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Transforming the Letters

Age 7 to 11 Challenge Level:

Transforming the Letters

In Miss Chan's class, a group were working with a box of large wooden capital letters. They were exploring what happened when they rotated them one half turn, or flipped them sideways and from top to bottom.
They started with "F". They found four Fs in the box.
"Billy, you just push yours into the middle of the table," said Katie who was rather bossy, "then we can see how the others change."
Here is Billy's F:

capital letter F

"I'll turn my F upside-down," continued Katie, "that's half a turn."
"A $180^o$ turn about its centre," remarked Ali.
This is what Katie's looked like:

capital F after a 180 degree turn about its centre

George said, "I'll flip mine over sideways."
Here is George's F:

Capital F after a flip sideways

"That leaves me to flip my F from top to bottom," said Ali.
So then Ali's looked like this:

capital F after a top to bottom flip

"Look, they are all different. I wonder if all the letters are like that. Which ones shall we try?"
Katie had spelt out Miss Chan's name with four of the letters:

C-H-A-N in capital letters

"Let's try with those," suggested George. So they did.

What did they find out?

"What happens if you do a half turn followed by a sideways flip?" wondered Ali. "Do you think any of the letters in the box get back to the same as they were to begin with?"

capital letters of the alphabet

They did find some which did just that. Which letters are they?

Do these letters also go back to the same if you do a half turn followed by a flip from top to bottom?

Why do this problem?

This problem uses the letters of the alphabet to study the effects of transformations such as rotations and reflections. It requires learners to visualise and predict outcomes. It could help learners to acquire and practise the language of both symmetry and transformations such as vertical and horizontal reflections, and turning through $180^o$.

Key questions

Will it look the same after you have rotated it through $180^o$?
How will it look after you have flipped it sideways/from top to bottom?
Why don't you try using a mirror to see if you are right?
Do these letters have a horizontal/vertical line of symmetry?

Possible extension

Learners could systematically go through the letters of the whole alphabet.

Possible support

Suggest using a mirror or cutting out some letters and trying them.