# Good teaching

To develop a sound understanding of fractions, students need to explore the various meanings for fractions, as explained in *Big Ideas*, and the ways in which they can be represented. Emphasis should be placed on developing a deep conceptual understanding of fractions, rather than relying on learned procedures or rules.

Effective assessment of student thinking informs good teaching, and helps to identify misunderstandings that need to be addressed through instruction.

Many of the key understandings have been grouped together under the four topics of fraction sense, dividing, equivalence and addition and subtraction. The information and student activities have been designed to support the development of reliable strategies for working with fractions, as students gradually move towards achieving proportional reasoning.

## Fraction sense

Fraction sense refers to a collection of connected fundamental concepts about fractions. It involves a variety of ways in which fractions can be represented, including symbolic notation.

## Dividing

Fractions express the process of dividing, as well as being the outcome of division (the quotient). Students explore fractions through modelling sharing-as-division problems.

## Equivalence

Understanding the equivalence of fractions is fundamental to the development of proportional reasoning. It begins with exploring physical models of fractions, gradually connecting with knowledge of factors and multiples.

## Adding and subtracting

Students should have opportunities to continue developing their fraction sense as they begin adding and subtracting fractions. Moving too quickly into standard procedures can inhibit understanding of strategies.