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.