Three a̶w̶f̶u̶l̶ awesome mistakes

Mr Gregg drew this shape with Geogebra:

and asked, "What do you notice?"

We wrote things down on whiteboards:

"It's a hexagon."

"It's an L."

"There's all right angles."  - "No, what about E?" - "All right angles except E."

"It's an irregular hexagon."

"All lines - no, most lines - are different."

And then, Anabel:

"It's made of a rectangle and a square."

Some people disputed this claim. We decided it was wrong. But it made us see that the L was made of two rectangles.

Well done Anabel!

We noticed the side lengths marked on. We worked out another side length for the side AB: 11. We estimated AF and ED - most of us thought they were 3 long.

And then Samyak:

"BF is 11 too."

The red diagonal line in the picture below. 

Mr Gregg drew a circle with it's centre at B, and stretching as far as F.

We could see that the diagonal line was longer than AB now.

So Samyak was wrong, a little wrong anyway. But he had got us looking at the diagonal lines.

Well done Samyak!

We left this, and went on to look at Christopher Danielson's Which One Doesn't Belong? book.

The idea is to chose a shape and say a way in which it's the odd one out. We had lots of ideas.

And then Marie: 

"I think the top left one is different because it has no lines of symmetry and the others do have them."

We looked closely.

Most people thought it did have lines of symmetry. Three, in fact.

And, after some discussion we agreed that the "diamonds" have two lines of symmetry, and the square has four. So Marie was wrong. But she'd got us thinking about lines of symmetry.

Well done Marie!

All three of these "mistakes" turned out to be reminding us about another thing to notice. Mr Gregg said because they were so good he was going to remember them and write them down. 

And now he has. From now on he's going to be looking out for how mistakes are actually a good thing! not a̶w̶f̶u̶l̶ ... awesome!