Keeping it in Proportion: Fractions and Decimals

This learning sequence aims to develop student understanding of fractions and decimals. Fractions underpin the development of proportional reasoning and are important for future mathematics study, including that of algebra and probability (Clarke, Roche, and Mitchell, 2011). This sequence aims to equip students with the skills required to compare and order fractions and decimals and to represent fractions in decimal form, and vice versa.

The sequence has been written by teachers for teachers, in collaboration with mathematics experts. It has been designed to provide students with rich, engaging learning experiences that address the Victorian Curriculum. The sequence consists of five stages, including suggested learning intentions.

There is a strong focus within this sequence on supporting students to develop the four mathematical proficiencies set out in the curriculum: Understanding, Fluency, Problem Solving and Reasoning, as well as their capacity for Critical and Creative Thinking.

Before you commence this sequence, it is suggested that you ensure your students are familiar with the terms numerator and denominator, common unit fractions such as ¹/₂, ¹/₃, ¹/₄, ¹/₅ and how to partition areas, lengths and sets to illustrate common unit fractions.

You can find support for building students’ understanding of these concepts in the Mathematics Curriculum Companion. The Teaching Context and Teaching Ideas related to content descriptions VCMNA157, VCMNA159, VCMNA187, VCMNA188, VCMNA189, VCMNA190, and VCMNA211 may be particularly useful.

The Mathematics Curriculum Companion is an additional resource that you could refer to when you are planning how you might use the sequence in your school. The Companion provides teachers with content knowledge, suggested teaching and learning ideas as well as links to other resources. Resources are organised by Mathematics strands and sub-strands and incorporate the proficiencies: understanding, fluency, problem solving and reasoning.

In addition, the Literacy in Mathematics section of the Literacy Teaching Toolkit contains an extensive range of strategies for teaching the literacy demands of mathematics. 

The sequence highlights opportunities to apply the High Impact Teaching Strategies (HITS), which are a component of the Victorian Teaching and Learning Model. 

The sequence highlights the use of a variety of scaffolding practices to help support students in the learning process, in particular:

• Collaborating
• Modelling
• Guiding
• Orienting

Students should be able to understand and use the following concepts and terms by the end of the learning sequence:

You can find definitions of some of these terms in the F-10 Victorian Curriculum Mathematics Glossary.

It is recommended that the explicit teaching of vocabulary occur throughout the learning sequence. The Literacy in Mathematics section of the Literacy Teaching Toolkit provides several teaching strategies with worked examples demonstrating how teachers can use literacy to support student understanding of mathematical language. A further set of strategies demonstrate how can develop students' literacy skills to support their mathematical problem solving.

Opportunities for formative and summative assessment are identified at different stages of the learning sequence. Look for the 'Assessment Opportunity' icon.

You may want to develop a rubric to assess students’ progress. A range of Formative Assessment resources are available from the Victorian Curriculum and Assessment Authority. This includes a Guide to Formative Assessment Rubrics, a series of modules to support you to develop your own formative assessment rubrics, and sample rubrics across six curriculum areas that demonstrate how you can put formative assessment rubrics into practice in the classroom.

In developing a rubric, you may wish to co-construct assessment criteria with your students. Each stage of the sequence provides sample success criteria for students working at Level 6.

The Victorian Curriculum and Assessment Authority has also published annotated student work samples that provide teachers with examples of student learning achievement in each strand of the Mathematics curriculum.