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Defining Mathematics Education

Defining Mathematics Education

The Seventy-fifth Yearbook is a celebration and reflection of the history of the NCTM yearbooks, and is a great resource on the key issues of mathematics education through the years.

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Home > Topdrawer > Fractions > Good teaching > Equivalence

Equivalence

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.

Three circles, one divided into halves, one into quarters, one into eighths.

Subdividing with related denominators.

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

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.