1 Mathematical sentences and algebraic expressions

It is tempting to define algebra as the strand of mathematics that uses letters for numbers. However, the roots of algebraic thinking lie in paying attention to quantities and their structural relationships. One definition that respects this broader view holds that algebraic thinking can be can characterised by:

• Indeterminacy: the problem involves unknown quantities.
• Denotation: the unknown quantities are represented, for example by words or symbols.
• Analyticity: the unknown quantities are operated on as if they were known numbers (Radford, 2014).

In the next section you will be asked to have a go at an algebraic task. At the end of the section you will consider how it meets these three requirements.