Objectives (5 - 10 minutes)

1. Understand the concept of mutually exclusive and non-mutually exclusive events: Students should be able to distinguish between events that can or cannot occur together.
2. Identify and classify events: Students should be able to identify events in everyday situations and classify them as mutually exclusive or non-mutually exclusive.
3. Apply event classification in problem situations: Students should be able to apply the concept of event classification in problem situations, making decisions based on the evaluation of events.

Optional Secondary Objectives:

1. Develop critical thinking skills: By discussing and solving problems related to event classification, students should be encouraged to think critically and justify their answers.
2. Promote teamwork: Through group activities, students should be encouraged to collaborate with each other, share ideas, and solve problems cooperatively.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher starts the lesson by reminding students about the concept of events and the difference between possible and impossible events. For this, simple problem situations can be proposed, and students can be asked to identify if they are possible or impossible events. For example, 'Is it possible to rain in the classroom?' or 'Is it possible for all students to levitate at the same time?'

2. Problem Situation 1: The teacher proposes the following situation: 'Imagine you are in a room with two doors, one red and one blue. The teacher puts two balls, one red and one blue, inside a box and asks you to guess which color ball is at each door. What could happen?' Students should discuss in small groups and then share their answers.

3. Problem Situation 2: The teacher presents another situation: 'If we have a box with 3 pencils, one blue, one red, and one yellow, and we take out a pencil without looking, what could happen?' Students again discuss in small groups and share their answers.

4. Contextualization of the importance of the subject: The teacher explains that these situations may seem simple, but they are examples of events that may or may not occur together. This is an important skill in mathematics and also in many everyday situations, such as when we need to make choices or predict outcomes. For example, when choosing an outfit to wear, we can consider if it is appropriate for the weather (event) and if it matches the rest of our look (another event), which are non-mutually exclusive events.

5. Introduction to the lesson topic: The teacher introduces the lesson topic - Event Classification - explaining that they will learn to classify events as mutually exclusive (that cannot occur together) and non-mutually exclusive (that can occur together). For this, the teacher can use simple examples from everyday life, such as the situation of choosing between two doors or removing an object from a box. Additionally, the teacher can mention that this classification is used in many areas, such as statistics, probability, and even in games and activities.

Development (15 - 20 minutes)

The teacher should choose one of the activities below to develop the lesson topic. Activities can be carried out individually, in pairs, or in small groups, according to the class dynamics and the teacher's preference.

1. 'Colored Doors' Activity:

   • Materials: Two small boxes, one red ball, and one blue ball.
   • Procedure: The teacher divides the class into groups and provides each group with the two boxes and the two balls (one red and one blue).
   • The teacher places one of the balls in each box, without the students seeing (the red ball in one box and the blue ball in the other).
   • The teacher then places the boxes on opposite sides of the room and challenges the groups to guess which color ball is in each box, without opening them.
   • The important aspect of this activity is that students will realize that, depending on their strategy, they can classify their guesses as mutually exclusive (only one color of ball in each box) or non-mutually exclusive (different color combinations in each box).
   • Groups should discuss and justify their choices. Then, the teacher reveals the colors of the balls and confirms if each group's answers are correct.

2. 'Color Bingo' Activity:

   • Materials: Sheets of paper, colored pencils or markers.
   • Procedure: The teacher distributes a sheet of paper and colored pencils to each student. On the sheet, the teacher should instruct the students to draw a grid with 4 rows and 4 columns.
   • Next, the teacher announces the rules of 'Color Bingo': the teacher will say a color and a position in the grid (for example: 'red, row 3, column 2'). The student who has the announced color and position on their grid must mark an 'X' in that position.
   • The game continues until a student completes a line, column, or diagonal with 'X'. This student then wins the game.
   • The key to this activity is that students must understand that the position (row and column) and the color are mutually exclusive events, as when a position is called, it cannot be called again. The color, on the other hand, is a non-mutually exclusive event, as the same color can be called multiple times.
   • Students should play silently, and the teacher can move around the room to check if they understand the difference between mutually exclusive and non-mutually exclusive events.

At the end of the activity, the teacher should gather the students in a large discussion circle to share their solutions and strategies. The teacher should emphasize the concept of mutually exclusive and non-mutually exclusive events, using the experiences from the activities to illustrate the two concepts. Additionally, the teacher should encourage students to explain their answers and reasoning, promoting critical thinking and effective communication.

Feedback (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes): After the activities, the teacher gathers all students in a large discussion circle. Each group or pair will have the opportunity to share their answers, solutions, and strategies. The teacher should encourage students to explain the reasoning behind their choices and justify their answers. During the discussion, the teacher should ask questions to promote reflection and critical thinking, such as 'Why do you think these events are mutually exclusive?' or 'How did you decide that these events are not mutually exclusive?'. The teacher should reinforce the importance of event classification and how it can be applied in different situations.

2. Connection to Theory (3 - 5 minutes): After discussing the answers, the teacher revisits the theory of the lesson, reinforcing the concept of mutually exclusive and non-mutually exclusive events. The teacher should refer to the activities carried out, explaining how they illustrate these concepts. For example, the teacher can say: 'In the 'Colored Doors' activity, you noticed that depending on the strategy you chose, your guesses were either mutually exclusive or non-mutually exclusive. This is because you considered if only one color of ball could be in each box or if there could be different color combinations.' The teacher should make this connection clear and simple, using examples from students' daily lives, so they can understand and apply the concept in the future.

3. Final Reflection (2 - 3 minutes): To conclude the lesson, the teacher proposes that students reflect on what they have learned. The teacher asks two simple and direct questions:

   • 'Can you think of a situation in everyday life where you need to classify events as mutually exclusive or non-mutually exclusive?'
   • 'Why is it important to know if events are mutually exclusive or non-mutually exclusive?'

   Students have a minute to think about their answers. Then, the teacher chooses some students to share their reflections with the class. The teacher should value all answers, reinforcing the importance of critical thinking and active participation.

At the end of the lesson, the teacher should take a moment to assess the students' learning. This can be done informally, through the teacher's observation during activities and group discussion, or more formally, through a small task or questionnaire. This assessment will help the teacher verify if the learning objectives were achieved and plan for the next lessons.

Conclusion (5 - 10 minutes)

1. Summary (2 - 3 minutes): The teacher reinforces the main points covered during the lesson. They recap the concept of mutually exclusive and non-mutually exclusive events, explaining that mutually exclusive events are those that cannot occur together, while non-mutually exclusive events are those that can occur together. The teacher also reviews the activities carried out, highlighting how they helped students understand and apply these concepts.

2. Connection to Theory (1 - 2 minutes): The teacher highlights how the lesson connected theory, activities, and practice. They explain that through the activities, students were able to experience and explore in practice the concept of mutually exclusive and non-mutually exclusive events. This helped make learning more meaningful and concrete for students.

3. Additional Materials (1 - 2 minutes): The teacher suggests additional materials for students who wish to deepen their knowledge on the topic. This may include textbooks, educational websites with interactive games, explanatory videos, and math apps. The teacher can also recommend practical activities at home, such as observing and recording mutually exclusive and non-mutually exclusive events that occur in their daily routines.

4. Importance of the Topic (1 - 2 minutes): Finally, the teacher emphasizes the importance of the topic for students' daily lives. They explain that the ability to classify events as mutually exclusive or non-mutually exclusive is useful in many situations, from choosing clothes to solving more complex mathematical problems. Additionally, the teacher mentions how mathematics is present in various areas of knowledge and practice, and how understanding basic mathematical concepts can contribute to the development of cognitive and problem-solving skills.