Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.

Prime factors are the factors of a number that are, themselves, prime.

Prime factorisation is a method to find the prime factors of a given integer.

Checking and securing understanding of prime factorisation

Maths

Converting any recurring decimal to a fraction

Checking and securing understanding of LCM and HCF

Checking and securing understanding of roots and integer indices

The laws of indices - multiplication

The laws of indices - division

The laws of indices - raising a power to a power

The laws of indices - negative and zero exponents

The laws of indices - fractional exponents

Advanced problem solving with the laws of indices

In this unit, pupils formalised their understanding of the index laws. This understanding will allow them to perform calculations with values written in standard form more efficiently.

The conditions for standard form mean that pupils have explored how different powers of 10 can be written in the prior unit. In this unit, this understanding is generalised and the index laws formalised.

In this unit pupils learn how to manipulate indices and perform calculations without conversion by understanding index laws.

Arithmetic procedures: index laws

What number is written as $$2 × 5^2 × 19$$ as a product of its prime factors? 

What number is written as $$2 × 5 × 31$$ as a product of its prime factors? 

What number is written as $$3 × 5 × 11$$ as a product of its prime factors? 

Which of these is a prime factor of 10905? 

Which of these is the prime factorisation of 450? 

Which of these is the prime factorisation of 539? 

Calculate 0.25 × 0.94, giving your answer as a decimal.

Calculate 3.25 × 7.94, giving your answer as a decimal.

Calculate -0.3 + 9.1, giving your answer as a decimal.

Calculate 0.28 ÷ 0.04, giving your answer as a decimal.

Checking and securing understanding of prime factorisation

Lesson outcome