Objectives (5 - 7 minutes)

1. Understanding of probability concepts: Students should be able to understand and explain what probability is, including the difference between a certain event, an unlikely event, and an impossible event. They should also be able to use appropriate vocabulary to describe the probability of events.

2. Application of probability in practical contexts: Students should be able to apply the concept of probability to make predictions in real-world contexts. This includes the ability to use probability to predict outcomes of events, such as the chance that an event will or will not occur.

3. Problem-solving involving probability: Students should be able to solve problems involving probability, including identifying possible outcomes, determining the probability of an event occurring, and resolving problem situations involving predictions based on probabilities.

Secondary objectives:

• Development of critical thinking: When working with probability problems, students should be encouraged to think critically, evaluating the relevance of different variables and considering possible scenarios.
• Improvement of mathematical reasoning skills: Through solving problems involving probability, students should be able to improve their mathematical reasoning skills, including the ability to infer, analyze, and synthesize mathematical information.

Introduction (10 - 12 minutes)

1. Review of previous concepts: The teacher should start the lesson with a brief review of basic mathematical concepts that are relevant to the lesson, such as the difference between random and deterministic events, and the idea of proportion. This will ensure that all students are on the same page when starting to discuss probability. (2 - 3 minutes)

2. Initial problem situations:

   • Situation 1: The teacher can propose a scenario where students need to decide whether to take an umbrella to school or not, based on the weather forecast. The teacher can then ask: "How would you decide whether to take an umbrella or not? What factors would you consider? And how could you use mathematics to make that decision?"

   • Situation 2: The teacher can propose a scenario where students are playing a board game and need to decide which move to make next. The teacher can ask: "How would you decide which move to make? Could you use mathematics to help make that decision?" (3 - 4 minutes)

3. Contextualization of the subject's importance:

   • Example 1: The teacher can mention how probability is used in the real world, such as in weather forecasting, in planning gambling games, in risk analysis in insurance, among others.

   • Example 2: The teacher can share how probability is used in various professions, such as statisticians, data scientists, economists, engineers, among others. (2 - 3 minutes)

4. Introduction of the topic and gaining attention:

   • Curiosity 1: The teacher can share how probability was used to find a sunken ship in the ocean. He can explain how scientists used the probability of certain events occurring, such as wind direction and ocean currents, to predict where the ship could be.

   • Curiosity 2: The teacher can talk about how probability is used to predict the outcome of elections. He can explain how political scientists use opinion polls, voting history, and other variables to calculate the probability of each candidate winning the election. (3 - 4 minutes)

Development (20 - 25 minutes)

1. Coin Toss Simulation Activity (10 - 12 minutes)

   • Preparation: The teacher should provide each group of students with a coin. He should explain that the activity involves conducting several rounds of coin tosses and recording the results (heads or tails).

   • Procedure: Students, in their groups, should perform the following steps:

     1. Decide who will toss the coin and who will record the results.

     2. Toss the coin 10 times and record the results.

     3. Calculate the proportion of times the coin landed heads and the proportion of times it landed tails.

     4. Compare the proportions with the initial predictions. If the predictions do not align with the results, discuss possible reasons for this.

     5. Repeat the procedure two more times, for a total of three rounds of tosses. Compare the proportions from each round and discuss whether they are consistent or vary.

   • Discussion: After the conclusion of the activity, the teacher should lead a classroom discussion, asking students what they learned from the activity. The teacher should highlight how the activity illustrates the idea of probability and how predictions can change based on observed results.

2. Weather Forecast Activity (10 - 12 minutes)

   • Preparation: The teacher should divide the class into groups of 3-4 students. Each group will receive a list of possible weather conditions for the next day (sunny, cloudy, rainy, etc.) and a list of factors that may influence the weather (temperature, humidity, atmospheric pressure, etc.).

   • Procedure: Each group should:

     1. Choose a weather condition to predict (e.g., sunny).

     2. List the factors they believe influence that condition (e.g., high temperature, low humidity, high pressure).

     3. Research the current conditions of these factors in their area (e.g., using a weather forecast app).

     4. Use probability to predict whether the chosen condition will occur based on the current conditions.

   • Discussion: After the conclusion of the activity, each group should share their predictions with the class. The teacher should then discuss how the activity illustrates the application of probability in real-world predictions and how different factors can influence predictions.

These playful and contextualized activities will help students understand and apply probability concepts in a practical and meaningful way. Additionally, group discussion will allow them to share their ideas and perspectives, which can lead to a deeper understanding of the topic.

Feedback (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes)

   • The teacher should ask each group to share their solutions or conclusions from the activities. Each group will have up to 3 minutes to present, ensuring that all students have the opportunity to speak.

   • During the presentations, the teacher should encourage other students to ask questions and provide constructive feedback. This will not only help clarify any misunderstandings but also promote participation from all students in the discussion.

2. Connection to Theory (2 - 3 minutes)

   • After the presentations, the teacher should summarize the main conclusions or patterns that emerged from the group discussions. He should then connect these conclusions back to the theory of probability, highlighting how the practical activities illustrated and applied theoretical concepts.

   • For example, the teacher can point out how the coin toss activity demonstrated the idea that, in a large number of tosses, the proportion of heads and tails should approach 1:1, regardless of any individual results. Or he can highlight how the weather forecast activity showed how probability can be used to predict uncertain events based on available evidence.

3. Individual Reflection (2 - 3 minutes)

   • Finally, the teacher should ask students to reflect individually on what they learned in the lesson. He can do this by asking questions like:

     1. "What was the most important concept you learned today?"

     2. "What questions have not been answered for you yet?"

   • The teacher should give students a minute to think about these questions silently. He can then ask for some volunteers to share their answers with the class.

This Feedback stage is crucial for consolidating students' learning and for the teacher to assess the effectiveness of the lesson. By listening to the group presentations, the teacher can identify any misunderstandings or areas of confusion that need to be addressed in future classes. Additionally, by asking students to reflect individually on what they learned, the teacher can help them internalize the knowledge and become aware of any gaps in their understanding that need to be filled.

Conclusion (5 - 7 minutes)

1. Lesson Summary (2 - 3 minutes)

   • The teacher should start the Conclusion by summarizing the main points discussed during the lesson, recalling the concepts of probability, the difference between certain, unlikely, and impossible events, and the application of probability to make predictions.

   • The teacher should highlight the main ideas and conclusions that emerged during the practical activities, reinforcing how they illustrated and applied theoretical concepts. For example, it can be recalled how the coin toss activity demonstrated the idea that the probability of an event occurring can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

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

   • The teacher should explain how the lesson connected the theory of probability with the practice of weather forecast and coin toss activities. He should emphasize that mathematics is not just a set of abstract rules and formulas, but a powerful tool for understanding and predicting the world around us.

   • The teacher should also reinforce the practical applications of probability, mentioning again examples such as weather forecasting, risk analysis in insurance, and predicting election results. He should emphasize that the ability to understand and use probability is a valuable skill that can be applied in many different contexts.

3. Additional Materials (1 - 2 minutes)

   • The teacher should suggest additional study materials for students who wish to deepen their understanding of probability. This may include textbooks, math websites, educational videos, and online probability games. The teacher can also recommend probability exercises for students to practice at home.

   • Additionally, the teacher can provide students with a list of real-life applications of probability, encouraging them to seek out more examples on their own. This will help reinforce the relevance and importance of probability in the real world.

4. Subject Relevance (1 minute)

   • Finally, the teacher should emphasize the importance of probability in everyday life, highlighting how the ability to predict and assess risks and uncertainties is crucial in many situations. He can illustrate this with concrete examples, such as the decision to take an umbrella based on the weather forecast, or the assessment of the risk of contracting a disease based on factors like infection rate and the effectiveness of protective measures.

The Conclusion of the lesson is an opportunity to consolidate students' learning, reinforce the relevance of the subject, and provide guidance for future studies. By doing this, the teacher can help students understand and appreciate the importance of probability, both as a valuable mathematical tool and as an essential practical skill for life.