In this section, students develop a general algorithm for dividing a fraction by a fraction, pulling together the thread of reasoning from earlier lessons.

First, students use tape diagrams to reason repeatedly about division of a whole number by a unit fraction. They look for structure and regularity in the process. Then, they do the same with division by a...

In this section, students make sense of division situations involving fractions, gradually building an understanding that can later be generalized into an algorithm.

The first four lessons explore “How many groups?” questions in various contexts. In the first lesson, the size of a group is a fraction and the number of groups is a whole number. This lesson is optional...

In this section, students apply their insights about multiplication and division, as well as prior knowledge about area and volume, to solve geometric problems.

Students first solve multiplicative comparison problems in contexts that involve fractional lengths in one dimension. They use their understanding of division to answer questions such as “How many times as tall or as far is this...

In this section, students investigate the quantities in a division situation, recall the relationship between multiplication and division, and revisit ways to represent this relationship.

First, students look at how the numbers in a division situation are related. Students observe—in concrete and abstract situations—how the size of the dividend and the divisor affect the size of the quotient. Next, students...

In this final section, students have the opportunity to apply their thinking from throughout the unit. As this is a short section followed by an End-of-Unit Assessment, there are no section goals or checkpoint questions. The first lesson in this section is optional because it consolidates the concepts from this unit with those of an earlier course. It offers additional...