A. The first two entries in a table of numbers are given on the right. Write five more numbers in the table to create a linear relationship. Write five more numbers in the table to create an exponential relationship. Write five more numbers in the table to create a quadratic relationship.

B. Explain how you generated the numbers.

C. Write an equation for each relationship and explain how you got your equation.

1, 4, 7, 10, 13, 16, 19; 1, 4, 9, 16, 25, 36, 49 and 1, 4, 6, 7, 6, 4, 1; 1, 4, 16, 64, 256, 1024, 4096.

This problem was used as a professional development tool for teachers. Some believed that the quadratic pattern was unique because the other two were. On the other hand, some believed that any pattern that rose and then fell symmetrically would be a quadratic pattern; e.g., 1, 4, 6, 7, 7, 6, 4, 1. Discussions among the teachers about student solutions were very productive.