Objectives (5 - 10 minutes)

1. To introduce the concept of congruent figures and help students identify different examples around them in the real world.

2. To teach students how to identify congruent figures, focusing on characteristics such as shape and size.

3. To encourage students to use appropriate and precise mathematical language when describing congruent figures.

Secondary objectives:

• To promote critical thinking and problem-solving skills through identifying congruent figures.

• To encourage students to work together and share ideas when discussing congruent figures.

• To spark students’ curiosity, encouraging them to further explore geometry in their everyday lives.

Introduction (10 - 15 minutes)

1. Review of Prior Knowledge: The teacher begins by reviewing basic geometric shapes (square, rectangle, triangle, circle), and exploring with students how they can identify them in the real world. A shape hunt activity can be conducted, where students have to find objects in the classroom corresponding to each geometric shape. This will set the stage for introducing the concept of congruent figures.

2. Problem-Based Scenarios: To pique students’ interest, the teacher presents two problem-based scenarios:

   • Scenario 1: The teacher draws two triangles on the board, one large and one small, and asks students if they are the same. Then, the teacher draws two triangles of the same size, but in different orientations, and asks if they are the same. This will illustrate the idea that two figures can be the same, even if they are different in size or orientation.

   • Scenario 2: The teacher shows two images, one of a red square and one of a blue square. He asks students if they can tell whether the squares are the same just by looking at the images. This will introduce the idea that two figures are congruent if they have the same shape and size, regardless of their position or color.

3. Relevance and Importance: The teacher explains that being able to recognize congruent figures is important because it helps us recognize patterns, solve problems, and better understand the world around us. He can share examples of how geometry is used in different fields, such as architecture, art, and even games and puzzles.

4. Introduction of the Topic: The teacher formally introduces the concept of congruent figures, explaining that two figures are congruent if they have the same shape and size, regardless of their position or orientation. He can use simple examples, such as folding a piece of paper in half to show that the two halves are congruent, or showing two puzzle pieces that fit together perfectly as an example of congruent figures. The teacher can also mention that the word "congruent" comes from the Latin word for "equal."

Development (20 - 25 minutes)

Activity 1: "Discovering Congruent Figures"

1. The teacher divides the class into groups of 4 or 5 and distributes paper and pencils to each group.

2. Each group receives a set of cards with drawings of different geometric shapes (squares, rectangles, triangles, circles) in various sizes and orientations.

3. The teacher explains that the challenge is to find pairs of congruent figures from the set of cards.

4. Students must carefully observe each card, discuss as a group, and mark the pairs they believe are congruent.

5. After a few minutes, the teacher asks groups to share their findings. They should give reasons for their answers, explaining why they believe the figures are congruent.

Activity 2: "Congruent Figures Around the World"

1. The teacher encourages students to find congruent figures in their surroundings.

2. Each group is given a tablet or a smartphone with the camera enabled. They must walk around the classroom or the school, take pictures of objects they believe are congruent, and return to their starting location.

3. The students then share their photos with the class. They should explain why they believe the objects in their photos are congruent.

4. The teacher provides feedback on students’ answers, clarifies any misconceptions, and reinforces the concepts of congruent figures.

Activity 3: "Congruent Figures Puzzle"

1. The teacher gives each group a puzzle with pieces in different shapes and sizes. The puzzle pieces are all congruent figures, but they are all mixed up.

2. The challenge for students is to reassemble the puzzle, forming a complete picture with the congruent pieces.

3. The teacher observes groups as they progress, offering guidance and clarifying doubts when needed.

4. As groups complete the puzzle, the teacher checks if the pieces are correctly placed, confirming that they are indeed all congruent figures.

These activities are designed to be fun and engaging, allowing students to explore the concept of congruent figures in a hands-on, meaningful way. The teacher should guide the discussion after each activity, reinforcing key concepts and correcting any misconceptions.

Wrap-Up (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes): The teacher gathers all students in a large circle and initiates a group discussion on the teams’ findings. Each group is invited to share the congruent figures they found during the "Discovering Congruent Figures" activity and explain why they believe these figures are congruent. Then, the groups who participated in the "Congruent Figures Around the World" activity present their pictures and justify why they determined the objects in the pictures to be congruent figures. Throughout the discussion, the teacher should observe students’ answers, ask probing questions to deepen understanding, and correct any misconceptions.

2. Connecting to Theory (2 - 3 minutes): After the group discussion, the teacher revisits the main theoretical concepts covered in the class, reinforcing the definition of congruent figures and the characteristics they share, such as shape and size. The teacher can use the examples found by students during the hands-on activities to illustrate these concepts. For instance, if a group presented a pair of triangles as congruent figures, the teacher can emphasize that even though the triangles are in different positions or orientations, they are still congruent if they have the same shape and size.

3. Individual Reflection (3 - 5 minutes): To conclude the lesson, the teacher asks students to reflect on what they have learned, individually. He provides two simple questions to guide this reflection:

   • Question 1: "What does it mean to say that two figures are congruent?"

   • Question 2: "Give an example of two figures that are congruent, and explain why they are congruent."

   Students are encouraged to silently think about these questions for a minute. Then, the teacher gives an opportunity for any student who wishes to share their answers with the class. This final reflection and sharing helps solidify students’ learning and allows the teacher to assess the effectiveness of the lesson.

Throughout the wrap-up, the teacher should maintain an encouraging and respectful environment, promoting participation from all students and valuing their contributions. In addition, he should be attentive to any challenges or gaps in understanding that may arise and be ready to address them individually or collectively.

Conclusion (5 - 10 minutes)

1. Summary of Main Points (2 - 3 minutes): The teacher begins the conclusion by recapping the main points of the lesson. He emphasizes that congruent figures are those that have the same shape and size, regardless of their position or orientation. He also reiterates that geometry is all around us, from the architecture of buildings to the cartoons we watch. The teacher can do this by briefly reviewing the definitions and key concepts discussed during the lesson.

2. Connecting Theory and Practice (1 - 2 minutes): The teacher highlights how the lesson connected the theory of congruent figures to practical, hands-on activities. He emphasizes that, by observing and discussing examples of congruent figures in their surroundings, students were able to apply and solidify what they had learned in class.

3. Extension Materials (1 - 2 minutes): The teacher suggests supplemental materials for students who wish to further their understanding of congruent figures. These can include math books with clear and illustrative explanations on the topic, interactive online games that help reinforce the identification of congruent figures, or even educational videos that present the concept in a fun and engaging way.

4. Relevance and Importance (1 - 2 minutes): Finally, the teacher discusses the relevance of the topic to students’ learning. He explains that being able to recognize congruent figures is foundational to developing spatial reasoning, a skill that is useful in many areas of life, such as solving puzzles, drawing, designing, or assembling objects. Furthermore, the teacher reinforces that mathematics is not just an academic subject, but also a practical tool that we use daily to understand and interact with the world around us.

5. Closing Remarks (1 minute): The teacher concludes the lesson by thanking the students for their active participation and reinforcing that they can always seek clarification or further their understanding of the topic. He also encourages them to continue exploring the world of mathematics in their everyday lives.