Mathematics · Grade 5

Active learning ideas

Understanding Volume with Unit Cubes

Active learning works for this topic because hands-on experiences with unit cubes help students visualize the three-dimensional space inside prisms. By physically packing cubes, students move from abstract formulas to concrete understanding, making volume measurable rather than just a calculation.

• Ontario Curriculum Expectations
• 5.MD.C.3.A
• 5.MD.C.3.B
• 5.MD.C.4

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 35 min · Pairs

Layering Challenge: Build to Volume

Provide students with unit cubes and cards specifying volumes like 24 cubic units. They build rectangular prisms by layering bases, measure dimensions, and record volume as length x width x height. Pairs verify each other's builds by repacking cubes.

Explain why volume is measured in cubic units.

Facilitation Tip

During Layering Challenge, circulate with guiding questions like, 'How many cubes fit on the bottom layer? How many layers do you need for 24 cubes?' to reinforce layer-based counting.

What to look for

Provide students with a collection of unit cubes. Ask them to build a rectangular prism with a volume of 12 cubic units. Observe if they can construct a valid prism and ask them to explain how they know the volume is 12.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 02

• Experiential Learning
• 30 min · Small Groups

Prism Decomposition: Break and Rebuild

Give students a pre-built prism of 36 unit cubes. They disassemble it into layers, sketch each layer, and rebuild into a different prism with the same volume. Discuss how base changes affect height.

Construct a rectangular prism with a given volume using unit cubes.

Facilitation Tip

For Prism Decomposition, ask students to sketch their broken-down prisms before rebuilding to connect visual decomposition with numerical volume.

What to look for

On one side of an index card, draw a rectangular prism made of 8 unit cubes. On the other side, ask students to write one sentence explaining why this prism has a volume of 8 cubic units, not 8 square units.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 03

• Experiential Learning
• 45 min · Small Groups

Volume Scavenger Hunt: Classroom Objects

Students select classroom items like boxes, fill with unit cubes or predict volume, then measure and compare actual versus estimated volumes. Record findings on a class chart.

Compare the concept of area to the concept of volume.

Facilitation Tip

In the Volume Scavenger Hunt, provide a mix of regular and irregular objects to push students to estimate before measuring with cubes.

What to look for

Pose the question: 'Imagine you have two boxes. Box A is 3 cm x 3 cm x 3 cm. Box B is 2 cm x 4 cm x 4 cm. Which box has a larger volume? How do you know?' Facilitate a discussion where students justify their answers by visualizing or calculating the volumes.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Experiential Learning
• 25 min · Pairs

Cube Packing Race: Irregular Shapes

Provide trays with irregular outlines; students pack with unit cubes, count without gaps, and calculate volume. Time pairs competitively then share strategies.

Explain why volume is measured in cubic units.

Facilitation Tip

During Cube Packing Race, set a time limit and encourage students to strategize by comparing their shapes to rectangular prisms they already know.

What to look for

Provide students with a collection of unit cubes. Ask them to build a rectangular prism with a volume of 12 cubic units. Observe if they can construct a valid prism and ask them to explain how they know the volume is 12.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

Teach this topic by starting with physical models before introducing formulas. Avoid rushing to abstract calculations; instead, emphasize the process of counting cubes layer by layer to build conceptual understanding. Research shows that students who build prisms first, then generalize the formula, retain the concept better than those who start with memorization.

Successful learning looks like students using unit cubes to build prisms with accuracy and confidence, articulating why volume is measured in cubic units and how layers contribute to total volume. They should explain their reasoning using terms like base area and height without mixing up volume with surface area.

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Watch Out for These Misconceptions

• During Layering Challenge, watch for students who count only the visible cubes on the surface.

  Have them build a prism, then remove one layer at a time, counting cubes as they go to show that volume measures interior space, not just the outside.

• During Prism Decomposition, watch for students who add the dimensions instead of multiplying them.

  Ask them to rebuild their prism and count the cubes in the base, then multiply by the number of layers to verify their answer.

• During Volume Scavenger Hunt, watch for students who treat the cubes as squares.

  Have them stack cubes vertically to show that depth requires filling all three dimensions, not just covering two.

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Methods used in this brief

• Experiential Learning