ALEX Lesson Plans
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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] 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.
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Title: Land Surveying ProjectEnhancing mathematics in the career/technical classroom and providing relevance in the mathematics classroom.
Description:
This project resulted from of the collaboration of a computer aided drafting teacher, Chris Bond, and a math teacher, Lee Cable, (HewittTrussville High School) to provide higher math expectations in CT and real life application in mathematics.
In this handson and technology based project, CT students will learn the basics of civil engineering in land surveying while applying algebraic and geometric concepts. The current technology used by survey crews, for example AutoCAD, will be utilized and applied by students. With assistance from a local civil engineering firm, students will record length and angle measurements of an assigned area and calculate unknown measures using math concepts that include solving general and right triangles, setting up and solving proportions, determining scale, and using the Law of Cosines. A topographical map will then be plotted using AutoCAD and a presentation made to the engineering firm for grading and feedback. The embedded math will be cotaught with a math teacher using the real world data to make the topics relevant. In the math classroom, the math teacher will use land surveying problems designed in this project to show students how math concepts are used in realworld applications.
Standard(s): [MA2013] GEO (912) 23: (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces).
[GSRT11]
Subject: Mathematics (9  12), or Science, Technology, Engineering, and Mathematics (9  12)
Title: Land Surveying ProjectEnhancing mathematics in the career/technical classroom and providing relevance in the mathematics classroom.
Description: This project resulted from of the collaboration of a computer aided drafting teacher, Chris Bond, and a math teacher, Lee Cable, (HewittTrussville High School) to provide higher math expectations in CT and real life application in mathematics.
In this handson and technology based project, CT students will learn the basics of civil engineering in land surveying while applying algebraic and geometric concepts. The current technology used by survey crews, for example AutoCAD, will be utilized and applied by students. With assistance from a local civil engineering firm, students will record length and angle measurements of an assigned area and calculate unknown measures using math concepts that include solving general and right triangles, setting up and solving proportions, determining scale, and using the Law of Cosines. A topographical map will then be plotted using AutoCAD and a presentation made to the engineering firm for grading and feedback. The embedded math will be cotaught with a math teacher using the real world data to make the topics relevant. In the math classroom, the math teacher will use land surveying problems designed in this project to show students how math concepts are used in realworld applications.
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Title: The Clock TowerEnhancing mathematics in the career/technical classroom and providing relevance in the mathematics classroom.
Description:
This project resulted from the collaboration of a computer aided drafting teacher (preengineering), Chris Bond, and a math teacher, Lee Cable, (HewittTrussville High School) to provide higher math expectations in CT and real life application in mathematics.
As a handson, technology based project this activity demonstrates use of the Pythagorean Theorem, Sine, Cosine and Tangent to find unknown heights of objects and can be adapted for use by the computer aided drafting or mathematics teacher. Clinometers are used as a surveying tool and AutoCAD is used as a drawing tool. Students use a clinometer and a ruler or a tape measure to find and then record the length and angle measurements of a right triangle to determine unknowns. This information is then used to find unknown lengths and angles and to then create a drawing in AutoCAD. Proportion and scale will be used to draw a scale drawing of the clock tower at the new HewittTrussville High School. In the mathematics classroom, students will produce scale drawings using graph paper instead of AutoCAD. This lesson will need to be adapted for use by other schools by selecting a different building structure for measure.
Standard(s): [MA2013] GEO (912) 21: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [GSRT8]
Subject: Architecture and Construction (9  12), or Mathematics (9  12)
Title: The Clock TowerEnhancing mathematics in the career/technical classroom and providing relevance in the mathematics classroom.
Description: This project resulted from the collaboration of a computer aided drafting teacher (preengineering), Chris Bond, and a math teacher, Lee Cable, (HewittTrussville High School) to provide higher math expectations in CT and real life application in mathematics.
As a handson, technology based project this activity demonstrates use of the Pythagorean Theorem, Sine, Cosine and Tangent to find unknown heights of objects and can be adapted for use by the computer aided drafting or mathematics teacher. Clinometers are used as a surveying tool and AutoCAD is used as a drawing tool. Students use a clinometer and a ruler or a tape measure to find and then record the length and angle measurements of a right triangle to determine unknowns. This information is then used to find unknown lengths and angles and to then create a drawing in AutoCAD. Proportion and scale will be used to draw a scale drawing of the clock tower at the new HewittTrussville High School. In the mathematics classroom, students will produce scale drawings using graph paper instead of AutoCAD. This lesson will need to be adapted for use by other schools by selecting a different building structure for measure.
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Title: Geometric Mean and Indirect Measurement
Description:
In this inquirybased lesson, students will work in groups to gather measurements needed to approximate the height of a building. Students will discover how geometric mean can be used to find the lengths of missing sides of right triangles.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
Standard(s): [MA2013] GEO (912) 21: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* [GSRT8]
Subject: Mathematics (9  12)
Title: Geometric Mean and Indirect Measurement
Description: In this inquirybased lesson, students will work in groups to gather measurements needed to approximate the height of a building. Students will discover how geometric mean can be used to find the lengths of missing sides of right triangles.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.
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Title: I Can Determine The Height Of A Rocket!
Description:
The lesson is intended to give students a fun realworld experience in applying their math skills. They will use trigonometric ratios to calculate heights of tall structures. They will also use the Internet to convert their calculations from standard to metric units and visa versa.
Standard(s): [MA2013] GEO (912) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [GMG1]
Subject: Mathematics (9  12), or Technology Education (9  12)
Title: I Can Determine The Height Of A Rocket!
Description: The lesson is intended to give students a fun realworld experience in applying their math skills. They will use trigonometric ratios to calculate heights of tall structures. They will also use the Internet to convert their calculations from standard to metric units and visa versa.
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Title: How tall is the school's flagpole?
Description:
The purpose of this lesson is to help students apply math concepts concerning similar triangles and trigonometric functions to real life situations. The students learn how to take these concepts and use them to find measurements of objects that they are unable to measure in conventional ways.
Standard(s):
Subject: Mathematics (9  12)
Title: How tall is the school's flagpole?
Description: The purpose of this lesson is to help students apply math concepts concerning similar triangles and trigonometric functions to real life situations. The students learn how to take these concepts and use them to find measurements of objects that they are unable to measure in conventional ways.
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] 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] 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: Geometry StepbyStep
Description:
This site provides a mix of sound, science, and Incan history in order to raise students' interest in Euclidean geometry. Visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, "scientific speculation", and more.
Standard(s): [MA2013] GEO (912) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama)
Geometry StepbyStep
http://agutie.homest...
This site provides a mix of sound, science, and Incan history in order to raise students' interest in Euclidean geometry. Visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, "scientific speculation", and more.
Learning Activities
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Title: Geometry StepbyStep
Description:
This site provides a mix of sound, science, and Incan history in order to raise students' interest in Euclidean geometry. Visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, "scientific speculation", and more.
Standard(s): [MA2013] GEO (912) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama)
Geometry StepbyStep
http://agutie.homest...
This site provides a mix of sound, science, and Incan history in order to raise students' interest in Euclidean geometry. Visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, "scientific speculation", and more.
Teacher Tools
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Title: Geometry StepbyStep
Description:
This site provides a mix of sound, science, and Incan history in order to raise students' interest in Euclidean geometry. Visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, "scientific speculation", and more.
Standard(s): [MA2013] GEO (912) 37: Determine the relationship between surface areas of similar figures and volumes of similar figures. (Alabama)
Geometry StepbyStep
http://agutie.homest...
This site provides a mix of sound, science, and Incan history in order to raise students' interest in Euclidean geometry. Visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, "scientific speculation", and more.
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Show Details
Title: The Pythagorean Theorem TV
Description:
This website shows videos to help students and teachers understand the Pythagorean Theorem.
Standard(s): [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.

