Sequence IV: LT level for sharing multiple wholes
During this sequence, teachers worked on two activities that addressed equipartitioning
multiples wholes among multiple people. The goal was to identify the various strategies
students use to share multiple wholes and to relate these strategies to the ways that
resulting shares are named. For the engagement prompt, teachers described the strategies
and naming practices that students use when sharing multiple wholes. For the exploration
activity, the teachers were paired and conducted clinical interviews with each other. The
interview protocol asked for sharing five cookies fairly among four, ten cookies among
seven, two pizzas among three, and then four pizzas among six. In the formalizing discussion,
the teachers’ strategies were compiled and related to strategies documented in the
EPLT. The sequence culminated in an application task where teachers analyzed student
work on assessment items that targeted this EPLT level. From the formalizing discussion
and application task of the sequence, we highlight the ways that the participants’ SMK
supported their participation.