We run a variety of events for school students.
The pop-maths quiz is an annual quiz for teams of students representing various schools. The quiz takes place in one of the big lecture theatres in a similar format to a pub quiz: the questions are read out at intervals, and they marked at the end of the session while the teams wait. There is a small prize for the winning team.
Lanacster University's Higher Education Summer School runs hands-on maths puzzle sessions.
Students from Millom School attended a master class in which they learnt about graph theory. A newspaper article about this may be found here.
They started by considering a simple problem from 1736. The diagram below represents the 7 bridges in the town of Königsberg. Can you design a walk to cross all 7 bridges and return to your starting point?

It turns out that this puzzle, and a wide range of seemingly unrelated puzzles, can be solved using graph theory.
Other problems that can be solved in this way include solving mazes, designing shortest routes for delivering the post and a fiendish puzzle known ``Instant Insanity'' (shown below).
The puzzle consists of four cubes, each face of which is decorated by a spot of one of four colours. The object is to stack the cubes on top of each other in such a way that each pair of touching faces are the same colour. The problem is quite hard to solve by trial and error but becomes much easier using techniques from graph theory.
In addition to events aimed specifically at school students, Lancaster University has occasional popular lectures that are of general mathematical interest. Recent lectures include ``Statistics in Sport'' by John Haigh and a lecture on codebreaking by noted science writer Simon Singh (pictured below).

We recently hosted the excellent Holgate lecture by Nick Gilbert on connections which attracted over 100 local school children