# Lesson 10

Rectangles and Triangles with Fractional Lengths

### Lesson Narrative

This lesson builds on students’ work on area and fractions in grade 5. Students solve problems involving the relationship between area and side lengths of rectangles, in cases where these measurements can be fractions. Knowing that the area of a rectangle can be found by multiplying its side lengths, and knowing the relationship between multiplication and division, they use division to find an unknown side length when the other side length and the area are given.

Then, they extend their work on area to include triangles, using division to find the length of a base or a height in a triangle when the area is known.

### Learning Goals

Teacher Facing

• Apply dividing by fractions to calculate the base or height of a triangle, given its area and the other measurement.
• Apply dividing by fractions to calculate the side length of a rectangle, given its area and the other side length.

### Student Facing

Let’s explore rectangles and triangles that have fractional measurements.

### Required Preparation

Consider having the objects mentioned in the How Many Would it Take? activity available for students to verify their answers. These objects are: $$\frac34$$-inch square stickers, $$\frac58$$-binder clips, and $$1\frac34$$-inch paper clips.

### Student Facing

• I can use division and multiplication to solve problems involving areas of rectangles with fractional side lengths.
• I can use division and multiplication to solve problems involving areas of triangles with fractional bases and heights.

Building On