Lesson plan of Triangles: Angular Classification

Objectives (5-7 minutes)

1. Understanding the concept of triangle angle classification: The main objective is for students to understand and explain the concept of triangle angle classification, identifying the different types of triangles (acute, obtuse, and right) based on their angle measurements.

2. Ability to calculate the angle measurements of a triangle: In this secondary objective, students should be able to perform calculations to determine the angle measurements of a triangle, using the properties of the internal angles of a triangle.

3. Development of problem-solving skills: Finally, the goal is for students to apply the knowledge acquired to solve problems involving the angle classification of triangles, developing their mathematical problem-solving skills.

Secondary objectives:

• Development of critical and logical thinking: Through problem-solving, students will be encouraged to think critically and logically, applying the acquired knowledge effectively.

• Improvement of communication skills: During classroom discussions, students will have the opportunity to improve their communication skills, expressing their ideas and understanding in a clear and coherent manner.

• Stimulating interest in mathematics: By making the class interactive and relevant to the students' daily lives, it is expected to encourage interest in mathematics and the perception of its importance and applicability.

Introduction (10-15 minutes)

1. Review of Previous Concepts (3-5 minutes): The teacher should recall basic concepts of plane geometry, such as the definition of a triangle (a plane figure formed by three sides and three angles) and the properties of the angles of a triangle (the sum of the internal angles of a triangle is always 180°). This review can be done through direct questions to students or through a quick quiz.

2. Contextualization (2-3 minutes): The teacher should then explain the importance of angle classification of triangles, showing some practical applications, such as in architecture (where the classification of triangle angles is essential for the construction of stable structures) and in cartography (where the classification of triangle angles is used to determine distances and areas on maps).

3. Problem Situation (3-5 minutes): To arouse the interest of the students, the teacher may present two problem situations: a) "How do architects manage to design such tall and complex buildings without them falling over?" and b) "Why are the maps of a globe different from the maps on a flat surface?" The teacher can then question the students on how the angle classification of triangles can be relevant to solving these problems.

4. Introduction to the Topic (2-3 minutes): Finally, the teacher should introduce the topic of the lesson - Angle Classification of Triangles - explaining that by classifying a triangle according to the measurement of its angles, we can better understand its characteristics and properties. The teacher can, for example, show some images of different types of triangles (acute, obtuse, and right) and ask students if they can identify them and why. This activity will help spark students' curiosity and prepare them for the next stage of the lesson plan.

Development (20-25 minutes)

1. Activity "Building Triangles" (10-12 minutes):

1.1. Preparation: The teacher should divide the class into groups of up to five students and provide each group with a set of geometric materials (ruler, protractor, and compass) and a sheet of cardboard.

1.2. Instructions: The teacher should explain that the group's task is to construct three different triangles: an acute triangle, an obtuse triangle, and a right triangle, using the materials provided.

1.3. Execution: The students should then start building the triangles, following the teacher's instructions. To verify if the triangles have been constructed correctly, students should measure the internal angles of each triangle with the protractor and write down the measurements on the cardboard sheet.

1.4. Discussion: After completing the activity, the teacher should ask a representative from each group to display the constructed triangles and explain how they determined the angle classification of each one. The teacher should correct any errors and clarify any questions.

2. Activity "Discovering Properties" (10-12 minutes):

2.1. Preparation: The teacher should provide each group with a list of triangles (drawn on paper or projected onto slides) with the measurements of their sides, but without the angle classification.

2.2. Instructions: The teacher should explain that the group's task is to determine the angle classification of each triangle, using the side measurements and the properties of triangles.

2.3. Execution: The students should then start analyzing the triangles, calculating the angle measurements (using the properties of triangles) and determining the angle classification of each one.

2.4. Discussion: After completing the activity, the teacher should ask a representative from each group to explain how they determined the angle classification of each triangle. The teacher should correct any errors and clarify any questions.

3. Activity "Real-World Problems" (5-7 minutes):

3.1. Preparation: The teacher should provide each group with a list of real-world problems involving the angle classification of triangles. These problems can be related to areas such as architecture, engineering, design, cartography, among others.

3.2. Instructions: The teacher should explain that the group's task is to solve the problems, using the knowledge acquired about the angle classification of triangles.

3.3. Execution: The students should then start solving the problems, discussing them in a group and applying the problem-solving strategies learned.

3.4. Discussion: After completing the activity, the teacher should ask a representative from each group to explain how they solved each problem. The teacher should correct any errors and clarify any questions.

These fun and contextualized activities are designed to actively engage students, promoting meaningful learning and comprehension of the topic. They also allow students to apply the acquired knowledge in practical and relevant ways, developing their problem-solving skills and critical thinking.

Feedback (8-10 minutes)

1. Group Discussion (3-4 minutes): The teacher should promote a group discussion with all students. Each group should share their solutions and conclusions from the activities performed. The goal is for students to hear different perspectives and approaches to solving problems, thus enriching their understanding of the topic. During this discussion, the teacher should act as a moderator, asking questions to stimulate critical thinking and deepen students' understanding.

2. Connection to Theory (2-3 minutes): After the group discussion, the teacher should make the connection between the practical activities performed and the theory presented at the beginning of the class. The teacher could, for example, demonstrate how the triangle properties (such as the sum of internal angles always being 180°) were used to determine the angle classification of the triangles in the activities. This will help students understand the relevance of theory and how it is applied in practice.

3. Individual Reflection (2-3 minutes): The teacher should, therefore, propose the student reflect individually on what was learned in class. To do this, the teacher can ask questions such as:

3.1. "What was the most important concept you learned today?"

3.2. "What questions have yet to be answered?"

3.3. "How can you apply what you learned today to everyday situations?"

3.4. "What were the main difficulties you encountered during the activities and how did you overcome them?"

3.5. "Which problem-solving strategies did you find most effective, and why?"

This individual reflection will allow students to consolidate what they have learned, identify possible gaps in their understanding, and begin to think about how they can apply the acquired knowledge. The teacher may optionally ask students to share their reflections with the class, prompting a final discussion.

4. Teacher Feedback (1-2 minutes): Finally, the teacher should provide general feedback on student participation and performance during the class. The teacher should praise students' efforts, highlight the main ideas and concepts learned, and offer suggestions for improvement, if necessary. The objective is to encourage and motivate students, reinforcing the importance of the topic and the relevance of the activities performed. The teacher should also encourage students to continue studying the topic and clarify any doubts they may have.

This Feedback phase is crucial for consolidating learning, clarifying doubts, promoting reflection, and motivating students for future learning. At the end of this stage, students should be able to explain the concept of triangle angle classification, calculate the angle measurements of a triangle, and solve problems involving the angle classification of triangles.

Conclusion (5-7 minutes)

1. Summary of Content (2-3 minutes): The teacher should recap the main points covered during the lesson, reinforcing the concept of triangle angle classification and the properties of triangles that were used to determine angle classification. The teacher should also recall the problem-solving strategies that were discussed and applied during the practical activities. In addition, the teacher should emphasize the importance of triangle angle classification and how it can be applied in different contexts, such as in architecture, engineering, design, cartography, among others.

2. Connection Between Theory, Practice, and Applications (1-2 minutes): The teacher should explain how the class connected theory (the definition of a triangle and its properties) with practice (activities of building triangles, determining their angle classifications, and solving problems) and with real-world applications (the real-world problem situations that were discussed). The teacher should emphasize that mathematics is not just a set of abstract rules and formulas, but rather a powerful tool for understanding and solving real-world problems.

3. Extra Materials (1-2 minutes): The teacher should suggest some extra materials for students who want to delve deeper into their studies of triangle angle classification. These materials may include explanatory videos, interactive math websites, reference books, additional exercises, among others. For example, the teacher may recommend using interactive geometry apps, such as Geogebra, that allow students to explore and manipulate triangles of different shapes and sizes.

4. Relevance of the Subject Matter (1 minute): Finally, the teacher should emphasize the importance of the presented subject matter for students' everyday lives. It should be stressed that understanding the angle classification of triangles is essential for various areas, such as in building stable structures, determining distances and areas on maps, creating designs, and much more. In addition, the teacher may reinforce that the development of problem-solving skills and critical thinking, which were stimulated during the lesson, are valuable skills not only for mathematics but for life in general.