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Mathematical Challenge Week Three

04 november 2015

This week, Mr Westwood introduces some ideas related to probability and how we might challenge students at IGCSE or IB by thinking about the mathematics in reverse. Mr Westwood believes that a great way of developing understanding is to take a standard problem and ask students to try and do it backwards. 

  • Maths Challenge Week Three

Linking multiple topics together is also a way of encouraging deeper learning and developing problem solving techniques. For this week’s challenge we are looking at a tree diagram which combines both probability and the manipulation of fractions. Rather than the standard tree diagram question, this one makes no reference to a real situation and instead asks students to think about the mathematics in reverse.


  1. Can you find each of the values of a, b, c, d, e and f?

If that is not enough, we can then ask some extension questions.

In this problem we are given 5 fractions.

  1. How many do you need to solve the problem? 
  2. Are all of the fractions equally important?

Please email your answers to Mr Westwood.

Martin Brown, Head of Mathematics