It's All in the Numbers

This learning sequence aims to build students’ capability to work with and classify whole numbers.  It aims to develop student understanding of whole number operations – including addition, subtraction, multiplication, order of operations, factors, and multiples – by providing opportunities for students to use these concepts in new and challenging ways. The sequence also broadens students’ understanding of number through exposure to prime and composite numbers, square and triangular numbers, and integers.

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

There is a strong focus within the 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 three stages are contextually based and are dedicated to ‘sense-making’, allowing students to develop the proficiency of Understanding.
• The fourth stage has a strong focus on skill development, enabling students to develop the proficiency of Fluency.
• The fifth and sixth stages provide opportunities for students to work on open-ended problem-solving tasks, requiring students to use the proficiencies of Problem Solving and Reasoning, as well as some of the skills developed throughout the first two stages.

While Fluency is the particular focus of the fourth stage, each task provides opportunities for students to develop fluency in a range of concepts and ideas.

Before you commence this sequence, it is suggested that you ensure your students are familiar with odd and even numbers, common multiplication and division facts, and factors and multiples.

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 VCMNA151, VCMNA155 and VCMNA181 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. 

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

• Excavating (used specifically in Operation overload)
• Guiding (used specifically in Visualising multiplication)
• Orienting (used specifically in Daniel’s great flight)

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 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 6.

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.