# It's All in the Numbers

Mathematics

Level 5Level 6Level 7

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.

 Big understandings We need a deep understanding of numbers and how to manipulate them to solve every day mathematical problems.

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.

Overview of stages

• 1. Visualising Multiplication

Suggested Learning Intentions

• To multiply two-digit numbers by partitioning them into smaller numbers, using a visual model as a support

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• 3. Daniel's Great Flight

Suggested Learning Intentions

• To position and compare positive and negative numbers on a number line
• To develop strategies for adding and subtracting positive and negative numbers

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• 5. Number Puzzles

Suggested Learning Intentions

• To use recognised problem-solving strategies to solve a number puzzle

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• 2. Liquorice Factory

Suggested Learning Intentions

• To develop an understanding and definition of prime numbers

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Suggested Learning Intentions

• To improve fluency when working with a range of mathematical operations
• To learn how to correctly use different operations to evaluate mathematical statements

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• 6. Number Properties

Suggested Learning Intentions

• To explore a range of number properties and use these properties to arrange numbers into sets
• To recognise that some pairs of sets can have common numbers, and some pairs of sets do not have common numbers

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• Prior knowledge

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.

Teaching strategies

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)

Vocabulary

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:

 Array Square root Prime numbers Factorial Prime factors Composite number Divisibility Square number Integers Triangular number Sets of numbers

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.

Assessment

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.

Victorian Curriculum connections

Contents

Level 5

This sequence addresses content from the Victorian Curriculum in Mathematics and Critical and Creative Thinking. It is primarily designed for Level 6, but also addresses the following content descriptions from Level 5:

 Content description Stage Mathematics Identify and describe factors and multiples of whole numbers and use them to solve problems (VCMNA181) Visualising Multiplication Liquorice Factory Number Properties Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (VCMNA183) Visualising Multiplication Operation Overload Critical and Creative Thinking Investigate thinking processes using visual models and language strategies (VCCCTM029) Visualising Multiplication Daniel’s Great Flight Operation Overload Number Puzzles

The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum in Mathematics Level 5:

• Students solve simple problems involving the four operations using a range of strategies
• Students identify and describe factors and multiples.

Level 6

This sequence addresses content from the Victorian Curriculum in Mathematics and Critical and Creative Thinking. It is primarily designed for Level 6, addressing the following content descriptions:

 Content description Stage Mathematics Identify and describe properties of prime, composite, square and triangular numbers (VCMNA208) Liquorice Factory Number Properties Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers and make estimates for these computations (VCMNA209) Visualising Multiplication Operation Overload Number Puzzles Investigate everyday situations that use integers. Locate and represent these numbers on a number line (VCMNA210) Daniel’s Great Flight Explore the use of brackets and order of operations to write number sentences (VCMNA220) Operation Overload Critical and Creative Thinking Investigate thinking processes using visual models and language strategies (VCCCTM029) Visualising multiplication Daniel’s great flight Operation overload Number puzzles

The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum in Mathematics Level 6:

• Students recognise the properties of prime, composite, square and triangular numbers and determine sets of these numbers
• Students solve problems that involve all four operations with whole numbers and describe the use of integers in everyday contexts
• Students locate … integers on a number line
• Students write number sentences using brackets and order of operations.

Level 7

This sequence addresses content from the Victorian Curriculum in Mathematics and Critical and Creative Thinking. It is primarily designed for Level 6, but also addresses the following content descriptions from Level 7:

 Content description Stage Mathematics Investigate and use square roots of perfect square numbers (VCMNA239) Operation Overload Apply the associative, commutative and distributive laws to aid mental and written computation and make estimates for these computations (VCMNA240) Visualising Multiplication Operation Overload Number Puzzles Compare, order, add and subtract integers (VCMNA241) Daniel’s Great Flight Operation Overload

The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum in Mathematics Level 7:

• Students solve problems involving the order, addition and subtraction of integers
• Students make the connections between whole numbers and index notation and the relationship between perfect squares and square roots.

Learning Progressions

The Numeracy Learning Progressions support teachers to develop a comprehensive view of how numeracy develops over time. You can use the Numeracy Learning Progressions to:

• identify the numeracy capability of your students
• plan targeted teaching strategies, especially for students achieving above or below the age-equivalent expected level in the Victorian Curriculum: Mathematics
• provide targeted feedback to students about their learning within and across the progressions.

The sequence is related to the following progressions:

 Learning Progression Level 5 Level 6 Level 7 Quantifying number Understanding place value Understanding place value (directed numbers) N/A

Click on the Learning Progression to access more detailed descriptions of student learning at each level.