Lesson 7

The purpose of this lesson is for students to solve problems involving multiplication of whole numbers by unit fractions and represent the problems with equations and diagrams.

In this lesson students interpret situations and solve problems that involve products of a whole number and a fraction. Students solve story problems in a way that makes sense to them and match stories with diagrams and expressions. They work with expressions and flexibly interpret a diagram to extend their understanding of the relationship between fractions and multiplication and division. For example, consider this image:

It shows $4 \div 3$ because there are 4 whole squares divided into 3 equal parts with 1 of those parts shaded. It also shows $\frac{4}{3}$ as there are 4 pieces shaded and each is $\frac{1}{3}$ of a unit rectangle. It shows the multiplication expression $4 \times \frac{1}{3}$ because there are 4 groups of $\frac{1}{3}$ shaded. It shows the multiplication expression $\frac{1}{3} \times 4$ since there is a total of 4, and $\frac{1}{3}$ of that is shaded.

Activity 1: How Far Did They Run?

• Create a set of cards from the blackline master for each group of 2.

Which student responses did you anticipate from today’s lesson? Which student responses surprised you in today’s lesson?