There are several concepts that support a sense of fractions as numbers, and that also support the development of strategies for comparing the size of fractions.
Students should be able to:
- reason that the larger the denominator of a fraction, the smaller the parts of the whole. This leads to a useful strategy for comparing the relative size of unit fractions with different denominators, such as \frac{1}{4} and \frac{1}{6}
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understand that the larger the difference between the numerator and the denominator, the closer the fraction is to zero; for example: \frac{1}{4} is close to 0, and \frac{1}{8} is even closer.
Similarly, the smaller the difference between the numerator and the denominator, the closer the fraction is to one whole; for example: \frac{6}{8} is close to 1, and \frac{7}{8} is even closer
- count by fractions of the same denominator (e.g. \frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4}, \frac{5}{4})
- realise that fractions are numbers and therefore have a position on a number line.
