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|Lesson Title: Pythagorean Theorem |Date: |
|Subject: Math |Grade Level(s): 8 |
|Teacher: |Time Frame: 60 minutes |
|Lesson Summary: |
|Students will be able to use the Pythagorean Theorem to find the length of the third side of any right triangle given the lengths of two of its sides. |
|Lesson Objectives |
| The students will know… |
|That the Pythagorean Theorem applies to right triangles only. |
|How to find the length of the hypotenuse given the length of the legs of a right triangle. |
|How to find the length of one leg of a right triangle given the length of the other leg and the hypotenuse. |
|That the Distance Formula can be developed from the Pythagorean Theorem. |
| |
|The students will be able to… |
|Use the Pythagorean Theorem to find the length of the third side of any right triangle given the length of two of its sides. |
|Lesson Plan |
|Time: |Procedure: |Materials Needed: |
|5 minutes |Warm-up Exercise: |PowerPoint Presentation, slide 2 |
| |Show slide 2. Discuss with students the parts of a right triangle. | |
| |Explain that the legs form the right angle and the hypotenuse is | |
| |opposite the right angle. Draw several right triangles, in various | |
| |positions, on the chalkboard. Ask students to identify the parts of| |
| |each triangle. | |
|15 minutes |Motivation (Real-world Applications): |Paper rectangles; centimeter rulers; PowerPoint Presentation, slide 3 |
| |Provide each student with a paper rectangle and a centimeter ruler.| |
| |Challenge students to find the length of the diagonal of their | |
| |rectangle without measuring it. Explain that they can only measure | |
| |the length and width of their rectangle with their ruler. | |
| | | |
| |Show slide 3. Discuss how the sides of a right triangle are | |
| |related. | |
| | | |
| |Encourage students to think of when they might need to use the | |
| |Pythagorean Theorem in the real world. | |
|10 minutes |Presentation of New Material: |PowerPoint Presentation slides 4–6 |
| |Show slides 4–6. As you work through the PowerPoint presentation | |
| |for this lesson, be sure to point out how to write and solve an | |
| |equation for a variable, how to square a number, and how to find | |
| |the square root of a number. | |
|15 minutes |Guided Practice: | |
| |Have students work in pairs. One partner should label two sides of | |
| |a right triangle. The other partner should find the length of the | |
| |third side. Have the students switch roles. Remind students that | |
| |the hypotenuse is the longest side of a right triangle. | |
|10 minutes |Independent Practice: |Paper and pencil; coordinate grid paper; PowerPoint Presentation, |
| |Challenge students to use a coordinate grid and the Pythagorean |slide 7 |
| |Theorem to develop the distance formula. They should write their | |
| |calculations on a sheet of paper. After giving students time to | |
| |think about it, discuss slide 7. | |
|5 minutes |Closing Activities: |Copies of the Study Island Worksheet on the Pythagorean Theorem |
| |Have students begin the Study Island Worksheet on the Pythagorean | |
| |Theorem. Circulate around the classroom to offer guidance as | |
| |needed. | |
|Homework: Have students complete the Study Island Worksheet on the Pythagorean Theorem. |
|Differentiation: For extra support, have students perform hands-on measurement of paper right triangles, whose sides are each a whole number of inches, to confirm|
|the Pythagorean Theorem for themselves. Give students needing an extra challenge a square and the measurement of its diagonal. Have students find the length of the|
|sides and then use their findings to develop a formula for an isosceles right triangle. |
|Teacher Reflection: |
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