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Mathematics Enhanced Scope and Sequence ­ Grade Eight

The Pythagorean Theorem

Reporting category Overview Related Standard of Learning Objectives

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Geometry Students verify and apply the Pythagorean Theorem. 8.10

The student will use square units to verify the Pythagorean Theorem. The student will find the measure of a missing side in a right triangle. The student will solve real-life problems involving right triangles.

Prerequisite Understandings/Knowledge/Skills

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The student must understand the concept of square numbers and their physical representations. The student must be able to work with the computation of squaring a number and taking the square root of a number (using a calculator is suggested). The student must be able to recognize a perfect square. The student has to know the components of a right triangle. The student must be able to work with variables in algebraic equations/formulas and use a replacement set for the variables. The student must be able to solve a quadratic equation. After verifying the Pythagorean Theorem Model, the students must be able to transfer the concrete/pictorial model to other triangles and find missing terms.

Materials needed

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"The Pythagorean Theorem Model," on copy for each student Scissors "The Pythagorean Theorem Exercises," one copy for each student

Instructional activity 1. Give a copy of "The Pythagorean Theorem Model" worksheet to each student. Discuss the parts of the right triangle, including the hypotenuse and the legs. 2. Review the concept of a perfect square, and emphasize that the square units on each side of the triangle are the perfect squares of those sides. 3. Have each student cut out only the square units of the legs of the triangle. Once all of the squares have been cut apart, have the students place them on the square units of the hypotenuse. All of the squares will be filled. Discuss the variables in the Pythagorean Theorem at this time. (a and b are the measures of the legs, and c is the measure of the hypotenuse.) 4. Hand out a copy of "The Pythagorean Theorem Exercises" worksheet to each student. Do a couple of the problems with the students. Have the students complete the worksheet. Sample assessment

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Circulate among the students as they are cutting the square units and rearranging them on the square of the hypotenuse. Check the answers to the exercises on the worksheet.

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Virginia Department of Education 2004

Mathematics Enhanced Scope and Sequence ­ Grade Eight

Follow-up/extension

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Have the students make up their own real-life problem that involves the Pythagorean Theorem to solve.

Specific options for differentiating this lesson Technology · Use of a calculator is encouraged (and allowed for this portion of the SOL testing). · Use of online interactive sites is encouraged (check www.google.com) · Use interactive electronic white boards to complete the activity. Multisensory · Use 3-dimensional squares to "fill in" the Pythagorean Theorem Model to allow tactile/kinesthetic learning. · Graph paper or geoboards can be used to assist in illustrating this concept. Community Connections · Take a field trip to a park, where sidewalks come in a right triangle form and student can measure and verify the Pythagorean Theorem. Small Group Learning · Students can work in pairs with the concrete/pictorial models. Vocabulary · The following vocabulary should be emphasized: right triangle, hypotenuse triangle, legs, perfect square, and Pythagorean Theorem. · Students should add new vocabulary to an interactive notebook, with the vocabulary word written on the left side of the notebook, and the definition and a picture on the right side. · Given a picture of a right triangle, students need to identify its components. Student Organization of Content · Students should be encouraged to keep a Math notebook with a section for right triangles and the Pythagorean Theorem.

Virginia Department of Education 2004

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Mathematics Enhanced Scope and Sequence ­ Grade Eight

The Pythagorean Theorem Model

Virginia Department of Education 2004

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Mathematics Enhanced Scope and Sequence ­ Grade Eight

The Pythagorean Theorem Exercises Find the length of the missing side in the following examples. Round answers to the nearest tenth, if necessary.

1. x 5 in.

2. x 5 cm

3. 2 ft x

3 in 4. 2.4 m 5.2 m x

12 cm

4 ft

5.

A 10-foot ladder is leaning against the side of a house. If the base of the ladder is 3 feet away from the house, how high up the side of the house will the ladder reach?

6.

Rebecca left her house and walked 2 blocks east. She turned and walked 5 blocks north to get to 1 the library. If each block is of a mile, how far is the direct route from Rebecca's house to the 4 library?

Virginia Department of Education 2004

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The Pythagorean Theorem

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