A level and Further Maths
Rich Starting Points (RISPs)
We asked A-level teachers for sites they use with their students and James from Manchester said he finds the RISPs site (Rich Starting Points for A-level Core Mathematics – A Collection of Forty Open-ended Investigative Activities for the A-level Pure Mathematics Classroom) really useful.
The RISPs site is written and maintained by Jonny Griffiths from Paston College in North Walsham, Norfolk, and was originally written as part of a Gatsby Teacher Fellowship 2005-6, supported by the Gatsby Foundation.
A RISP can be used as a starting point for a new topic, for consolidation of a topic or for revision. For example:
RISP 28: Modelling the Spread of a Disease
A population is threatened by an infectious disease. Imagine that the population splits into two groups, the infected and the healthy. Each year, the probability that a healthy person catches the disease is c, and the probability that an infected person recovers is r. Each of you is going to model what happens to ten people over a period of ten years.
Everyone starts with eight healthy people and two infected people. Year zero on your list is 8 Hs and 2 Is.
We are going to assume that no-one dies (of any cause) over this ten year period.
For each person roll a die, for each year. If you roll a 1 or 2 for a healthy person, then they become infected that year (c = 1/3). If you roll a 1 for an infected person, then they recover that year (r = 1/6).
For everything else, there is no change.
When you have each completed 100 rolls of the dice, we can pool our data, to arrive at the total numbers of H/I people for the population for each year.
Let x = proportion of population that are infected.
What happens if we plot a graph of x against time?
What happens as x tends to infinity?
Can we model this situation with a differential equation?
Can you solve the differential equation?
What happens to the solution if we vary c and r?
Could you use this RISP with your students? When would you use it and how would you use it? Each RISP is backed by teacher’s notes. There are also articles on ‘How to use a RISP’ and on ‘What can go wrong.’
The site lists RISPs organised by topic and also in numerical order 1-40.
If you know of any other sites to recommend to other teachers of A-level or Further Maths, please let us know!