The Finger Counting Problem

I was intrigued by this problem posted on the computer forum last night and I used it with my groups this morning.

count 1, 2, 3, ... on your fingers, starting with your thumb and going back and forth on your hand. On what finger will you reach 1704? 2476? 3121? When counting, be sure not to "double count" on any fingers.

To keep solutions consistent, let P be your pinky finger, R be your ring finger, M be your middle finger, I be your index finger, and T be your thumb. Use these variables when you write your solutions.

I had students trace their hands and write the numbers on the fingers they would count on, telling them they should be looking for a pattern. On each finger a clear pattern emerged which helped them to answer what fingers the larger number would land on. Then we divided the larger number by 5 (the number of fingers on the hand) and found that the remainder also helps identify which finger the number will land on. From there, we went on to looking at patterns in charts and continuing them and also writing them as an algebraic expression.