Lesson plan of Congruent Figures

Objectives (5 - 7 minutes)

1. Identify congruent figures: Students should be able to recognize congruent figures, understanding that they are figures that have the same shape and size, even if they are rotated, flipped, or translated. This will be developed through the observation and comparison of different figures.

2. Separate congruent from non-congruent figures: Students should be able to differentiate between congruent and non-congruent figures. To do so, they will be challenged to classify a set of figures into two categories: congruent and non-congruent.

3. Construct congruent figures: Finally, students will be encouraged to construct congruent figures using different materials, such as paper, pencils, and scissors. This will help consolidate the concept of congruence in a practical and fun way.

Introduction (10 - 12 minutes)

1. Review of concepts: The teacher begins the lesson by reviewing the concepts of basic geometric shapes that students should have already learned, such as squares, rectangles, triangles, and circles. This can be done through flashcards or small games to engage students. (2 - 3 minutes)

2. Problem situations: Next, the teacher presents two problem situations to introduce the concept of congruent figures. The first can be a puzzle, where students must discover which pieces fit together to form a square. The second can be a memory game, where students must find pairs of congruent figures. (3 - 4 minutes)

3. Contextualization: The teacher explains that congruent figures are very important in mathematics and in everyday life. For example, when we build a house, the bricks need to be congruent so that the walls are straight. Similarly, when we play a board game, the pieces need to be congruent so that the game works correctly. (2 - 3 minutes)

4. Gaining attention: To spark students' interest, the teacher can share curiosities about congruent figures. For example, in ancient times, architects used the concept of congruence to build perfectly symmetrical temples and pyramids. In addition, the teacher can show images of animals and challenge students to find pairs of animals that are congruent. (3 - 4 minutes)

Development (20 - 25 minutes)

1. Activity: Fitting pieces (10 - 12 minutes)

   • The teacher prepares a series of geometric figures on paper or card stock, such as squares, rectangles, triangles, and circles. These figures should be large enough for students to easily manipulate.
   • In groups of 3 or 4, students are given a set of figures and the task of fitting them together to form a rectangle, a square, and a triangle.
   • Students are encouraged to experiment with different combinations, discuss within the group, and check if the shapes they have built are indeed rectangles, squares, and triangles. This helps develop problem-solving and critical thinking skills.
   • After the completion of the activity, the teacher guides a whole-class discussion, asking students about the figures they found and how they know that their shapes are correct.

2. Activity: Congruent memory game (10 - 12 minutes)

   • The teacher prepares a set of cards containing images of various geometric figures, with half of them being congruent.
   • Students are divided into groups, and each group receives a set of cards.
   • The aim of the game is to find pairs of cards that represent congruent figures.
   • Students can take turns flipping the cards, but they need to justify why they think the figures are congruent.
   • At the end of the game, the teacher promotes a discussion so that students can justify their choices and explain what they understand by congruence.

3. Activity: Constructing congruent figures (10 - 12 minutes)

   • The teacher provides each group of students with a set of geometric figures similar to those used in the previous activity, but this time on thicker paper.
   • Students are encouraged to experiment with different manipulations of the figures, such as rotations, reflections, and translations, in order to create new figures.
   • The challenge is to construct a pair of congruent figures and explain how they know that the two figures are congruent.
   • The teacher circulates around the classroom, providing guidance and clarifying doubts, if necessary.
   • At the end of the activity, students share their creations with the class, explaining the process they used to construct the congruent figures.

The teacher should choose one or two of these activities, depending on the time available and the needs of the students. Each activity is designed to be interactive, engaging, and promote collaboration among students.

Wrap Up (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes)

   • The teacher gathers all students in a circle and starts a group discussion about the solutions and conclusions found in each activity.
   • He/she asks students to share their answers, explaining how they arrived at them. This helps promote communication and critical thinking.
   • During the discussion, the teacher reinforces important concepts, such as what makes two figures congruent and how figures can be transformed (rotated, flipped, or translated) while maintaining their congruence.

2. Connection to Theory (3 - 4 minutes)

   • The teacher briefly reviews the theoretical concepts discussed at the beginning of the class on congruent figures and their importance in mathematics and everyday life.
   • Next, he/she makes the connection between the theory and the practical activities carried out during the class, reinforcing how the students applied these concepts in practice.
   • The teacher can also highlight everyday situations where the congruence of figures is important, such as in the construction of objects, in the organization of spaces, and even in games and puzzles.

3. Final Reflection (2 - 4 minutes)

   • To conclude the lesson, the teacher asks students to reflect on what they have learned. He/she can do this through two simple questions:
     1. "What did you find most interesting about congruent figures and why?"
     2. "How could you use what you learned today in your everyday life?"
   • Students are encouraged to share their answers with the class, thus promoting self-assessment and the consolidation of learning.

4. Teacher Feedback (1 - 2 minutes)

   • Finally, the teacher gives general feedback on the students' performance during the class, highlighting the strengths and areas that need more attention.
   • He/she also congratulates the students on their effort and participation, encouraging them to continue exploring and learning about congruent figures.

The wrap up is a crucial step to consolidate learning, allowing students to reflect on what they have learned and identify possible knowledge gaps. Moreover, it promotes the connection between theory and practice, helping students see the relevance of what they have learned.

Conclusion (5 - 7 minutes)

1. Lesson Summary (2 - 3 minutes)

   • The teacher begins the conclusion by summarizing the main points covered in the lesson. He/she reinforces the concept of congruent figures, reminding students that these figures have the same shape and size, even if they are rotated, flipped, or translated.
   • The teacher also highlights the different ways to identify congruent figures, such as by comparing their dimensions and applying geometric transformations.
   • To reinforce learning, the teacher can ask quick questions for students to answer on these points, such as: "What makes two figures congruent?" and "How can we transform a figure while maintaining its congruence?"

2. The Connection of Theory to Practice (1 - 2 minutes)

   • The teacher emphasizes how the lesson connected the theory on congruent figures with practice. He/she reminds the students of the activities carried out, such as the congruent memory game and the construction of congruent figures, which allowed students to apply the concept of congruence in a practical and fun way.
   • The teacher also highlights everyday situations where the congruence of figures is important, such as in the construction of objects and in the organization of spaces, reinforcing the relevance of what was learned.

3. Extra Materials (1 - 2 minutes)

   • The teacher suggests extra materials for students who wish to deepen their knowledge of congruent figures. These materials may include textbooks, educational websites with interactive congruence games, and explanatory videos.
   • For example, the teacher might suggest using the website "Fun Mathematics" (www.funmathematics.com), which offers a variety of interactive activities on geometry, including a section dedicated to congruent figures.

4. Importance of the Subject (1 minute)

   • Finally, the teacher stresses the importance of studying congruent figures, explaining that this skill not only helps in understanding geometry better but is also useful in many practical everyday situations.
   • The teacher can cite examples of professions that use the concept of congruence, such as architects and designers, and games and toys that involve the congruence of figures, such as puzzles and building blocks.
   • To conclude, the teacher encourages students to continue exploring the world of congruent figures and to apply their knowledge in different contexts.

The conclusion is an important step to consolidate learning, reinforce the relevance of what was learned, and encourage the continuation of studies. By connecting theory to practice and providing extra materials, the teacher helps students solidify their knowledge and expand their understanding of the subject.