Lesson 10

The purpose of this lesson is for students to find the area of rectangles with one non-unit fractional side length and one whole number side length.

In the previous lesson, students extended their understanding of multiplication to find the area of rectangles with a side length that is a unit fraction. In this lesson, students will find the area of rectangles with a whole number side length and a non-unit fraction side length. Students will apply what they learned in earlier lessons to area representations and recognize that a side length of \(\frac{a}{b}\) is equivalent to a side length of \(a \times \frac{1}{b}\). This allows them to find areas by counting the number of pieces covering the area and then multiplying this by the unit fractional area of each piece. For example, in the image below, there are 8 shaded pieces and each piece has an area of \(\frac{1}{3}\) square unit.

In the next lesson, students will find the area of a rectangle where one of the side lengths is a fraction greater than 1. Try finding the area of a rectangle that is \(\frac{5}{4}\) by 6. How do the understandings in today’s lesson support how you found the area of that rectangle?