Objectives (5 - 7 minutes)

1. Understanding Conditional Probability: The main objective is for students to understand the concept of conditional probability, that is, the probability of an event occurring given that another event has already occurred. Students should be able to apply this concept in practical situations and understand how it differs from simple probability.

2. Calculation of Conditional Probability: Students should learn how to calculate conditional probability using the appropriate formula. They should understand that conditional probability is calculated by dividing the probability of events A and B occurring together by the probability of B occurring.

3. Problem Solving: Students should be able to apply the concept and calculation of conditional probability to solve complex problems. This includes the ability to interpret the problem, identify relevant events, and calculate conditional probability correctly.

   • Secondary Objectives:

     • Development of Logical Thinking: Through the study of conditional probability, students will be exposed to situations that require logical reasoning. This will help develop their critical thinking and analytical skills.

     • Improvement of Problem-Solving Skills: Problem-solving is a fundamental skill that students must develop. Applying conditional probability to real problems will help enhance this skill.

Introduction (10 - 15 minutes)

1. Review of Previous Content: The teacher should start the lesson by briefly reviewing the concepts of simple probability and probability calculation. This is essential for students to understand and correctly apply the concept of conditional probability. The review may include practical examples and the resolution of some quick exercises. (3 - 5 minutes)

2. Problem Situation 1: The teacher should propose the following situation: "If we toss two coins, what is the probability that both coins land on the same face, given that at least one of them landed face up?" This situation will help introduce the concept of conditional probability and show students its practical application. (3 - 5 minutes)

3. Problem Situation 2: Next, the teacher should present another situation: "If we draw a card from a standard deck of 52 cards, without replacement, what is the probability that the second card drawn is an Ace, knowing that the first card drawn was an Ace?" This situation will reinforce the concept of conditional probability and give students another opportunity to practice its application. (3 - 5 minutes)

4. Contextualization: The teacher should explain that conditional probability is an important tool in many areas, including science, medicine, economics, and even everyday decision-making. For example, in medicine, conditional probability is used to calculate the probability of having a disease given certain symptoms. In economics, conditional probability is used to predict the behavior of the stock market given past performance. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Activity 1 - "The Dice Game" (10 - 12 minutes)

   • Scenario: The teacher will present a scenario in which students are participants in a board game where progress in the game depends on the outcome of rolling a die. However, there are conditional rules that must be applied.

   • Preparation: The teacher will prepare a game board with a continuous path marked in spaces. Each space will have a number from 1 to 6, representing the possible outcomes of rolling a die.

   • Execution: Students will be divided into groups of 5, and each group will receive a set of cards. Each card will have a specific conditional rule, such as "if the result of the last roll was odd, move forward 2 spaces" or "if the result of the last roll was less than 4, move back 1 space." Students will have to calculate the conditional probabilities of progress in the game, given the rules on their cards.

   • Objective: The goal of the game is to move through the board to the end, correctly applying the conditional rules and calculating the conditional probabilities of progress. The first group to reach the end of the board wins.

2. Activity 2 - "Investigating the Ball Box" (10 - 12 minutes)

   • Scenario: The teacher will present a scenario in which students are scientists investigating a box full of balls of different colors. Each ball color represents an "event" type, and students will have to calculate the probability of an event occurring, given that another event has already occurred.

   • Preparation: The teacher will prepare a box with balls of different colors. Each ball color will have a different proportion in the box, representing the probability of an event occurring.

   • Execution: Students will be divided into groups of 5. Each group will receive a box of balls and will have to choose two events and calculate the probability of one occurring, given that the other has already occurred. They will have to justify their choices and calculations.

   • Objective: The goal of the activity is for students to understand and apply the concept of conditional probability in a realistic scenario. They will have to use logical thinking and problem-solving skills to complete the activity.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes)

   • The teacher should gather all students and promote a group discussion about the solutions or conclusions found by each group during the activities. This will allow students to share their ideas, understand different approaches to the same problem, and learn from the mistakes and successes of others.

   • The teacher should ask targeted questions to each group, asking them to explain how they arrived at their answers and what strategies they used. This will help clarify any misunderstandings and deepen students' understanding of the concept of conditional probability.

2. Connection to Theory (2 - 3 minutes)

   • After the discussion, the teacher should make the connection between the activities carried out and the theory presented at the beginning of the lesson. The teacher can highlight how the problem situations in the activities reflect the practical application of the concept of conditional probability.

   • The teacher can briefly review the formula for calculating conditional probability and show how it was applied in the activities. The teacher should emphasize that conditional probability is calculated by dividing the probability of events A and B occurring together by the probability of B occurring.

3. Final Reflection (3 - 4 minutes)

   • The teacher should ask students to reflect individually on what they learned in the lesson. The teacher can ask questions like: "What was the most important concept you learned today?" and "What questions have not been answered yet?".

   • Students should be encouraged to express their reflections and doubts. This will help the teacher assess the effectiveness of the lesson and plan possible revisions or clarifications for the next class.

4. Teacher's Feedback (1 minute)

   • Finally, the teacher should provide feedback on the students' participation and performance during the lesson. The teacher can praise students' efforts, highlight strengths, and offer suggestions for improvement. This will help motivate students and guide them to the next topic.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes)

   • The teacher should summarize the main points covered during the lesson, reinforcing the concept of conditional probability and the formula for its calculation.
   • The teacher can briefly recap the problem situations presented, highlighting how conditional probability was applied in solving each one.
   • It is important for the teacher to ensure that all students have understood the fundamental concepts before moving on to the next stage.

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

   • The teacher should explain how the lesson connected the theory of conditional probability with practice, through the activities "The Dice Game" and "Investigating the Ball Box".
   • The teacher should highlight the relevance of applying conditional probability in various contexts, such as medicine, economics, and everyday decision-making.
   • The teacher can encourage students to look for more examples of conditional probability in their daily lives to strengthen the connection between mathematics and the real world.

3. Additional Materials (1 minute)

   • The teacher should suggest additional study materials for students who wish to deepen their knowledge of conditional probability.
   • These materials may include explanatory videos, interactive math websites, online exercises, and textbooks.
   • The teacher can also recommend that students practice calculating conditional probability in everyday situations, such as watching a soccer game or making decisions based on partial information.

4. Importance of the Subject (1 minute)

   • In conclusion, the teacher should emphasize the importance of the subject presented for students' lives.
   • The teacher should explain that the ability to calculate and understand conditional probability is useful in many situations, from solving complex mathematical problems to making informed decisions in daily life.
   • The teacher can encourage students to apply what they have learned to improve their logical thinking, problem-solving skills, and decision-making.