The concept of equivalence begins with noticing the equality of representations of particular fractions. Often an area model is used, like partitioning circles into equal parts.
An essential skill at this stage is that of re-unitising: subdividing a whole into smaller and smaller parts. Focussing on fractions with related denominators at first — halves, quarters and eighths — makes these relationships easier to notice and explain.
Activities with linear models, like folding paper strips or placing familiar fractions on a number line, will help develop flexibility in thinking about what equivalence means.
Modelling fractions using grids and arrays supports the exploration of fractions with related denominators, and makes the connection to factors and multiples knowledge. This lays the foundation for effective strategies for creating equivalent fractions without relying on physical models.
Further information about students’ thinking about equivalence can be found in the article Assessing Students' Understanding of Fraction Equivalence on the AAMT website.
Linear models of fractions connect with students' concept of length. Equivalent fractions are recognised as being represented by equal lengths.
Grids and arrays
Using grids and arrays to represent fractions begins to focus attention on the multiplicative relationships between pairs of equivalent fractions.