Lesson Plan | Active Learning | Polygons: Introduction

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)

This stage of the lesson plan is essential to establish the theoretical and practical foundations that students need to apply the knowledge acquired at home about polygons. Through the proposed objectives, students will be prepared for a deeper and more applied understanding of the concept of regular polygons, gaining skills that can be utilized in more complex mathematical activities in the future.

Main Objectives:

1. Enable students to write and understand a flowchart or algorithm for constructing a regular polygon based on the given side measurement.

2. Develop the ability to identify and describe the properties of regular polygons, reinforcing theoretical understanding through practical applications.

Side Objectives:

1. Encourage logical reasoning and students' problem-solving ability when manipulating formulas and mathematical procedures.

Introduction

Duration: (15 - 20 minutes)

This stage of the lesson plan is designed to engage students through problem situations that make them think critically about the subject being studied, using prior knowledge to solve practical and theoretical issues. The contextualization aims to show the applicability of polygons in the real world, increasing students' interest and motivation to learn about the subject.

Problem-Based Situations

1. Imagine you are an architect and need to design a square with several flower beds, all in the shape of regular polygons. How would you decide the size of each side of the flower beds so that they are visually pleasing and proportional to each other?

2. Consider that you work in a card factory and have the task of cutting cards into regular polygon shapes for a special campaign. How would you ensure that all cards had the same sides and angles without the need to measure each one individually?

Contextualization

Polygons are geometric figures that are widely present in our daily lives, from architecture to graphic design. For example, the shape of football fields is a regular polygon: the pentagon. Understanding how to calculate and draw regular polygons not only helps in mathematics, but also in practical applications such as logo design or architectural arrangements. These practical applications help to realize the relevance of the study of polygons in solving real problems and in the construction of things we see and use every day.

Development

Duration: (65 - 75 minutes)

The Development stage is fundamental to consolidate students' prior knowledge about regular polygons through practical and playful applications. By working in groups, students not only apply mathematical concepts but also develop communication, collaboration, and critical thinking skills. Each proposed activity aims to reinforce understanding of regular polygons in different ways, ensuring a holistic approach to the subject.

Activity Suggestions

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

Activity 1 - Geometric Garden Challenge

> Duration: (60 - 70 minutes)

- Objective: Apply knowledge about regular polygons in practice, developing teamwork skills, creativity, and planning.

- Description: Students will be divided into groups of up to 5 people to design a mini geometric garden. Each group will receive a designated area on the classroom floor and materials such as sticks, rubber bands, and colored cardboard. The challenge is to create a layout that maximizes the use of regular polygons, such as squares, triangles, and pentagons, with sides of pre-defined measurements.

- Instructions:

• Organize into groups of up to 5 students.

• Receive the materials kit containing sticks, rubber bands, and cardboard.

• Choose the side lengths of each polygon that will be used to construct the garden.

• Draw the layout of the garden on paper, marking where each polygon will be positioned.

• Use the materials to build the garden within the designated area.

• Present the created geometric garden to the class, explaining the reasoning behind the design choices.

Activity 2 - Polygonal City Builders

> Duration: (60 - 70 minutes)

- Objective: Develop practical geometry skills, stimulating spatial reasoning and the ability to apply mathematical concepts in design and construction activities.

- Description: In this activity, each group of students receives a large transparent plastic sheet with a grid drawn on it. The challenge is to use straws of different sizes to build three-dimensional models of buildings in the shape of regular polygons, respecting the provided measurements. Students must calculate and adjust the measurements so that the straws form polygons with correct angles and sides.

- Instructions:

• Divide the class into groups of no more than 5 students.

• Distribute the plastics with grids and straws to each group.

• Choose a type of polygon - triangle, square, pentagon - to begin construction.

• Calculate and adjust the size of the straws to form the correct sides of the polygon.

• Build the three-dimensional model of the building using the straws.

• Present the final model, explaining the construction process and the challenges faced.

Activity 3 - The Great Polygon Tournament

> Duration: (60 - 70 minutes)

- Objective: Encourage the use of mathematical strategies in a game context, promoting healthy competition and deepening understanding of the properties of regular polygons.

- Description: This activity turns the classroom into a large competition board. Each group of students, representing a 'house' in a strategy game, must use their knowledge about regular polygons to 'conquer territories' on the board, positioning polygons with specific measurements in specific areas.

- Instructions:

• Divide the class into groups of up to 5 students, each representing a 'house'.

• Explain the game rules, which involve the strategic use of polygons to occupy the board.

• Distribute cards with measurements of polygon sides and determine the areas on the board for each house.

• Groups must use the cards to form polygons that fit into the designated areas.

• Each group presents its strategy and justifies its mathematical choices.

• The group that manages to position the most polygons correctly within the stipulated time is declared the winner.

Feedback

Duration: (15 - 20 minutes)

The purpose of this stage is to consolidate students' learning, allowing them to articulate the knowledge acquired and share insights with their peers. This not only reinforces understanding of the concepts of regular polygons but also develops communication and critical thinking skills. The group discussion helps identify gaps in understanding and reinforces the importance of the practical application of mathematics in everyday life.

Group Discussion

At the end of the practical activities, gather all students for a group discussion. This stage is crucial for students to reflect on what they have learned and share their experiences. Start the discussion with a brief introduction, highlighting the importance of understanding and applying mathematical concepts in practical situations. Encourage each group to discuss the challenges faced, the creative solutions adopted, and what they learned about constructing regular polygons.

Key Questions

1. What were the main challenges your group faced when constructing the polygons and how did you overcome them?

2. How did understanding properties such as sides and angles help in the construction of your models?

3. In what way did the practical activities alter or reinforce your theoretical understanding of regular polygons?

Conclusion

Duration: (5 - 10 minutes)

The purpose of this stage of the lesson plan is to ensure that students have a clear and consolidated understanding of the concepts covered, as well as recognizing the importance and applicability of regular polygons in real situations. The conclusion serves to reinforce learning, ensuring that students can relate theory to practice and value mathematics as an essential tool in their academic and professional lives.

Summary

In this final stage, the teacher should conduct a comprehensive summary of the activities and discussions held in class, recapping the concepts of regular polygons, their properties, and practical applications. It is essential for students to visualize how theoretical content was applied in practical activities and how this knowledge is relevant in everyday situations.

Theory Connection

Today’s lesson was carefully structured to connect the theory of regular polygons with practice, through activities that simulate real situations where geometric knowledge is crucial. This was done not only to solidify learning but also to show the relevance of mathematics in varied contexts, from architecture to graphic design.

Closing

Finally, it is essential to highlight that the study of polygons is not just an isolated mathematical discipline. Understanding these figures is essential in many areas of knowledge and everyday life, such as civil construction, industrial design, and many other practical applications. Therefore, what was learned today has a direct and significant applicability, reinforcing the importance of mathematics as an essential tool in the modern world.