Square Corners

'Square Corners' printed from https://nrich.maths.org/

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Have a look at the three grids below.

What do you see?
What do you notice?

Once you have had chance to think, talk to someone else about your noticings.

Click below to read what some children noticed.

Miles said:

There are lots of spots. And I can see some of the spots are blue. The blue spots are joined to make shapes.

Freya said:

All the shapes have four sides. Some of the shapes are turned round.

Omar said:

I can see three red squares! They're different sizes.

Do you agree with Miles, Freya and Omar? Why or why not?

Now it is your turn...

Use the interactivity below to put blue counters on the grid.
Your challenge is to put as many counters on the grid as you can but none of them must lie at the corners of a square.

How many counters can you use without making a square?
How do you know that you cannot have more counters?

You're doing really well if you can place 8 or 9 counters.
We think 10 is the maximum number possible, but do let us know if you can find a way of placing 11!

If you would prefer to work away from the computer, you might like to use a printable sheet (square grid or array of circles) with counters.

We would love to hear how you are going about this task!

This problem is taken from 'Mathematical Challenges for Able Pupils Key Stages 1 and 2', published by DfES.