Grade 5 · Measurement & Data · MAT-05-MD-008
Solve Measurement and Volume Word Problems
Represent and solve solve measurement and volume word problems problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve solve measurement and volume word problems problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for solve measurement and volume word problems works and verify the result with an independent check.
Prerequisite check
Make sure the foundation is ready.
The new lesson builds directly on this prior concept, so the prerequisite should be usable rather than merely familiar.
The new lesson builds directly on this prior concept, so the prerequisite should be usable rather than merely familiar.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Solve Measurement and Volume Word Problems measures three-dimensional space with cubic units. A rectangular prism can be understood as equal layers of unit cubes, connecting volume directly to multiplication.
Represent the idea
The Math Box uses geometry workspace as the primary representation. Translate the situation into numbers or geometry first, identify what stays fixed, then change one quantity at a time and observe which relationships remain invariant.
Reason, calculate, and verify
A convincing solution names the quantities, shows the mathematical relationship, computes accurately, and includes a reasonableness check rather than relying on an unsupported answer.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Volume Layer Lab
Build a rectangular prism from equal layers of unit cubes.
- Build one example of solve measurement and volume word problems in the Math Box.
- Change one input and predict the effect before moving the control.
- Explain which mathematical relationship stayed invariant after the change.
Worked examples
Twenty different ways to see the concept work.
A rectangular prism measures 2 by 4 by 5 units. Find its volume.
2 × 4 × 5 = 40 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 3 by 5 by 2 units. Find its volume.
3 × 5 × 2 = 30 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 4 by 6 by 3 units. Find its volume.
4 × 6 × 3 = 72 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 5 by 2 by 4 units. Find its volume.
5 × 2 × 4 = 40 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 6 by 3 by 5 units. Find its volume.
6 × 3 × 5 = 90 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 7 by 4 by 2 units. Find its volume.
7 × 4 × 2 = 56 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 2 by 5 by 3 units. Find its volume.
2 × 5 × 3 = 30 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 3 by 6 by 4 units. Find its volume.
3 × 6 × 4 = 72 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 4 by 2 by 5 units. Find its volume.
4 × 2 × 5 = 40 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 5 by 3 by 2 units. Find its volume.
5 × 3 × 2 = 30 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 6 by 4 by 3 units. Find its volume.
6 × 4 × 3 = 72 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 7 by 5 by 4 units. Find its volume.
7 × 5 × 4 = 140 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 2 by 6 by 5 units. Find its volume.
2 × 6 × 5 = 60 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 3 by 2 by 2 units. Find its volume.
3 × 2 × 2 = 12 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 4 by 3 by 3 units. Find its volume.
4 × 3 × 3 = 36 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 5 by 4 by 4 units. Find its volume.
5 × 4 × 4 = 80 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 6 by 5 by 5 units. Find its volume.
6 × 5 × 5 = 150 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 7 by 6 by 2 units. Find its volume.
7 × 6 × 2 = 84 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 2 by 2 by 3 units. Find its volume.
2 × 2 × 3 = 12 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
A rectangular prism measures 3 by 3 by 4 units. Find its volume.
3 × 3 × 4 = 36 cubic unitsVolume counts unit cubes arranged in layers; length × width gives cubes per layer, then height counts the layers.
Practice
Guided practice with hints
01A rectangular prism measures 4 by 4 by 5 units. Find its volume.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4 × 4 × 5 = 80 cubic units
02A rectangular prism measures 5 by 5 by 2 units. Find its volume.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 5 × 5 × 2 = 50 cubic units
03A rectangular prism measures 6 by 6 by 3 units. Find its volume.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 6 × 6 × 3 = 108 cubic units
04A rectangular prism measures 7 by 2 by 4 units. Find its volume.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 7 × 2 × 4 = 56 cubic units
05A rectangular prism measures 2 by 3 by 5 units. Find its volume.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 2 × 3 × 5 = 30 cubic units
06A rectangular prism measures 3 by 4 by 2 units. Find its volume.
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 3 × 4 × 2 = 24 cubic units
Practice
Independent practice
01A rectangular prism measures 4 by 5 by 3 units. Find its volume.
Answer: 4 × 5 × 3 = 60 cubic units
02A rectangular prism measures 5 by 6 by 4 units. Find its volume.
Answer: 5 × 6 × 4 = 120 cubic units
03A rectangular prism measures 6 by 2 by 5 units. Find its volume.
Answer: 6 × 2 × 5 = 60 cubic units
04A rectangular prism measures 7 by 3 by 2 units. Find its volume.
Answer: 7 × 3 × 2 = 42 cubic units
05A rectangular prism measures 2 by 4 by 5 units. Find its volume.
Answer: 2 × 4 × 5 = 40 cubic units
06A rectangular prism measures 3 by 5 by 2 units. Find its volume.
Answer: 3 × 5 × 2 = 30 cubic units
07A rectangular prism measures 4 by 6 by 3 units. Find its volume.
Answer: 4 × 6 × 3 = 72 cubic units
08A rectangular prism measures 5 by 2 by 4 units. Find its volume.
Answer: 5 × 2 × 4 = 40 cubic units
Common mistakes
Learn to catch the error, not just the answer.
Volume counts three-dimensional unit cubes, so use cubic units.
For a rectangular prism, multiply length × width × height.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Estimate storage capacity, packing space, aquariums, boxes, and building materials.
- Compare three-dimensional designs by decomposing them into rectangular prisms.
Challenge problems
A rectangular prism measures 6 by 3 by 5 units. Find its volume.
6 × 3 × 5 = 90 cubic units
A rectangular prism measures 7 by 4 by 2 units. Find its volume.
7 × 4 × 2 = 56 cubic units
A rectangular prism measures 2 by 5 by 3 units. Find its volume.
2 × 5 × 3 = 30 cubic units
A rectangular prism measures 3 by 6 by 4 units. Find its volume.
3 × 6 × 4 = 72 cubic units
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 5 Math Strategy Sprint
Solve and explain solve measurement and volume word problems problems accurately, then check each result with a second method.
Practice
Mastery check
01A rectangular prism measures 4 by 2 by 5 units. Find its volume.
Answer: 4 × 2 × 5 = 40 cubic units
02A rectangular prism measures 5 by 3 by 2 units. Find its volume.
Answer: 5 × 3 × 2 = 30 cubic units
03A rectangular prism measures 6 by 4 by 3 units. Find its volume.
Answer: 6 × 4 × 3 = 72 cubic units
04A rectangular prism measures 7 by 5 by 4 units. Find its volume.
Answer: 7 × 5 × 4 = 140 cubic units
05A rectangular prism measures 2 by 6 by 5 units. Find its volume.
Answer: 2 × 6 × 5 = 60 cubic units
06A rectangular prism measures 3 by 2 by 2 units. Find its volume.
Answer: 3 × 2 × 2 = 12 cubic units
07A rectangular prism measures 4 by 3 by 3 units. Find its volume.
Answer: 4 × 3 × 3 = 36 cubic units
08A rectangular prism measures 5 by 4 by 4 units. Find its volume.
Answer: 5 × 4 × 4 = 80 cubic units
Terminology
Words to know
- volume
- The amount of three-dimensional space an object occupies.
- unit cube
- A cube with edge length one unit, used to measure volume.
- cubic unit
- A unit of volume such as cubic centimeters or cubic inches.
- rectangular prism
- A solid with rectangular faces whose volume can be found with length × width × height.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade-level instructional guidance, mathematical practices, and coherent progression.Common Core State Standards for Mathematics — Grades 4–5
Grade-level expectations for operations, number and fraction work, measurement, data, and geometry.Principles to Actions: Ensuring Mathematical Success for All
Evidence-based emphasis on reasoning, representations, discourse, and conceptual understanding.