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Professor Sharma’s Fractions Cut lots of equal width strips of A4 paper in a variety of colours. Ten strips per A4 sheet works well. Give each learner several different coloured strips. Ask learners to construct their own fraction board bit by bit, using a whole strip to represent ‘one whole’ and another new strip to fold and tear for each different fraction, halves, thirds, quarters etc. as you put the strip through the ‘fraction machine’. Each time writing the names of the fractions on one side as in the top diagram …………… 1 1 2 1 2 1 3 1 3 1 4 1 3 1 4 1 6 1 6 1 8 1 8 1 4 1 6 1 8 1 4 1 6 1 8 1 6 1 8 1 6 1 8 1 8 1 8 …………. and alternative ways of writing the fractions on the other side of the fraction strips. whole 1 out of 2 1 out of 2 1 out of 3 1 out of 3 1 out of 4 1 out of 6 1 out of 8 1 out of 4 1 out of 6 1 out of 8 ¼ of a ½ ½ of 1/3 ¼ of a ½ 1 out of 3 ½ of a ½ ½ of 1/3 ½ of a ¼ ½ of a ½ 1/3 of ½ ½ of a ¼ ½ of a ½ of a ½ 1/3 of ½ ½ of a ½ of a ½ Talk about the fractions as you are making them – put a strip through the ‘third’ machine – how many parts are there – are they equal? 1 Now ask the students to write 5 true and 5 untrue statements about the fractions e.g. 1/3 > ½ untrue ½ > 1/3 true 1 = ½ untrue 2/3 > 1/3 true etc. Note that: 1 = 2/2 = 3/3 = 4/4 = 6/6 = 8/8 = 15/15 = / = (A + B)/(A + B) Fractions can be added if they are of the same type i.e. if they have had the same experience. Demonstrate first with CONCRETE examples, followed by PICTORIAL, followed by ABSTRACT methods. At concrete level, put the half through the third machine ….. show that you get sixths by tearing the (half) strip of paper into three sixths, and the third through the half machine ….. show that you get sixths by tearing the (third) strip of paper into two sixths. At pictorial level ½ = 1/3 of ½ 1/3 = ½ of 1/3 1/6 1/6 1/6 At symbolic or abstract level ½ = 3/3 of ½ = 3/6 } + 1/3 = 2/2 of 1/3 = 2/6 } = 5/6 Common experience common denominator Ideas developed by Professor Mahesh Sharma, President and Professor of Education at Cambridge College, Cambridge MA, USA. For further information see - www.berkshiremathematics.com 2