I was doodling the other day and drew a little square like this:-
So I went on!
A new square appeared, now red!
Extend that one. . .
I really liked what was happening here!
and so on. . . .
I had to stop there because it had up to the size of the paper.
I suggest that you print these pages out so far and have a good look at the way that the pattern has grown and see what things you notice in this last picture.
When I looked at this shape I could imagine that I was looking through a square window at a pattern of squares but could only see the one square in the middle.
So I printed out these:-
Then I printed out the bigger square . . . .
This one I traced onto a "see through" sheet and placed it in different places over the grid of smaller squares.
This was great fun and led to some interesting conversations. Have a GO!
I think that this is one of the most exciting shape investigations that I've put on the NRICH site, so let's have a lot of workings sent to Cambridge U.K. from all over the world so that we can show how people from different countries are thinking and working in their maths. Pester your teachers to collect some results and send them off.