Square and cube numbers: what children learn
Year 5 pupils learn to recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³). A square number is a whole number multiplied by itself: 6² = 6 × 6 = 36. A cube number is a whole number used three times in a multiplication: 4³ = 4 × 4 × 4 = 64.
This sprint covers the squares from 1² to 12² and the cubes from 1³ to 5³. Children type each answer, and the time limit encourages them to remember the facts rather than work them out each time.
This topic covers the Year 5 statutory requirement in the National Curriculum in England (Number – multiplication and division): pupils should be taught to “recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)”. Year 5 pupils are usually aged 9–10.
For families following US standards, the closest Common Core standard is 6.EE.A.1, which is taught in Grade 6. Common Core introduces exponents in Grade 6.
How to play
How many can you answer in 60 seconds? Type the answer and press Enter. Questions keep coming for 60 seconds. Type each answer and press Enter, or choose Skip. Answers can be typed with or without commas.
Step by step
- Picture a square. 6² can be drawn as a square of dots, 6 rows of 6. That is why it is called a 'square' number.
- Picture a cube. 3³ is a cube made from small cubes, 3 long, 3 wide and 3 high: 27 small cubes in total.
- Read the small number carefully. The small raised number tells you how many times to use the number in the multiplication, not what to multiply by. 5² is 5 × 5, not 5 × 2.
- Work out cubes in two steps. For 4³, first find 4 × 4 = 16, then multiply by 4 again: 16 × 4 = 64.
Worked examples
Example 1: 9² = ?
Working: 9 × 9.
Answer: 81
Example 2: 5³ = ?
Working: 5 × 5 = 25, then 25 × 5 = 125.
Answer: 125
Example 3: 12² = ?
Working: 12 × 12 = 120 + 24.
Answer: 144
Common mistakes and how to fix them
- Working out 6² as 6 × 2 = 12. Say it as '6 squared means 6 times itself'. Drawing the square of dots helps.
- Working out 4³ as 4 × 3 = 12. Write it out in full first: 4 × 4 × 4.
- Forgetting that 1² = 1 and 1³ = 1. 1 × 1 = 1 and 1 × 1 × 1 = 1. They are square and cube numbers too.
Activities to try at home
- Build squares and cubes with Lego or sugar cubes and count the pieces.
- Look for square numbers on a multiplication square: they run along the diagonal.
- Find a number that is both square and cube (64 = 8² = 4³).
Ideas for the classroom
- Investigate the pattern of differences between square numbers: 1, 4, 9, 16 go up by 3, 5, 7…
- Use multilink cubes to build the first five cube numbers.
- Link to factors: square numbers are the only numbers with an odd number of factors.
Printable worksheet
The printable worksheet uses the same question generator as the game, so it practises exactly the same skills. It comes with a separate answer sheet on the second page. Print it, or save it as a PDF from your browser's print menu.
Frequently asked questions
What are the square numbers up to 144?
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144.
What are the first five cube numbers?
1, 8, 27, 64 and 125.
Do Year 5 pupils learn square roots?
Square roots are formally introduced at Key Stage 3, though many teachers discuss them alongside square numbers in upper Key Stage 2.
What is the US equivalent?
Common Core introduces whole-number exponents in Grade 6 (6.EE.A.1), so this is earlier in England.