Let’s Experiment: Discovering Area and Volume Formulas

This learning sequence aims to develop students’ conceptual understanding of perimeter, area and volume. When students are given the chance to develop measurement formulas, they acquire a deeper conceptual understanding of the relationships involved in measuring and they engage with an authentic mathematical process (Siemon, 2015). By investigating and forming relationships, students will see how area and volume formulas are derived and make sense of them in context.

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 five flexible stages, including suggested learning intentions.

Before you commence this sequence, it is suggested that you ensure your students are familiar with converting between common metric units of length (such as from cm to mm), calculating the perimeter and area of rectangles and constructing and deconstructing three-dimensional shapes from their nets.

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

• VCMMG196
• VCMMG198
• VCMMG223
• VCMMG228

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 you 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, usually under ‘Reflect and consolidate’.

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.