Lesson Plan | Active Learning | Sets

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 of the lesson plan is crucial for establishing a clear focus for the educational session. By defining specific objectives, we outline what is expected for the students to achieve by the end of the lesson. This not only guides the teaching process but also helps in evaluating the effectiveness of learning. In this case, the objectives were selected to cover the essential points of the study of sets, allowing students to manipulate and apply the concepts in a practical and theoretical manner.

Main Objectives:

1. Ensure that students understand the concept of sets and elements, including the relationships of belonging and inclusion.

2. Ensure that students understand and know how to apply operations on sets, as well as identify subsets and understand the concept of the power set and Cartesian product.

Side Objectives:

1. Develop logical and mathematical reasoning skills through solving practical problems involving sets.

Introduction

Duration: (15 - 20 minutes)

The introduction stage serves to engage students with the theme of the lesson by using problem situations that stimulate the practical application of the concepts studied earlier. Furthermore, by contextualizing the subject with real examples and historical curiosities, students can see the relevance and utility of sets in the real world, increasing their interest and motivation for learning.

Problem-Based Situations

1. Imagine you are organizing a birthday party and need to send invitations to your friends. Create a set that represents different groups of friends who may or may not attend the party.

2. Consider a store that sells fruits, and the manager wants to organize the products according to their colors: red, yellow, and green. Use sets to classify the fruits available in the store.

Contextualization

Set theory is a powerful tool for organizing ideas and data, with applications ranging from organizing information in databases to solving problems in computer science. Moreover, the study of sets has a rich history, with many foundational concepts developed in the 19th century by mathematicians like Georg Cantor. This contextualization helps students realize the relevance of sets in real-world situations and appreciate the depth of the mathematical field they are about to explore.

Development

Duration: (65 - 75 minutes)

The development stage is designed to allow students to practically and playfully apply their prior knowledge about sets. By working in groups to solve problems and challenges, students not only solidify their theoretical understanding but also develop collaboration and critical thinking skills. Each proposed activity aims to explore different aspects of sets, from simple classification to more complex operations, ensuring a comprehensive understanding of the topic.

Activity Suggestions

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

Activity 1 - Sets Mission: The Treasure of Elements

> Duration: (60 - 70 minutes)

- Objective: Apply knowledge about belonging, inclusion, operations on sets, and subsets in a playful and collaborative manner.

- Description: In this activity, students will be divided into groups of up to 5 people to solve a mathematical riddle involving the discovery of the 'Treasure of Elements'. Each group will receive a map with clues spread across the classroom, representing different sets and subsets. The clues will be related to everyday situations, such as dividing items into categories.

- Instructions:

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

• Distribute maps to each group, highlighting the positions of the clues.

• Each clue will lead to an envelope containing a mathematical challenge related to operations on sets.

• Students must solve the challenge to obtain the next clue.

• The group that reaches the 'Treasure of Elements' first, correctly solving all the challenges, will be the winner.

Activity 2 - Set Builders

> Duration: (60 - 70 minutes)

- Objective: Develop understanding of sets as organized structures and the ability to apply operations on sets visually and practically.

- Description: Students, in groups, will assume the role of architects who need to build 'cities' made of sets. Each construction must represent a unique characteristic (for example, colors of fruits at a market). The challenge will be to organize the elements (houses) in such a way that they belong to specific sets and subsets, following rules of operations on sets.

- Instructions:

• Organize students into groups of up to 5.

• Distribute cards with different characteristics (colors, sizes, types) that the elements of the city can have.

• Groups must use these cards to build 'houses' on a large whiteboard, organizing them into sets and subsets.

• Each group must present its 'city' and explain how the elements are organized into the sets.

• At the end, each group votes on the city that best demonstrated the understanding of the concepts.

Activity 3 - The Subset Show

> Duration: (60 - 70 minutes)

- Objective: Explore the concept of subsets in a creative and engaging way, reinforcing students' understanding of inclusion and belonging in sets.

- Description: Students, in groups, will create and present a 'show' where each 'act' will visually represent a mathematical concept about subsets. Using music, dances, or short plays, they should illustrate how elements can belong to more than one set and how sets can be contained within others.

- Instructions:

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

• Each group chooses a subset concept to represent in a creative and fun way.

• Groups have 40 minutes to prepare their presentation, using available materials in the classroom such as paper, pens, and musical instruments (if desired).

• Each group presents its 'show' to the class, explaining the mathematical concept they are representing.

• After the presentations, discuss with the class the different ways to represent mathematical concepts and how this helps in understanding.

Feedback

Duration: (15 - 20 minutes)

The purpose of this feedback stage is to consolidate learning, allowing students to articulate verbally what they have learned and share insights with their peers. This discussion helps not only reinforce the understanding of set concepts but also develop communication and critical analysis skills. Furthermore, it allows the teacher to assess students' understanding and clarify any remaining doubts.

Group Discussion

After completing the activities, gather all students for a group discussion. Start the discussion with a brief introduction, explaining that the goal of this stage is to share experiences and learnings gained during the practical activities. Encourage each group to present a summary of what they accomplished, highlighting the challenges faced and the strategies used to overcome them. Stimulate students to reflect on how the concepts of sets apply in everyday situations and other subjects.

Key Questions

1. What were the main challenges when applying the concepts of sets during the activities and how did you overcome them?

2. How can the concepts of belonging, inclusion, and operations on sets be applied outside the mathematical context?

3. Was there any situation during the activities where the definition of subsets was particularly useful for solving a problem?

Conclusion

Duration: (5 - 10 minutes)

The purpose of the Conclusion is to consolidate learning, ensuring that students have a clear and comprehensive understanding of the set concepts studied. Moreover, it aims to reinforce the connection between theory and practice, helping students to perceive mathematics as a discipline integrated with their daily life and other areas of study. This stage also serves to clarify how the knowledge acquired is relevant and applicable, encouraging students to continue exploring and using the concepts of sets in various contexts.

Summary

In this final stage, the teacher should summarize the main contents covered about sets, reinforcing students' understanding of the notions of belonging, inclusion, operations on sets, subsets, and the power set. It is essential to recap the definitions and properties discussed, ensuring that students have consolidated the knowledge acquired during the practical activities.

Theory Connection

The teacher should also explain how the lesson connected theory with practice, highlighting how the activities carried out helped visualize and apply the mathematical concepts of sets concretely. This connection is crucial to show the relevance of theoretical concepts in everyday life and other subjects, such as physics, computer science, and even common situations.

Closing

Finally, it is important for the teacher to emphasize the importance of sets in everyday life, whether in organizing data, structuring logical problems, or even in decision-making. This understanding helps students value mathematical learning and see mathematics as an essential and applicable tool, not just an abstract theory.