Objectives (5 - 7 minutes)

1. Recognize and identify the different types of triangles: equilateral, isosceles, and scalene.
2. Understand the characteristics and properties of each type of triangle: number of equal sides, internal and external angles.
3. Apply the acquired knowledge in the identification and classification of triangles in everyday situations and mathematical problems.

Secondary Objectives:

• Develop observation, comparison, and classification skills.
• Promote logical reasoning and problem-solving abilities.
• Encourage active and collaborative participation of students through discussions and group activities.
• Foster the connection between mathematics and the real world through examples and practical applications.

Introduction (10 - 12 minutes)

1. Review of previous contents: The teacher should start the lesson by reminding students about the concepts of basic geometric shapes, such as square, rectangle, and circle. They should be encouraged to identify these shapes in everyday objects or in the classroom environment.

2. Problem situation: The teacher can present the following situation to the students:

   • "Imagine you are architects designing a new park for the city. You need to decide which shape to use for the park's playground equipment. Do you think all the playground equipment should have the same shape? Why?"

3. Contextualization: The teacher should explain that, just like in the park example, in many everyday situations, knowing how to identify and classify geometric shapes is important.

   • "For example, engineers need to know what type of triangle is most suitable for building a bridge. Or when we are cutting a pizza into slices, we are actually dividing a circle into equal parts."

4. Introduction to the topic: The teacher should then introduce the topic of the lesson - "Components of Triangles" - in this way:

   • "Today we are going to learn more about one of the most important geometric shapes: the triangle. Did you know that there are different types of triangles? Triangles that have all sides equal, triangles that have two sides equal, and triangles that have all sides different. Let's find out more about them and their characteristics."
   • The teacher can show illustrations of the different types of triangles and explain that each one has special characteristics that differentiate them from each other.
   • "Our mission today is to become true detectives of triangles, capable of identifying and classifying each one!"

This stage should be conducted in an engaging and interactive manner, encouraging active student participation and sparking their interest in the subject. The teacher can use visual resources such as posters, images, or even three-dimensional objects to make the introduction more concrete and tangible.

Development (20 - 25 minutes)

Activity 1: Building Triangles

1. Step 1: The Pencil and Ruler Game

   • In pairs, each student receives a sheet of paper, a pencil, and a ruler.
   • The teacher explains that they should draw several "line segments" (similar to "straight lines" they already know) on their sheets of paper. Each line segment can be of any length, but all must have a start and an end.
   • Next, the teacher asks the students to try to combine three line segments to form a triangle. They should mark the starting and ending points of each line segment with a dot and then connect the dots to form a triangle.
   • The teacher circulates around the room, offering support and guidance as needed.

2. Step 2: Checking the Triangles

   • After all students have drawn at least one triangle, the teacher asks them to check if their triangles satisfy the condition that the sum of the measures of two sides of a triangle is always greater than the measure of the third side.
   • To do this, students measure each of the three sides of their triangles using the ruler, and sum the measures of two sides. Then they compare this sum with the measure of the third side. If the sum is greater, they have a triangle. If not, they need to try again.

3. Step 3: Naming the Triangles

   • After students build and check several triangles, the teacher explains that they can classify their triangles into three types: equilateral, isosceles, and scalene.
   • The teacher shows examples of each type of triangle on the board or on posters, and discusses the characteristics of each. The students then classify their own triangles according to the characteristics and write the classification next to each triangle.

Activity 2: Super Triangle Detectives

1. Step 1: The Card Game

   • In groups of 4 or 5, each student receives a card with a triangle drawn on it, but without the classification written.
   • The teacher explains that they are "Super Triangle Detectives" and must discover what type of triangle they have on their cards.
   • Each student, in turn, must ask a question to the group that can only be answered with "yes" or "no". For example: "Does my triangle have two equal sides?"
   • The teacher circulates around the room, helping students formulate their questions and ensuring that the answers are accurate.

2. Step 2: Discovering the Triangle

   • With each question, students discard the triangles that do not match the description. They should use what they have learned about the characteristics of different types of triangles to make their decisions.
   • The game continues until all triangles have been correctly classified.
   • At the end of the game, the teacher discusses the strategies used by the students to discover the classification of their triangles.

Both activities are designed to be fun and engaging, while allowing students to apply and deepen their knowledge of the different types of triangles. The teacher should closely monitor the students' progress, offering support and guidance as needed.

Feedback (10 - 15 minutes)

1. Group Discussion: The teacher should gather all students in a large circle and promote a group discussion about the solutions or conclusions found by each team in the activities. Each group should share the triangles they built, how they classified them, and what strategies they used to reach their conclusions.

2. Connection to theory: After each group shares, the teacher should then review the characteristics of each type of triangle (equilateral, isosceles, and scalene) and check if the students were able to make the connection between practice and theory. For example, the teacher can ask: "What characteristics did you observe in your triangles that led you to classify them this way?"

3. Reflection on learning: Next, the teacher should guide the students to reflect on what they learned in the lesson. For this, the teacher can ask two simple questions:

   • "What was the most fun part of today's lesson and why?"
   • "What did you learn about triangles that you didn't know before?"

4. Learning assessment: To conclude, the teacher should propose that students apply what they learned in a problem-solving situation. The situation could be something like:

   • "You have been invited to create a poster for the classroom that explains the different types of triangles. How would you do that? What information would you include on the poster?"

This feedback stage is essential to consolidate students' learning, allowing them to reflect on what they have learned, make connections to the real world, and apply their knowledge in new situations. Additionally, group discussion and individual reflection promote oral expression and self-assessment, important skills for students' development.

Conclusion (5 - 7 minutes)

1. Summary of contents: The teacher should start the conclusion by recapping the main points covered during the lesson. For example, reminding students about the three main types of triangles - equilateral, isosceles, and scalene - and their distinct characteristics: equilateral has all sides with the same measure and all angles with the same measure (60°); isosceles has two sides with the same measure and two angles with the same measure; and scalene has all sides and angles with different measures.

2. Connection between theory and practice: The teacher should then highlight how the lesson connected theory with practice. For instance, mentioning that students had the opportunity to build their own triangles, measure their sides and angles, and apply what they learned to classify them correctly. Additionally, the game "Super Triangle Detectives" allowed students to apply their knowledge in a fun and challenging way.

3. Suggestion of additional materials: To enrich learning, the teacher can suggest some extra resources to students. These may include children's math books that explore the topic of triangles, educational websites with games and interactive activities about triangles, and short videos that explain the characteristics of triangles in a simple and visual way.

4. Importance of the topic for everyday life: Finally, the teacher should emphasize the importance of the topic for students' daily lives. For example, explaining that the ability to identify and classify triangles can be useful in various situations, from building physical structures (such as bridges and buildings) to solving mathematical problems and appreciating art and design. Additionally, the teacher can remind students that, as in all forms of mathematics, the ability to observe, compare, and classify is a skill that can be applied in many aspects of everyday life.

This conclusion stage is crucial to reinforce students' learning, encourage them to continue exploring the topic on their own, and understand the relevance of mathematics in their lives. Furthermore, by connecting theory with practice, the teacher helps students solidify their understanding of the topic and apply what they have learned in new situations.