Math problem set Grade 5 Math

Elmswick Lot Storage Crates: A Grade 5 Volume Problem Set

A grade 5 problem set counting unit cubes and applying V = l x w x h to the buried stormwater crates under a fictional town's community center lot.

Grade: Grade 5
Subject: Math
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator (optional)

Standards

5.MD.C.4 Common Core Math

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

How this material aligns: Problems 1 through 3 measure the volume of a crate bed by counting one-cubic-foot crates layer by layer before any formula is introduced.

All materials for 5.MD.C.4 →

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 4, 5, 7, and 8 apply V = l x w x h to a crate bed, solve for a missing number of layers, and add the volumes of two separate beds.

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: Problem 6 multiplies a whole-number cubic-foot volume by the decimal 7.48 to express a crate bed's capacity in gallons.

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 2026-09-03.

Objectives

Students will find the volume of a stack of unit cubes by counting cubes layer by layer.
Students will apply V = l x w x h to a rectangular crate bed and check it against the cube count.
Students will find a missing number of layers by dividing a required volume by the floor area.

Vocabulary

Stormwater: Stormwater is rain or melted snow that flows off roofs, streets, and parking lots. In most towns it goes into storm drains and flows to a stream without being treated, carrying whatever it picked up.

Also: crate, unit cube, layer, volume

Teacher overview

Elmswick is a fictional town that is rebuilding the parking lot at its community center. Rain used to run straight off that lot into the street, so the crew is burying open plastic crates under the new pavement to hold the rain until it soaks into the ground below. In our scenario every crate is a cube one foot on each side, so each crate holds exactly one cubic foot and a bed of crates is a stack of unit cubes. The misconception this set corrects is counting only the crates a person can see along the outside of a stack, which leaves out every crate buried in the middle and makes a two-layer bed look smaller than it is.

Elmswick Lot Storage Crates: A Grade 5 Volume Problem Set — Grade 5 Math

Name: ____________________________ Date: ______________

Problems

Elmswick is burying crates under its parking lot. Each crate is a cube one foot on every side, so each crate holds one cubic foot of water. Show your work.

The crew sets the first layer of crates 10 crates long and 6 crates wide. How many crates are in that one layer?
The crew stacks a second layer of the same size on top of the first. How many crates are in the bed now?
Each crate holds one cubic foot. How many cubic feet does the two-layer bed in problem 2 hold?
The two-layer bed measures 10 feet long, 6 feet wide, and 2 feet tall. Use V = l x w x h to find its volume in cubic feet.
A second bed is 12 crates long, 8 crates wide, and 3 crates tall. How many cubic feet does it hold?
One cubic foot holds 7.48 gallons. How many gallons does the 288-cubic-foot bed from problem 5 hold?
A third bed must hold 360 cubic feet. Its floor is 15 crates long and 8 crates wide. How many layers tall must it be?
A small bed is 6 crates long, 5 crates wide, and 2 crates tall. What do the small bed and the 288-cubic-foot second bed hold together?

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: 60 crates.
One layer is a rectangle of crates, so 10 x 6 = 60 crates.
Answer: 120 crates.
Each layer holds 60 crates and there are 2 layers, so 60 x 2 = 120 crates. Every crate in the lower layer counts, including the ones hidden under the top layer.
Answer: 120 cubic feet.
Each of the 120 crates holds one cubic foot, so the bed holds 120 x 1 = 120 cubic feet.
Answer: 120 cubic feet.
The floor covers 10 x 6 = 60 square feet, and 60 x 2 = 120 cubic feet. The formula gives the same answer as counting the crates in problem 3.
Answer: 288 cubic feet.
One layer holds 12 x 8 = 96 crates. Three layers hold 96 x 3 = 288 crates, and each crate holds one cubic foot, so the bed holds 288 cubic feet.
Answer: 2,154.24 gallons.
Multiply 288 x 7.48. Since 288 x 7 = 2,016 and 288 x 0.48 = 138.24, the total is 2,016 plus 138.24 = 2,154.24 gallons.
Answer: 3 layers.
The floor holds 15 x 8 = 120 crates in one layer, which is 120 cubic feet. Dividing the required volume by that layer gives 360 divided by 120 = 3 layers.
Answer: 348 cubic feet.
The small bed holds 6 x 5 = 30 crates in a layer and 30 x 2 = 60 crates in all, which is 60 cubic feet. Adding the two beds gives 60 plus 288 = 348 cubic feet.

Differentiation

Support

Give these students interlocking cubes and have them build the bed in problem 1 and add the second layer by hand before writing any numbers, so the hidden crates are ones they placed themselves. Provide a recording table with columns for crates in one layer, number of layers, and total crates, which turns problems 1 through 5 into a fill-in task.

Extension

Ask students to design two different crate beds that each hold exactly 240 cubic feet, using whole numbers of crates and no more than 4 layers. Have them write which design would fit better under a lot that is long and narrow, and explain the choice using both sets of dimensions.

ELL supports

Build a three-crate-by-two-crate model out of sugar cubes or interlocking cubes and label the parts "layer," "long," "wide," and "tall" in English and, where possible, in students' home languages. Provide a sentence frame for problem 7: "One layer holds ___ cubic feet, so the bed needs ___ layers."

Extensions

Have students measure a paved area at their own school, such as a basketball court or a bus loop when no buses are present, and find how many one-foot crates would fit in a single layer under it. Ask them to state how many cubic feet that layer would hold and to write two sentences about where the rain that falls on that pavement goes today.