What are cube numbers?
Here you can find out what cube numbers are, why they are called cube numbers and how you can help children to understand cube numbers as part of their maths learning at home.
What is a cube number?
A cube number is found when we multiply a number by itself and then itself again. The symbol for cubed is 3.
For example, 8 is a cube number because it’s 2 x 2 x 2; this is also written as 23 (“two cubed”).
Another example of a cube number is 27 because it’s 33 (3 x 3 x 3, or “three cubed”).
A cube number can also be called a number cubed.
- 2³ = 2 × 2 × 2 = 8
- 3³ = 3 × 3 × 3 = 27
- 4³ = 4 × 4 × 4 = 64
- 5³ = 5 × 5 × 5 = 125
Watch this video to find out how to teach cube numbers and square numbers to primary aged children.
This works for all numbers.
So for example 11 cubed is 113 or 11 x 11 x 11 which is 1331.
Another example could be 2563 or 256 x 256 x 256 which is 16,777,216
As you can see when you cube a whole number, you’ll find the numbers get very big very quickly!
Why are they called cube numbers
They are named cube numbers (or cubed numbers) because they can also be used to calculate the volume of a cube: since a cube is a 3d shape with sides of the same length, width and height, you calculate its volume by multiplying the side length by itself and then itself again (or ‘cubing’ it).
As cubes have equal sides (length, height and width), calculating the volume is simple – just “cube” one of its sides!
For example, a cube with side length 2cm would have a volume of 8cm3 (as 23 = 8). In reverse, if we knew a cube had a volume of 27cm3, we’d know that each side would measure 3cm (as 33 = 27).
See the diagrams below to demonstrate these cube number examples.
- A cube with side length 2 units, volume 8 units ie 2 x 2 x 2 – we can also see there are 8 cubes.
2. A cube with side length 3 units, volume 27 units ie 3 x 3 x 3 – we can also see there are 27 cubes)
3 x 3 x 3 cube
When will children learn about cube numbers in primary school?
As part of the multiplication and division topic, the national curriculum for Key Stage 2 states that Year 5 pupils should be taught to:
- recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3)
- solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes
In the non-statutory notes and guidance, the curriculum advises that children understand the terms factor, multiple and prime, square and cube numbers and use them to construct equivalence statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 92 x 10).
This knowledge of square numbers will be built on in Year 6, particularly when learning about BIDMAS and the order of operations when children may learn the term ‘indices’ (an ‘index number’ is the name for the little 2 used to mean ‘squared’, or the little 3 used to mean ‘cubed’).
Cube roots, like square roots, or working with squares and cubes of decimals are not generally tackled by children until secondary school closer to GCSE.
How do cube numbers relate to other areas of maths?
Cube numbers are particularly useful when finding the volume of cubes, which children begin to do in Year 5 (pupils should be taught to estimate volume [for example, using 1cm3 blocks to build cuboids (including cubes)])
In Year 6, pupils should be taught to calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm3) and cubic metres (m3), and extending to other units [for example, mm3 and km3].
By Year 6 maths pupils will be taught to use their knowledge of the order of operations to carry out calculations and problem solving questions with cubed numbers, including two-step and multi-step word problems.
Wondering how to explain other key numeracy vocabulary to your children? Check out our Maths Dictionary For Kids, or try the following explanations for parents of children following a maths mastery approach in their primary school:
- What Is Pemdas?
- What Is The Lowest Common Multiple?
- What Is The Highest Common Factor?
- What Are Prime Numbers?
- What Is Place Value?
questions and answers
1. Order these from smallest to largest: 52 32 33 23
(Answer: 23 (8), 32 (9), 52 (25), 33 (27))
2. Which of these numbers are also square numbers? 13 23 33 43 53
(Answer: 13 (1), 43 (64))
3. Find two cube numbers that total 152.
(Answer: 125 (53) + 27 (33))
4. Write a number less than 100 in each space in this sorting diagram.
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What are Cube Numbers? Explained by PlanBee
What are cube numbers?
A cube number is the product of three identical factors (e.g. 2 x 2 x 2 = 8). So, a cube number is any number which has been multiplied by itself, twice.
Sometimes, the language ‘cubed’ is used (e.g. ‘2 cubed’ = 2 x 2 x 2 = 8).
How to calculate cube numbers
Calculating a cube number is simple. To generate a cube number, multiply a number by itself. Then, multiply the product by the number again!
Why are cube numbers called cube numbers?
Cube numbers are called cube numbers (or ‘cubed numbers’) because they can be visually represented as a three-dimensional cube: a shape with an equal number of units along its length, width, and height.
Cube number notation
The symbol to demonstrate that a number is cubed is 3 (e.g. 23 =8). This superscript symbol shows that the number represents three dimensions (length, height and width).
The symbol that represents the cube root is 3√ (e.g.3√8 = 2) . However, in Key Stage Two children only need to know the notation for cubed (‘3‘).
Factor = a whole number that divides into another whole number, with no remainder.
Product = the result when two or more numbers are multiplied together.
Cube number = a number multiplied by itself twice.
Cube root = the factor which can be multiplied by itself twice to produce the cube number.
Cube numbers up to 1000
The first ten cube numbers are: 8, 27, 64, 125, 216, 343, 512, 729, 1000. The table below shows the relationship between cube numbers and cube roots.
Children are first introduced to cube numbers in Year 5. Here, children are expected to recognise cube numbers and to know the notation for cubed (‘3‘). Children should also recognise the application of cubed numbers in units used to measure volume (mm3, cm3, km3).
In Year 6, children consolidate their understanding and are expected to solve problems using different cubic units, such as: mm3, cm3, m3 and km3.
Before introducing cube numbers, ensure that children have a solid understanding of multiplication and division and that they are familiar with square numbers (the product of a number multiplied by itself). Make sure that children know the vocabulary: factor, product, square, cube and inverse as this will make it much easier for them to understand teaching input related to cube numbers. Use manipulatives to start
Use our complete Squares, Cubes and Factors lesson pack to teach your class how to identify and use squared and cubed numbers, as well as how to find factor pairs. Revisit the children’s understanding in the context of area and volume with our Primes, Squares and Cubes series of lessons.
Investigations involving cube numbers
Children develop more secure understanding when they have the oppotunity to find out the answers for themselves. So, when you come to teach cube numbers to your class, why not try one of these investigations:
1. «What do the following numbers have in common: 8, 27, 64, 125, 216, 343, 512, 729, 1000?