Lesson Plan | Active Learning | Possible Outcomes

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 crucial for guiding students' focus and establishing clear learning goals for the lesson. By defining specific objectives, students can better understand the importance of the topic and how it applies to practical everyday situations. This stage also serves to reinforce prior concepts that will be essential for the development of subsequent activities, ensuring a solid foundation for a complete understanding of the theme.

Main Objectives:

1. Empower students to identify and list all possible outcomes of a random experiment.

2. Develop the ability to estimate whether the outcomes of an experiment are equally likely or not.

Side Objectives:

1. Encourage critical thinking and logical analysis through the comparison of experimental results.

Introduction

Duration: (15 - 20 minutes)

The Introduction serves to engage students with the theme through problem situations that facilitate the connection of previously studied concepts with the content that will be explored in the lesson. Additionally, the contextualization aims to show the practical relevance of the concepts of possible outcomes and probability, illustrating how they are applied in real and everyday situations, enhancing students' interest and understanding of the subject.

Problem-Based Situations

1. Imagine you have a box with colored marbles: red, green, blue, and yellow. If you draw a marble from the box without looking, what are the possible outcomes? Are they equally likely?

2. Think of a bag containing playing cards from just two suits: hearts and spades. If you randomly select a card, what outcomes are possible? Do all cards have the same chance of being chosen?

Contextualization

The ability to predict outcomes in uncertain situations is a valuable tool in everyday life and in various professions, such as meteorology, economics, and sports. For instance, when trying to predict the weather, meteorologists use models based on possible outcomes to make critical decisions. Understanding and calculating these outcomes not only improves our daily decision-making but also sparks curiosity and interest in the exact sciences and statistics.

Development

Duration: (70 - 75 minutes)

This Development section aims to provide students with practical experience with random experiments through playful and contextual activities. By working in groups, they will have the opportunity to apply the concepts studied at home, practice data collection and analysis, and discuss their findings, thereby reinforcing their understanding of the theme of possible outcomes and probability.

Activity Suggestions

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

Activity 1 - Dice Party!

> Duration: (60 - 70 minutes)

- Objective: Understand the frequency distribution of a random event and practice the graphical representation of data.

- Description: Students will be divided into groups of up to 5 people. Each group will receive a standard six-sided die and a recording sheet. They will roll the die 50 times, recording each result. After data collection, each group will create a bar graph to represent the frequency of each side of the die.

- Instructions:

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

• Distribute a die and a recording sheet to each group.

• Instruct students to roll the die 50 times, recording each result on the sheet.

• After rolling, each group must count how many times each number appeared.

• Students should then create a bar graph on paper to visualize the frequency of each number.

• Lead a discussion on whether the results seem equally likely or not.

Activity 2 - Race of Possible Outcomes

> Duration: (60 - 70 minutes)

- Objective: Explore the idea of probability with practical experiments and understand that some outcomes may not be equally likely.

- Description: In this activity, students, divided into groups, will use playing cards to explore probability. Each group will receive a deck with cards from only two suits (hearts and spades). They will draw a card from the deck 30 times, noting the suit with each draw, to then analyze the probability of each suit being chosen.

- Instructions:

• Form groups of up to 5 students.

• Hand out a modified deck (only hearts and spades) to each group.

• Ask each group to draw a card from the deck 30 times, recording the suit of each drawn card.

• After data collection, each group should calculate the frequency of each suit.

• Students should discuss whether one suit is more likely to appear than the other and why.

• Each group presents its conclusions to the class.

Activity 3 - Mystery in the Surprise Box

> Duration: (60 - 70 minutes)

- Objective: Practice recording and analyzing data in random experiment situations and understand probability concepts.

- Description: Each group of students will receive a box containing various small objects (buttons, clips, erasers, etc.), all of different colors and shapes. They must, without looking, draw an object from the box and record the event in a table. After several draws, they will analyze the data to determine which objects are more likely to be drawn.

- Instructions:

• Organize students into groups of up to 5.

• Give each group a box with assorted objects.

• Each student, in turn, must draw an object from the box without looking and record it in a table.

• Repeat the procedure until each student has drawn 5 objects.

• The groups should then analyze the table to see which object was drawn the most and discuss the results.

• Conclude whether some objects are easier to draw than others and why.

Feedback

Duration: (15 - 20 minutes)

The purpose of the Feedback stage is to consolidate students' learning, allowing them to share and reflect on their experiences and discoveries. This group discussion helps to assess students' understanding of the concepts of possible outcomes and probability, as well as promote communication and argumentation skills as they discuss their conclusions with peers.

Group Discussion

Promote a group discussion with all students after completing the practical activities. Each group should present its findings and conclusions. Use the following outline to guide this discussion: Start by asking each group to share what they observed during the experiments, discuss the differences between each group's results, and conclude by questioning how these experiences help understand probability and possible outcomes in everyday situations.

Key Questions

1. What were the main differences in the results obtained by the different groups?

2. How did these activities help to better understand the idea of possible outcomes and probability?

3. Are there situations in daily life where you can apply what you learned today about probability?

Conclusion

Duration: (5 - 10 minutes)

The purpose of the Conclusion stage is to ensure that students have grasped the main concepts of the lesson, connecting theory with practice and demonstrating the relevance of the themes to everyday situations. This recap helps consolidate learning and ensures that students leave the lesson with a clear understanding of how possible outcomes and probability apply in their lives.

Summary

In summary, in this lesson we explored the concepts of possible outcomes in random experiments and the probability of each outcome. Students had practical opportunities with dice, cards, and surprise boxes to identify and list outcomes, as well as estimate the equality of probability among them.

Theory Connection

The lesson connected theory with practice by allowing students to apply prior knowledge in playful and interactive activities. This not only reinforced theoretical understanding but also demonstrated how mathematics can be applied in real situations, stimulating critical thinking and logical analysis.

Closing

Understanding probability and possible outcomes is crucial, as these concepts are frequently applied in everyday decisions, from predicting the weather to making financial choices. This understanding will help students develop important analytical skills for adulthood.