Objectives (5 - 7 minutes)

1. Understand the concept of a matrix: Students should be able to understand what a matrix is, how it is represented, and what its elements are. Additionally, they should be able to identify a matrix in a problem situation.

2. Identify the order of a matrix: Students should learn to identify the order of a matrix, that is, the number of rows and columns it consists of.

3. Classify a matrix: After understanding the concept and order of a matrix, students should be able to classify it according to the quantity of null, equal, and non-zero elements.

   Secondary objectives:

   • Develop critical thinking skills: Through the proposed activities, students will be encouraged to think critically and analytically, developing the necessary mathematical skills to solve problems.
   • Promote interaction and teamwork: The proposed activities should be carried out in groups, promoting interaction among students and encouraging teamwork.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher should start the lesson by briefly reviewing the concepts of matrices that were previously seen, such as the representation of a matrix, its elements, and the difference between row, column, and square matrices. This can be done through a quick oral questionnaire to activate students' prior knowledge. (3 - 5 minutes)

2. Problem situation 1: The teacher should present the following problem to the students: 'Imagine that you are organizing a chess tournament, where each team has 5 players. You would like to record the number of wins and losses of each player in a matrix. How would you do that?'. The teacher should encourage students to think about the organization of the matrix, its order, and classification. (2 - 3 minutes)

3. Contextualization: The teacher should explain that matrices are widely used in applied mathematics and in various areas of science and engineering, such as image processing, cryptography, programming, and physics. Organizing data in matrices allows for more efficient and structured analysis. (2 - 3 minutes)

4. Problem situation 2: The teacher should present a second problem to the students: 'Suppose that in a board game, each player can move their piece on a 3x3 board. You would like to record the positions of the pieces of each player in a matrix. How would you do that?'. This will serve to reinforce the concept of order and the practical application of matrices. (2 - 3 minutes)

5. Introduction of the topic: The teacher should introduce the topic of the lesson - matrix classifications - explaining that, just like in a tournament, the analysis of data in a matrix can reveal important information. Matrix classifications help to understand and interpret this data. (1 - 2 minutes)

Development (20 - 25 minutes)

1. Activity 1 - Championship Matrix (10 - 12 minutes):

   • Description: The teacher should divide the class into groups of 5 students. Each group will receive a sheet with a 5x5 grid, representing a matrix. Each cell in the grid represents a player and the number of wins and losses. Some values will be null, others different from zero. Students must fill in the matrix according to the provided results.

   • Objective: The objective of this activity is for students to apply the concepts of matrix, order, and classification to organize the data from the chess tournament.

   • Step by step:

     1. Students should analyze the provided results and distribute them in the matrix.
     2. After filling in the matrix, students must identify the order of the matrix and classify it according to the null, equal, and non-zero elements.
     3. Each group must present their matrix to the class, explaining how they organized the data and the classification of the matrix.
     4. The teacher should provide collective correction, highlighting the different ways of filling in the matrix and the different classifications obtained.

2. Activity 2 - Board Game Matrix (10 - 12 minutes):

   • Description: The teacher should present a new 3x3 grid to the students, representing the board of a board game. Each cell in the grid represents the position of a piece. Students, in their groups, must fill in the matrix according to the positions of the pieces on the board.

   • Objective: The objective of this activity is for students to apply the concepts of matrix and order to organize the data from the board game.

   • Step by step:

     1. The teacher should present the rules of the board game to the students and explain how the positions of the pieces should be recorded in the matrix.
     2. Students, in their groups, must fill in the matrix according to the positions of the pieces on the board.
     3. After filling in the matrix, students must identify the order of the matrix.
     4. Each group must present their matrix to the class, explaining how they recorded the positions of the pieces and the order of the matrix.
     5. The teacher should provide collective correction, highlighting the different ways of filling in the matrix and the different orders obtained.

3. Group Discussion (5 - 7 minutes):

   • Description: The teacher should propose a group discussion for students to share their perceptions and learnings from the activities carried out. Students should be encouraged to make connections between the activities and the real world.

   • Objective: The objective of this discussion is for students to reflect on the importance of matrices in organizing and analyzing data in different everyday situations.

   • Step by step:

     1. The teacher should propose some questions to guide the discussion, such as: 'How can matrices be useful in solving everyday problems?', 'What other everyday situations could be represented through matrices?'.
     2. Students, in their groups, should discuss the questions and develop answers.
     3. The teacher should choose some groups to share their answers with the class.
     4. The teacher should summarize the answers, highlighting the main ideas and the importance of matrices in solving everyday problems.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher should promote a group discussion for students to share their solutions and conclusions from the activities carried out. Each group should have a maximum of 3 minutes to present their filled matrices and the classifications made. During the presentation, the teacher should encourage other groups to ask questions and make comments, thus promoting interaction and the exchange of ideas among students.

2. Connection with Theory (2 - 3 minutes): After the presentations, the teacher should make a brief connection between the practical activities and the theory studied. The teacher should reinforce the concepts of matrix, order, and classification, explaining how they were applied in the activities. The teacher should also highlight the importance of organizing and analyzing data in matrices, reinforcing the applicability of these concepts in various areas of knowledge.

3. Individual Reflection (1 - 2 minutes): The teacher should propose that students make an individual reflection on what they learned in the lesson. For this, the teacher should ask the following questions:

   1. 'What was the most important concept you learned today?'
   2. 'What questions have not been answered yet?' The teacher should give a minute for students to think about the questions and then ask some students to share their answers with the class.

4. Feedback (2 - 3 minutes): Finally, the teacher should give feedback on the lesson, reinforcing the main points and clarifying any doubts that may still exist. The teacher should also praise the students' effort and participation, encouraging them to continue studying and dedicating themselves to the subject.

Conclusion (5 - 7 minutes)

1. Lesson Summary (1 - 2 minutes): The teacher should start the Conclusion of the lesson by briefly summarizing the main points covered. Should recall the concept of matrix, what is the order of a matrix, and how to classify it. Should also highlight the main ideas raised during the practical activities and group discussion, reinforcing the importance of organizing and analyzing data in matrices.

2. Connection of Theory with Practice (1 - 2 minutes): Next, the teacher should explain how the presented theory connects with the practical activities carried out. Should highlight how the concepts of matrix, order, and classification were applied in solving the problems of the chess tournament and the board game. Additionally, should reinforce the importance of understanding the theory for the performance of practical activities and problem-solving.

3. Extra Materials (1 minute): The teacher should then suggest some extra materials for students who wish to deepen their knowledge on the subject. These materials may include books, websites, videos, and online activities on the topic. The teacher should encourage students to explore these materials outside of class time as a way to review and consolidate what they have learned.

4. Importance of the Subject (1 - 2 minutes): Finally, the teacher should emphasize the importance of the subject for students' daily lives. Should explain that the ability to organize and analyze data in matrices is fundamental for various areas of knowledge and practical life, such as science, engineering, finance, and even games. The teacher should encourage students to perceive the practical applications of the concepts learned and to use them in everyday situations.

5. Closing (1 minute): To end the lesson, the teacher should thank the students for their participation, praise their effort, and reinforce the importance of continuous study and engagement in the subject. Should also remind students of the next topics to be studied and the activities to be carried out.