When a number is multiplied by itself multiple times, it can be written more simply in exponential form.

An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

Checking and securing understanding of multiples of 10

Maths

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

In the prior unit, pupils learnt how to factorise multiples of 10 in order to simplify calculations. This understanding is built on in this unit as values are converted to meet the conditions for standard form. 

In this unit pupils learn to recognise, interpret and write in standard form. Pupils then extend this knowledge so that they can order numbers written in standard form.

Standard form

A prime number is an integer greater than one with exactly 2 factors. All integers greater than 1 are either composite or prime.

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 further securing understanding of the commutative law

Multiples of 10 involving negative exponents

Standard form is when a number is written in the form A × 10^n, (where 1 ≤ A < 10 and n is an integer).

Writing large numbers in standard form

The associative law states that a repeated application of the operation produces the same result regardless of how pairs of values are grouped. We can group using brackets.

Standard form

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These lessons will be removed by end of Summer Term 2025.