# 1. Use area models to show the Pythagorean Theorem (C)

teaches Common Core State Standards CCSS.Math.Content.8.G.B.6 http://corestandards.org/Math/Content/8/G/B/6
teaches Common Core State Standards CCSS.Math.Practice.MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards CCSS.Math.Practice.MP8 http://corestandards.org/Math/Practice/MP8

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Lesson objective: Understand that area models can be used to explain why $$a^2 + b^2 =c^2$$

Students bring prior knowledge of properties of area and area models from 6.EE.A.2c, 6.G.A.1. This prior knowledge is extended to use the area of squares as students compare the relationship between the squares on the legs and the square on the hypotenuse of a right triangle. A conceptual challenge students may encounter is quantifying the amount of area covered by two squares as the same as the amount of area covered by the other square.

The concept is developed through work with calculations of area, which are shown to be equivalent.

This work helps students deepen their understanding of operations and equivalence because students must understand the usage of exponents in squaring a number, while applying that understanding to a balanced equation in the form $$a^2 + b^2 =c^2$$.

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they discover the relationship between the three legs on a right trianlgle.

Key vocabulary:

• area
• exponent
• hypotenuse
• legs
• Pythagorean Theorem
• squared

Special materials needed:

• print out of three triangles, which can be found here
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