This research was centered on exploring the multiplication of varying sums of ones. Given any number of ones, the first step in this exploration was to group them in different sized boxes. For example, we started with ten ones. One possible grouping was three in one box, two in another, and five in another. This yielded the product 3∙2∙5=30. Alternatively, another grouping was four in one box, four in another, one in a third box, and one in a fourth, which yielded the product 4∙4∙1∙1=16. The goal was to find the configuration of boxes that led to the largest product for any given amount of ones. Many examples led to a generalization about how to find that product. Throughout this workshop participants will be given the opportunity to experience the exploration firsthand using manipulatives. Following the exploration, they will then be convinced of the validity of the generalization.
