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### Math Tools Grades 3–12 (2nd edition)

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Home > Topdrawer > Fractions

# Fractions

Students' first experiences of number are with positive integers — counting numbers and the operations of addition and subtraction. When they begin working with multiplication and division they are also introduced to rational numbers — more specifically, fractions. Many young students find the transition from whole-number thinking to rational-number thinking quite difficult.

It can be unsettling for students to discover that there are many more numbers between zero and one. To then extend that understanding beyond one (to include improper fractions and mixed numerals) can be a challenge.

One source of confusion is the fact that the symbols for fractions involve two numerals rather than just one. Two numerals are needed because a fraction expresses a mathematical relationship between two quantities.

To further complicate learning about fractions, there are various meanings and uses for fractions, such as part-whole, division and ratio. There is also a huge variety in the ways fractions can be represented, such as area diagrams, lengths, volumes and discrete items.

All of these complications make good quality teaching essential. Attention must be given to developing conceptual understanding and 'fraction sense', rather than relying on procedural understanding and practised 'rules'.

A conceptual understanding of fractions is essential for problem solving, proportional reasoning, probability and algebra.

## Big ideas

What is a fraction?

Think beyond your immediate response. Are there other ways fractions are used in mathematics?

## Misunderstandings

Research into student thinking has revealed that many students have misconceptions that hamper understanding and restrict the development of effective strategies for working with fractions.

## Good teaching

Good teaching of fractions involves learning experiences that enable students to build a strong sense of what fractions mean in a variety of contexts and using a variety of representations to develop effective strategies.

## Assessment

Assessment of students' understanding of mathematics serves two main purposes — to inform further teaching, and to provide feedback to students on their own learning.

## Activities

Student activities that appear in other parts of the drawer have been collected here.