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  • Subject Area

    • Math: Middle Grades Math: Algebraic Thinking
    • Math: Middle Grades Math: Basic Facts
    • Math: Middle Grades Math: Measurement
    • Math: Middle Grades Math: Number Sense
    • Math: PreAlgebra: Number Sense and Operations
    • Math: PreAlgebra: Measurement

  • Author

    Texas Instruments

  • Level


  • Activity Time

    60 Minutes

  • Device
    • TI-30X IIB
    • TI-30X IIS
    • TI-34 II Explorer Plus™
  • Other Materials
      This is Activity 6 from the EXPLORATIONS Book:
      Math Investigations with the TI-30X IIS: Activities for Secondary Mathematics

      The following materials are required for this activity:
    • Scissors and paper
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The Tortoise and the Hare

Activity Overview

Students develop patterns using two or more rational number quantities. They comprehend the concept of functions by understanding the relationship between these quantities and their sums.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 60 - 62 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the activity procedures:

  • Fold a paper in half and cut along the crease
  • Determine the fractional part of the whole sheet that each equal half represents
  • Continue the process for each resulting sheet of paper, and use the calculator to find the fractional part
  • Understand that dividing a number by 2 is the same as multiplying it by 1/2
  • Try to reconstruct the whole sheet by arranging the smaller sheets of paper
  • Use the calculator to represent the sum of the pieces in the reconstructed rectangle
  • Observe that the sum of fractions approaches 1 as more fractions are added
  • Determine the decimal approximations of the sum of pieces at each stage
  • Generate a similar pattern for fractions 1/3 and 1/4
  • After the Activity

    Students complete the Student Activity pages and use the results to answer questions about the race between the tortoise and the hare.

  • Review student results
  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary