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Lesson Plans > Mathematics > Grades 6 - 8 > Pythagoreum Theorem
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Kinesthetic Learner
Kinesthetic Learner
Visual Learner
Visual Learner
Auditory Learner
Auditory Learner
Technology Integration
Technology Integration

Pythagoreum Theorem

Learn how to apply the formulas for the area of parallelograms and triangles

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:
  • recount the contributions of Pythagoras
  • apply knowledge of the Pythagorean theorem
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:
  • for various grade levelsVarying academic levels: uses mixed-ability groups allow students to learn from one another, small and whole group participation
  • for visual learnersVisual learners: incorporates drawings of figures that allow students to test the Pythagorean theorem
  • for auditory learnersAuditory learners: uses guided questioning and discussion to help students articulate the relationship between the sides and the hypotenuse
  • for kinesthetic learnersKinesthetic 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
  • Recount the story of Pythagoras’ life and accomplishments. (A Google search will turn up many resources.)
  • for auditory learners 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.
  • If available, display pictures of the pyramids to illustrate the geometric accomplishments of ancient civilizations.
Direct Instruction
  • for visual learners On a white board (or chalk board), define hypotenuse and right angle.
  • Draw a series of triangles and ask students to identify the hypotenuse.
  • for visual learners for kinesthetic learners Have students draw a right triangle on grid paper with one side three units long and another four units long. Ask students to use the grid paper to figure out the length of the hypotenuse.
  • for auditory learners Have students turn to a partner and describe the relationship between the hypotenuse and the two sides in terms of length.
  • for visual learners On a white board, write the formula for the length of a hypotenuse.
  • for visual learners On a white board, define square and square root.
  • for kinesthetic learnersAsk students to create their own right triangles to test Pythagoras’ theorem.
  • Randomly call on students to share their triangles and explain whether their results support the theorem.
Practice
  • Explain that ancient peoples used the Pythagorean theorem to help them survey lands, construct buildings, and study the night sky.
  • for visual learners Distribute drawings of geometric figures that can be broken down into multiple right triangles.
  • 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.
  • for visual learners 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
  • for visual learners Invite each group to illustrate their solution on the board.
  • for auditory learners Ask other students to explain how to find other solutions to the problem.
Closure
  • Ask students to choose from a variety of enrichment activities:
  • Give an oral presentation on the development of geometry in the ancient world
  • write a short history of Pythagoras, his followers, and their influence
  • create a collage of pictures of architectural structures in the ancient world
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