*Tessellation*

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## September 28, 2010

### Week 52: Tuesday

This morning we started with the task of contructing dynamic quadrilaterals using geogebra.

htp://www.geogebra.org/cms/

Basically we had to construct the shapes so that you can drag the corners around and the shape will still be the same. Despite not knowing anything about geogebra (whoops I just admitted I hadn't done my session preparation. I hope Jenni's not reading this...) I managed to get to grips with it pretty quickly.

Next we were given some activities and told to plan a lesson around them. Jenni emphasised that in planning lessons it is often a good idea to base your lessons around pre-prepared materials rather than planning a lesson and then trying to make the activities yourself. I'll try to bear that in mind.

The activities were about semi-regular tilings, which is where you put different shapes together (in this case, hexagons, squares and triangles) so that at every corner of each shape the sequence of shapes is the same. First we had to make 5 different tilings using the shapes we were given. That was easy enough with some trial and error. I'm not entirely sure why there are only 5 possible tilings though. I need to engage my higher order thinking skills, methinks.

The next activity was, given a semi-regular tiling, work out the ratio of triangles to squares to hexagons. Paul managed to work it out by looking at the pattern within each row, but Giulian's method of finding the minimum building block was in my opinion the most elegant way of proving the ratio was correct.

We worked through the lesson plan outline and discussed how we were going to structure the lesson, how we would differentiate, etc. The lesson plan can be found on Lydia's blog here:

http://www.blogs.warwick.ac.uk/lydiaclarke/entry/geometry_lesson_plan/

Writing a topic plan was harder, because we had to consider which things should go before and after this lesson. Should we include area and perimeter? Symmetry? Should that come in a seperate topic?

After lunch we did an exercise where we all had to close our eyes as Jenni described an everyday object using mathematical terminology. This was fun and also helped calm the class down because closing your eyes is very relaxing. Then we opened our eyes as Jenni described a picture made up of squares, which we had to draw on our whiteboards. She demonstrated how hard it is to give precise enough instructions so that everyone is picturing the same thing. She then started asking questions about the hands of a clock, about the angle they make at different times. I think the point of this was to demonstrate how hard it is to visualise and manipulate in your mind moving objects. Which brings us swiftly on to...

Dynamic geometry. Using Geogebra we worked through some worksheets as if we were pupils. We had to construct a kite and connect the midpoints of each edge and conjecture that it forms a rectangle. Then we had to justify the conjecture by changing the shape of the kite and seeing that it's always a rectangle.

Next we worked on preparing a Geogebra animated picture demonstrating the circle theorems. I had no trouble drawing the circle theorems and dragging corners to show that they're always true, but I couldn't work out the animation bit. I will work on that in my spare time. (Spare time? What's that?)

The last thing we did was a weird exercise involving wool. In groups of 12-ish, we stood in a circle and tried to make patterns by passing the wool to every second person, then every third, and so on. The idea is it forms a regular polygon in the middle. I don't know if it's because I'm ridiculously short, but I couldn't really see what was going on in my circle. There might well be kids who get a lot out of an exercise like that, but clearly I am not one of them.

I'm about to start my reading for tomorrow and get ready for my tutorial.

Emma x x x