1
Prime Factorisation
Classify numbers as prime, composite or neither using divisibility and factor checks
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Real Numbers
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2
Prime Factorisation
Write a natural number uniquely as a product of prime factors
3
Fundamental Theorem of Arithmetic
Explain existence and uniqueness of prime factorisation with examples
4
Fundamental Theorem of Arithmetic
Compare and reason about numbers using their prime factor forms
5
HCF and LCM
Calculate highest common factor from common prime powers
6
HCF and LCM
Calculate least common multiple from maximum prime powers
7
HCF and LCM
Use HCF × LCM = product of two numbers and check when it applies
8
HCF and LCM
Model grouping, sharing and arrangement situations using HCF
9
HCF and LCM
Model repetition, timing and synchronization situations using LCM
10
Irrationality Proofs
Follow the contradiction structure used in irrationality proofs
11
Irrationality Proofs
Write a complete algebraic proof that √2 is irrational
12
Irrationality Proofs
Adapt the irrationality proof method to √3 and √5
13
Irrationality Proofs
Use closure and contradiction to prove expressions involving surds are irrational
14
Real Number Reasoning
Detect invalid assumptions and incomplete contradiction steps
15
Real Number Applications
Use prime factors to explain packaging, tiling and repetition patterns
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