Objectives (5 minutes)

1. Recognize and classify triangles - Students should be able to identify and differentiate the three types of triangles (equilateral, isosceles, and scalene) based on their distinct characteristics, such as sides and angles.

2. Identify and describe the components of a triangle - Students should be able to identify and name the components of a triangle: vertices, sides, and angles. They should also be able to describe how each of these components relates to the others.

3. Solve problems involving triangles - In addition to identifying and describing triangles and their components, students should be able to apply this knowledge to solve simple mathematical problems involving triangles. This may include tasks such as identifying the type of triangle given a set of measurements or determining the measure of an unknown angle in a triangle.

Students will be encouraged to work in teams to achieve these objectives, promoting collaboration and critical thinking.

Introduction (10 - 15 minutes)

1. Review of geometric shapes - The teacher should start the lesson by reminding students of the basic geometric shapes they already know, such as squares, rectangles, and circles. This will help prepare them for the introduction of the concept of triangles, which is a more complex geometric shape.

2. Problem Situations - The teacher will present two problem situations to spark students' interest:

   • "Can you think of a situation in which you use triangles? For example, when you fly a kite, what happens to the string when the kite is flying high? And when it's falling down?"

   • "And at snack time? Have you ever thought about how the sandwiches in your lunchbox are cut? Are they all the same size? Why?"

3. Contextualization - The teacher will explain that triangles are very important in mathematics and everyday life. For example, in the construction of houses, architects and engineers use triangles a lot to calculate angles and distances. In addition, many games, such as tangram, are based on triangles.

4. Introduction to the topic - To spark students' curiosity, the teacher can share some fun facts about triangles:

   • "Did you know that the triangle is the strongest geometric figure? This is because when we apply a force to a triangle, it distributes that force equally on all sides, making it very resistant."

   • "And that many famous artists, like Leonardo da Vinci and Salvador Dalí, used triangles a lot in their artworks? This is because the triangle is a very balanced and harmonious shape to our eyes."

The teacher should ensure that all students have understood the information presented, encouraging them to ask questions and share their own experiences with triangles. Additionally, it is important to remind students that there are no right or wrong answers at this stage, as the goal is to spark curiosity and a desire to learn more about the subject.

Development (20 - 25 minutes)

1. Activity: Building Triangles - The teacher should organize students into groups of 4 to 5, distributing a kit of materials to each group. Each kit should contain toothpicks (or cut straws) and modeling clay (or clay). The students' task will be to build different types of triangles using these materials.

   • Step 1: Each group will receive a sheet with drawings of triangles (equilateral, isosceles, and scalene) and should try to replicate the figure with the toothpicks and clay.

   • Step 2: The teacher will circulate around the room, checking each group's work, asking questions to encourage discussion and reflection on the characteristics of each type of triangle.

   • Step 3: When all groups finish, the teacher will conduct a review together, asking each group to show their constructions, explaining what they learned about the different types of triangles and their characteristics.

2. Activity: Triangle Mission - The teacher presents a playful activity involving triangles:

   • Step 1: The teacher divides the class into two teams and positions one triangle of each type (equilateral, isosceles, scalene) in different locations in the room.

   • Step 2: One representative from each team at a time is called and must run to one of the triangles, identify it, and say the type of triangle it is. If correct, they earn a point for their team.

   • Step 3: The game continues until everyone has had the opportunity to participate and the triangles have been identified several times.

   • Step 4: The teacher then gathers the class and discusses the observations made during the game, reinforcing the concepts learned about the different types of triangles.

3. Activity: Triangular Puzzle - To review the lesson content, the teacher proposes a puzzle activity:

   • Step 1: The teacher divides the class into groups and distributes triangular puzzles, each group receiving a different puzzle.

   • Step 2: Each puzzle consists of a disassembled triangle and a set of cards with the characteristics of the triangles (equal sides, different sides, angles).

   • Step 3: Students must work together to solve the puzzle, matching the characteristics of the triangles on the cards with the shape of the disassembled triangle.

   • Step 4: The first group to complete the puzzle correctly wins the activity. The teacher then discusses with the class the solutions found, clarifying doubts and reinforcing the concepts learned.

The teacher should choose one of the activities developed, according to the pace and interest of the students, to ensure that there is enough time for the completion of the activity. Throughout all activities, the teacher should circulate around the room, observing the interactions of the students, offering support when necessary, and promoting discussion and questioning to deepen the students' understanding of the topic.

Feedback (10 - 15 minutes)

1. Group Discussion - The teacher should gather all students in a large circle and start a group discussion about the activities carried out. Each group should have the opportunity to share their solutions, discoveries, and challenges encountered during the activities. The teacher should encourage all students to participate, asking open-ended questions and promoting active listening among peers.

   • Step 1: The teacher should ask a representative from each group to briefly share the solution or conclusion they found during the activity. For example: "Group 1, what did you conclude about the different types of triangles after the construction activity?"

   • Step 2: The teacher should then ask questions to stimulate students' reflection on what they have learned. For example: "Group 2, did you encounter any challenges when identifying the triangles during the game? What did you do to overcome this challenge?"

   • Step 3: The teacher should encourage students to ask each other questions and to offer compliments and constructive suggestions. For example: "Group 3, what did you think of what Group 2 presented? Do you have any questions or comments for them?"

2. Connection to Theory - After discussing the activities, the teacher should revisit the theoretical concepts presented at the beginning of the lesson and make connections with the students' discoveries and conclusions.

   • Step 1: The teacher can ask: "Based on what we saw today about the different types of triangles, how would you describe an equilateral triangle? And an isosceles triangle? And a scalene triangle?"

   • Step 2: The teacher should reinforce the technical terms and definitions presented, using the students' conclusions as examples. For example: "Remember we talked about an equilateral triangle having all sides equal? Can you think of an example of an equilateral triangle that you built during the activity?"

3. Final Reflection - To conclude the lesson, the teacher should propose that students make an individual reflection on what they have learned. This can be done through two simple questions:

   • Step 1: The teacher should ask students to close their eyes (if they feel comfortable) and silently think about the following question: "What was the most interesting thing you learned today about triangles?"

   • Step 2: The teacher should then ask the second question: "How can you use what you learned today about triangles in your lives? Think of an example."

4. Sharing Reflections - To wrap up the lesson, the teacher can ask some students to share their reflections with the class. This can help reinforce learning and the connection of the content to everyday life.

   • Step 1: The teacher can say: "Who would like to share the most interesting thing they learned today about triangles?"

   • Step 2: The teacher can then ask: "Who wants to share how they can use what they learned today about triangles in their lives?"

Throughout the feedback session, the teacher should maintain a welcoming and respectful environment, valuing the contributions of all students and clarifying any doubts that may arise. Additionally, the teacher should take the opportunity to assess students' understanding of the topic and identify any areas that may need reinforcement or review in future lessons.

Conclusion (5 - 10 minutes)

1. Lesson Summary - The teacher should start the conclusion by summarizing the main points covered during the lesson. They can review the different types of triangles (equilateral, isosceles, and scalene) and their distinct characteristics, such as the relationship between sides and angles. Additionally, the teacher should recap the components of triangles (vertices, sides, and angles) and how they relate to each other.

2. Connection Between Theory, Activities, and Applications - Next, the teacher should reinforce the connection between the theory presented at the beginning of the lesson, the practical activities carried out, and the applications of triangle knowledge in everyday life. They can highlight how the triangle construction activities, the game "Triangle Mission," and the "Triangular" puzzle allowed students to apply theory in a practical and fun way. Additionally, the teacher can recall the applications of triangles in different contexts, such as in construction, art, and even in organizing a lunchbox.

3. Additional Materials - The teacher can suggest additional materials for students who wish to deepen their knowledge on the subject. This may include children's books on geometry, educational websites with interactive geometry games, and explanatory videos about triangles. The teacher should emphasize that exploring these materials is optional and that the most important thing is for students to have understood the basic concepts presented in the lesson.

4. Importance of the Subject - Finally, the teacher should emphasize the importance of studying triangles. They can explain that in mathematics, triangles are one of the most basic and fundamental geometric shapes, and that understanding their characteristics and properties is essential for the study of geometry and many other fields of mathematics. Additionally, the teacher can reinforce that knowledge of triangles is also very useful in everyday life, as it can be applied in diverse situations such as building a house, solving a puzzle, or even organizing a snack.

Throughout the conclusion, the teacher should encourage students to ask questions, share their opinions, and express any difficulties they may have regarding the lesson's topic. Additionally, the teacher should emphasize that learning is a continuous process, and that students will have many future opportunities to explore and deepen their knowledge of triangles and other mathematical topics.