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Fixing wholes
Concrete experiences that challenge students' thinking about comparing fractions can be helpful for drawing attention to the 'whole'.
For example, students could create models of the same fractions with a variety of different wholes and attempt to compare the sizes of the parts they have created.
Contexts for fractions can help to clarify the difference between situations where the wholes are different, and situations where the wholes are the same.
For example, students could explore the problem:
Mum had a cupcake and a big round cake. How did she give equal shares to each of the six people in the family?
Explicit teaching is needed to draw attention to the fact that when no context is provided for fractions, it is assumed that the fractions relate to the same whole.
For example, the question:
Which fraction is larger, \(\frac{2}{3}\) or \(\frac{5}{6}\)?
is an abstract task.
We do not need to know 'two thirds of what?' or 'five sixths of what?' However, if we choose to represent the fractions to help with our thinking, the wholes we use must be the same size.
