Flip
Can you picture where this letter "F" will be on the grid if you flip it in these different ways?
Problem
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 × 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.
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?
Can you tell where the triangle will be?
Move around the blue dots to see what happens when you flip using different lines.
Here you can move the line and try different triangles.
Getting Started
You could focus on one part of the F, or just one point. Where that will be on the grid once you have flipped the F? Can you build up a picture of the F after the flip in this way?
You might like to have some dotty paper to hand to draw the F after you've talked to someone else about it.
You could draw the grid and the F on an overhead transparency, then flip it to check what you have pictured in your head.
Student Solutions
Cong from St Peter's Roman Catholic Primary School worked hard at this problem. He sent us these pictures to show the flips:
Horizontal flip:
Vertical flip:
First diagonal flip:
I'm not sure this first diagonal flipped one is quite right - have another go.
Second diagonal flip:
And for the triangle, here is the horizontal flip:
The vertical flip:
First diagonal flip:
And finally, the second digaonal flip:
Very well done, Cong!
Teachers' Resources
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 × 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.
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.