Stage 3 – volume and capacity
Strategy
Students can:
- determine how many cubes were used in a simple, solid rectangular construction
- illustrate two constructions and write how they estimated the number of cubes in each
- compare the volumes of the two constructions
- discuss the strategies used to calculate the volume of the construction
Activities to support the strategy
1. Students are given a collection of interlocking cubes (centicubes).
Ask:
- How long is the side of each cube?
- What is the volume of each cube? How did you know?
Students make a rectangular prism using 24 cubes and record the dimensions (length, breadth, height). Determine the volume is 24 cubic units. Look at the relationship between the volume, length, breadth and height.
- What is the volume of each prism? 24 cubic units/cubic centimetres
- How can we calculate the volume using the length, breadth and height of the prism?
- Can you make other rectangular prisms with a volume of 24 cubic units?
Students attempt to make other prisms, record the results and describe what they notice. Discuss:
- How is your second prism different from your first prism?
- How is your second prism similar to your first prism?
- What is the length, breadth and height of each prism?
- What generalisations can you make?
- How do know that you have made all the possible prisms?
Students draw some of the models they have made.
2. Students use centicubes to construct a rectangular prism which is 3 cm long, 2 cm wide and 1 cm high.
Students add more cubes to the prism by following the steps below. After each step they must add the details to the table.
- What is the volume of the prism? Complete row a) of the table.
- Add another layer to this prism so the height is now 2 cm. Complete row b) of the table.
- Add another layer to this prism so the height is now 3 cm. Complete row c) of the table.
- Repeat with a height of 4 cm. Complete row d) of the table.
- Repeat with a height of 5 cm. Complete row e) of the table.
- Students choose their own measurement for the height and complete row f).
| Ref | Length | Breadth | Height | Volume (cm3) |
|---|---|---|---|---|
| a | 3 cm | 2 cm | 1 cm | enter answer |
| b | 3 cm | 2 cm | 2 cm | enter answer |
| c | 3 cm | 2 cm | 3 cm | enter answer |
| d | 3 cm | 2 cm | 4 cm | enter answer |
| e | 3 cm | 2 cm | 5 cm | enter answer |
| f | 3 cm | 2 cm | enter answer | enter answer |
3. Students complete similar tables where they are given two dimensions and the volume of a prism. Students have to calculate the missing dimension, e.g.
| Length | Breadth | Height | Volume (cm3) |
|---|---|---|---|
| enter answer | 5 cm | 2 cm | 80 cm |
4. Provide students with drawings of a variety of rectangular prisms which have the dimensions labelled. Students have to determine the volume of each prism and give reasons for their answer.
Exploring higher-order thinking (QTF)
Pose this problem. Imagine a box which is 1 metre long, 1 metre wide and 1 metre high.
Ask:
- What is the volume of the box in cubic metres?
- What is the volume of the box in cubic centimetres?
- How did you work out this answer?
- How many centicubes would be needed to fill the box?
References
Australian curriculum
ACMMG108: Choose appropriate units of measurement for length, area, volume, capacity and mass
NSW syllabus
MA3-11MG: Selects and uses the appropriate unit to estimate, measure and calculate volumes and capacities, and converts between units of capacity.
Resources
- primaryresources.co.uk/maths/mathsE1 - select Capacity | Volume then Volume Visuals (DOC) and Volume (PPT)