Mathematics · Grade 5

Active learning ideas

Volume of Composite Figures

Active learning works for this topic because students need to see and touch the concept of volume as a measurable space, not just a formula. Handling physical blocks or measuring classroom objects makes the abstract idea of decomposing shapes concrete and memorable.

• Ontario Curriculum Expectations
• 5.MD.C.5.C

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

Activity 01

• Project-Based Learning
• 35 min · Pairs

Block Building Challenge: Composite Creations

Provide linking cubes or unit blocks. Pairs build a composite figure from two prisms, sketch it with dimensions, decompose it on grid paper, and calculate total volume. Partners swap builds to verify each other's work.

Differentiate between a simple rectangular prism and a composite figure.

Facilitation Tip

During Block Building Challenge: Composite Creations, ask students to share their building plans aloud before they start so peers can spot missing dimensions.

What to look for

Provide students with a diagram of a composite figure made of two rectangular prisms. Ask them to label the dimensions of each prism and write the formula they will use to calculate the volume of each part. Then, have them write the final step to find the total volume.

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

Activity 02

• Stations Rotation
• 45 min · Small Groups

Stations Rotation: Decompose and Measure

Set up stations with pre-made composite models from foam or wood. Small groups measure each prism's dimensions at one station, compute volumes at the next, add totals at a third, and explain decomposition at the last. Rotate every 10 minutes.

Explain how to decompose a complex shape into simpler rectangular prisms to find its total volume.

Facilitation Tip

For Station Rotation: Decompose and Measure, provide a checklist with each station that reminds students to measure length, width, and height before calculating.

What to look for

Present students with an image of a composite figure. Ask them to draw lines on the figure to show how they would decompose it into two rectangular prisms. Then, have them write one sentence explaining why adding the volumes of these two parts gives the total volume of the figure.

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

Activity 03

• Project-Based Learning
• 30 min · Pairs

Real-World Hunt: Classroom Composites

Individuals or pairs identify composite objects like desks or bookshelves. Measure and decompose into prisms, calculate volumes, and share findings in a whole-class gallery walk with sticky note feedback.

Construct a plan to calculate the volume of an irregular 3D object.

Facilitation Tip

In Real-World Hunt: Classroom Composites, assign roles like measurer, recorder, and presenter to keep groups organized and accountable.

What to look for

Pose the question: 'Imagine you have two identical boxes. If you stack them one on top of the other, how does the volume of the new shape compare to the volume of one box? What if you placed them side by side?' Guide students to explain how decomposition helps find the volume in each scenario.

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

Activity 04

• Project-Based Learning
• 25 min · Pairs

Volume Puzzle Partners

Give partners isometric dot paper puzzles of composites. They draw nets, identify prisms, label dimensions, and compute volumes. Discuss strategies before checking with physical models.

Differentiate between a simple rectangular prism and a composite figure.

Facilitation Tip

During Volume Puzzle Partners, give students a timer for each puzzle to focus their thinking and prevent rushing through calculations.

What to look for

Provide students with a diagram of a composite figure made of two rectangular prisms. Ask them to label the dimensions of each prism and write the formula they will use to calculate the volume of each part. Then, have them write the final step to find the total volume.

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

A few notes on teaching this unit

Teach this topic by starting with physical models before moving to diagrams. Use guided questions to push students toward decomposition, such as, 'How could you split this figure into parts you can measure?' Avoid rushing to the formula; emphasize the reasoning behind the steps. Research shows that students who manipulate objects perform better on volume tasks than those who only see 2D drawings.

Successful learning looks like students confidently breaking composite figures into rectangular prisms, calculating each volume accurately, and combining results correctly. They should explain their process verbally and in writing, showing they understand why decomposition is necessary.

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Watch Out for These Misconceptions

• During Block Building Challenge: Composite Creations, watch for students who try to use overall dimensions instead of breaking the figure into separate prisms.

  Ask them to physically separate the blocks into groups and label each prism’s dimensions before calculating. Have them explain why using overall dimensions would give an incorrect answer.

• During Station Rotation: Decompose and Measure, watch for students who assume overlapping parts must be subtracted even when the prisms are non-overlapping.

  Use transparent grids over the prisms to show clean joins. Have students trace the outline of each prism to verify no overlap exists before adding volumes.

• During Real-World Hunt: Classroom Composites, watch for students who dismiss irregular classroom objects as impossible to decompose.

  Provide examples like a bookshelf or a pencil case and model splitting them into rectangular prisms. Ask students to sketch their decomposition before measuring.

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Methods used in this brief

• Project-Based Learning
• Stations Rotation