Unit 1, Lesson 7
Area of Triangles
Accelerated 6
Preparation
Lesson Narrative
In this lesson, students reason about areas of triangles. They see that they can find the area of a triangle by applying strategies such as decomposing and rearranging, or enclosing and subtracting. They can also use the relationship between parallelograms and triangles.
Students observe that the area of a triangle is half of the area of a parallelogram that shares the same base as the triangle and has the same height. Students arrive at this observation by:
- Recalling that two copies of a triangle can be composed into a parallelogram
- Reasoning about one or more rectangles that have the same height as the triangle.
An optional activity is included to help students make another, related observation: that a triangle can be decomposed and rearranged into a parallelogram that shares the same base but is half the triangle’s height.
In making these observations and applying them to find the areas of triangles on and off a grid, students practice looking for and making use of structure (MP7).
A note about terminology:
At this point, students have not yet learned about bases and height in a triangle. They are not expected to use these terms when referring to measurements used to find the area of a triangle or when describing the connections between a triangle and a related parallelogram. While students may use the terms intuitively, the meanings of a triangle’s base and height will be formalized in the next lesson.
Today, students use sticky notes to document actions in the “Doing Math” sections of the Math Community Chart that they see or hear throughout the lesson. During the Lesson Synthesis, students share what they noticed, and then they suggest additions for the chart as part of the Cool-down. The work today continues to build a foundation for developing math community norms in a later exercise and is the start of students identifying strengths in the actions of their peers.
- Draw a diagram to show that the area of a triangle is half the area of an associated parallelogram.
- Explain (orally and in writing) strategies for using the base and height of an associated parallelogram to determine the area of a triangle.
Let’s use what we know about parallelograms to find the area of triangles.
Required Materials
Activity 2
Activity 3
Required Preparation
Each copy of the blackline master contains two copies of each of Parallelograms A, B, C, and D. Prepare enough copies so that each student receives two copies of a parallelogram.
Students need access to tape or glue; it is not necessary to have both.