Volume of Prisms

Active learning works well for volume of prisms because young children need to physically manipulate objects to understand three-dimensional space. Filling prisms with unit cubes helps students connect abstract ideas to tangible experiences, making volume an intuitive concept rather than a memorized formula.

• Junior Infants
• Foundations of Mathematical Thinking
• 4 activities
• 25 min–45 min

Learning Objectives

1. Identify the unit cube as the standard measure for volume.
2. Calculate the volume of a rectangular prism by counting unit cubes.
3. Compare the volumes of two different prisms by counting the unit cubes required to fill them.
4. Explain how doubling the height of a rectangular prism affects its volume.
5. Distinguish between the concepts of surface area and volume through hands-on manipulation.

Stations Rotation

⏱ 45 min·Small Groups

Stations Rotation: Prism Filling Stations

Prepare stations with empty rectangular and triangular prisms made from card or foam. Students fill each with unit cubes, count layers for base area, then multiply by height to find volume. Groups rotate every 10 minutes and record findings on simple charts.

Prepare & details

Explain the difference between surface area and volume.

Facilitation Tip: During Prism Filling Stations, circulate while students fill prisms and ask them to predict how many cubes they will use before starting.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 30 min·Pairs

Build and Measure: Rectangular Boxes

Pairs construct rectangular prisms using multilink cubes of varying dimensions. They fill the shapes, count total cubes, and discuss how doubling length or height changes volume. Share predictions with the class.

Prepare & details

Analyze how the base area and height determine the volume of a prism.

Facilitation Tip: For Build and Measure, provide clear measurements for rectangular boxes to help students connect their cube counts to real dimensions.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 35 min·Small Groups

Triangular Prism Challenge: Group Towers

Small groups layer unit cubes to form triangular prism towers of different heights. They calculate volume by counting base cubes per layer times layers. Compare towers and predict taller versions.

Prepare & details

Predict how doubling the dimensions of a rectangular prism affects its volume.

Facilitation Tip: In Triangular Prism Challenge, encourage groups to discuss why their towers need different numbers of cubes even when they look similar.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 25 min·Whole Class

Prediction Walk: Volume Hunt

Whole class walks around the room to find prism-like objects, like cereal boxes. Individually predict volume in cubic units, then verify by filling with cubes or estimating layers.

Prepare & details

Explain the difference between surface area and volume.

Facilitation Tip: During the Prediction Walk, assign pairs to measure and record volumes so they can compare findings later.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Teaching This Topic

When teaching volume of prisms, start with physical manipulatives to build foundational understanding before introducing any formulas. Use guided questions to prompt reasoning, such as asking students to explain why two prisms with different shapes might hold the same number of cubes. Avoid rushing to abstract symbols; let students discover the multiplicative relationship between base and height through repeated hands-on experiences. Research shows hands-on exploration leads to deeper understanding than worksheets alone.

What to Expect

Successful learning looks like students accurately counting unit cubes to fill prisms, describing how base size and height affect volume in simple terms, and using correct vocabulary such as 'layer' and 'cubic units' when explaining their work. Students should also demonstrate an understanding that volume is the space inside a shape by comparing different prisms with their peers.

Watch Out for These Misconceptions

Common Misconception

During Prism Filling Stations, watch for students who assume a wider prism always holds more cubes without considering height. Redirect by having them fill two prisms with different bases but same height to compare volumes directly.

What to Teach Instead

During Prism Filling Stations, provide two prisms with different bases but the same height and ask students to fill them completely. Guide them to observe that while the base area differs, the volume matches if the height is equal.

Common Misconception

During Build and Measure, watch for students who focus only on the height of the prism when describing volume. Redirect by asking them to fill the prism completely with cubes and count all layers.

What to Teach Instead

During Build and Measure, have students fill the prism with cubes layer by layer and ask, 'How many cubes are in each layer? How many layers did you stack?' This reinforces that all three dimensions contribute to volume.

Common Misconception

During Triangular Prism Challenge, watch for students who confuse volume with surface area when comparing towers. Redirect by tracing the outline of the prism on paper and then filling it with cubes to show the difference.

What to Teach Instead

During Triangular Prism Challenge, ask students to trace the outline of their prism on paper to represent surface area, then fill it with cubes to measure volume. Discuss how the two measurements describe different things.

Assessment Ideas

Quick Check

After Prism Filling Stations, provide two different-sized rectangular prisms and a collection of unit cubes. Ask, 'Which prism holds more cubes? How do you know?' Observe students' counting strategies and listen to their explanations.

Exit Ticket

After Build and Measure, give each student a drawing of a rectangular prism and 12 unit cubes. Ask them to draw how they would arrange the cubes to fill the prism. Then ask, 'If we added another layer of cubes, would the volume be bigger or smaller?'

Discussion Prompt

During Triangular Prism Challenge, show students two identical boxes, one filled with small packing peanuts and the other with larger packing peanuts. Ask, 'Which box has more space inside? Does it matter what we use to fill it? How is this like measuring volume with cubes?'

Extensions & Scaffolding

• Challenge students to fill prisms with half-units (e.g., half cubes) to explore fractional volume.
• Scaffolding: Provide prisms with marked layers or a grid overlay to help students count cubes more easily.
• Deeper exploration: Ask students to create their own prisms using unit cubes and compare volumes with classmates’ designs.

Key Vocabulary

Volume	The amount of space a three-dimensional object occupies. We measure volume using cubic units.
Cubic Unit	A standard-sized cube used to measure volume. For example, a small block or a snap cube.
Rectangular Prism	A solid shape with six rectangular faces. Think of a box or a brick.
Triangular Prism	A solid shape with two triangular bases and three rectangular sides. Imagine a Toblerone box.
Layer	A set of unit cubes arranged to cover the base of a prism, forming one level of height.