Making fractions with Cuisenaire rods

This practice material is suitable for any learner who does not yet have a deep, confident grasp of what a fraction is. It consists of practice-items (a mixture of tasks and questions) that have been sequenced and varied to help pupils develop deep understanding of the nature of fractions by 'drawing-out' for themselves some basic 'observations'. For example, they should ‘see’ that not only are fractions used to denote various particular numbers of other particular numbers of equal parts of 'wholes', but they are very useful 'tools' when we want to express comparisons between numbers and quantities (‘that number/length/weight/etc is half/two-thirds/one tenth/etc of this number/length/weight/etc’). This kind of practice should help them, later, understand fundamental links between the concepts of ‘fraction’ and ‘ratio’. The various ways of seing the same multiplicative relationships should also help them grasp what is meant by ‘equivalent fractions’. This material is intended to be used flexibly; it is easily-extended by pupils making-up their own examples. Pupils who 'fall-behind' in mathematics often make un-anticipated progress when they are encouraged to make choices, as they have to do when they set themselves their own tasks. Also, the possibility of using physical objects (in this case actual Cuisenaire rods) to represent and explore number-relationships in their own (concrete) ways can significantly improve pupils' attitudes to their learning.