Marcy’s Dots - sequence

Date February 2006
Class Algebra
Teacher Joyce Cook

Marcy’s Dots activity. 

I asked students to answer the following 2 questions:
1.  How many dots are in the 20th step?
2.  Write an expression for the number of dots in any step.

I passed out the papers and told them to make a chart of the steps.  I saw many struggling, so I told them to go by dimensions of the dots, rather than total dots.  I gave them 10 minutes to work on it. Out of 15, 6 answered both questions correctly, 5 could find the 20th step but not the general expression, and only 4 could not answer either question.  I was rather pleased with the results, particularly that 3 of the 4 were lower students.  I think the 4th student was just having a bad day. I am still somewhat concerned that so many students cannot think in terms of general expressions.  Some of the middle group described how to find the total number of dots for any step, but could not write it in terms of a variable.