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