Lesson Plan | Active Learning | Polygons: Sum of Angles

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 objective stage is essential to direct the focus of students and the teacher towards the key competencies that will be developed during the lesson. By clearly establishing what is expected to be achieved, this section serves as a guide for subsequent activities, ensuring that both the prior preparation and the application in the classroom are aligned with the expected learning outcomes.

Main Objectives:

1. Empower students to solve problems that involve the calculation and application of the sum of the internal angles of polygons, as exemplified by the hexagon (720º).

2. Develop logical reasoning skills and the application of mathematical formulas to determine the sum of the internal angles of different polygons.

Side Objectives:

1. Encourage cooperation and dialogue among students during practical activities to promote collaborative learning.
2. Stimulate curiosity and interest in mathematics through practical applications and challenges.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students with the content they previously studied, bridging the gap between theory and practice. The proposed problem situations encourage students to apply prior knowledge in a practical and relevant way, preparing them for classroom activities. The contextualization, in turn, shows how the theme is applied in the real world, increasing awareness of its importance and usefulness, and motivating students to explore the subject in more depth.

Problem-Based Situations

1. Imagine you are designing a rug with a pattern based on geometric shapes. To ensure that the design is harmonious, it is necessary to calculate the angles of the triangles, squares, and hexagons that make up the pattern. How would you use your knowledge of the sum of the internal angles to solve this problem?

2. The architect who designed the ceiling of a building wants the beams to form a hexagonal pattern. When joining the beams, each intersection forms an angle. What should the angle between the beams be for the pattern to be symmetrical and the sum of the internal angles to be correct, based on the mathematical knowledge of the sum of the internal angles of a hexagon?

Contextualization

The sum of the internal angles of polygons is not just an abstract mathematical concept but has practical applications in various fields such as architecture, art, and games. For example, in the construction of floors with tiles, the correct arrangement of the tiles in patterns brings beauty and functionality to the environment, which depends on the accurate calculation of the angles. Furthermore, understanding this concept helps visualize and comprehend complex geometric structures, such as church domes and crystal shapes, making mathematics a vital tool in the real world.

Development

Duration: (70 - 80 minutes)

The development stage is designed to allow students to practically and engagingly apply the knowledge acquired about the sum of the internal angles of polygons. Working in groups, students will face challenges that require critical thinking, collaboration, and direct application of mathematical formulas. These activities will not only solidify students' understanding of the topic but will also develop teamwork and problem-solving skills in varied and fun contexts.

Activity Suggestions

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

Activity 1 - Geometric Explorers

> Duration: (60 - 70 minutes)

- Objective: Apply knowledge about the sum of the internal angles of polygons in a practical and playful way, encouraging teamwork and spatial reasoning.

- Description: Students will be divided into groups of up to 5 people, and each group will receive a map of the 'Polygonal Territory'. On this map, different polygons, such as triangles, squares, pentagons, and hexagons, are drawn in various sizes and orientations. The challenge is to calculate the sum of the internal angles of each polygon on the map and then use these angles to navigate pathways that lead to 'hidden treasures', which are marked by intersection points of the polygons on the map.

- Instructions:

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

• Distribute the maps and explain that each polygon on the map needs to have its internal angles calculated.

• Students must use their prior knowledge about the sum of the internal angles to calculate and note the angles of each polygon.

• After calculating the angles, students must plan a path that passes through intersections of polygons, using the angles as a guide.

• The first group to find all 'treasures' and return to the starting point using the correct path will be the winner.

Activity 2 - Polygon Builders

> Duration: (60 - 70 minutes)

- Objective: Develop calculation and construction skills, applying mathematical concepts of spatial geometry in a practical and visual manner.

- Description: In this activity, students will use sticks and play dough to build three-dimensional models of regular polygons. Each group will receive a specific amount of material and a drawing that represents the base of a prism, where the sides must be formed by regular polygons. The challenge is to construct the prism so that the sum of the internal angles of each polygon is correct and, at the end, present a model that is symmetrical and mathematically viable.

- Instructions:

• Divide students into groups of up to 5 people.

• Distribute the materials (sticks and play dough) and the base drawing of the prism to each group.

• Students must first calculate the sum of the internal angles of the polygons that will form the sides of the prism.

• Based on the calculations, students must construct the prism, ensuring that the angles are correct and that the structure is symmetrical.

• At the end, each group will present their prism and explain how they ensured that the sum of the internal angles was correct.

Activity 3 - Polygon Circus

> Duration: (60 - 70 minutes)

- Objective: Promote interactive and collaborative learning, where students teach and learn from each other about the sum of the internal angles of different polygons in a playful and engaging manner.

- Description: Transform the classroom into a grand circus, where each student group will be responsible for a different 'attraction'. Each attraction is a different polygon, where students must draw on the floor or on large poster boards, inviting their classmates to discover the sum of the internal angles. Colorful tape can be used to highlight the lines of the polygons. The objective is for each attraction to be interactive, with visitors (other students) participating in the discovery of the angles and learning from the mistakes and successes of the polygon 'artists'.

- Instructions:

• Organize the room into stations, each representing a type of polygon (triangle, square, etc.).

• Each group selects a type of polygon and draws it on the floor or large poster board, using tape.

• Students must then calculate and mark the internal angles on the polygon so that it is visible to visitors.

• Visitors, in different groups, must try to discover the sum of the internal angles of the visited polygon.

• At the end, each group of 'artists' explains how they arrived at the correct calculations and what they learned from interacting with the visitors.

Feedback

Duration: (10 - 15 minutes)

The purpose of this stage is to consolidate learning, allowing students to verbalize and reflect on what they accomplished. The group discussion helps reinforce the acquired knowledge, as well as promotes communication and argumentation skills. This moment also serves for the teacher to assess students' understanding of the topic and clarify any remaining doubts, ensuring that everyone has a clear and complete understanding of the subject.

Group Discussion

After completing the activities, gather all students for a group discussion. Start the conversation by highlighting the importance of sharing the discoveries and learnings made during the activities. Suggest that each group share their main difficulties, strategies used, and how they arrived at solutions. Encourage students to discuss different approaches and what they learned from their classmates' mistakes and successes.

Key Questions

1. What were the main challenges in calculating the sum of the internal angles of the polygons in the different contexts of the activities?

2. How did collaborating with your classmates help in solving problems during the practical activities?

3. Was there a situation where prior knowledge of the sum of the internal angles was essential in solving an unexpected problem?

Conclusion

Duration: (5 - 10 minutes)

The conclusion stage serves to consolidate learning, ensuring that students have understood the key concepts discussed and applied during the lesson. Additionally, by connecting theory with practice and discussing real-world applications of the studied concepts, this section aims to reinforce the relevance of mathematics in everyday life and motivate students to continue exploring and applying the acquired knowledge.

Summary

To conclude, the teacher should summarize the main points discussed in the lesson, reiterating the importance and practical application of the sum of the internal angles of polygons, such as the specific case of the hexagon with 720º. Review the calculation methods and curiosities explored during the activities, ensuring that students have a clear understanding of the subject.

Theory Connection

It is crucial to explain how today's lesson connected theory with practice. Students had the opportunity to directly apply mathematical concepts through playful and challenging activities, which not only solidified theoretical understanding but also demonstrated the relevance of geometry in everyday life, such as in architecture and design projects.

Closing

Finally, the teacher should emphasize the importance of the sum of the internal angles of polygons in real situations, such as in construction, art, and design, highlighting how understanding these concepts can positively impact practical problem-solving. This moment is crucial to ensure that students comprehend the usefulness of mathematical concepts beyond the school environment.