What is a cubed number?

When you multiply a whole number (not a fraction) by itself, and then by itself again the result is a cube number. For example 3 x 3 x 3 = 27.

An easy way to write 3 cubed is 33. This means three multiplied by itself three times.

The easiest way to do this calculation is to do the first multiplication (3×3) and then to multiply your answer by the same number you started with; 3 x 3 x 3 = 9 x 3 = 27.

 

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Learning Cube Numbers

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:

 

What is a cubed number

 

To calculate the number of blocks (the squared number) we would simply multiply 4 x 4 or 42equalling 24.

 

Here is a 3D 4 x 4 cube:

 

What is a cubed number

 

To calculate the number of blocks (the cubed number) this time we would multiply 4 x 10 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 12×12:

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

 

Finding the Cube of a Negative Number.

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.

 

Finding the Cube of a Decimal.

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

 

Worksheets and Practice

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

 

Further Learning

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. 

What is a cubed number?