My lovely Year 11s are currently revising for the wonderful AQA Level 2 GCSE Further Maths qualification. One of the topics that is completely new to them is the trigonometry ratios that they need to know without the use of a calculator.

Of course, we have derived them in a traditional way using triangles:

But being able to produce this is proving quite difficult and time consuming for the students. “Is it sin(30) that is 0.5 or cos(30), sir?” is a question I have heard more than once in the last few weeks.

So, imagine my delight when I stumbled upon this piece of mathematical gold from the wonderful Mike Ollerton maths blog:

I picked up the following idea during some work I did in Mongolia when I asked a small group of teachers/teachers trainers to present their best idea for use in the equivalent of A-level classrooms. Tsogtolmaa presented the following idea:

Step 1  Draw around a hand

Step 2 Designate the values 0, 1, 2, 3 and 4 to the thumb and fingers as in diagram 1

Step 3 – take the square root of each of these assigned values

Step 4 – divide each of these by 2

Step 5 – allocate angles 0⁰, 30⁰, 45⁰, 60⁰ and 90⁰ as in diagram 4

Step 6 – label the direction of travel

I thought that was lovely! 🙂

I am going to try it out with my Year 11s this afternoon.

There are numerous other delights on Mike’s blog that are definitely worth checking out.