What Are Cube Numbers?
Cube numbers are the result of multiplying a number by itself twice e.g. 3 x 3 x 3.
They are named cube numbers because they can also be used to calculate the volume of a cube: since a cube has sides of the same length, width and height, you calculate its volume by multiplying the side length by itself twice (or ‘cubing’ it).
This blog is part of our series of blogs designed for parents supporting home learning and looking for free home learning resources during the Covid-19 epidemic.
What are cube numbers?
A cube number is the result when a number has been multiplied by itself twice. For example, 8 is a cube number because it’s 2 x 2 x 2 (2 multiplied by itself twice); this is also written as 23 (“two cubed”). 27 is also a cube number because it’s 33 (3 x 3 x 3, or “three cubed”). The first 10 cube numbers are:
1 (1x1x1, or 13)
8 (2x2x2, or 23)
27 (33)
64 (43)
125 (53)
216 (63)
343 (73)
512 (83)
729 (93)
1,000 (103)
They are called cube numbers because they form the volume of a cube. As cubes have equal sides (length, height and width), calculating the volume is simple – just “cube” (multiply by itself twice) 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 examples.
A cube with side length 2 units, volume 8 units (2x2x2 – we can also see there are 8 cubes)
A cube with side length 3 units, volume 27 units (3x3x3 – we can also see there are 27 cubes)
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When will my child learn about cube numbers in primary school?
As part of the multiplication and division topic, the national curriculum 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 will be built on in Year 6, particularly when learning about 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’).
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)]) but which is built on further 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]).
As previously mentioned, knowledge of cube numbers is built on in Year 6 when pupils should be taught to use their knowledge of the order of operations to carry out calculations.
Wondering about how to explain other key maths vocabulary to your children? Check out our Primary Maths Dictionary, or try these primary maths terms:
- What Is A Square Number: Explained For Primary Parents and Kids
- What Is The Lowest Common Multiple: Explained For Primary Parents And Kids
- What Is The Highest Common Factor: Explained For Primary Parents And Kids
- What Is Long Multiplication: Explained For Primary Parents And Kids
Practice questions
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.
Answer:
5. Explain why 125 is a cube number.
(Answer: Because it’s 5 x 5 x 5, or 53)
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