ALEX Lesson Plans
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Title: Pythagorean Theorem: Prove It
Description:
During this lesson, eighth grade students will be introduced to the Pythagorean Theorem: a2+b2=c2. They will construct a right triangle on graph paper and draw squares on each side of the triangle.
Standard(s): [MA2013] (8) 21: Explain a proof of the Pythagorean Theorem and its converse. [8G6] [MA2013] (8) 22: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [8G7] [MA2013] (8) 21: Explain a proof of the Pythagorean Theorem and its converse. [8G6] [MA2013] (8) 22: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [8G7]
Subject: Mathematics (8)
Title: Pythagorean Theorem: Prove It
Description: During this lesson, eighth grade students will be introduced to the Pythagorean Theorem: a2+b2=c2. They will construct a right triangle on graph paper and draw squares on each side of the triangle.
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Title: Pythagorean Theorem: Prove It (Part 2)
Description:
In this lesson, eighth grade students will use their new found knowledge of the Pythagorean Theorem and relate it to the world around them. They will work in cooperative groups to solve problems using the Pythagorean Theorem.
Standard(s): [MA2013] (8) 21: Explain a proof of the Pythagorean Theorem and its converse. [8G6] [MA2013] (8) 22: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [8G7]
Subject: Mathematics (8)
Title: Pythagorean Theorem: Prove It (Part 2)
Description: In this lesson, eighth grade students will use their new found knowledge of the Pythagorean Theorem and relate it to the world around them. They will work in cooperative groups to solve problems using the Pythagorean Theorem.
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Title: Growing in a Triangle
Description:
Middle school students explore the Pythagorean Theorem by measuring and calculating diagonal lengths using the Pythagorean Theorem. Students view an animated proof of the Pythagorean Theorem. They access an Internet site to view and discuss three examples of the Pythagorean Theorem. Students apply knowledge of the Pythagorean Theorem to create a scale drawing of a plan to build a triangular raised bed garden for an outdoor classroom. Each group will present their plan to the class.
Standard(s): [MA2013] (8) 21: Explain a proof of the Pythagorean Theorem and its converse. [8G6] [MA2013] (8) 22: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [8G7] [TC2] (02) 7: Use digital tools to access and retrieve information. [TC2] (02) 10: Design original works using digital tools. [TC2] (35) 5: Practice safe use of technology systems and applications.
Subject: Mathematics (8), or Technology Education (K  5)
Title: Growing in a Triangle
Description: Middle school students explore the Pythagorean Theorem by measuring and calculating diagonal lengths using the Pythagorean Theorem. Students view an animated proof of the Pythagorean Theorem. They access an Internet site to view and discuss three examples of the Pythagorean Theorem. Students apply knowledge of the Pythagorean Theorem to create a scale drawing of a plan to build a triangular raised bed garden for an outdoor classroom. Each group will present their plan to the class.
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Title: Quilting With My Pal, Pythagoras!
Description:
In this unit lesson, students will learn about the Pythagorean Theorem and how it is evident in our everyday world. Students will apply the concept of the Pythagorean Theorem to the squares of a quilt. Each quilt square will be designed and crafted by a student. In the end, a beautiful quilt will be made with the help of Pythagoras himself!
Standard(s): [MA2013] (8) 22: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [8G7] [EDT] ED03 (8) 13: Demonstrate basic sewing construction skills to complete a project.
Subject: Education and Training (8), or Mathematics (8)
Title: Quilting With My Pal, Pythagoras!
Description: In this unit lesson, students will learn about the Pythagorean Theorem and how it is evident in our everyday world. Students will apply the concept of the Pythagorean Theorem to the squares of a quilt. Each quilt square will be designed and crafted by a student. In the end, a beautiful quilt will be made with the help of Pythagoras himself!
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Title: Proofs into Practice: The Pythagorean Theorem in the Real World
Description:
The introduction of this lesson has students verifying the famous Pythagorean Theorem with a handson proof. Students will then apply the Theorem in one of two ways: by solving for the side lengths of a right triangle and by determining whether three side lengths could possibly form a right triangle. Finally, students will choose one of two reallife applicataions to explore, using the Pythagorean Theorem.
Standard(s): [MA2013] (8) 22: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [8G7] [MA2013] (8) 21: Explain a proof of the Pythagorean Theorem and its converse. [8G6] [MA2013] (8) 23: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8G8] [MA2013] ALC (912) 8: Determine missing information in an applicationbased situation using properties of right triangles, including trigonometric ratios and the Pythagorean Theorem. (Alabama) [MA2013] GEO (912) 17: Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [GSRT4] [MA2013] GEO (912) 21: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [GSRT8]
Subject: Mathematics (8  12)
Title: Proofs into Practice: The Pythagorean Theorem in the Real World
Description: The introduction of this lesson has students verifying the famous Pythagorean Theorem with a handson proof. Students will then apply the Theorem in one of two ways: by solving for the side lengths of a right triangle and by determining whether three side lengths could possibly form a right triangle. Finally, students will choose one of two reallife applicataions to explore, using the Pythagorean Theorem.
Web Resources
Podcasts
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Title: The Pythagorean Theorem TV
Description:
This website shows videos to help students and teachers understand the Pythagorean Theorem.
Standard(s): [MA2013] (8) 21: Explain a proof of the Pythagorean Theorem and its converse. [8G6] [MA2013] (8) 22: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [8G7] [MA2013] (8) 23: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8G8] [MA2013] GEO (912) 17: Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [GSRT4] [MA2013] GEO (912) 21: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [GSRT8] [MA2013] GEO (912) 29: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. [GGPE1] [MA2013] GEO (912) 30: Use coordinates to prove simple geometric theorems algebraically. [GGPE4] [MA2013] ALC (912) 8: Determine missing information in an applicationbased situation using properties of right triangles, including trigonometric ratios and the Pythagorean Theorem. (Alabama) [MA2013] MI1 (912) 10: Determine the mathematical impact of the ancient Greeks, including Archimedes, Eratosthenes, Euclid, Hypatia, Pythagoras, and the Pythagorean Society. (Alabama)
The Pythagorean Theorem TV
http://www.mathtv.co...
This website shows videos to help students and teachers understand the Pythagorean Theorem.
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Title: Pythagorean Theorem Rap Song
Description:
This video puts the Pythagorean theorem in realworld terms, helping students visualize examples in which the formula comes into play. The professionally produced music and video is highly engaging for students. For teachers, there are links to song lyrics, activities, and questions. Many Flocabulary videos are only accessible through a paid subscription. *This particular video is available for free and without the need for an account signup.
Standard(s): [MA2013] (8) 22: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [8G7] [MA2013] GEO (912) 21: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [GSRT8] [MA2013] ALC (912) 8: Determine missing information in an applicationbased situation using properties of right triangles, including trigonometric ratios and the Pythagorean Theorem. (Alabama) [MA2013] MI1 (912) 10: Determine the mathematical impact of the ancient Greeks, including Archimedes, Eratosthenes, Euclid, Hypatia, Pythagoras, and the Pythagorean Society. (Alabama)
Pythagorean Theorem Rap Song
http://www.flocabula...
This video puts the Pythagorean theorem in realworld terms, helping students visualize examples in which the formula comes into play. The professionally produced music and video is highly engaging for students. For teachers, there are links to song lyrics, activities, and questions. Many Flocabulary videos are only accessible through a paid subscription. *This particular video is available for free and without the need for an account signup.
Interactives/Games
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Title: Pythagorean Theorem game
Description:
The pythagorean theorem game is a fun way for students to practice using the pythagorean theorem.
Standard(s): [MA2013] (8) 22: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [8G7]
Pythagorean Theorem game
http://www.mathplay...
The pythagorean theorem game is a fun way for students to practice using the pythagorean theorem.
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Title: Pythagorean Theorem Jeopardy
Description:
In this Pythagorean Theorem Game, students will practice calculating the hypotenuse and the unknown leg in a right triangle. The converse of the Pythagorean Theorem will also be utilized to verify if three numbers could be the sides of a right triangle.
Standard(s): [MA2013] (8) 22: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [8G7]
Pythagorean Theorem Jeopardy
http://www.mathplay...
In this Pythagorean Theorem Game, students will practice calculating the hypotenuse and the unknown leg in a right triangle. The converse of the Pythagorean Theorem will also be utilized to verify if three numbers could be the sides of a right triangle.
Teacher Tools
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Title: The Pythagorean Theorem TV
Description:
This website shows videos to help students and teachers understand the Pythagorean Theorem.
Standard(s): [MA2013] (8) 21: Explain a proof of the Pythagorean Theorem and its converse. [8G6] [MA2013] (8) 22: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [8G7] [MA2013] (8) 23: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8G8] [MA2013] GEO (912) 17: Prove theorems about triangles. Theorems include a line parallel to one side of a triangle divides the other two proportionally, and conversely; and the Pythagorean Theorem proved using triangle similarity. [GSRT4] [MA2013] GEO (912) 21: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [GSRT8] [MA2013] GEO (912) 29: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. [GGPE1] [MA2013] GEO (912) 30: Use coordinates to prove simple geometric theorems algebraically. [GGPE4] [MA2013] ALC (912) 8: Determine missing information in an applicationbased situation using properties of right triangles, including trigonometric ratios and the Pythagorean Theorem. (Alabama) [MA2013] MI1 (912) 10: Determine the mathematical impact of the ancient Greeks, including Archimedes, Eratosthenes, Euclid, Hypatia, Pythagoras, and the Pythagorean Society. (Alabama)
The Pythagorean Theorem TV
http://www.mathtv.co...
This website shows videos to help students and teachers understand the Pythagorean Theorem.
Thinkfinity Learning Activities
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Title: Understanding the Pythagorean Relationship Using Interactive Figures
Description:
The Pythagorean relationship, a2 + b2 = c2 (where a and b are the lengths of the legs of a right triangle and c is the hypotenuse), can be demonstrated in many ways, including with visual 'proofs' that require little or no symbolism or explanation. The activity in this example from Illuminations presents one dynamic version of a demonstration of this relationship. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations.
Standard(s): [MA2013] (8) 22: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [8G7] [MA2013] (8) 23: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8G8]
Subject: Mathematics Title: Understanding the Pythagorean Relationship Using Interactive Figures
Description: The Pythagorean relationship, a2 + b2 = c2 (where a and b are the lengths of the legs of a right triangle and c is the hypotenuse), can be demonstrated in many ways, including with visual 'proofs' that require little or no symbolism or explanation. The activity in this example from Illuminations presents one dynamic version of a demonstration of this relationship. eMath Investigations are selected eexamples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The eexamples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the eexamples are natural companions to the iMath investigations. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Proof Without Words: Pythagorean Theorem
Description:
In this student interactive, from Illuminations, students watch a dynamic, geometric '' proof without words'' of the Pythagorean Theorem. By clicking on a button, students can see the theorem in action; they are then challenged to explain the proof.
Standard(s): [MA2013] (8) 21: Explain a proof of the Pythagorean Theorem and its converse. [8G6] [MA2013] (8) 22: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [8G7] [MA2013] (8) 23: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [8G8]
Subject: Mathematics Title: Proof Without Words: Pythagorean Theorem
Description: In this student interactive, from Illuminations, students watch a dynamic, geometric '' proof without words'' of the Pythagorean Theorem. By clicking on a button, students can see the theorem in action; they are then challenged to explain the proof. Thinkfinity Partner: Illuminations Grade Span: 6,7,8

