Math problem set Grade 6 Math

Cobblemere's Settling Basin: Volume with a Fractional Depth

A grade 6 problem set in which students find the volume of two rectangular settling basins with fractional depths and convert cubic feet to gallons.

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

Standards

6.G.A.2 Common Core Math

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

How this material aligns: Problems 2 and 6 apply the formula for the volume of a right rectangular prism to basins whose depths are 6 and one quarter feet and 7 and one half feet.

All materials for 6.G.A.2 →

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 3 through 5 convert cubic feet to gallons and gallons per hour to gallons per minute, and problem 9 finds one basin's volume as a percent of the other.

All materials for 6.RP.A.3 →

Download Word file

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 find the volume of a rectangular basin with a fractional depth.
Students will convert a volume in cubic feet to gallons.
Students will compare two basin volumes using a ratio and a percent.

Vocabulary

Key words: volume, rectangular prism, settling basin, cubic foot

Teacher overview

After chemicals are mixed into raw water at a drinking water plant, the water moves slowly through a long rectangular basin so that heavy clumps of dirt can settle to the bottom. This problem set uses two such basins at the plant serving the fictional town of Cobblemere, one of them 6 and one quarter feet deep and the other 7 and one half feet deep. Plant designers expect water to spend roughly 2 to 4 hours in a settling basin, and problem 4 checks the Cobblemere basin against that range. The misconception this set targets is treating the fraction in a depth of 6 and one quarter feet as something to add on after multiplying, rather than as part of the number that gets multiplied.

Cobblemere's Settling Basin: Volume with a Fractional Depth — Grade 6 Math

Name: ____________________________ Date: ______________

Problems

The town of Cobblemere's water plant has two rectangular settling basins. Basin A is 45 feet long, 16 feet wide, and 6 and one quarter feet deep.

Find the area of the floor of Basin A in square feet.
Find the volume of Basin A in cubic feet. Use the formula volume equals length times width times depth.
One cubic foot holds 7.48 gallons. How many gallons does Basin A hold when it is full?
Water takes 3 hours to travel from one end of Basin A to the other. How many gallons pass through the basin each hour?
Using your answer from problem 4, how many gallons pass through the basin each minute?
Basin B has the same length and width as Basin A but is 7 and one half feet deep. Find the volume of Basin B in cubic feet.
How many more gallons does Basin B hold than Basin A?
Write the ratio of the depth of Basin A to the depth of Basin B in simplest form.
The volume of Basin A is what percent of the volume of Basin B? Round to the nearest whole percent.
A student found the volume of Basin A by multiplying 45 times 16 times 6 and then adding one quarter to the result. Explain the mistake and state what the student should have done.

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: 720 square feet.
45 feet times 16 feet equals 720 square feet.
Answer: 4,500 cubic feet.
The depth 6 and one quarter feet equals 6.25 feet. 720 square feet times 6.25 feet equals 4,500 cubic feet.
Answer: 33,660 gallons.
4,500 cubic feet times 7.48 gallons per cubic foot equals 33,660 gallons.
Answer: 11,220 gallons per hour.
33,660 gallons divided by 3 hours equals 11,220 gallons per hour. A travel time of 3 hours sits inside the 2-to-4-hour range designers plan for.
Answer: 187 gallons per minute.
11,220 gallons per hour divided by 60 minutes per hour equals 187 gallons per minute.
Answer: 5,400 cubic feet.
The depth 7 and one half feet equals 7.5 feet. 720 square feet times 7.5 feet equals 5,400 cubic feet.
Answer: 6,732 gallons.
Basin B holds 5,400 minus 4,500, or 900 more cubic feet. 900 cubic feet times 7.48 gallons per cubic foot equals 6,732 gallons.
Answer: 5 to 6.
The depths 6.25 and 7.5 can both be multiplied by 4 to give 25 and 30. Dividing both by 5 gives 5 to 6.
Answer: 83 percent.
4,500 divided by 5,400 equals 0.8333..., which rounds to 83 percent.
Answer: The quarter foot belongs inside the multiplication, not after it.
The student found the volume of a basin 6 feet deep, which is 4,320 cubic feet, then added 0.25 cubic feet for a total of 4,320.25. The extra quarter foot of depth covers the whole 720 square foot floor, so it adds 180 cubic feet. Multiplying 720 by 6.25 gives the correct 4,500 cubic feet.

Differentiation

Support

Provide a sketch of Basin A labeled with its length, width, and depth, and write the depth as both a mixed number and a decimal beside the drawing. Work problem 1 with the class so students begin problem 2 with the floor area already in hand, and allow a calculator throughout.

Extension

Ask students to design a Basin C that holds exactly twice as many gallons as Basin A while keeping the same 45-foot length. They must state the width and depth they chose, at least one of which uses a fraction, and show the volume calculation that proves the answer.

ELL supports

Give a visual glossary card for "settle," "basin," "depth," and "cubic foot," with a drawing of a one-foot cube beside a drawing of the long basin. Provide the frame "The volume is ___ times ___ times ___, which equals ___ cubic feet" for problems 2 and 6.

Extensions

Students can compare the two basins by drawing them to scale on grid paper, using one square for each 5 feet of length and width. Seeing that the two basins differ only in depth helps explain why the ratio of their volumes matches the ratio of their depths.