Lesson plan of Sum of the Interior Angles of a Triangle

Objectives (5 - 7 minutes)

1. Understand the sum of the interior angles of a triangle: This objective asks students to understand the fundamental property of Maths which states that the sum of the interior angles of a triangle is always equal to 180 degrees. Students must be able to explain this property in their own words and apply it to various examples of triangles.

2. Apply the sum of interior angles formula: Students should be able to apply the sum of the interior angles formula to find the value of an unknown angle in a triangle. This involves using simple equations to solve problems as well as the ability to manipulate variables and constants.

3. Solve problems involving the sum of the interior angles of a triangle: This objective is an extension of the second objective and asks students to use their newly acquired skills to solve more complex problems that involve the sum of the interior angles of a triangle. This includes solving problems that require the application of prior knowledge, logical reasoning, and the ability to interpret and solve mathematical problems.

Secondary objectives:

• Develop critical thinking and problem solving skills: Although the main focus of the lesson is the sum of the interior angles of a triangle, the teacher should take the opportunity to develop students' critical thinking and problem solving skills. This can be done by presenting challenging problems that require the concepts learned to be solved.

• Promote classroom interaction: The teacher should encourage active student participation to promote classroom interaction. This can be done through group discussions, team problem solving, and presenting solutions to the class.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher should start the class by reviewing the concepts of angles and triangles, previously studied in earlier classes. This review may include the definition of angles, types of angles (acute, obtuse, right), the sum of the angles of a point, among others. This will serve as the basis for the Introduction of the new concept.

2. Problem situation 1: The pyramid challenge: The teacher can propose a situation in which students need to find the value of an interior angle of a pyramid, which is a complex figure composed of several triangular faces. This situation will instigate students to think about the sum of the interior angles of a triangle and how it can be applied to other geometric figures.

3. Problem situation 2: The triangle puzzle: The teacher can present a problem in which students need to find the value of one of the angles of a triangle, but only by knowing the values of the other two angles. This situation will challenge students to apply the concept of the sum of the interior angles of a triangle and the corresponding formula.

4. Contextualizing the importance of the subject: The teacher should explain that the sum of the interior angles of a triangle is a fundamental property of geometry that has practical applications in various areas, such as architecture, engineering, art, among others. For example, understanding this property is essential for building stable structures, such as bridges and buildings.

5. Introduction of the topic with curiosities: To spark students' interest, the teacher can share some curiosities about the sum of the interior angles of a triangle. For example, he may mention that this property is so fundamental that it is considered an axiom, that is, a truth that does not need to be demonstrated. Furthermore, the teacher may mention that this property also applies to other geometric figures, such as quadrilaterals (sum of the interior angles = 360 degrees) and polygons in general (sum of the interior angles = (n - 2) x 180 degrees, where n is the number of sides).

Development (20 - 25 minutes)

1. Explanation of the property of the sum of the interior angles of a triangle (5 - 7 minutes): The teacher should start by explaining the fundamental property of the sum of the interior angles of a triangle. He can do this through a theoretical explanation, using the blackboard or a whiteboard to draw and demonstrate examples.

   • The teacher should start by drawing a triangle on the board and marking the interior angles as A, B and C.
   • Then, he should explain that the sum of these three angles, A + B + C, is always equal to 180 degrees, regardless of the size or shape of the triangle.
   • The teacher can demonstrate this with an example: draw a right triangle, an equilateral triangle, and a scalene triangle, and calculate the sum of its interior angles in each case. The results should always be 180 degrees.

2. Presentation of the formula for the sum of the interior angles of a triangle (5 - 7 minutes): The teacher should then present the formula for the sum of the interior angles of a triangle, which is a way to calculate this sum without having to measure the angles.

   • The teacher should write the formula on the board: A + B + C = 180.
   • Then, he should explain that this formula can be used to find the value of an unknown angle in a triangle, as long as the values of the other two angles are known.
   • The teacher can demonstrate this with an example: write the formula on the board, substitute the values of two angles (for example, A = 60 and B = 30), and solve the equation to find the value of the third angle (C = 90).

3. Solving problem situation 1: The pyramid challenge (5 - 7 minutes): The teacher should now go back to the problem situation presented in the Introduction and guide students in solving the problem.

   • The teacher should draw the pyramid figure on the board and mark the interior angles that students need to find.
   • Then, he should remind students of the property of the sum of the interior angles of a triangle and the corresponding formula.
   • Students should then work in groups to try to solve the problem. The teacher should circulate the room, offering help and clarifying doubts.
   • When students find the solution, the teacher should ask one or two groups to share their strategies and answers with the class.

4. Solving problem situation 2: The triangle puzzle (5 - 7 minutes): The teacher should now present the second problem situation and guide students in solving this new challenge.

   • The teacher should draw the triangle on the board and write the values of the two known angles.
   • Then, he should remind students of the formula for the sum of the interior angles of a triangle and explain how to use it to find the value of the unknown angle.
   • Students should then work in groups to solve the problem. The teacher should again circulate the room, offering help and clarifying doubts.
   • When students find the solution, the teacher should ask one or two groups to share their strategies and answers with the class.

5. Reflection on the importance of the subject and preparation for the next step (3 - 5 minutes): The teacher should conclude the Development step by making a brief reflection on the importance of the subject, reinforcing how the sum of the interior angles of a triangle is a fundamental property of geometry with practical applications in various areas. Then, he should prepare students for the next step, which will involve solving more problems and applying the concept learned to other geometric figures.

Feedback (8 - 10 minutes)

1. Group discussion (3 - 4 minutes): The teacher should promote a group discussion with all students, where each group will share their solutions or conclusions from the problem situations solved in the Development stage. This will allow students to compare their strategies, identify different approaches, and learn from each other. During the discussion, the teacher should ask questions to deepen students' understanding of the topic and clarify possible doubts that may arise.

2. Connection with theory (2 - 3 minutes): After the group discussion, the teacher should return to the theoretical concepts presented in the Introduction and explain how they connect with the solutions found by the students. For example, the teacher may highlight how the property of the sum of the interior angles of a triangle and the corresponding formula were applied to find the value of the unknown angles in the problem situations.

3. Individual reflection (2 - 3 minutes): The teacher should propose that students reflect individually on what they have learned in the class. He can do this by asking questions such as:

   1. "What was the most important concept you learned today?"
   2. "What questions have not yet been answered?"
   3. "How can you apply what you learned today in everyday situations?"

   Students should be encouraged to write down their answers, which can be shared with the class or used as a basis for the next class.

4. Feedback and clarification of doubts (1 - 2 minutes): Finally, the teacher should make time for students to provide feedback on the lesson and clarify any questions they may still have. This is important to ensure that all students have understood the concepts presented and feel confident to continue learning about the subject. The teacher should encourage students to express their opinions and doubts freely, creating an open and welcoming learning environment.

Conclusion (5 - 7 minutes)

1. Content summary (2 - 3 minutes): The teacher should begin the Conclusion by recalling the main points covered in the class. This includes the property of the sum of the interior angles of a triangle, the corresponding formula (A + B + C = 180), the application of this formula to find the value of an unknown angle, and the solution of the problem situations presented. The teacher can do this through a brief oral summary and/or written on the board.

2. Connection of theory with practice (1 - 2 minutes): Then, the teacher should explain how the class connected theory and practice. He should mention that, after the theoretical review, students had the opportunity to apply these concepts in solving practical problems, which helped to solidify their understanding. The teacher can also highlight how the problem situations presented were similar to real problems that may arise in everyday life or in other disciplines.

3. Extra materials (1 - 2 minutes): The teacher should then suggest some extra materials for students who want to deepen their knowledge on the topic. These materials may include explanatory videos, interactive math websites, textbooks, among others. For example, the teacher may recommend an online video that explains the sum of the interior angles of a triangle in a fun and engaging way, or a website that offers interactive exercises to practice applying the formula.

4. Relevance of the topic (1 minute): Finally, the teacher should emphasize the importance of the topic presented for daily life and for other disciplines. He may mention, for example, that the sum of the interior angles of a triangle is fundamental for understanding several other properties and theorems of geometry, and that this property has practical applications in various areas, such as architecture, engineering, art, among others. In addition, the teacher may emphasize that the ability to solve problems involving the sum of the interior angles of a triangle is an important skill that can be useful in many aspects of life.