This story provides the scenario for playing a game on a graph. It
can be played on the graph of Land of Many Ponds or on any other graph
available here, or on graphs that students draw themselves. At the end
of the story the Monster and Superperson have begun to solve their
problem, but it is not completely clear what they should do next. The
students who play the role of Superperson and the Monster will have to
decide what to do. The planning and strategies that the characters
will need to do will change when the game is played on different
graphs. Playing the same game on different graphs helps students
understand the structure of graphs in general, and to make inferences
about properties that can be used to distinguish one from another.
If students have not heard or read the story of how Superperson Saves the Monster it may help to give them a little bit of background. (For example, to explain how each of the characters flies. ) Tell the students that the adventures of Gertrude, Superperson and
the Monster continue, and that you will read them a different story
that explains a game that can be played by the three characters.
Select students to play the roles of Gertrude, Superperson, and
the Monster. Encourage them to play their parts with as much drama as
possible.
When the story ends, Superperson and the Monster have managed to
clear one pond of pollution. Now they must do the rest. The precise
strategy that they used to clear the first pond will not work in
exactly the same way again. The students will have to figure out what
to do to force Gertrude to fly into all of the ponds one at a time.
Remind Superperson and the Monster that they can only talk to each
other and make plans about where they will go next when they are in
the same pond together. Be aware that before they set out each time they have to
agree the following:
the route by which they will each return to Gertrude's
pond so
that they can force her to fly into the next pond they want to clear
out.
where they will have to fly in order to return to Gertrude's
pond by that route
how to time their flight so that they both arrive in
Gertrude's pond at exactly the same time.
Help the students to articulate the strategies that they want to
use.
Ask the students what will happen if they play the game on
different graphs. Have them experiment with different graphs to see
if their predictions are correct. Below are a few graphs you can try, and there are many others as well.
Draw some graphs that you think will be interesting to try the game on.
Consider some of the variations for the other games and stories. Which ones will be interesting to try here? What do you think will happen?
Invent new variations. Send in your favorite ones.
Materials 
