I. In this investigation, we will use graphing calculators to determine the total number of pennies needed to build a "pyramid" 20 rows high.

 

II. Use you pennies to create pyramids that grow one row at a time. Then fill in the table below:

table

III. Use the lists on your calculator to determine a formula for the number of pennies needed to construct a pyramid "n" rows high:

IV. Now use your formula to answer the following questions:

  1. How many pennies are needed for 33 rows:
  2. How much money would you have if you had a pyramid 59 rows high?
  3. George has $4.00 worth of pennies. How large of a penny pyramid can he make. How many pennies will he have left over?

V. Triangular numbers are important mathematically because they represent the sum of the first "n" integers. On the back, we will analyze a mathematical pattern with a science connection.