In 6F–2 pupils learnt to compare any 2 fractions by expressing them with a common denominator. However, fractions can often be compared by reasoning, without the need to express them with a common denominator. Pupils can already compare unit fractions.
Language focus “If the numerators are both 1, then the larger the denominator, the smaller the fraction.”
Pupils should now extend this to compare other fractions with the same numerator, for example, because 1/5 is greater than 1/6 we know that 2/5 is greater than 2/6.
Language focus “If the numerators are the same, then the larger the denominator, the smaller the fraction.”
Pupils should be able to use reasoning in other ways when comparing fractions:
- For each fraction they should be able to visualise where it is positioned on a number line, for example, thinking about whether it is greater than or less than 1/2 or whether it is close to 0 or 1.
- Pupils should be able to reason about the relationship between the numerator and the denominator of each fraction, asking themselves ‘Is this fraction a large or small part of the whole?’. They should be able to reason, for example, 5/6 is greater than 7/11 because 5 is a larger part of 6 than 7 is of 11.
- For fractions that are a large part of the whole, pupils should be able to reason about how close each fraction is to the whole.
For example, 7/8 is 1/8 less than the whole, while 6/7 is 1/7 less than the whole. Since 1/8 is less than 1/7, 7/8 must be larger than 6/7.
For a given pair or set of fractions, pupils must learn to assess whether it is more appropriate to compare them using reasoning or to express them in a common denomination