To add and subtract fractions, pupils must already understand that non-unit fractions are repeated additions of unit fractions, for example, three-eighths is 3 one-eighths. In other words, pupils must have begun to unitise with unit fractions in the same way that they learnt to unitise, for example, in tens (30 is 3 tens). Addition and subtraction of fractions with the same denominator then follows logically: just as pupils learnt that 3 tens plus 2 tens is 5 tens, they can reason that 3 one-eighths plus 2 one-eighths is equal to 5 one-eighths.
Language focus: “3 one-eighths plus 2 one-eighths is equal to 5 one-eighths.” “5 one-eighths minus 2 one-eighths is equal to 3 one-eighths.”
Pupils should be able to understand and use the following generalisations.
Language focus: “When adding fractions with the same denominators, just add the numerators.” “When subtracting fractions with the same denominators, just subtract the numerators.”