Math problem set Grade 6 Math

Foxwell Reservoir: Flow, Ratio, and Percent Problems

A grade 6 problem set on the fictional Foxwell Reservoir, converting acre-feet, cfs, and gpm and finding percent increase and a ratio split of released water.

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

Standards

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: Problems 1, 2, 3, 4, and 5 convert measurement units, find a percent increase, and split water in a 3 to 1 ratio, the measurement and percent work this standard covers.

All materials for 6.RP.A.3 →

6.RP.A.2 Common Core Math

Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship.

How this material aligns: Problems 7 and 8 have students use a per-minute release rate and a per-day loss rate to find totals, applying the unit-rate reasoning this standard defines.

All materials for 6.RP.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 convert reservoir storage and release rates between acre-feet, gallons, cfs, and gpm.
Students will find a percent increase and a part of a ratio for released reservoir water.

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: cfs, unit rate, percent

Teacher overview

Foxwell Reservoir is a fictional storage lake held back by Foxwell Dam. This problem set uses its water to practice unit conversion, percent increase, ratios, and unit rates at grade 6. The dam releases 50 cfs, and students convert that and other quantities using two standard water conversions. A common misconception to watch for: when finding a percent increase, students often divide the change by the new, larger amount instead of by the original amount, which gives too small an answer.

Foxwell Reservoir: Flow, Ratio, and Percent Problems — Grade 6 Math

Name: ____________________________ Date: ______________

Problems

Foxwell Reservoir is a fictional lake. Use these facts for every problem:

One acre-foot equals 325,851 gallons.
One cfs equals 448.8 gpm.
The lake now holds 300 acre-feet. Its maximum is 400 acre-feet.
The dam releases water at 50 cfs.

The lake holds 300 acre-feet. Using 325,851 gallons per acre-foot, how many gallons is that?
The dam releases water at 50 cfs. Using 448.8 gpm per cfs, how many gallons per minute is that?
The lake's 300 acre-feet is 75 percent of its maximum. What is the maximum in acre-feet?
Last month the lake rose from 240 to 300 acre-feet. What was the percent increase?
The dam splits its water between farms and the town in a 3 to 1 ratio. Over one season, including inflow from the river, the dam releases 800 acre-feet in all. How many acre-feet go to farms?
The power plant runs 18 hours each day. What percent of a full 24-hour day is that?
Use your gpm answer from problem 2. How many gallons does the dam release in one hour?
The lake loses 2 acre-feet each day to evaporation. How many acre-feet does it lose in a 30-day month?

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: 97,755,300 gallons.
300 acre-feet × 325,851 gallons per acre-foot = 97,755,300 gallons.
Answer: 22,440 gpm.
50 cfs × 448.8 gpm per cfs = 22,440 gpm.
Answer: 400 acre-feet.
300 is 75 percent of the maximum, so maximum = 300 ÷ 0.75 = 400 acre-feet.
Answer: 25 percent.
The change is 300 - 240 = 60 acre-feet. 60 ÷ 240 = 0.25, which is 25 percent. Note that dividing by the original 240, not the new 300, is what makes this correct.
Answer: 600 acre-feet.
A 3 to 1 ratio has 3 + 1 = 4 parts. 800 ÷ 4 = 200 acre-feet per part. Farms get 3 parts: 3 × 200 = 600 acre-feet.
Answer: 75 percent.
18 ÷ 24 = 0.75, which is 75 percent of the day.
Answer: 1,346,400 gallons.
From problem 2 the release is 22,440 gpm. In one hour: 22,440 × 60 = 1,346,400 gallons.
Answer: 60 acre-feet.
2 acre-feet per day × 30 days = 60 acre-feet lost in the month.

Differentiation

Support

Give students a small conversion card listing "1 acre-foot = 325,851 gallons" and "1 cfs = 448.8 gpm" so recall is not the barrier. For problem 4, show the setup "60 ÷ 240" already written, leaving students to finish and convert to a percent.

Extension

Ask students to imagine the dam raising its release from 50 cfs to 60 cfs. Have them find the new gpm and the percent increase in the release rate, then explain which quantity the percent describes.

ELL supports

Provide a labeled diagram of a dam and lake with arrows for water going in and water being released, and pair each unit (acre-foot, gallon, cfs, gpm) with a short definition in simple language before students begin.

Extensions

Have students compare their gallons-per-hour answer from problem 7 to how much water their own school might use in a day, using a figure your building manager can provide, to give the reservoir's output a familiar size.