This 7th century visualisation of quadratic algebra, thanks to Islamic scholars, is a great place to start the academic year in mathematics.
Problems with straight line graphs
Rules of Indices provide an excellent first look at a developing mathematical structure. You start with a definition which provides a nice rule. You then generalise, trying to preserve the rule. What you get is a marvellous structure which is all a consequence of the first definition.
Arithmetic Progressions, much loved by students of AS Core Mathematic, is an early result in my favourite Victorian textbook and has a good visual proof too.