Real World, Real Numbers: Ratio and Proportions

Proportional reasoning is important as it forms the basis of student learning in other mathematical domains such as measurement and geometry and financial mathematics (Siemon et al., 2018). It is a skill we often rely on daily when comparing the relationship of proportions.

This learning sequence aims to develop student understanding of the relationships between ratio and proportion in a range of everyday situations. Students will extend their understanding of fraction equivalence, fraction quantities and percentages to make sense of the multiplicative relationships that underpin proportional reasoning. By investigating proportional situations in real world contexts, students will have opportunities to simplify and compare ratios, divide quantities into ratios, and explore simple rates with a focus on the proficiency strands of problem solving and reasoning.

The sequence has been written by teachers for teachers. It has been designed to provide students with rich, engaging learning experiences that address the Victorian Curriculum. The sequence consists of four flexible 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 calculating equivalent fractions, simplifying fractions and comparing fractions. Students should also have some familiarity with making connections between fractions, decimals and percentages.

You can find support for building students’ understanding of these concepts in the following sections of the Mathematics Curriculum Companion:

• VCMNA242
• VCMNA245
• VCMNA247

The Mathematics Curriculum 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. The Companion is an additional resource that you could refer to when you are planning how you might use the sequence in your school.

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

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 Glossary for the Mathematics Curriculum.

It is recommended that the explicit teaching of vocabulary occur throughout this 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 teachers 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 7.

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