Volume and surface area of cuboids

New Zealand Curriculum: Level 3 to early Level 4

Learning Progression Frameworks: Measurement sense, Signpost 5 to Signpost 7

Target students 

These activities are intended for students who understand how to use units of measure to find length and areas of rectangles. They should understand the following characteristics of units:

  • Relate to the attribute being measured (area is measured with a part of area, usually a square, volume is measured with a unit of volume, usually a cube)
  • Identical
  • Tiled with no gaps or overlaps to create a measure
  • Sub-dividable (equally partitioned when greater accuracy is needed)

Students should also know how to use a measurement scale, such as a ruler or tape measure. They should be familiar with the most common metric units of length, metres, centimetres, and possibly millimetres, though they may not be able to convert measures (e.g., 45cm = 450mm). Students should have a partial or full grasp of their basic multiplication facts and the division equivalents.

The following diagnostic questions indicate students’ understanding of, and ability to find the volumes and surface area of cuboids (rectangular prisms). Allow access to pencil and paper and to a calculator if students need it (show diagnostic questions).

Teaching activities