The X Factor: Using Algebra to Solve Problems

This learning sequence aims to build students’ capability to develop and use algebraic generalisations to solve problems accurately and efficiently. It aims to equip students with the skills to express generalisations in multiple ways. By looking for and noticing patterns, students will be able to describe relationships using variables in spoken, written and symbolic form, and make sense of them in context.

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 four flexible stages.

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.

• The first two stages provide opportunities for open-ended, contextually based mathematical investigations, through which students can explore concepts of algebra sense, and making meaning of algebra. These stages are dedicated to ‘sense-making’, allowing students to develop the proficiency of Understanding.
• The third and fourth stages are open-ended problem-solving tasks, requiring students to use the proficiencies of Problem Solving and Reasoning, as well as some of the understandings developed throughout the first two stages; specifically, the recognition that generalisations are critically useful to efficient problem solving.

Each task provides opportunities for students to develop Fluency in a range of algebraic concepts and ideas, notably: variable and generalisation; symbolic representation using variables, constants, and operations; substitution; solving equations; equivalent expressions; and graphs of algebraic relationships.

Before you commence this sequence, it is suggested that you ensure your students are familiar with general number operations (addition, subtraction, multiplication, and division) and, in particular, number patterns (numbers changing, successively, through the repeated application of one or more operations).

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 VCMNA138, VCMNA161 and VCMNA219 may be particularly useful.

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. 

This sequence makes reference to multiple teaching strategies, including modelling 'think-alouds' and scaffolding practices.

More information about modelling 'think-alouds' can be found in the Literacy Teaching Toolkit and from nzmaths. This strategy is used in Paths in the Park and Garden Beds. 

The Victorian Department of Education and Training provides information on scaffolding practices, as part of numeracy and maths supports for teachers.

Depending on the progress made, 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 7.

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