Though we taught this lesson in a fourth grade classroom, we crafted it in response to a different classroom of fifth grade students who were struggling with story problems requiring division. Several teachers, Linda Fisher, and I then opted to introduce the “Singapore Bar Model” to students who had never seen it in before. We used the context of solving “division” story problems to introduce the model. In a neighboring classroom we taught a parallel lesson with the same content, but a “direct teaching” instructional style. Our intent was to compare student responses from the two lessons. We instructed the multiplication/division launch similarly in both lessons. Our goal in this was formative assessment of students’ understanding of these concepts and opportunity to engage in the foundational idea of equal parts. The role of the “number talk” was to connect the basic components of the Bar Model with students’ original thinking, thus front-loading students with several applications of the Bar Model as a representation of equal parts. For this lesson only, we designed the exploration of one or more story problems (we only got to one) with original pictorial representations in order to introduce the Bar Model as simply another representation to further our understanding of the problem and of division.
Students are challenged by interpreting language. In the exploration problem the words “three times” becomes a division problem or a missing factor problem. Students with fragile understanding of how multiplication and division are connected are challenged by this language. The intermediary step of drawing a “math picture” or model of the problem, poses a challenge for many students who have limited exposure to models. These students tend toward calculations without models or very detailed pictures which do not necessarily aid in understanding the mathematics of the story. It is an engaging challenge for students of all levels to attempt to make sense of someone else’s model or strategy. For some students, multi-digit multiplication became a challenge and distraction from the problem (which did not require multi-digit multiplication).