Fractions as numbers

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 $\frac{1}{6}$
• 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.