- Know and use the formula for the volume of a cuboid; calculate volumes and surface areas of cuboids and shapes made from cuboids
Examples of what pupils should know and be able to do
- Secondary mathematics exemplification: Deduce and use formulae to calculate volume
Probing questions
- How do you go about finding the volume of a cuboid?
- How do you go about finding the surface area of a cuboid?
- 'You can build a solid cuboid using any number of interlocking cubes.' Is this statement always, sometimes or never true? If it is sometimes true, when is it true and when is it false?
- For what numbers can you only make one cube? For what numbers can you make several different cubes?
What if pupils find this a barrier?
Ensure that pupils know the correct formulae for areas, perimeters and volumes and how to work them out.
Encourage pupils to use interlocking cubes to make shapes with various volumes. Ensure that pupils realise that three-dimensional objects have surface area as well as volume.
Give pupils opportunities to explore problems of fixed volume, e.g. 'A cuboid is made from 72 cubes. What is the largest surface area?'
- Deduce and use formulae for the area of a triangle, a parallelogram and a trapezium; calculate areas of compound shapes made from rectangles and triangles
Examples of what pupils should know and be able to do
- Secondary mathematics exemplification: Deduce and use formulae to calculate lengths, perimeters, areas and volume
Probing questions
- Why do you have to multiply the base by the perpendicular height to find the area of a parallelogram?
- Right-angled triangles have half the area of the surrounding rectangle with the same base and height. What about non-right angled triangles?
- The area of a triangle is . What are the possible lengths of the base and height?
- What other formulae for the area of two-dimensional shapes do you know?
- Is there a formula for every two-dimensional shape?
What if pupils find this a barrier?
For areas of triangles start with right-angled triangles and establish that the area is half the area of the surrounding rectangle. Extend to any triangle; focus on pupils identifying a base and perpendicular height. Give more information in diagrams than needed. Discuss strategies to identify the necessary information.
Similarly for compound shapes.
- Lesson idea: Area and perimeter
- Example questions: Area and perimeter (DOC-317 KB) Attachments
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