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).
calculate the missing values
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

View/print (PDF 33.39KB)

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.

Calculate the missing length
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

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