I end work on the risp to have a plenary, gathering together what has been discovered in a whole class setting.
I would note that this is not a lecture, which is guaranteed to kill off student interest,
but rather a joint construction of the theory that emerges from the risp.
I am always aware of the need to improvise here.
Although I have in mind the theory I wish to head towards,
each class requires me to construct a different route to my goal.
I could invite a student to address the class at this point.

I tend to do the note-taking on IWB while the students watch as they contribute.
Asking the students to make comprehensive notes themselves as we do this gives the illusion of useful work,
but while they are note-taking, they cannot really think.
Sometimes looking afterwards at notes students have taken,
I am shocked by how two or three slight errors can render the notes near to useless.
Mathematics is so concise a language that this can often happen.

I can now introduce related new theory that the risp does not immediately address.
I find that students quite happily accept this part of the work with great concentration:
the fact that they have asked to think independently at the start of the lesson
somehow legitimates this more teacher-centred part of the lesson.

I save these notes from the IWB as a pdf, and email this to the class.
Thus each student is given a summary of the theory, to which they have contributed,
that is unique to that particular class and that particular lesson.
They may then need to engage with these notes, by underlining, highlighting, linking and so on, to make them their own.

Now it is time to consolidate the theory of the lesson.
This does not have to mean exercises from books:
the kind of group work, often involving games, that the Standards Unit promoted in 2005 would be ideal.