Lesson Plan | Active Learning | Probable and Improbable

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 10 minutes)

The objectives stage is fundamental to establish a clear foundation of what is expected to be achieved by the end of the lesson. This section focuses on defining the skills that students should acquire, ensuring that all participants are aligned with educational goals. Additionally, it serves to guide the development of subsequent activities, ensuring that all covered content is directly related to the skills students need to develop.

Main Objectives:

1. Empower students to recognize and differentiate between the most probable and improbable events using practical examples such as dice rolls, coins, and playing cards.

2. Develop logical-mathematical reasoning skills when analyzing and justifying the probabilities of event occurrence.

Side Objectives:

1. Encourage active participation from students through group discussions about the different proposed scenarios.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to activate students' prior knowledge and introduce the topic in an engaging and contextualized manner. The proposed problem situations encourage students to think critically about the concept of probability, while the contextualization demonstrates the relevance of mathematical studies in real situations, increasing student engagement and curiosity.

Problem-Based Situations

1. Imagine you are playing 'heads or tails' with a coin. If the coin is fair, meaning it has the same chance of landing heads up or tails up, which is more probable: heads or tails?

2. Let's roll a six-sided die. If we want to find out which number is more likely to roll, the 3 or the 6, what do you think we can do to find that out? Discuss in groups and see if you can reach a conclusion.

Contextualization

Understanding probable and improbable events is crucial not only in mathematical situations but also in daily life. For example, when deciding whether to take an umbrella based on the weather forecast, we are considering the probability of rain. In addition, large companies use probability concepts to predict the success of products in the market, showcasing how these concepts are applied in various fields.

Development

Duration: (70 - 75 minutes)

The development stage is designed to allow students to apply the probability concepts they studied previously in a practical and engaging way. By working in groups, students are encouraged to discuss and collaborate, which promotes a deeper understanding of the concepts. Each proposed activity aims to solidify students' knowledge of probable and improbable events, using real and fun examples to make learning more effective and memorable.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - The Great Coin Calculation

> Duration: (60 - 70 minutes)

- Objective: Develop forecasting and probability calculation skills through practical experiments and group discussions.

- Description: In this activity, students will be challenged to predict the probability of different outcomes when tossing coins. Coins that students already have in their possession or that they can create on paper will be used, made in an equitable manner.

- Instructions:

• Divide the class into groups of up to 5 students.

• Distribute three identical coins to each group.

• Ask each group to toss the coins 30 times and record the results of each toss (heads or tails).

• After all tosses, ask each group to calculate the proportion of heads and tails and discuss the differences observed.

• Conclude the activity with a class discussion about why some proportions may have been closer to 50% and others farther away, linking to probability concepts.

Activity 2 - The Dice Race

> Duration: (60 - 70 minutes)

- Objective: Visualize and understand the probabilities of rolling a die and how the number of attempts affects those probabilities.

- Description: Students will participate in a simulation race among different numbers on a six-sided die to visualize and calculate the probabilities of each number winning. This activity combines math with action, making learning more dynamic.

- Instructions:

• Organize the room into an imaginary racetrack, with six 'paths' representing each face of a die.

• Divide students into groups and assign each group a number from 1 to 6.

• Ask each group to simulate 30 rolls of a die, and each time their number is rolled, they advance one step on the track.

• At the end of the rolls, calculate the percentage of times each number won the race.

• Discuss with the class the findings and the relationships between the number of rolls and the probability of each number winning.

Activity 3 - Deck of Surprises

> Duration: (60 - 70 minutes)

- Objective: Enhance understanding of probability through a fun game, encouraging strategic thinking and data analysis.

- Description: Using a standard deck of cards, students will explore the probability of drawing certain cards and winning a guessing game. This activity is a playful way of learning about probability and logical reasoning.

- Instructions:

• Distribute a deck of cards to each student group.

• Explain that they must draw cards from the deck and try to guess if it will be a specific suit (or a specific number in the case of numbered cards).

• Ask each group to record their predictions and the actual results.

• After several rounds, ask each group to calculate the percentage of correct guesses for each type of card.

• Discuss with the class the strategies used and how probability influences the game.

Feedback

Duration: (15 - 20 minutes)

The purpose of this stage is to consolidate learning by allowing students to articulate and share their understandings and questions, promoting a deeper reflection on the concepts of probability and probable and improbable events. This discussion also serves to assess students' understanding and clarify any remaining doubts, ensuring that everyone has a clear and consistent understanding of the topics discussed.

Group Discussion

To begin the group discussion, it is suggested that the teacher gather all the students and ask each group to share their findings and conclusions from the activities conducted. The teacher can guide the discussion by asking questions such as: 'What were the most surprising results you observed in the experiments?' and 'How does the number of times an event is repeated affect the probability of the outcome?'

Key Questions

1. What strategies did your group use to predict which events were more probable?

2. How did the number of attempts influence the conclusion about the probabilities of events?

3. Was there any outcome that contradicted your initial expectations? Why?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to consolidate learning, ensuring that students have understood and are able to apply the concepts of probability in varied contexts. Additionally, the conclusion serves to reinforce the importance of studying mathematics, showing how the knowledge acquired is relevant and applicable in everyday life.

Summary

To conclude, the teacher should summarize the main points discussed about probable and improbable events, reiterating the differences and calculations made during the activities. Emphasis should be placed on the probabilities involved in games such as 'heads or tails', dice rolls, and card draws, illustrating how these concepts are applied in practical situations.

Theory Connection

During the class, the connection between theory and practice was established through activities that simulated real situations of gambling games and daily decision-making based on probabilities. This allowed students not only to understand the mathematical concepts but also to visualize their applicability in daily life, reinforcing the importance of studying probabilities.

Closing

Finally, it is crucial to highlight the relevance of probability concepts in everyday life, such as in weather forecasting, system security, and informed decision-making. These concepts help develop critical thinking and the ability to assess risks, essential skills in various areas of life.