Explain how to calculate the volume of compound shapes | Maths

Starter quiz

Which of these are the correct properties of a cuboid?

8 vertices, 8 faces, 8 edges

12 vertices, 8 faces, 8 edges

12 edges, 6 faces, 8 vertices ✓

12 vertices, 6 faces, 12 edges
Which of these is the correct way to calculate the volume of a cuboid?

Multiply the height, length and width measurements together. ✓

Multiply the height and width measurements and add the length.

Multiply the height and width measurements and divide by the length.

Add the height, length and width measurements together.
What is the volume of this cuboid? ______ cm $^3$

'110' ✓
What is the volume of this cuboid? ______ cm $^3$

'320' ✓
What is the volume of this cuboid? ______ cm $^3$

'52' ✓
What is the difference in volume between cuboid A and cuboid B? ______ cm $^3$

'4' ✓

Exit quiz

What is the name given to a shape made by combining two or more basic shapes?

rectangle

compound shape ✓

cube

cuboid
Use the complete and subtract strategy to find the volume of this shape. ______cm $^3$

'47' ✓
Jacob partitioned the compound shape into two cuboids. What is the volume of the smaller cuboid? ______ cm $^3$

'30' ✓
Use an efficient strategy to calculate the volume of this compound shape. ______ cm $^3$

'352' ✓
Use an efficient strategy to calculate the volume of this compound shape. ______ cm $^3$

'340' ✓
Use an efficient strategy to calculate the volume of this compound shape. ______ cm $^3$

'664' ✓

Worksheet

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Lesson Details

Key learning points

Compound shapes can be split into cubes and cuboids in different ways.
Compound shapes can be split in different ways but the volume stays the same.

Common misconception

Pupils may default to trying to use the same strategy for every shape, for example, the 'partition and add' can be applied to most shapes although it might not be the most efficient.

Spend time exploring each strategy with basic dimensions for compound shapes at first. Explore different strategies for the same shape and encourage children to reason which strategy might be most efficient to use.

Keywords

Compound shape - A compound shape is a shape created with two or more basic shapes.
Strategy - A strategy is a planned approach used to solve a problem.