## Lesson abstract

This lesson introduces prime factorisation. Students search for factor strings using the context of a puzzle and then justify that the longest factor string for a number is made up of primes. This introduces The Fundamental Theorem of Arithmetic: that all whole numbers greater than 1 can be represented as a product of prime numbers in exactly one way. Students then create similar puzzles and participate in a short class challenge to look at why prime factorisation is used to encrypt information.

## Mathematical purpose (for students)

To find strings of factors that make up a composite number and investigate how different strings are related to each other.

## Mathematical purpose (for teachers)

This lesson introduces *The Fundamental Theorem of Arithmetic:* that all whole numbers greater than 1 can be represented as a product of prime numbers in exactly one way. It provides experience in writing numbers as products of prime numbers and in other ways, including with index notation.

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