There are many elements of architecture that provide teachers and students useful opportunities for mathematical explorations. In this article I have only touched on a few aspects of what is possible with only one structure, the brick wall. More could be said about the patterns formed using coloured bricks, or the frieze patterns that are found at the edges of walls, or the patterns possible with non-rectangular bricks. The fact that even something as seemingly simple as a brick wall is rich in mathematics is a lesson I try to teach to future teachers, as an example of a way they might make their future students more aware of the presence of mathematics in the world around them.