We analyze how middle grades teachers in a professional development program reasoned about fraction arithmetic using length and area models. We discovered that teachers' abilities to partition length and area quantities were critical. In particular, we focus on ways that teachers' used multiplication factor/product relationships, distributive reasoning, and levels of units. Our findings contribute to the learning sciences' growing understanding of what teachers must know in order to use drawn representations effectively in instruction.
['Chandra Hawley Orrill', 'Andrew Izsák', 'Erik Jacobson', 'Zandra de Araujo']
Teachers' understanding of partitioning when modeling fraction arithmetic