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What to create	Lesson plan
Which subject	Mathematics
What topic	Pythagorean theorem
What length (min)	30
What age group	Year or Grade 8
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Lesson Plan: Pythagorean Theorem

Subject: Mathematics

Grade Level: 8

Duration: 30 Minutes

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Objective

Students will understand the Pythagorean Theorem and how to apply it to find the lengths of sides in right triangles.

Materials Needed

• Whiteboard and markers
• Graph paper
• Ruler
• Protractor
• Worksheets with practice problems

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Lesson Outline

Introduction (5 minutes)

• Begin with a question: “What do you know about right triangles?”
• Discuss the properties of right triangles and introduce the Pythagorean theorem:
  • The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
  • Mathematically, this is represented as:
    [ c^2 = a^2 + b^2 ]

Explanation and Demonstration (10 minutes)

• Provide examples on the whiteboard.
  1. Example 1
     • Given a right triangle with legs of lengths 3 cm and 4 cm, calculate the hypotenuse.
     • Calculation:
       [ c^2 = 3^2 + 4^2 ]
       [ c^2 = 9 + 16 ]
       [ c^2 = 25 ]
       [ c = 5 ]
  2. Example 2
     • Given a hypotenuse length of 10 cm and a leg of 6 cm, find the length of the other leg.
     • Calculation:
       [ 10^2 = 6^2 + b^2 ]
       [ 100 = 36 + b^2 ]
       [ b^2 = 64 ]
       [ b = 8 ]

Guided Practice (10 minutes)

• Distribute graph paper and have students draw a right triangle with given leg lengths (for example, 5 cm and 12 cm).
• In pairs, have them calculate the hypotenuse using the Pythagorean theorem and then verify their results with a ruler.

Independent Practice (5 minutes)

• Hand out a worksheet with the following problems:

  Worksheet Problems:

  1. Find the hypotenuse of a right triangle with legs of lengths 8 cm and 15 cm.
  2. If one leg of a right triangle is 9 cm and the hypotenuse is 15 cm, find the length of the other leg.
  3. A right triangle has a hypotenuse of 13 cm, and one leg is 5 cm. Find the length of the other leg.

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Conclusion (5 minutes)

• Recap the Pythagorean theorem and its applications.
• Ask a few students to share their answers from the independent practice and discuss any challenges encountered.

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Homework

Homework Assignment

Complete the following problems at home:

1. A right triangle has legs measuring 7 cm and 24 cm. What is the length of the hypotenuse?
2. If one leg of a right triangle is 8 cm and the hypotenuse is 10 cm, find the length of the other leg.
3. The legs of a right triangle measure 9 cm and 12 cm. Check if it is a right triangle using the Pythagorean theorem.

Answers

1. Hypotenuse:
   [ c^2 = 7^2 + 24^2 ]
   [ c^2 = 49 + 576 ]
   [ c^2 = 625 ]
   [ c = 25 \, \text{cm} ]

2. Other leg:
   [ 10^2 = 8^2 + b^2 ]
   [ 100 = 64 + b^2 ]
   [ b^2 = 36 ]
   [ b = 6 \, \text{cm} ]

3. Check:
   [ c^2 = 9^2 + 12^2 ]
   [ c^2 = 81 + 144 ]
   [ c^2 = 225 ]

   • Yes, it is a right triangle since ( c = 15 \, \text{cm} ) (using ( 15^2 = 225 )).

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Reflection

After conducting the lesson, reflect on student engagement and understanding of the Pythagorean theorem. Assess whether adjustments are needed for future classes.