Why do this problem?
This problem is a good way to engage students with many ideas in
statistics. It can be accessed at a variety of levels.
The activity works well as a group discussion. The most important
features are the questions raised by the process. Students may come
up with their own statistical questions in using this activity. It
can be related to basic intuitive
probability or more formal expectation analysis. Questions of
convergence of the expression for the area can also be adressed
informally or related to ideas surrounding the central limit
theorem and the law of large numbers.
- What is the chance of a randomly thrown cell falling under a
- Are there any cells which might be problematic? How might we
deal with those?
- How reliable would you think that this method might be?
Able students will want to focus on the question of creating an
algorithm for deciding when to stop generating random squares. They
can also relate this to work on the central limit theorem. They
might like to consider a refinement of the algorithm which takes
into account the boundary of the shape.
Just using the activity in a hands-on fashion to find areas by
recording whether randomly generated squares fall under or to the
side of a shape can really reinforce the understanding of basic
ideas in statistics. Encourage students to note when questions or
uncertainties in the process arise.