Where is the middle?

Finding an easy Geogebra challenge for Year 5s that's just right is itself a challenge, but this one went well.

Where is the centre of a regular pentagon?

We know how to make these, because we've had a go at making stars (another interesting and more open-ended challenge).

Some of the children remembered how to find the mid-point between two points (we'd done this finding the parallelograms inside any quadrilateral).

So they found the mid-point between A and B. Here it is, F. Then they found the midpoint between F and D and "I've found it!"

There it is - G.

Except that it isn't.

We checked and, doing the same thing on the four other sides, we got four other "centres":

So, it's got us close, but not close enough. After a bit more experimenting, some of the class did it with lines: We were now pretty confident that we'd found the centre! To finish off, I asked the children to play a little, and see what they could create from that. Later on, some of them had a bit of spare time to colour in their creations on Paint.