# Activities

• • • ##### 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 9-12

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

## 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.

• 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