Circle Theorems

My students will be writing their IGCSE´s this year and last week I had them sit a past paper in order to spot gaps in their knowledge and see what we should revise.  Even though we had thoroughly studied circle theorems for the past two years, very few of my students remembered what they needed to in order to get full marks on the topic.  So, back to the drawing board.  I looked for inspiration on the net and found a great idea on Mr. Reddy´s Maths Blog and so I thought I would try it and it worked a treat.  

Prior to the lesson, I prepared two hula hoops with strings attached in order to demonstrate two different theorems.  I handed out a sheet of paper for students which has all of the theorems they need to know on it.  I´ve tried lots of different approaches to this topic.  In the past, I started by getting students to draw the circles with compasses first, then fill in the diagram according to the theorem.  I found this time consuming and exhausting as I ran around the room ensuring the diagrams were filled in properly, providing new pencils for the compasses and trying to help those...ahem...less coordinated students use the compass in the first place.  It was all too much, especially considering the lesson was about them learning circle theorems.  The next time I taught the topic, I created a worksheet with circles on it and had the students label the diagrams accordingly while I explained each one and asked leading questions hoping that students would notice patterns, and then remember the theorem.  This was a big better, but still I didn´t find the note taking interactive enough to make it really stick in their memory.  I´ve decided with this lesson to keep the learning part as interactive as possible and I provided them with a sheet which they eventually glued into their books. 

Next they worked with partners or in small groups of three and were given a theorem they had to teach the class.  I provided a pile of supplies including art straws, protractors, string and paper and I let them decide how they would use their hula hoops to teach the class.  Here are some examples of what students came up with:

I can´t say yet whether this teaching approach has helped my students remember their theorems any better.  What I can say though, is that the lesson was far more enjoyable than any other I´ve taught on this topic.  Also, there was very little input from me and when it was time to tackle the worksheets after the demonstrations had been given, students were readily engaged and from what I could see accurate in answering their questions.  There was a buzz about the room as students were helping each other, asking questions and were really productive.  Happy maths students means a happy teacher...especially period 7 on a Thursday afternoon!

As a plenary for follow up, I recently found this site which I think would be more FUN ways to practice circle theorems.  http://mathsbox.org.uk/shape.php.  It´s all just too much right?  On this site there are treasure hunts and bingo games. 

Check out my original inspiration amongst other great ideas at: http://mrreddy.com/blog/2012/12/guest-blog-circle-theorems-and-hula-hoops/