Grade Level: 6-8
Concept: Learn to apply the formulas for the area of parallelograms and triangles.
Estimated Duration: 50 minutes
Objectives
Students will be able to:
Materials
White board (or chalk board)
Markers
Grid paper, pencil
Handouts of geometric shapes that can be broken down into right triangles
Differentiation Strategies
These strategies are used to meet the varied needs of all learners:
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Varying academic levels: uses mixed-ability groups allow students to learn from one another, small and whole group participation
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Visual learners: incorporates drawings of figures that allow students to test the Pythagorean theorem
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Auditory learners: uses guided questioning and discussion to help students articulate the relationship between the sides and the hypotenuse
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Kinesthetic learners: engages students in group project to calculate the perimeter of ancient fields using the Pythagorean theorem
Key Vocabulary
Right triangle
Hypotenuse
Square
Square root
Procedures
Warm Up
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Recount the story of Pythagoras’ life and accomplishments. (A Google search will turn up many resources.)
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Explain that while the relationship between the sides and the hypotenuse of a right triangle were known in Babylonia hundreds of years before Pythagoras was born, Pythagoras is thought to have been the first to have proven this relationship.
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If available, display pictures of the pyramids to illustrate the geometric accomplishments of ancient civilizations.
Direct Instruction
Practice
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Explain that ancient peoples used the Pythagorean theorem to help them survey lands, construct buildings, and study the night sky.
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Distribute drawings of geometric figures that can be broken down into multiple right triangles.
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Create mixed ability pairs and ask them to create math problems for each other that involve computing the lengths of the hypotenuse. Pair up stronger academic students with challenged students.
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Explain that these drawings represent fields of landowners of ancient times, and have the groups work together to calculate the perimeter of the field by breaking down the geometric figure into simpler shapes, including right triangles.
Assessment
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Invite each group to illustrate their solution on the board.
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Ask other students to explain how to find other solutions to the problem.
Closure
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Ask students to choose from a variety of enrichment activities:
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Give an oral presentation on the development of geometry in the ancient world
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write a short history of Pythagoras, his followers, and their influence
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create a collage of pictures of architectural structures in the ancient world