Lesson plan

# Lesson 9: Formula for the Area of a Triangle

teaches Arizona State Standards 6.G.A.1
teaches Common Core State Standards MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards MP8 http://corestandards.org/Math/Practice/MP8
teaches Common Core State Standards 6.EE.A.2.c http://corestandards.org/Math/Content/6/EE/A/2/c
teaches Common Core State Standards 6.EE.A.2.a http://corestandards.org/Math/Content/6/EE/A/2/a
teaches Common Core State Standards 6.G.A.1 http://corestandards.org/Math/Content/6/G/A/1
teaches Georgia State Standards MGSE6.G.1.
teaches Kansas State Standards 6.G.1.
teaches New York State Standards NY-6.G.1.
teaches New York State Standards NY-6.EE.2c.
teaches New York State Standards NY-6.EE.2a.
teaches Ohio State Standards 6.G.1.
teaches Pennsylvania State Standards CC.2.3.6.A.1.

# Lesson 9: Formula for the Area of a Triangle

In this lesson students begin to reason about area of triangles more methodically: by generalizing their observations up to this point and expressing the area of a triangle in terms of its base and height.

Students first learn about bases and heights in a triangle by studying examples and counterexamples. They then identify base-height measurements of triangles, use them to determine area, and look for a pattern in their reasoning to help them write a general formula for finding area (MP8). Students also have a chance to build an informal argument about why the formula works for any triangle (MP3).

Lesson overview

• 9.1 Warm-up: Bases and Heights of a Triangle (10 minutes)
• 9.2 Activity: Finding the Formula for Area of a Triangle (20 minutes)
• 9.3 Activity: Applying the Formula for Area of Triangles (10 minutes)
• Lesson Synthesis
• 9.4 Cool-down: Two More Triangles (5 minutes)

Learning goals:

• Compare, contrast, and critique (orally) different strategies for determining the area of a triangle.
• Generalize a process for finding the area of a triangle, and justify (orally and in writing) why this can be abstracted as $$\frac12 \cdot b \cdot h$$.
• Recognize that any side of a triangle can be considered its base, choose a side to use as the base when calculating the area of a triangle, and identify the corresponding height.

Learning goals (student facing):

• Let’s write and use a formula to find the area of a triangle.

Learning targets (student facing):

• I can use the area formula to find the area of any triangle.
• I can write and explain the formula for the area of a triangle.
• I know what the terms “base” and “height” refer to in a triangle.

Required materials:

• geometry toolkits

Glossary:

• opposite vertex - For each side of a triangle, there is one vertex that is not on that side. This is the opposite vertex. For example, point $$A$$ is the opposite vertex to side $$BC$$.

• Access the complete Grade 6 glossary.

Standards

• This lesson builds towards the standard:CCSS.6.G.A.1MS.6.G.1MO.6.GM.A.1

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.