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Square on a Number Grid - Investigation

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activity of the week 16 - Square on a Nu
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Key Skills and Concepts

Optimising GCSE


Topics Covered:

Factors and Multiples


Understanding Place Value

Problem Solving

Investigation Work


Equipment needed:

A number grid up to 100 (the one in the image)

A Pen and Paper to make notes



This is an investigation that can be used for children as long as they can add numbers together. It is extremely open ended and can be made really complicated up to a high GCSE level based on how efficient a solution a child wants to reach (a generalised algebraic formula)). There are plenty of opportunities for children to change the rules showing that there is no ceiling on a maths investigation and that they will achieve as much as they want to. It really is up to them!


Follow the instructions on the image below. You may wish to print it out so you at least have a number grid to use. Please use the prompts below to encourage children to move the investigation onward. The ultimate aim of these number and algebra investigations is to create a formula that links (in this case) the top left number of each square to the total for that square. Any pattern spotting at this point is brilliant though.

Example – Can you work out what number between 1 and 20 I am thinking of in this example game below?

Q1: Is your number a multiple of 2?

A1: No

Q2: Is 3 a factor of your number?

A2: Yes

Q3: Is your number a multiple of 5?

A2: Yes

Q4: Is your number a factor of 20?

A4: No

Try and encourage your child to alternate between factor and multiple questions so they get used to the two different (yet very connected) terms.

Key Questions/Prompts:

Can you explain what a multiple is?

Can you explain what a factor is?

(Child: Is your number a multiple of 4?) Can you ask that same thing using a factor question instead of a multiple question?

Which numbers do you think it could be?

Which numbers do you know it can’t be?



You can easily extend the challenge by allowing numbers that are higher than 20. You can also turn it into a race where you both pick a number and take it in turns to ask a question. See who can guess the other person’s number first.

You should also open up the discussion about which numbers are harder to guess. The language of factors is really important in this discussion and can even open up a great way of understanding prime numbers.

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