Math problem set Grade 5 Careers & CTE

Trainee Operator at Pennwick: A Basin Volume Problem Set

A grade 5 careers math set where students act as trainee plant operators and find the volume of rectangular treatment basins in cubic feet and gallons.

Grade: Grade 5
Subject: Careers & CTE
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

5.MD.C.5 Common Core Math

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume, including applying the formulas V = l x w x h and V = b x h for rectangular prisms.

How this material aligns: Problems 1, 2, 3, and 7 apply the volume formula length times width times depth to rectangular basins, the real-world volume work this standard names.

All materials for 5.MD.C.5 →

5.NBT.B.7 Common Core Math

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

How this material aligns: Problems 4 and 5 multiply the cubic-foot volume by the decimal 7.48 to convert to gallons, the decimal multiplication this standard requires.

All materials for 5.NBT.B.7 →

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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 find the volume of a rectangular basin using length times width times depth.
Students will convert a volume in cubic feet to gallons using the factor 7.48.
Students will use a fill rate to estimate how long a basin takes to fill.

Vocabulary

Key words: volume, basin, cubic foot, gallon

Teacher overview

At the Pennwick water plant, a made-up plant for this set, water rests in rectangular settling basins so the dirt can sink before the water moves on. Students act as trainee operators and find how much each basin holds, first in cubic feet and then in gallons. A common mistake in this set is multiplying only length times width, which gives the floor area, not the volume; the volume needs length times width times depth, and the worked answers show the full three-number product each time.

Trainee Operator at Pennwick: A Basin Volume Problem Set — Grade 5 Careers & CTE

Name: ____________________________ Date: ______________

Problems

The Pennwick plant has two rectangular settling basins. Use the formula Volume = length times width times depth. One cubic foot holds 7.48 gallons.

Basin A is 30 feet long, 10 feet wide, and 8 feet deep. Find its volume in cubic feet.
Basin B is 20 feet long, 10 feet wide, and 8 feet deep. Find its volume in cubic feet.
What is the total volume of Basin A and Basin B together, in cubic feet?
How many gallons does Basin A hold? Use your answer from problem 1 and the fact that one cubic foot holds 7.48 gallons.
How many gallons do both basins hold together? Use the total from problem 3.
A pump fills Basin A at 200 gallons per minute. About how many minutes will it take to fill Basin A? Use your answer from problem 4 and round to the nearest minute.
A new Basin C is planned. It would be 30 feet long and 10 feet wide, but only 4 feet deep, which is half the depth of Basin A. Find Basin C's volume in cubic feet, and tell whether it is exactly half of Basin A's volume.
In one day, enough water flows through Basin A to fill it 3 times. How many gallons pass through Basin A that day? Use your answer from problem 4.

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: 2,400 cubic feet. Multiply length times width times depth: 30 times 10 equals 300, and 300 times 8 equals 2,400 cubic feet.
Answer: 1,600 cubic feet. Multiply 20 times 10 equals 200, and 200 times 8 equals 1,600 cubic feet.
Answer: 4,000 cubic feet. Add the two volumes: 2,400 plus 1,600 equals 4,000 cubic feet.
Answer: 17,952 gallons. Multiply the volume by 7.48: 2,400 times 7.48 equals 17,952 gallons.
Answer: 29,920 gallons. Multiply the total volume by 7.48: 4,000 times 7.48 equals 29,920 gallons.
Answer: 90 minutes. Divide the gallons by the fill rate: 17,952 divided by 200 equals 89.76, which rounds to about 90 minutes.
Answer: 1,200 cubic feet. Multiply 30 times 10 equals 300, and 300 times 4 equals 1,200 cubic feet. Because only the depth was cut in half, the volume is exactly half of Basin A's 2,400 cubic feet.
Answer: 53,856 gallons. Multiply one basin's gallons by 3 fills: 17,952 times 3 equals 53,856 gallons.

Differentiation

Support

Give these students a basin diagram labeled with length, width, and depth as three separate arrows, so they see the three numbers to multiply. Provide the fill-in "30 times 10 times 8" for problem 1 already set up, and allow a calculator for every step.

Extension

Ask students to find the fill rate, in gallons per minute, that would fill Basin A in exactly 60 minutes, working backward from the gallons in problem 4, and to show the division they used.

ELL supports

Pre-teach "volume," "basin," "cubic foot," and "gallon" with a labeled drawing of a rectangular basin. Provide a short reference line that reads "one cubic foot holds 7.48 gallons," and allow answers to be shown as the number sentence plus the result.