Lion Hunting
Why do this problem?
Spotting the patterns underlying apparently random data is one of
the most important jobs of industrial mathematicians and
statisticians. This problem allows students first to identify
different sorts of patterns and then to try to refine their notions
of these patterns. They will use a wide variety of mathematical and
statistical problem solving skills in this activity. It can be
approached on a variety of levels, from quite simplistic to very
detailed.
Possible approach
First approach the problem as a game. If the activity is being
done individually, try to guess the location grid square in as few
guesses /sightings as possible. If the activity is being done as a
group, try taking turns to guess with a new sighting being given on
each turn. The group will need to try to describe in words the
square of interest if they do not have control of the whiteboard.
This will help to focus their minds on the variable parameters in
the problem.
Next try to repeat for a few different lions. Can the group
spot any recurring themes in the types of pattern exhibited? Once
you have some suggestions for the patterns, make and test your
hypothesis.
Once the distributions have clearly been discovered, try to
estimate the parameters involved.
At each stage, try to be as presicse as possible with any
statistical / probabilistic statements.
Key questions
- In trying to maximise a score on the game, what features do we
look for when making the decision to make a guess?
- How would you describe the configuration of sightings at each
stage?
Possible extension
Estimate the parameters used by the program to determine the
behaviour of the lions by building up a set of data from several
sets of sightings.
Possible support
Playing the game several times is the best way into this
activity. It will naturally raise statistical questions even if
these are not formally explored. If several computers are
available, see who can obtain the highest score in, say, a five
minute period.