Lesson plan of Sum of the Interior Angles of a Triangle

Objectives (5 - 7 minutes)

1. Understanding the concept of interior angles of a triangle: The teacher should ensure that students understand what interior angles of a triangle are and how they are formed. This can be done through visual and practical examples.

2. Recognition of the formula for the sum of interior angles: Students should be able to identify and apply the formula for the sum of interior angles of a triangle. This can be achieved through practical exercises and problem-solving.

3. Application of the formula to solve problems: Students should be able to apply the formula for the sum of interior angles to real-world problems. This can be done through practical examples and classroom discussions.

Secondary objectives:

• Development of logical reasoning and problem-solving skills: Through the study of the sum of interior angles of a triangle, students will have the opportunity to enhance their logical reasoning and problem-solving skills, which are essential skills in mathematics and many other disciplines.

• Promotion of collaboration and classroom discussion: By working on problems and exercises in groups, students will have the opportunity to collaborate and discuss ideas, thus fostering a collaborative and interactive learning environment.

Introduction (10 - 12 minutes)

1. Review of previous concepts: The teacher should begin the lesson by briefly reviewing the concepts of angles, triangles, and the sum of the angles of a triangle. This review will serve as a foundation for the introduction of the new concept of the sum of interior angles of a triangle. (3 - 4 minutes)

2. Problem situation 1: The teacher can present students with a drawing of a triangle with one of the interior angles missing. He can then ask students: "How can we find the value of the missing interior angle?" This problem situation will help to pique students' interest and prepare them for the new concept that will be introduced. (2 - 3 minutes)

3. Contextualizing the importance of the subject: The teacher should explain to students that the sum of interior angles of a triangle is a fundamental concept in mathematics and has practical applications in various areas, including geometry, physics, architecture, and engineering. For example, engineers and architects use this concept to calculate and build stable and safe structures. (2 - 3 minutes)

4. Curiosity: To capture students' attention, the teacher can share two curiosities related to the topic:

• Curiosity 1: "Did you know that the sum of the interior angles of any triangle is always equal to 180 degrees? This means that if we have the measure of two interior angles of a triangle, we can easily find the measure of the third angle."
• Curiosity 2: "Have you ever heard of the flat surface hypothesis? It says that the sum of the interior angles of a triangle is equal to 180 degrees, regardless of the type of triangle or its size. This is one of the things that makes geometry so fascinating and useful!" (2 - 3 minutes)

5. Introduction to the topic: The teacher should then introduce the topic of the lesson, explaining that they will learn how to calculate the sum of interior angles of a triangle and apply this formula to solve problems. (1 minute)

Development (20 - 25 minutes)

1. Practical Activity - "The Triangle Challenge":

   • Description: The teacher should divide the class into groups of no more than 5 students. Each group will receive a sheet of paper with the figure of a triangle, but without the angles marked. The challenge will be to find the measure of the three interior angles of the triangle. The teacher can provide rulers and compasses to assist in the activity.

   • Step by step:

   1. The teacher should distribute the sheets of paper and explain the activity to the students.

   2. The students, in their groups, should start working on finding the measures of the interior angles. They can use the ruler to measure the sides of the triangle and the compass to draw the angles.

   3. The teacher should circulate around the room, assisting the groups that have difficulties and encouraging discussion and exchange of ideas among the students.

   4. When all the groups have finished the activity, the teacher should gather the class and discuss the solutions. He can ask the groups to present their findings and explain how they arrived at them.

   • Objective: This activity aims to have students apply the formula for the sum of interior angles of a triangle in a practical and contextualized way.

2. Fun Activity - "Angle Scavenger Hunt":

   • Description: In this activity, the teacher will spread around the classroom cards with different types of triangles (equilateral, isosceles, scalene) and angles of different measures. The students, divided into their groups, will have to find the cards that correspond to the sum of the interior angles of a triangle (180º). The group that finds all the cards correctly first will be the winner.

   • Step by step:

   1. The teacher should prepare the cards in advance, ensuring that there is a variety of types of triangles and angle measures.

   2. When the activity starts, the teacher should spread the cards around the room, ensuring that they are well mixed.

   3. The groups should then start looking for the cards that correspond to the sum of the interior angles of a triangle. They should calculate the sum of the angles of each triangle and compare it to 180º.

   4. The teacher should circulate around the room, observing the work of the groups and clarifying doubts.

   5. The first group that finds all the cards correctly will be the winner.

   • Objective: This activity aims to reinforce the concept of the sum of interior angles of a triangle in a fun and playful way, encouraging collaboration and healthy competition among the groups.

Feedback (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher should gather the whole class and promote a group discussion. Each group will have up to 2 minutes to share their solutions or conclusions from the activities carried out. During the presentations, the teacher should encourage students to explain the reasoning they used to arrive at their answers, as well as the strategies they adopted to solve the proposed problems. This discussion will allow students to see different approaches to the same problem, thus fostering mutual understanding and respect for different ideas and ways of thinking.

2. Connection with the Theory (2 - 3 minutes): After the presentations, the teacher should make the connection between the activities carried out and the theory on the sum of interior angles of a triangle. He should reinforce the essential concepts, explaining how the activities illustrate and apply these concepts. For example, he can highlight how the activity "The Triangle Challenge" allowed students to apply the formula for the sum of interior angles of a triangle in a practical way, and how the activity "Angle Scavenger Hunt" helped to reinforce this concept in a fun and playful way.

3. Individual Reflection (1 - 2 minutes): Finally, the teacher should propose that students reflect individually on what they have learned in the lesson. He can ask questions such as: "What was the most important concept you learned today?" and "What questions have not yet been answered?" Students will have one minute to think about these questions. This reflection will allow students to consolidate what they have learned and identify any doubts or areas that need further study or practice.

4. Feedback and Clarification of Doubts (2 - 3 minutes): After the individual reflection, the teacher should open a space for students to share their answers and doubts, if they wish. He should answer the doubts and provide feedback, reinforcing the positive points and pointing out areas that need improvement. He should also clarify any misconceptions or misunderstandings that may have arisen during the lesson. This feedback and clarification of doubts will help students to better understand the subject and to prepare for the next lesson.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes): The teacher should begin the Conclusion by recalling the main points covered during the lesson. He should emphasize the concept of interior angles of a triangle, the formula for the sum of interior angles, and how this formula can be applied to solve practical problems. In addition, he should recap the activities carried out and how they contributed to the understanding of the subject.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes): Next, the teacher should explain how the lesson connected theory, practice, and applications. He can mention how the theory was introduced and explained, how the practical activities allowed students to apply this theory in a concrete way, and how the discussions and reflections helped to connect the theory and the practice. In addition, he should reinforce the applications of the subject, reminding students how the concept of the sum of interior angles of a triangle is useful in various areas of knowledge.

3. Complementary Materials (1 minute): The teacher should suggest some complementary study materials for students who wish to deepen their understanding of the subject. These materials may include math books, online explanatory videos, websites with exercises and math problems, among others.

4. Importance of the Subject (1 - 2 minutes): Finally, the teacher should highlight the importance of the subject for students' daily lives. He can mention some everyday situations where knowledge about the sum of interior angles of a triangle can be useful, such as solving geometry problems, understanding maps and floor plans, construction, and engineering, among others. In addition, he should reinforce that the development of logical reasoning and problem-solving skills, which were exercised during the lesson, are valuable and useful skills in various areas of life.