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Averages and The Phantom Tollbooth

  • Lesson
Data Analysis and Probability
Location: Unknown

Students participate in activities in which they focus on connections between mathematics and children's literature. Using The Phantom Tollbooth as a literature basis, students explore the concept of averages.

In the delightfully fantastic The Phantom Tollbooth, Milo and his watchdog, Tock, travel through Dictionopolis and Digitpolis. Milo's mission is to reunite the princesses of Dictionopolis (Rhyme) and Digitopolis (Reason) so that the world will once again have rhyme and reason. While completing his mission, Milo and his companions experience many language and mathematical concepts.

This lesson should be completed after students have had the opportunity to read The Phantom Tollbooth. Teachers may wish to read portions of the story aloud in class each day, or students may be assigned the book as independent reading.

Discuss the meaning of averaging as a "leveling" process. Ask students to identify situations where they have experienced averaging the past (grades, baseball statistics, and so on).

Distribute copies of the Can It Be? Activity Sheet.

pdficonCan It Be? Activity Sheet

Direct students to read each scenario from The Phantom Tollbooth and to write their explanations in the spaces provided. Encourage students to share their responses in a class discussion.

For the third question on the activity sheet, students will need access to newspapers or online newspaper resources. They may work individually or in pairs to complete this activity.


  • Hopkins, Martha. "Ideas: Mathematics and Children’s Literature." The Arithmetic Teacher. May, 1993.  pp 512 - 520.
  • Juster, Norton. The Phantom Tollbooth. New York: Random House, 1961.


  1. Ask students to find other discussions of averaging the The Phantom Tollbooth and to decide if Milo's friends are telling him the truth.
  2. Students can use almanacs and online resources (such as census information) to research the current average number of children per family. How does this number compare to the number found in the story?

Learning Objectives

Students will:
  • Explore and interpret the concept of averages.

NCTM Standards and Expectations

  • Find, use, and interpret measures of center and spread, including mean and interquartile range.
  • Use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken.

Common Core State Standards – Mathematics

Grade 6, Stats & Probability

  • CCSS.Math.Content.6.SP.A.3
    Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.