Lesson Plan | Active Learning | Regular Polygon: Construction

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 stage of defining objectives is crucial to guide both the teacher and students about what will be achieved during the lesson. This stage focuses on clearly establishing the skills that students should acquire, providing a clear direction for subsequent activities. This ensures that all involved are aligned with expectations and understand the importance of each step in the learning process.

Main Objectives:

1. Empower students to describe, through a flowchart, an algorithm that allows the construction of a regular polygon from a known side length.

2. Encourage the development of algorithmic and logical thinking skills in practical geometry situations.

Side Objectives:

1. Encourage collaboration and communication among students during practical activities in the classroom.
2. Promote the application of mathematical concepts in diverse contexts, stimulating critical reasoning and problem-solving.

Introduction

Duration: (15-20 minutes)

The introduction phase aims to engage students and connect prior knowledge with the real-world application of the content through problem situations that simulate practical challenges. These situations help stimulate critical thinking and curiosity, preparing students for practical activities in class. The contextualization seeks to show the relevance of the topic in the real world, increasing students' motivation as they realize the utility of what they have learned.

Problem-Based Situations

1. Suppose you are an architect and need to design the base of a tower that will be built in a hexagonal shape, where each side must measure 10 meters. How could you use knowledge about the construction of regular polygons to accurately draw this base?

2. Imagine you are a game designer and need to create a board for a new game that will have an octagonal shape. Each side of the board must be identical and measure 15 centimeters. What steps would you take to build this board quickly and accurately?

Contextualization

The construction of regular polygons is not just a mathematical skill but an essential tool in various professions and practical applications, such as architecture, graphic design, and engineering. For example, famous architect Renzo Piano applied concepts of polygons in his projects to create complex and efficient structures. Moreover, understanding how polygons are constructed helps develop logical and algorithmic thinking skills, which are crucial in the digital world we live in.

Development

Duration: (75-80 minutes)

The development phase is designed to allow students to practically and collaboratively apply the concepts studied about regular polygons. This stage aims to consolidate the theoretical knowledge acquired through playful and challenging activities, fostering the development of critical thinking skills, teamwork, and mathematical precision. The proposed activities aim to engage students in real and practical contexts, increasing content retention and motivation for learning.

Activity Suggestions

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

Activity 1 - Architects in Action

> Duration: (60-70 minutes)

- Objective: Apply regular polygon construction knowledge in a practical and collaborative context, developing teamwork and mathematical precision skills.

- Description: In this activity, students will be divided into groups of up to 5 people and will assume the role of architects. They will be tasked with designing the floor plan of a building that must include a leisure area in the shape of a regular polygon with 7 sides, known as a heptagon. Each side of the heptagon must measure 5 meters. Students should use graph paper and a ruler to draw the project, considering precise measurements and correct angles.

- Instructions:

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

• Distribute graph paper and rulers to each group.

• Explain that they must draw the floor plan of a building that includes a regular heptagon with 5-meter sides for the leisure area.

• Guide students to calculate the angles and line segments necessary to construct the heptagon, and to use prior knowledge about regular polygons.

• Encourage discussion and collaboration among group members to ensure the accuracy of measurements and the correct construction of the heptagon.

Activity 2 - The Polygonal Board Challenge

> Duration: (60-70 minutes)

- Objective: Develop technical drawing skills and precise application of geometry concepts in the construction of a regular polygon, also promoting cooperation and critical thinking.

- Description: Students, in groups of up to 5, will participate in a challenge to create the layout of a game board in the shape of an octagon, where each side of the octagon must measure 10 centimeters. They will use construction paper, colored pens, and protractors to draw the board, ensuring that all sides are identical and that the formed angles are correct.

- Instructions:

• Organize students into groups of no more than 5 people.

• Provide each group with construction paper, colored pens, and protractors.

• Explain that they must draw an octagonal game board, where each side measures 10 centimeters.

• Instruct students to use the protractor to draw the correct angles and measure the sides of the octagon accurately.

• Monitor the process and offer support as needed.

Activity 3 - Geometric Builders

> Duration: (60-70 minutes)

- Objective: Apply geometry concepts in the construction of a three-dimensional model, promoting practical understanding of regular polygons and improving calculation and construction skills.

- Description: In this activity, students will form groups of up to 5 people and will need to build a physical model of a regular polygon with 6 sides (hexagon) using popsicle sticks and modeling clay. Each side of the hexagon must be 8 centimeters. They will need to calculate the necessary angles and measurements and then build the model, ensuring it is symmetrical and stable.

- Instructions:

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

• Distribute popsicle sticks, modeling clay, and a measuring tape to each group.

• Ask each group to calculate the angles and measurements to build a hexagon with sides of 8 centimeters.

• Guide students to start building the hexagon, using modeling clay to hold the sticks together and form the correct angles.

• Encourage students to test the stability and symmetry of the final model.

Feedback

Duration: (10-15 minutes)

The feedback section is essential to consolidate students' learning, allowing them to reflect on the practical activities conducted and articulate theoretical knowledge with practical application. This discussion helps reinforce the understanding of regular polygon concepts and the importance of teamwork and mathematical precision. Furthermore, it allows students to verbalize their strategies and learnings, promoting a deeper and more critical understanding of the content.

Group Discussion

At the end of the activities, gather all groups for a collective discussion. Start the discussion with a brief introduction: 'Today, we explored the construction of regular polygons and applied this knowledge in practical situations such as architecture and game design. Now, it is time to share what each group has learned and discuss the challenges faced during the activities. Let's reflect on how these mathematical concepts can be used in various professional fields.'

Key Questions

1. What were the main challenges your group faced while constructing the regular polygon?

2. How did you apply the knowledge of angles and measurements to ensure accuracy in the construction of the polygons?

3. In what way did collaboration among group members contribute to the success of the activity?

Conclusion

Duration: (5-10 minutes)

The conclusion stage serves to reinforce learning, ensuring that students have absorbed the fundamental concepts of the lesson. Moreover, it provides an opportunity for students to reflect on the applicability of regular polygons in practical contexts and become aware of the relevance of mathematics in their lives and future careers. This section is vital to conclude the lesson in a structured way and ensure that learning objectives have been achieved.

Summary

In the final phase of the lesson, the teacher should summarize and recapitulate the main concepts covered regarding the construction of regular polygons, reinforcing the definition and characteristics of polygons such as the heptagon, hexagon, and octagon. Techniques for construction, angle calculation, and side measures applied in practical activities should be highlighted.

Theory Connection

During the lesson, the connection between theory and practice was clearly established through activities that simulated real situations, such as architectural planning and game design. Students were able to see how the mathematical concepts of regular polygons are applied in professional contexts, consolidating their learning.

Closing

Finally, it is crucial to emphasize the importance of regular polygons in everyday life and in various professions such as architecture, engineering, and design. This knowledge not only enriches students' mathematical understanding but also highlights the relevance of mathematics in solving practical problems and developing critical skills.