Graphs, Stories, and Games


Gertrude, Superperson and the Monster are the main characters in a series of stories. They are introduced in Superperson Saves the Monster, and their adventures continue in Gertrude, Superperson and the Monster Recover from a Disaster.

Each story can be acted out on a graph that is drawn on the floor, with a student taking the part of each one of the characters. The action and the situations in the stories explain the requirements and the constraints for how each of the characters moves about the graph. The endings of the stories remain somewhat open, because what Gertrude, Superperson and the Monster eventually do depends, not only on the choices that the students make as they act out their parts, but on the graphs that are chosen to play the games.

Play the games first with the graphs that are recommended, then try them on different graphs. As they play the games on various graphs, students can discover many different properties of the mathematical objects called graphs.

Students can also play the games on a table using a graph that is drawn on a piece of paper for a game board and moving marking pieces that show the actions of the characters.



Ideas for discussion

Varying the Game



  1. Explain to the students that the figure on the floor is a game board and that they are going to play a game which is best explained by a story. The story has three characters in it: Gertrude (a goose), Superperson, and a Monster. Select a student to play the role of each of these characters.

  2. Tell the students that the circles represent ponds in the land where Gertrude, Superperson and the Monster live. To begin the game, the three characters must select the ponds where they will start out. During the course of the game they will see that Gertrude has the least amount of moving power and she runs away from the Monster. So to give her as much advantage as possible, the Monster should select his place before Gertrude selects hers. Superperson chooses her place last.

  3. Read the story Superperson Saves the Monster and have the students act out their parts as the story moves along. The story serves as script and rule book for the game. Encourage the students to act out their parts with as much drama as possible.

  4. The game doesn't end when the story ends. The story simply provides enough information for the game to continue.

  5. After Superperson has saved the Monster from Gertrude, have a different group of students play the roles of the three characters. You can continue to read the story as they play, or a student might want to read the story. Once the students know the roles of all the characters, they might want to play without reading the whole story each time.

Ideas for Discussion

  1. Depending on the age and experience of the students, they will be able to figure out, after some number of rounds, that the Monster always catches up with Gertrude and that Superperson always saves the day.

  2. Help them to explore what difference various starting points for the three characters make.

  3. Help the students to articulate why it is easy to figure out what will happen. The concept of distance and diameter in a graph figure largely into the reason why. Provide them with that vocabulary when it will be useful to them in talking about their experience.

Varying the Game

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