An exploration of Euler's phi function, spotting patterns and building increasingly powerful rules for calculating its values.

The notation will not feel familiar to younger pupils. See notes below.

• Factors and prime numbers
• Index notation
• Substitution into simple formulae
• Basic familiarity with function notation*

*This may, however, be a good opportunity to gently introduce pupils to function notation. Perhaps it would be best suited as an end of term activity not long before pupils go on to study function notation.

1. Introduce pupils to the notation before handing out sheets. As per 'prior knowledge' this investigation would work best with pupils who are soon to move onto function notation.

2. Distribute one copy of attached A3 pupil sheet to each pupil, and have a copy of A3 teacher sheet printed for reference.

3. Pupils are instructed to check their answers at the end of section 3, but I suggest quickly reviewing the sheet to decide if you would like to check answers at another point.