Packing pennies onto a piece of paper provides perplexing problems for students to ponder. To set the stage for students to gain insight into penny-packing problems, we suggest that you provide groups of students with small sheets of paper and an ample supply of pennies. At the start of the investigation, a quarter of a standard-size 8.5 in.- by-11 in. sheet of paper is sufficient for each group. Ask the groups to cover their paper completely with pennies. Students typically choose one of the covering patterns shown in figure 1 and figure 2. As part of the task, students should determine the number of pennies needed to completely cover the paper using each pattern. The penny-packing problem is, Which pattern guarantees the most pennies on the page?
They are committed to designing and exploring rich problem settings, especially those with a historical context that enlivens mathematics content.