Cubes and cube roots: building with unit cubes
Build cubes from small unit cubes, 1, 2, 3 and up to 6 along each edge. Count the cubes, the squares on the outside and the cubes hidden inside, and find cube roots.
Core concept
The cube of a number n is n × n × n = n³, the number of unit cubes in a cube with n along each edge; the cube root ∛ undoes it, so ∛64 = 4 because 4³ = 64
Topic: Whole numbers
A square number counts the small squares in a square; a cube number counts the small cubes in a cube. A cube with 3 unit cubes along each edge has 3 layers of 3 × 3, so 3 × 3 × 3 = 3³ = 27 unit cubes. The numbers 1, 8, 27, 64, 125, 216, … are perfect cubes. The cube root is the opposite: ∛27 = 3, because 3³ = 27. To find the cube root of a bigger number, you can break it into prime factor: A number that divides another exactly. 3 is a factor of 12. All key words and group them in threes: 216 = 2 × 2 × 2 × 3 × 3 × 3 = (2 × 3)³, so ∛216 = 6.
What you will learn
- Find the cube of a number.
- Recognise perfect cubes.
- Find the cube root of a perfect cube.
- Explain why cubes grow much faster than the edge.
Before you start
- Know square numbers and square roots.
Materials
- Sugar cubes or small wooden blocks
Equipment
- None
Procedure
- Build a cube with 3 along each edge and record.
- Record cubes with four or more different edges.
- Find the cube whose number of unit cubes is 64.
How this simulation is simplified
- Every small cube is a unit cube, 1 cm along each edge.