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Understanding volume

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Last updated 26 October 2012 15:28 by NZTecAdmin
Understanding volume (PDF, 49 KB)

Measurement progression, 2nd–3rd steps

In this activity, the learners develop an understanding of volume as a description of the number of cubic units needed to fill a solid shape. They do this by finding the volume of rectangular solids, initially by counting cubic units and then by forming a mental image of the number of cubic units that fit into the shape.

The teaching points

  • Volume is the amount of space occupied by a solid expressed in cubic units.
  • A cube has equal sides and equal square faces. Image of a cube.
  • For a rectangular solid, working out how many squares fit on one level and how many levels there are is a faster way of calculating the volume than counting each cube.
  • Metric units for volume are cubic centimetres (cubes with sides of 1 centimetre) with the symbol of cm3 and cubic metres (cubes with sides of 1 metre) with the symbol of m3.
  • m3 means m x m x m and is said as metres cubed.
  • Discuss with the learners the situations in which they might want to measure volumes.


  • Nets with squares of 1 centimetre to build solid shapes (templates below).
  • Lots of centimetre cubes.
  • Rulers or measuring tapes that can measure 1 metre.
  • Scissors.
  • Sellotape.

The guided teaching and learning sequence

1. Ask the learners to build a solid from the net below (made from 1 centimetre squares) and to discuss how they might measure the space inside it. Listen for and encourage responses that suggest finding out how much fits in the solid.

Image of net made of 1cm squares.

2. Give each learner a 1 centimetre cube and ask them to describe its features. You may need to prompt them to measure the sides. Listen for and reinforce the fact that the length of the sides are all 1 centimetre and the faces are equal squares. Discuss the name “centimetre cube”.
3. Ask the learners to predict how many cubes will fit into the solid. Record their predictions.
4. Ask them to check their predictions by filling the solid with cubic centimetres and share their results. Discuss the fact that the number of cubes that fill the space inside the solid is a way of measuring that space/volume and that, in this example, the volume is 16 cubes or 16 cubic centimetres or 16 cm3.

5. Ask the learners to compare the results with their predictions. Encourage those with more accurate predictions to share their methods. Listen for and encourage, or prompt if necessary, comments like “8 cubes fit on the bottom, and they are stacked 2 high so there must be 16 cubes”.

6. Ask the learners to make a solid from a second net, predict its volume and, if necessary, check the prediction by filling the shape with centimetre cubes (volume equals 36 cm3).

Image of net made of 1cm squares.

7. Ask the learners to estimate the number of cubic centimetres that would fit into a freight container and whether cubic centimetres are an appropriate unit to measure its volume. Ask them to suggest an alternative unit. Listen for “cubic metres”.

8. Discuss with the learners what a cubic metre might look like and how they might demonstrate it with newspaper. Using square metres of newspaper (as they made in the activity “Understanding area”), ask four learners to make a cubic metre. The learners will each hold a side face of a cubic metre. The bottom and top faces are contained within other faces. Emphasise that a cubic metre is a cube with sides of 1 metre with the symbol m3, from 1 m x 1 m x 1 m. Emphasise that it is the unit used to describe the volume of larger shapes.

9. Ask the learners to estimate the volume of the room and other objects in the room (large cardboard box, carry bag, etc). You may need to discuss the use of fractions of a metre for objects with a volume smaller than 1 cubic metre.

Follow-up activity

Ask the learners to choose small and large solid objects in the room, decide which metric unit of measurement they would use to describe the volume and give an estimation of the volume of those objects.

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