a labeled side view of the reservoir showing the surface, the depth lost from the top, and the full pool line. Provide a filled-in unit chart pairing each quantity in the Tarrant Flats scenario with its unit, so students can check that their answers carry square feet, cubic feet, or gallons as appropriate.