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TheSchoolRun.com closure date

As we informed you a few months ago, TheSchoolRun has had to make the difficult decision to close due to financial pressures and the company has now ceased trading. We had hoped to keep our content available through a partnership with another educational provider, but this provider has since withdrawn from the agreement.

As a result, we now have to permanently close TheSchoolRun.com. However, to give subscribers time to download any content they’d like to keep, we will keep the website open until 31st July 2025. After this date, the site will be taken down and there will be no further access to any resources. We strongly encourage you to download and save any resources you think you may want to use in the future.

In particular, we suggest downloading:

You should already have received 16 primary school eBooks (worth £108.84) to download and keep. If you haven’t received these, please contact us at [email protected] before 31st July 2025, and we will send them to you.

We are very sorry that there is no way to continue offering access to resources and sincerely apologise for the inconvenience caused.

What are square numbers?

Square numbers
We explain what square numbers are and how children are taught to know square numbers plus the corresponding squares of multiples of 10. We also explain how knowledge of square numbers can help when it comes to working out the area of a square.

What are square numbers?

When you multiply a number by itself, the result is a square number:

1 x 1 = 1                           7 x 7 = 49
2 x 2 = 4                           8 x 8 = 64
3 x 3 = 9                           9 x 9 = 81
4 x 4 = 16                        10 x 10 = 100
5 x 5 = 25                        11 x 11 = 121
6 x 6 = 36                        12 x 12 = 144

and so on.

To write the mathematical formula for square numbers we add a small 2 next to and above the number, for example: 32.

Square numbers in Key Stage 2

Children in Years 5 and 6 are expected to know all the above square numbers, plus the corresponding squares of multiples of 10 (20 x 20 = 400, 30 x 30 = 900, 40 x 40 = 1600, etc.).

Knowledge of square numbers can help children when it comes to working out the area of a square. For example: they may be shown a square (not drawn to scale) and told the area of the square is 81cm². If they are asked to work out the length of each side, their knowledge of square numbers will mean they will know instantly that each side of the square is 9cm.
 

Children in Year 6 will need to solve puzzles and investigations involving square numbers. Here are some examples:

Karen has these number cards:

If she puts all the cards in a hat and picks one out at random, what is the probability she will pick a square number?

Answer: since there are 3 square numbers: 49, 100 and 16, the probability she will pick a square number is 3/8.

Another investigation example:

Two square numbers are added together to make another square number. What are they?

One possible answer is 16 + 9 which equals 25. 

Children in upper KS2 (but more usually KS3) will also learn about cube numbers.