Objectives (5 minutes)

1. Understand the classification of triangles based on the length of their sides: equilateral, isosceles, and scalene.
2. Identify and describe the characteristics of each type of triangle, including their specific properties.
3. Solve practical problems involving the application of the concept of triangle classification.

Secondary Objectives:

• Stimulate critical thinking and problem-solving through practical activities.
• Develop communication and collaboration skills, encouraging active student participation during the lesson.
• Integrate the use of digital technologies, such as geometry apps, to facilitate visualization and understanding of the content.

Introduction (10 - 15 minutes)

1. Review of Previous Content (5 minutes):

   • The teacher starts the lesson by reviewing the concepts of angles and sides of a triangle, which were covered in previous classes. It is important for students to have these concepts fresh in their minds as they form the basis for understanding the current topic.
   • The teacher can use simple and visual examples to reinforce these concepts, such as using toothpicks or straws to form triangles.

2. Contextualization (5 minutes):

   • The teacher then contextualizes the importance of studying the classification of triangles, explaining that this skill is fundamental in various fields such as architecture, engineering, design, among others.
   • The teacher may mention practical examples where the classification of triangles is applied, such as in the construction of bridges, towers, and buildings, in the design of projects, and in solving engineering problems.

3. Problem-Solving Scenarios (5 minutes):

   • The teacher proposes two problem-solving scenarios to pique students' interest. The first one could be: 'If a triangle has all sides of the same length, what would you call it?' The second one could be: 'If a triangle has two sides of the same length and one side of a different length, what would you call it?'
   • The teacher encourages students to think about these scenarios and share their answers and justifications with the class. This helps set the stage for the introduction of the concept of triangle classification.

Development (20 - 25 minutes)

1. Theory: Classification of Triangle Sides (10 - 12 minutes):

   • Definition of equilateral, isosceles, and scalene triangles (3 minutes): The teacher explains that an equilateral triangle is one that has all sides of the same length, an isosceles triangle is one that has two sides of the same length, and a scalene triangle is one in which all sides have different lengths.
   • Properties of each type of triangle (4 minutes): The teacher describes the properties of each type of triangle. For example, in an equilateral triangle, all angles are equal to 60 degrees; in an isosceles triangle, the angles opposite the equal sides are equal; and in a scalene triangle, all angles have different measures.
   • Differences between types of triangles (3 minutes): The teacher highlights the differences between equilateral, isosceles, and scalene triangles. For example, while an equilateral triangle has all sides and angles equal, an isosceles triangle has two sides and angles equal, and a scalene triangle has all sides and angles different.
   • Practical examples (2 minutes): The teacher presents visual and practical examples of each type of triangle, using geometric figures and real-world applications. Students are encouraged to ask questions and actively participate in the discussion.

2. Practice: Triangle Classification Exercises (10 - 13 minutes):

   • The teacher hands out a worksheet containing various triangles and asks students to classify each as equilateral, isosceles, or scalene.
   • Students work individually or in small groups to solve the exercises. They are encouraged to discuss their solutions and justify their classifications.
   • The teacher circulates around the room, offering help when needed and clarifying doubts.
   • After a designated time, the teacher asks some students to share their answers and justifications with the class. This promotes active student participation and allows the teacher to assess the class's level of understanding.

3. Application: Problem Solving (5 minutes):

   • The teacher presents some practical problems involving the classification of triangles and asks students to solve them.
   • The problems may include everyday situations, such as classifying triangles on a map, identifying the type of triangle in an architectural drawing, among others.
   • Students are encouraged to explain their problem-solving strategies and justify their answers. This helps reinforce the understanding of the concept and develop critical thinking and problem-solving skills.

Feedback (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes):

   • The teacher gathers all students for a group discussion on the solutions or conclusions reached by each one.
   • The teacher can start by asking different students how they classified the triangles in the exercises.
   • Then, he can ask each student to explain the reasoning behind their classification.
   • During this discussion, the teacher should encourage students to question each other's answers and defend their own answers.
   • The goal of this activity is to promote collective understanding of the concept of triangle classification and enhance students' communication and argumentation skills.

2. Connection to Theory (3 - 5 minutes):

   • The teacher then makes a connection between the students' answers and the theory presented.
   • He can highlight how the characteristics of equilateral, isosceles, and scalene triangles were applied in classifying the triangles in the exercises.
   • The teacher can also reinforce the differences between types of triangles, using practical examples provided by the students.
   • This step is important to consolidate students' understanding of triangle classification and reinforce the relevance of the topic for everyday applications.

3. Final Reflection (2 - 3 minutes):

   • To conclude the lesson, the teacher should ask students to reflect for a minute on what they have learned.
   • The teacher can ask questions such as: 'What was the most important concept learned today?' and 'What questions have not been answered yet?'
   • Students are encouraged to write down their reflections, which can serve as a starting point for the next lesson or for future studies.
   • The teacher can also ask some students to share their reflections with the class. This helps assess the effectiveness of the lesson and identify possible areas for improvement in future classes.

Conclusion (5 - 7 minutes)

1. Recap of Content (2 - 3 minutes):

   • The teacher begins the Conclusion phase by summarizing the main points covered in the lesson. He reiterates the classification of triangles according to the length of their sides, highlighting the distinct characteristics of each type: equilateral, isosceles, and scalene.
   • He also reinforces the properties of each type of triangle, such as the equality of sides and angles in an equilateral triangle, the equality of two sides and angles in an isosceles triangle, and the difference in sides and angles in a scalene triangle.
   • The teacher can use illustrations or drawings on the board to visually reinforce these concepts.

2. Theory-Practice Connection (1 - 2 minutes):

   • The teacher then makes the connection between the presented theory and the practical activities. He emphasizes how the triangle classification exercises and problem-solving helped students apply theoretical concepts in practice.
   • The teacher can mention concrete examples of how triangle classification is useful in different contexts, reinforcing the relevance of the topic for students' daily lives.

3. Extra Materials (1 - 2 minutes):

   • The teacher suggests additional study materials for students who wish to deepen their knowledge on the subject. This may include math books, educational websites, explanatory videos, among others.
   • For example, the teacher may recommend a geometry app that allows students to explore and manipulate different types of triangles virtually, which can help reinforce the understanding of the concept.

4. Importance of the Subject (1 minute):

   • Finally, the teacher emphasizes the importance of the subject covered for students' daily lives. He reiterates that the classification of triangles is not just an abstract mathematical concept, but a practical tool that can be applied in various fields, from architecture and engineering to design and art.
   • The teacher encourages students to see mathematics not only as a set of formulas and procedures, but as a discipline that provides powerful tools to understand and transform the world around them.