# Blog posts

### cosine of pi/518 February 2014

An interesting exercise for HL students is to prove that the cosine of (36 degrees) is exactly one-half of the golden ratio (phi). Students are aware of 'special' angles, such as and , for which... more

### Conditional Probability Brainteaser4 February 2014

You have two coins in your pocket. One of them is double-headed and the other is a fair coin (head-tail). You randomly choose one of the coins from your pocket. You look at one side of it. Given... more

### Unfamiliar Questions1 December 2013

A common comment from examiners that appears on Maths HL Subject Reports is that teachers are strongly encouraged to take measures to develop their students' problem solving skills and their ability... more

### Counting by Twelves22 July 2013

There are some very thought-provoking questions that can arise while discussing mathematical ideas with students. Some intriguing questions that have emerged at different times (some repeatedly) in... more

### Drawing a Line with Circles27 May 2013

I've always been fascinated with cycloids. It's a shape that is best illustrated not by a formula but by a particular type of motion. A cycloid is the shape that is traced out by a fixed point on a... more

### Do not completely trust your GDC21 April 2013

For a recent review lesson, I composed a question which I thought would nicely review using definite integrals to find areas and volumes and to illustrate the significant difference that could occur... more

### What About Computer Algebra Systems (CAS)?6 April 2013

I remember well the first time I saw a computer algebra system (CAS) in action. It was 1984 and I was in my first year of teaching. The head of the mathematics department at my school was excited... more

### quod erat demonstrandum23 February 2013

There is a great little book entitled QED - Beauty in Mathematical Proof that I keep on my desk at school - not as a resource for juicy example questions to use in class lectures, but as something to... more

### The Monty Hall Problem12 February 2013

Like much of mathematics, without much effort it is certainly possible to teach probability in a stale and uninteresting way. I find that engaging the students with some well known probability paradoxes... more

### Probability, Coincidences and Birthdays31 January 2013

On our past two family holidays, my family and I have experienced very unlikely (or at least what we felt to be very unlikely) coincidences - namely, having chance meetings with people we know well while... more