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 baseheight 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 Warmup: 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 Cooldown: 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 20172019 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/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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