In this lesson, students learn to use tape diagrams to represent and answer “How many groups?” questions. Tape diagrams are more abstract than are other visual representations that students have used or may have created, but they offer greater flexibility for making sense of problems that involve fractions. Students also continue to write multiplication and division equations for each situation, engaging in abstract and quantitative reasoning as they do so (MP2).

At the start of the lesson, students solve problems with a quotient that is a whole number or a multiple of one-half and with a blank tape pre-drawn on a grid. As the lesson progresses, students work with a wider range of numbers and with less scaffolding for creating diagrams. For instance, in the first main activity, a grid is given but students need to draw their own tapes. In the last activity, no grid is given.

As students use diagrams to show known values and to reason about unknown values, they practice communicating with precision (MP6).