Sequence II: LT level for composition of splits
In this sequence, the teachers explored emergent relationships from the EPLT through an
investigation of the ways that task parameters interact with students’ approaches to
equipartitioning a whole. The goal of the sequence was for teachers to examine how
students use composition of splits as described in the ELPT and come to understand the
ways various parameters of tasks influence difficulty for students. For the engaging prompt
of the sequence, teachers were asked to organize, according to the level of difficulty,
exercises of folding square and circular pieces of paper into a variety of numbers of equalsized
parts. The exploration activity required teachers to examine composition of splits
(Confrey 2011a) and was adapted from Empson and Turner (2006). Following a discussion
of the activity in which the specifics of the task parameters were formalized, teachers
applied this knowledge to order four assessment items in increasing difficulty and to