'Prime factor lock' is a reimagining of our 8.4 sequence 'Prime Factorisation', aligned to AC V9
- On the 'In this sequence' tab you'll find all the lessons in this sequence, a suggested implementation plan and curriculum alignment.
- The 'Behind this sequence' tab shows how key mathematical ideas develop over the sequence.
- Have you taught this sequence? Use the Feedback button to let us know how it went!
Lessons in this sequence
Task 1 • Factor lock
Students learn about prime number encryption and explore the number of possible pairs of primes in a grid. They explore how the number of combinations increases as the grid grows, and decide how many possible combinations are needed to create a secure lock.
Task 2 • Composite factor lock
Students test a composite-number lock where the numbers swiped must multiply to give the target product 480. They use factor pairs to find two-number swipes, then investigate how they can split factors to create three-number swipes with the same product.
Task 3 • Factor strings
Students express composite numbers as products of prime factors using exponent notation. They systematically generate and count factor strings for given composite numbers, then compare results to investigate how prime-factor structure affects the number of possible strings.
Task 4 • Designing a factor lock
Students design and justify a factor lock that balances security and practicality. They choose a composite lock number, organise its factor strings, select and populate a grid with factors, then use an interactive digital tool to test and refine their design.
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Curriculum and syllabus alignment
Year 7
Students represent natural numbers in expanded form and as products of prime factors, using exponent notation.
Number
Represent natural numbers as products of powers of prime numbers using exponent notation
The sequence begins with a short video about the role of prime numbers in banking security. This provides a hook for the idea that large numbers can be built from prime factors, but that working backwards to identify those factors can be difficult. Students then work with a simplified phone-lock context that allows them to explore these ideas with factor strings and grid designs.
Computational thinking is introduced through the mathematics rather than as a separate set of skills. Students decompose a lock number into smaller factors, recognise the fixed structure of the number’s prime factorisation, and develop a repeatable method for generating factor strings without omissions or duplicates. In Task 3, a branching tool for organising factor strings shows how to keep factors in ascending order and repeatedly split the final factor into two smaller factors. This makes the systematic process for generating and counting factor strings visible.
The final Build task brings these ideas together in an open design challenge. Students choose a lock number, grid size, and arrangement of values, then use an interactive tool to compare lock numbers, populate a grid and check which mathematical factor strings are available as connected swipes. They have flexibility in how they communicate their final design but must show the mathematical reasoning behind it: the prime factorisation, an organised record of factor strings, the final grid and a justification of how their choices balance security and practicality.
'Prime factor lock' is a reimagining of our 8.4 sequence 'Prime Factorisation', aligned to AC V9
- On the 'In this sequence' tab you'll find all the lessons in this sequence, a suggested implementation plan and curriculum alignment.
- The 'Behind this sequence' tab shows how key mathematical ideas develop over the sequence.
- Have you taught this sequence? Use the Feedback button to let us know how it went!