Home > Fractions > Good teaching > Adding and subtracting

# Adding and subtracting

Students begin by modelling addition and subtraction of fractions with the same denominator in years 4 and 5, then progress to working with fractions that have related denominators in year 6. This forms the foundation for being able to find common denominators for any fractions in year 7.

There are various approaches to take.

• Count by fractions and 'jump' forwards and backwards along a number line.
• Apply a sense of the size of fractions (e.g. Predict whether $$\frac{3}{4}$$ + $$\frac{1}{8}$$ will be less than, equal to, or greater than 1. Explain how you know.)
• Use familiar models such as area diagrams (circles and squares) or a fraction wall.
• Use grids and arrays to promote thinking about factors and multiples in the relationship between denominators.

Student learning can be further supported by attention to:

• expressing fractional numbers greater than one as improper fractions and mixed numbers
• working on problems that provide a context to make sense of adding and subtracting fractions
• further development of strategies for recognising and creating equivalent fractions.

## Same denominator

Addition and subtraction of fractions with the same denominator builds on the skills of sequencing fractions and counting forwards and backwards by fractions.

## Related denominators

Working with related denominators draws on students’ knowledge of factors and multiples, and their growing facility with creating equivalent fractions.

Year 4: Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line

Year 5: Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator

Year 6: Solve problems involving addition and subtraction of fractions with the same or related denominators

Source