Cube numbers can be a little bit more confusing than squared numbers, simply because of the extra multiplication. Essentially, you are calculating a 3D shape instead of a flat one.
Here is a flat (or 2D) 4 x 4 square:
To calculate the number of blocks (the squared number) we would simply multiply 4x 4 or 42,equalling 16.
Here is a 3D 4 x 4 cube:
To calculate the number of blocks (the cubed number) this time we would multiply 4 x 4 x 4 or 43 equalling 64.
In KS2, you won’t need to learn cube numbers off by heart, but you will have to have a basic understanding of what they are, and how to calculate them. Often children will be given a pattern of numbers, such as lower end cube numbers and may be asked to try to work out the pattern.
Here is a list of cubed numbers up to 12x12:
| 0 Cubed | = | 03 | = | 0 × 0 x 0 | = | 0 |
| 1 Cubed | = | 13 | = | 1 × 1 x 1 | = | 1 |
| 2 Cubed | = | 23 | = | 2 × 2 x 2 | = | 8 |
| 3 Cubed | = | 33 | = | 3 × 3 x 3 | = | 27 |
| 4 Cubed | = | 43 | = | 4 × 4 x 4 | = | 64 |
| 5 Cubed | = | 53 | = | 5 × 5 x 5 | = | 125 |
| 6 Cubed | = | 63 | = | 6 × 6 x 6 | = | 216 |
| 7 Cubed | = | 73 | = | 7 × 7 x 7 | = | 343 |
| 8 Cubed | = | 83 | = | 8 × 8 x 8 | = | 512 |
| 9 Cubed | = | 93 | = | 9 × 9 x 9 | = | 729 |
| 10 Cubed | = | 103 | = | 10 × 10 x 10 | = | 1,000 |
| 11 Cubed | = | 113 | = | 11 × 11 x 11 | = | 1,331 |
| 12 Cubed | = | 123 | = | 12 × 12 x 12 | = | 1,728 |
The cube of a negative number will always be negative, just like the cube of a positive number will always be positive.
For example; -53 = -5 x -5 x- -5 = (25 x -5) = -125.
Just like whole numbers (integers), it’s easy to cube a decimal number too. Don’t worry though, you won’t need to memorise these in key stage 2 (or probably even work them out)!
| 1.23 Cubed | = | 1.233 | = | 1.23 × 1.23 x 1.23 | = | 1.860867 | |
| 2.56 Cubed | = | 2.563 | = | 2.56 × 2.56 x 2.56 | = | 16.777216 |
Here are some worksheets aimed specifically at getting to grips with cube numbers and practising your skills.
Year 6 – Drawing dice dots on net cubes
Year 8 – Know your squares and your cubes
Year 8 – Cube numbers and cube roots
Year 8 – Practise finding cubes and cube roots on a calculator
If cube numbers and puzzles are your thing and you really want to give yourself a challenge, why not look at the BBC Bitesize website or try some of the puzzles and problems set by the NRich team at the University of Cambridge?
https://nrich.maths.org/public/leg.php?code=-308
http://www.bbc.co.uk/guides/z2ndsrd
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AUTHOR, MS ALISON – MATHS TEACHER.
