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Age 7 to 11 Challenge Level:


I'd like you to imagine a large square piece of rigid plastic, maybe perspex or pretend glass.
On it is marked a square made up of 6 x 6, that is 36, dots:


Someone marks a capital or big "F" in this way:


You are pretending to hold this in front of you.

You are going to flip it over in front of you along imaginary lines which I've drawn in blue on the diagrams below. You could do this by imagining you are holding each end of the blue line with a hand and turning the sheet over.

Each time start with the "F" as shown above, and in your mind find how it will look when you flip it along the blue line.

First this one:


Try to describe to someone how it will now look to you.


Now try this one:


If you feel you could go further try this one:


And my last suggestion as a different way of flipping is:


How did you get on?

Talk to others about the experience.

If that's been ok. then use this next shape instead of the "F" and do the same flips.

Can you tell where the triangle will be?


Why do this problem?

This challenge focuses entirely on visualising a process in your head, something which perhaps pupils have little experience of trying. Visualising in this way can be a very useful tool in solving problems, but of course children need to be encouraged to use it. Therefore it helps if they are given lots of opportunities to do so.

Possible approach

A good way to carry this out with young pupils is to set up a straight line on a small, maybe 4 x 4, dotted grid on an OHP sheet and quickly show them the flips required. To introduce this activity in the classroom, give everyone time to picture the flip for themselves, in silence first. Then ask them to talk to someone sitting near them about it. Can they describe where the F or triangle will be on the grid without drawing it and without gesticulating? Once they have had a chance to do this, share the descriptions with the whole group, again discouraging drawing and gesticulating! (Think-pair-share.) Talk about the effective ways that pupils have found to describe, not only the process and how they imagined it, but the final result.

Key questions

Possible extension

Possible support

It will help some pupils to provide them with a sheet of dotted paper once they have got an answer and have told someone about it, so that they can record their visualisation. You may find that others are able to rely completely on their own "mind's eye" and verbal descriptions.