Planning tool

Australian Curriculum Mathematics V9: AC9M3N02

Numeracy Progression: Interpreting fractions: P5

At this level, students will develop their understanding of multiple representations of fractions including  12 ,  13 ,  14 ,  15 and 16  using three different models: area models, length models and set models.

Area models are a useful starting point for the exploration of part-part-whole concepts, which include equal sharing and partitioning. Activities such as paper folding and the use of concrete materials, such as pattern blocks and fraction walls, can be used to scaffold thinking. Move beyond prototypical representations of fractions (typically, circular models) to support understanding. Additionally, provide opportunities for students to grapple with examples and non-examples (for example, ‘Which of these are equivalent to  14 ?') to challenge their thinking.

Length (or linear) models are based on relative length and are an important precursor to the use of fractional number lines in the future. The use of fraction strips (as seen in fraction walls), pieces of string, Unifix blocks and Cuisenaire rods are examples of length models which can be used to help students see fractional parts proportionally, enabling them to make comparisons and recognise equivalence. Online manipulative versions of Cuisenaire rods are also available.

Set models help students recognise the whole as a set of objects with the subsets making up the fractional parts. Concrete materials such as counters or similar items are useful in providing meaningful experiences of this form of thinking. 

Multiple exposures using all three models reinforce students’ ability to visualise, estimate and make connections between these representations of fractions. To develop abstract thinking, encourage students to visualise fractions and describe what they pictured in their mind. See if their descriptions connect to the representations of the models explored.

Encourage mathematical reasoning by exploring non-prototypical examples of fractions and ask students to justify their thinking.

Model correct fractional language that will help students understand fractions as one quantity rather than two separate whole numbers. For example, describe  13 as ‘one third’ rather than ‘1 over 3’. In later years, use of this language will help students make sense of improper fractions such as  73 which should be described as ‘seven thirds’.

Students will need to be familiar with both quarters and fourths, as they will encounter both in everyday situations.

Teaching and learning summary:

• Use area, length and set models to represent unit fractions and their multiples.
• Combine fractions using repeated addition to make wholes.
• Use correct mathematical language when discussing fractions (not ‘over’).