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Link to the inquiry on the Inquiry Maths website.

Link to triangular dotty paper.

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Learning Journey

Find the volume of a cuboid by counting cubes (with multi-link cubes).
Draw 2-d representations of cuboids.
Find the volume of a cuboid using layers (from a 2-d drawing).
Understand and apply the formula for volume of a cuboid.
Work out the area of the six faces of a cuboid (by drawing a net).
Distinguish between units of volume and surface area.
Understand and apply the formula for the surface area of a cuboid.
Create a particular case to test the prompt. Make a conjecture.
Use an algebraic approach to determine the truth of the prompt.
Find the volume and surface area of a cylinder using formulae.
Determine the truth of the prompt in the case of a cylinder. At what point is V > SA?
Deduce the length, area and volume scale factors.

The Learning Journey is a guide. Students will be at different stages of the journey. Not all students in a mixed attainment class will see all the stages. The journey might involve seeing the stages in a different order to the one on this slide.

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Lesson 1

Volume

The lesson divisions are suggestions only and will depend on the progress of the inquiry. The practice sheets are for students who want to defer creating their own examples until they are fluent in a procedure.

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Volume and surface area inquiry

The surface area of a cuboid can

never be less than its volume.

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Questions and observations

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Questions and observations

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Link to regulatory cards

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5 layers

Volume of a cuboid

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Volume of a cuboid

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Drawing a cuboid using the Y method

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Drawing a cuboid using the Y method

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Practice sheet

Draw the nets of the cuboids and work out their surface area. Is the surface area less than the volume for any of the cuboids?

1

2

3

4

6

5

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Lesson 2

Surface area

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Do now

The nets are folded to create a cuboid. What are the volumes of the cuboids?

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What is the volume of the cuboid?

front

back

side

top

bottom

What is the surface area of the cuboid?

Is the surface area less than the volume?

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front

back

side

top

bottom

Formula for the surface area of a cuboid

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Practice sheet

Draw the nets of the cuboids and work out their surface area. Is the surface area less than the volume for any of the cuboids?

1

2

3

4

6

5

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1

Practice sheet

Examples

4

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Can you find a cuboid that has a surface area less than its volume?

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An algebraic approach

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Lesson 3

Volume of a cylinder

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Do Now

Work out the area of the two shapes. What do you notice?

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The surface area of a cylinder can never be less than its surface area.

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Use the diagrams to explain how to work out the volume of a cylinder.

Think Pair Share

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Not drawn to scale.

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Practice sheet

Work out the volumes of the cylinders.

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Solutions

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Surface area of a cylinder

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Not drawn to scale.

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Practice sheet

Work out the volumes of the cylinders.

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Solutions

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An algebraic approach

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Lesson 4

Scale factors

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Cuboid	length	width	height	surface area	volume
1	3	2	1
2
3
4
5

What do you notice about the surface area and volume? Write down your observations.

Fill in the fourth and fifth rows without drawing the cuboids.

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Cuboid	length	width	height	surface area	volume
1
2
3
4
5

Choose your own starting cuboid.

Write down what you expect to happen to the surface area and volume before drawing the cuboids.

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