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