Objectives (5 - 7 minutes)

1. Introduce the concept of congruence of figures in a didactic and visual way, allowing students to understand that two figures are congruent when they have the same shape and size, even if they are in different positions.

2. Provide students with the opportunity to identify congruent figures in their environment, encouraging observation and critical analysis.

3. Develop students' ability to recognize and draw congruent figures, promoting logical-mathematical reasoning and motor coordination.

Secondary Objectives:

• Stimulate cooperation and exchange of ideas among students through group activities.
• Promote curiosity and interest in mathematics, showing the application of learned concepts in everyday life.

Introduction (10 - 12 minutes)

1. Content Review: The teacher starts the lesson by reviewing basic concepts of plane geometry, such as points, lines, curves, and basic geometric figures (triangle, square, rectangle, and circle). This review is important so that students can better understand the concept of congruence of figures.

2. Problem Situation 1: The teacher proposes the following situation: "Imagine you have two puzzle pieces. The two pieces have exactly the same shape and size. If you swap the pieces, what happens? Do the pieces remain the same or change?" The teacher expects students to realize that the pieces remain the same, even if they have been swapped, and that this is an example of congruent figures.

3. Problem Situation 2: The teacher poses the following question: "If you have two paper triangles and one plastic triangle, how can you tell if the paper triangles are congruent to each other and if they are congruent to the plastic triangle?" Here, the teacher expects students to understand that for two figures to be congruent, they must have the same shape and size.

4. Contextualization: The teacher explains that the concept of congruent figures is very important as it is used in various areas such as construction, toy industry, art, etc. For example, when an architect designs a house, they need to draw several congruent figures to represent the different parts of the house. Similarly, a toy designer needs to create congruent pieces for the toy to function correctly.

5. Introduction to the Topic: The teacher introduces the topic of the lesson, Congruent Figures, explaining that two figures are congruent when they have the same shape and size, even if they are in different positions. They also emphasize that for two figures to be congruent, all their corresponding sides and angles must be equal.

6. Curiosity: To spark students' interest, the teacher can share some curiosities, such as the word "congruent" coming from the Latin "congruens," which means "equal" or "similar." Additionally, they can mention that the study of congruence of figures was developed by ancient Greeks, like Euclid, who is considered the "father" of geometry.

By the end of this stage, students should have a basic understanding of the concept of congruence of figures and be ready to explore the topic in a more practical and fun way.

Development (20 - 25 minutes)

Suggested Activities:

1. Congruent Memory Game:

   • The teacher should prepare cards in advance with pairs of figures (triangles, squares, rectangles, circles) drawn, where one figure of each pair should be slightly different in size or orientation.
   • The cards are shuffled and placed on a table or on the floor, with the figures facing down.
   • Students, in groups of up to 4, must take turns flipping two cards.
   • If the figures on the flipped cards are congruent, the student can keep the cards and earn a point.
   • If the figures are not congruent, the student must return the cards to their original position.
   • The game continues until all cards have been flipped. The group with the most pairs of congruent cards wins.

2. Construction of Congruent Figures:

   • The teacher provides students with a variety of materials (popsicle sticks, modeling clay, colored paper, etc.) and a model of a simple geometric figure (e.g., triangle).
   • Students, in groups, must use the available materials to build figures congruent to the model figure.
   • The teacher circulates around the room, encouraging discussion and collaboration among students, and observing the strategies used by each group.
   • At the end of the activity, each group must present their congruent figures and explain how they arrived at the solution.

3. Congruent Treasure Hunt:

   • The teacher hides congruent figures made on bond paper or cardboard around the classroom or schoolyard.
   • Students, in groups, must find the hidden congruent figures.
   • Each time a group finds a pair of congruent figures, they must bring them to the teacher, who verifies if the figures are indeed congruent.
   • The group that finds the most pairs of congruent figures wins the activity.

It is important to note that the teacher can choose one or more of these activities, depending on the available time and the class profile. Each activity allows students to explore the concept of congruence of figures in a playful and practical way, stimulating critical thinking, collaboration, and creativity. By the end of this stage, students should have a deeper understanding of the concept of congruence of figures and be able to identify and construct congruent figures.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes)

   • The teacher gathers all students in a large circle and promotes a group discussion about the solutions and discoveries of each team in the previous activities.
   • Each group is encouraged to share the congruent figures they built, the pairs they found in the Memory Game, and the strategies they used.
   • During the discussion, the teacher reinforces the concepts of congruence of figures, highlighting the criteria of equality of corresponding sides and angles, and how these criteria were applied in the activities.
   • The teacher also takes the opportunity to correct any misconceptions and reinforce the most important points of the lesson.

2. Connection with Theory (3 - 5 minutes)

   • After the discussion, the teacher reviews the theoretical concepts presented at the beginning of the lesson, relating them to the practical activities carried out.
   • The teacher revisits the definition of congruence of figures, emphasizing that two figures are congruent when they have the same shape and size, even if they are in different positions.
   • The teacher also highlights that the congruence of figures is determined by the equality of all corresponding sides and angles.

3. Individual Reflection (2 - 3 minutes)

   • To conclude the lesson, the teacher proposes that students reflect individually on what they have learned.
   • The teacher asks two simple questions to guide students' reflection:
     1. "What did you enjoy learning the most about congruent figures today?"
     2. "How can you apply what you learned today about congruent figures in everyday situations?"
   • Students are encouraged to think about the answers and, if comfortable, to share their reflections with the class.

This return stage is essential to consolidate students' learning, allowing them to review and reflect on the concepts and skills acquired during the lesson. Furthermore, the group discussion and connection with theory promote a deeper understanding of the content, while individual reflection helps students realize the relevance and applicability of what they have learned.

Conclusion (5 - 7 minutes)

1. Summary of Key Points (2 - 3 minutes)

   • The teacher summarizes the key points covered during the lesson, recalling the definition of congruent figures, the importance of equality of corresponding sides and angles, and the practical application of the concept in different contexts.
   • The teacher reinforces the criteria that determine the congruence of figures, explaining that for two figures to be congruent, all their corresponding sides and angles must be equal.

2. Connection between Theory and Practice (1 - 2 minutes)

   • The teacher highlights how the lesson managed to connect the theory presented at the beginning with the practice through playful activities and group discussion.
   • The teacher emphasizes that by building and identifying congruent figures, students were able to directly apply theoretical concepts, which helps solidify learning.

3. Additional Materials (1 - 2 minutes)

   • The teacher suggests some extra materials for students to deepen their knowledge of congruent figures. This may include educational websites with interactive games, math books with practical exercises, and explanatory videos available online.
   • The teacher may also recommend that students look for congruent figures at home, on the way to school, in the park, etc., as a way to practice what they have learned and develop their observation and analysis skills.

4. Relevance of the Content (1 minute)

   • Finally, the teacher emphasizes the importance of understanding and recognizing congruent figures, explaining that this knowledge is fundamental for the comprehension of more advanced geometry concepts and for solving practical problems.
   • The teacher highlights that the ability to identify and construct congruent figures is useful not only in mathematics but also in many other areas such as art, architecture, toy industry, etc.
   • To reinforce this idea, the teacher can present examples of real-life situations where the congruence of figures is important, such as building a puzzle, assembling furniture, creating a cartoon, etc.

The conclusion is a crucial stage to effectively end the lesson, allowing students to consolidate their learning, understand the relevance of the content, and have resources to continue studying and practicing. Additionally, by connecting theory to practice, the conclusion helps promote a deeper and lasting understanding of the concept of congruent figures.