What is hybridisation and how can it be used to explain the shapes of molecules?

Before we start on exploring the implications of hybridisation, we should start with a definition. Hybridisation can be thought of as the mixing atomic orbitals into new hybrid orbitals suitable that can be used to create chemical bonds. It is an important part of valence bond theory.
When these orbitals are mixed, they take on new properties. The most important ones for us as the shape and energy of the new orbitals. This is most easily described using an example. Let's have a look at what happens when we mix s and p orbitals together.
[diagram of relative energies of s and p orbitals, and their shapes]
The easiest way to think about this is using the phases of the orbitals. If we add an s orbital to one of the p orbitals, the in-phase parts will add together and two new orbitals are produced. The other two p orbitals remain the same. The new orbitals are called "sp" orbitals, and they can be thought of as 50% s orbital, 50% p orbital. They are halfway between the energies of the s and p orbitals before they were mixed. They are collinear, and will form linear bonds. This is the type of bonding scene in alkenes. [diagrams to demonstrate these points].
In the lesson, I would ask the student to try and apply the same logic to sp2 and sp3 orbitals to demonstrate their understanding.