Pushing the limits

18th May 2007 at 01:00
Maths Ages 11 to 18

Teenagers want to know where the limits are - what they can get away with.

Turn that to a mathematical advantage with "possibility spaces". These are tables with different factors running horizontally and vertically, and the task is to see what is allowed and what isn't.

How far can you go before you bump into mathematical limits? For example, make one for different kinds of triangles.

Triangles can be classified according to the lengths of the sides (scalene, isosceles, equilateral) or their angles (acute, obtuse, right angle), but which of the nine boxes in your table are possible and which are impossible?

Photocopy a blank table on to A3 paper and get pupils in groups to draw an example in each space in the table. If some are impossible, pupils must justify why.

One that gets maths teachers thinking, as well as pupils from Year 7 upwards, is a table for order of rotational symmetry and number of lines of symmetry.

Pupils display great ingenuity trying to create shapes that satisfy the constraints or convincing one another that something cannot be done. There are moments when someone finds they can do one that they previously thought was impossible. And the possibility patterns in the finished tables provoke some interesting questions

Colin Foster teaches maths at King Henry VIII School in Coventry

Subscribe to get access to the content on this page.

If you are already a Tes/ Tes Scotland subscriber please log in with your username or email address to get full access to our back issues, CPD library and membership plus page.

Not a subscriber? Find out more about our subscription offers.
Subscribe now
Existing subscriber?
Enter subscription number

Comments

The guide by your side – ensuring you are always up to date with the latest in education.

Get Tes magazine online and delivered to your door. Stay up to date with the latest research, teacher innovation and insight, plus classroom tips and techniques with a Tes magazine subscription.
With a Tes magazine subscription you get exclusive access to our CPD library. Including our New Teachers’ special for NQTS, Ed Tech, How to Get a Job, Trip Planner, Ed Biz Special and all Tes back issues.

Subscribe now