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.

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

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. 

Standard form

A {{ }} number is an integer greater than one with exactly two factors.

Which of the following products only use prime numbers?

Write 200 as a product of its prime factors.

Use the fact that 60 = 2² × 3 × 5 to write 180 as a product of its prime factors.

Use the fact that 60 = 2² × 3 × 5 to write 20 as a product of its prime factors.

165 = 3 × 5 × 11 and 42 = 2 × 3 × 7. Which of the following is the most useful arrangement to calculate 165 × 42?

Using the Gattegno chart or otherwise, work out which of the following calculations equate to 48.

Using the Gattegno chart or otherwise, match each calculation to its correct answer.

Using the associative law to partition 5000 and 7000 into powers of 10, find the calculations that are equivalent to 7000 × 5000.

Which of the following calculations are equivalent to $$3000\times2000$$?

Without using a calculator, work out 0.007 × 30.

Which of the following calculations are equivalent to $$4.5\times0.05$$?

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