Fraction arithmetic

I don’t envisage this task as being a worksheet to be issued to classes. Rather as the focus of a class discussion and investigation into the nature of fractions.  The task aims to link the number line representation with the procedures for adding and subtracting fractions.  Further it is about building fluency in counting with fractions.  All too often, I’ve found pupils aren’t adept at mental approaches to this and overly rely on procedures.  I often write about developing “feel” for ideas.  The results of this task may not be immediately obvious, however, the discernments I hope may arise would be around familiarity with the family of fractions which is related to the twelfths, including halves, quarters, thirds and sixths.  Other possible extension is to extend the fraction line into improper fractions and or backwards into negative fractions.  

Credit: @ChrisMcGrane84

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