## Who is this Sequence for?

Students undertaking this sequence need a reasonable fluency with multiplication facts, although the sequence provides further practice. Multiplication and division are required to find factors of a number. Students also need to know the definition of prime and composite numbers and be able to give examples. Either lesson 3 or 4 or both can be used after lessons 1 and 2.

## Summary of learning goals

This sequence of four lessons explores prime factorisation and how it can be used to solve problems related to the properties of numbers. The activities demonstrate why prime numbers are important. Proficiency goals are to reason mathematically about properties of numbers, and to carry out a mathematical investigation related to prime factorisation.

## Rationale for this sequence

Prime numbers form the building blocks of numbers. Every whole number can be represented as the product of prime numbers. Factorising numbers provides students with a deeper understanding of number and, most particularly, the properties of these numbers. Students are provided with opportunities to participate in mathematical investigations revealing prime factorisations as a powerful and efficient tool for identifying common factors and common multiples which has connections to many areas of mathematics, particularly work with integers and fractions.

The first two lessons in the sequence develop some ideas related to prime factorisation. Lessons 3 and 4 are substantial mathematical investigations that involve students in looking for patterns, and in generating and testing hypotheses. Investigations such as these develop students’ strategic knowledge and positive dispositions such as persistence.

While prime factorisation is an interesting study in and of itself, this concept plays an ever increasing role in our world today. The prime factorisation of numbers is used to encrypt data and protect personal details.

**reSolve Mathematics is Purposeful**

Prime numbers have formed an exceedingly rich area of mathematical inquiry since ancient times. This sequence is designed to highlight mathematics as a creative human endeavour while inviting students to participate in a deep exploration of prime numbers and prime factorisations. The ability to represent numbers as a product of primes provides students with a powerful tool to solve problems.

**reSolve Tasks are Challenging Yet Accessible**

The tasks in this sequence are designed so that they are founded in concepts explored in the previous years of the Australian Curriculum and then build and create connections to new content. Students engage in experiences that provide a common point of access, and enabling and extending prompts are included to address the needs of different students. The stars investigation is accessible because all students can begin by drawing stars and collecting information systematically.

**reSolve Classrooms Have a Knowledge Building Culture**

This sequence uses a variety of strategies to support the development of a supportive knowledge building culture. Open-ended investigations allow students the opportunity to discuss their own solution methods and to develop more efficient ways to solve problems. Visual aids such as class wall charts and materials such as prime dice help to stimulate discussion and to allow students to observe and reflect on each other’s work. Consolidation exercises are included to reinforce knowledge developed during the open-ended investigations.