The Power of Numbers...

DESIGN OF THE PAY IT FORWARD ACTIVITY:
The activity will investigate the power of numbers by looking at exponential growth. Trevor's idea of "paying it forward" involves the mathematics of exponential growth.

LEARNING OUTCOMES:

• Students see how quickly powers of a number increase
  (exponential growth)
• Students practice using exponents
• Students recognize and extend patterns
• Students make connections to other curricular areas and their environment (science, pay it forward concept, etc.)

1. Students use a sheet of paper to show how quickly powers of numbers increase (exponential growth)
   • a) Fold a sheet of paper in half. Unfold the paper. Into how many parts has the paper been separated. (Fill in chart)
   • b) Refold the paper. Now fold it in half again. Unfold the paper. Into how many parts has the paper been separated? (Fill in chart)
   • c) Continue the process of folding and unfolding the paper. After each fold, open the paper and count the number of parts into which it has been separated. Record the results in a table like the one below.

   

   • d) Look at the data in the table and describe the numbers in the row labeled "Number of Parts". (numbers are powers of 2)
   • e) How many parts would the paper have if you could fold it seven times? Ten times? Twenty times?
   • f) At this point, it might be impossible to fold anymore but students can predict what the numbers might be by looking at the pattern that has developed. (22, 23, 24, 25, 26, etc.)

2. Pay It Forward Connection

   • a) Tell the basic story of "Pay It Forward". (A student, Trevor, chooses to help 3 people and asks them not to pay it back to him but to "pay it forward" to 3 other people. Those people then "pay it forward" to 3 more, etc.)
   • b) Using the same concept as the paper folding, students will look for patterns as they put the data into the table (sample below)

   

   • c) Continue with the pattern and filling in the table as students see how many people will be affected by acts of kindness started by ONE individual.
   • d) Have students find out the population of their school and/or community. How many cycles would it take before everyone in his/her school, community, state would be affected?

3. To illustrate the power of numbers, one student can give three students a blue dot that is pinned to their clothing (anything can be substituted for a blue dot). Those three give a blue dot to three other individuals, etc. Students are then able to visually see, as they walk around the school, how quickly the number of people affected grows.

RESULTS AND EVALUATION:

1. Performance Assessment:
   • The teacher assigns groups (three in a group) their task.
     • Design a project that demonstrates the power of numbers (exponential growth).
     • Include (1) Goal(s) (2) Procedure(3) Table illustrating the mathematics involved (4) Results

   • Share Back Projects