This video begins with an introduction to the preconceptions around the use of algebra and algebraic thinking and refers to early lessons for algebra, ‘unknown numbers’. Derek provides an anecdote relating to his time at secondary school and his misunderstanding of what algebra truly is. He presents his aim for this section as one that explains the meaning of algebra as first and foremost about ‘expressing generalisations’. Derek argues that thinking algebraically is about recognizing the patterns in numbers and relationships that always occur and expressing them.

The video then shows a definition on screen: a variable is a quantity than can vary. Derek provides an example of this by explain that he has 32 students in his class but the number that turns up each day is a variable and subject to change. This is explored further using a range of different expressions of generalisations with words. Algebra is explained as a way of expressing different quantities. Derek then uses the whiteboard to help visualise algebraic representation, attributing certain letters to certain amounts.