Unit 12: Surface area and volume of 3D shapes
Planning guidance
Unit objectives
Within this unit, students will learn to:
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Explore the surface area of cubes and cuboids
Explore the surface area of prisms, including cylinders
Find the volumes of cubes and cuboids
Find the volumes of prisms, including cylinders
Convert between measures of area and volume
The primary focus for this unit is on developing an understanding of volume and use of formulae within this
context. Although surface area is not covered in depth in this unit, students are expected to understand the
concept of surface area; they will work with this idea in the Year 9 Autumn Term project. For instance, when
creating shapes with the same volume, they need to be able to explain how the shapes differ - this may be
through different numbers of faces, vertices and edges or differing surface areas. At this stage, they are not
expected to abstractly determine the surface area of a prism given its dimensions.
This unit should take two weeks and there are two sections of work to cover, the first exploring volume
and the other looking at finding the volume of prisms.
Suggested Structure
The actual number of lessons spent on each section will depend on the individual class and the number of
lessons available to teachers. We suggest the following based on a total of 6, 8 or 10 lessons over two
weeks:
Section
Exploring volume
Finding the volume of prisms
6 lessons
2-3
3-4
8 lessons
3-4
4-5
10 lessons
4
6
Exploring volume
Objectives
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Understand the meaning of volume/capacity
Find simple volumes by counting cubes
Begin to appreciate how to find the volume of cuboids
Explore the surface area of cuboids
Convert between volume units
Students will spend the first part of this unit exploring the concept of volume, what it represents and how
it is measured. The should be able to find volumes of shapes made from 1 cm3 cubes by simple counting
and should begin to form strategies for finding the volume of a cuboid. Students should use multilink or
other similar objects to explore volume and to deepen their understanding further.
Copyright © Mathematics Mastery 2014
Surface area is not explicitly covered but should be discussed and explored since it involves revising areas
of rectangles and squares.
Unit conversions have been met earlier and can now be extended to volume. As before, students need to
gain a conceptual understanding through concrete and pictorial representations rather than learning
conversion rates. Dienes blocks are useful as students can compare ones with a thousand block for
volume comparison.
For further guidance, including the Department Tasks for this section, click Exploring volume on the
Planning resources on the main page for this unit.
Volume of a prism
Objectives:
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Explore and find the volume of prisms including cylinders
Find the volume of compound 3D shapes
Solve more complex problems involving volume
Solve problems involving surface area and volume
Explore dimensions (optional)
In this section students look at finding the volume of prisms, including cylinders.
There is a lot of opportunity here to challenge students and to consolidate work on a number of other
units such as similarity, percentages and ratio. Many of these tasks would work well as group tasks
allowing students to draw on earlier mathematics and to develop their problem solving skills.
We do not provide any formulae in the slides since the aim is for students to develop their understanding
that a prism is made up of identical layers and to find the volume we find the volume of one layer and
multiply by the height/length/depth depending on the shape’s orientation. It is important that this is
demonstrated either concretely or through pictorial representations (e.g. on the IWB) since some
students find it difficult to go from the 2D area of a face to 3D volume.
Again, surface area is not explicitly taught, but is included in many of the problems so that students can
be using their knowledge of finding areas throughout the unit.
For further guidance, including the Department Tasks for this section, click Finding the volume of prisms
under Planning resources on the main page for this unit.
Copyright © Mathematics Mastery 2014