Lesson plan of Polygon Angles

Objectives (5-7 minutes)

1. Understand the concept of the interior angle of a polygon: Students should be able to define and calculate the interior angle of a polygon. They should understand that the sum of the interior angles of a polygon is given by (n-2) * 180, where n is the number of sides of the polygon.

2. Identify and calculate interior angles of different polygons: Students should be able to identify different types of polygons (triangles, quadrilaterals, pentagons, hexagons, etc.) and calculate their interior angles. They should understand that for each type of polygon the formula for the sum of the interior angles is the same.

3. Apply the concept of interior angle of a polygon in practical situations: Students should be able to apply the concept of interior angle of a polygon in real-world situations, such as when constructing a prism or pyramid, or when drawing a map.

Secondary Objectives:

• Develop logical reasoning and abstract thinking skills: By working with interior angles of polygons, students will have the opportunity to develop their logical reasoning and abstract thinking skills, which are essential skills in mathematics and various other disciplines.

• Foster collaboration and teamwork: By working on hands-on activities and group discussions, students will have the opportunity to collaborate and develop teamwork skills.

Introduction (10-15 minutes)

1. Review of related concepts: The teacher begins the lesson with a brief review of the concepts of polygons, parallel lines, perpendicular lines, and angles. This review is essential to ensure that students have the necessary prior knowledge to understand the main topic of the lesson: interior angles of polygons. (3-5 minutes)

2. Problem situations: The teacher presents two problem situations that will serve as the starting point for the development of the topic:

   • Situation 1: Imagine you are building a building in the shape of a regular hexagon. How could you calculate the interior angles of each of the hexagon's sides?

   • Situation 2: Suppose you are drawing a labyrinth in the shape of an octagon. To ensure that the labyrinth is functional, the sum of the interior angles must be equal to 1080°. How could you calculate the value of each of the octagon's interior angles?(4-5 minutes)

3. Contextualization of the importance of the topic: The teacher highlights the importance of calculating interior angles of polygons in various practical situations, such as:

   • In architecture and engineering, when designing and constructing structures in the shape of polygons.

   • In cartography, when drawing maps.

   • In art and design, when creating patterns and geometric shapes.

   • In solid geometry, when calculating volumes and areas of solids. (3-5 minutes)

4. Introduction of the topic in a playful way: To arouse students' interest, the teacher can introduce the topic of interior angles of polygons in a fun and playful way. For example:

   • Curiosity 1: The teacher can show an image of a dodecahedron, which is a polyhedron with 12 faces, all of which are regular pentagons. The challenge would be to calculate the sum of the interior angles of each face of the dodecahedron and verify if the result is equal to 540°, as the formula for regular polygons suggests.

   • Curiosity 2: The teacher can tell the story of the German mathematician Carl Friedrich Gauss, who as a child amazed his teacher by quickly calculating the sum of all the interior angles of a polygon with 500 sides. The teacher expected him to perform an exhaustive sum, but Gauss realized he could use the formula (n-2) * 180 to obtain the result more quickly and efficiently. (4-5 minutes)

Development (20-25 minutes)

1. Activity: “Building Polygons” (10-12 minutes)

   • Description: The teacher divides the class into small groups and provides each group with toothpicks and modeling clay. The challenge is to build different polygons (triangle, quadrilateral, pentagon, hexagon, etc.) with the clay and toothpicks, ensuring that all the interior angles are correct.

   • Step by step:

     1. The teacher provides the necessary materials (toothpicks and modeling clay) to each group.
     2. The teacher instructs students to build each polygon, reminding them that all the interior angles must be correct.
     3. While students are building the polygons, the teacher circulates around the room, monitoring the work of the groups, and providing guidance when needed.
     4. After each polygon is built, the teacher asks a representative from each group to explain how they ensured that all the interior angles were correct.
     5. The teacher reinforces the concepts learned, making connections between the hands-on activity and the theory presented.

2. Activity: “Drawing the Treasure Map” (10-12 minutes)

   • Description: The teacher presents the problem situation: students are pirates in search of a treasure hidden on an island. They will be given a map that shows the location of the treasure, but the map is incomplete. The students need to complete the map by drawing the island, which must be a regular polygon, and indicating the location of the treasure. In addition, they must calculate the sum of the interior angles of the polygon to ensure that the map is correct.

   • Step by step:

     1. The teacher distributes a sheet of paper and colored pens to each group.
     2. The teacher presents the problem situation and the criteria for drawing the map (the island must be a regular polygon and the sum of the interior angles of the polygon must be equal to (n-2)*180, where n is the number of sides of the polygon).
     3. Students discuss in groups and decide on the number of sides of the polygon (5, 6, 7, ...).
     4. Next, students draw the island on the paper, ensuring that all the interior angles are correct.
     5. Finally, students indicate the location of the treasure on the map and present their work to the class. The teacher verifies if the sum of the interior angles is correct and if the location of the treasure is in accordance with the original map.
     6. The teacher reinforces the concepts learned, making connections between the hands-on activity and the theory presented.

3. Group discussion and conclusions: After completing the activities, the teacher leads a group discussion so that students can share their experiences, difficulties, and learnings. The teacher reinforces the concepts learned, clarifies possible doubts, and makes connections with real-world situations and other disciplines. (5-6 minutes)

These activities allow students to explore the concept of interior angles of polygons in a playful and contextualized way, develop logical reasoning and abstract thinking skills, and work in teams to solve problems. In addition, the activities promote active learning and student participation, who become the protagonists of their own learning.

Feedback (8-10 minutes)

1. Group discussion (3-4 minutes): The teacher leads a group discussion with all students so they can share their solutions and conclusions from the activities carried out. Each group has a maximum of 2 minutes to present their findings and strategies to the class.

   • The teacher should encourage students to explain how they arrived at their answers, what formulas or strategies they used, and what difficulties they encountered in the process. This allows students to learn from each other and develop communication and argumentation skills.

2. Connection with the theory (2-3 minutes): After the group presentations, the teacher reviews the theoretical concepts discussed at the beginning of the lesson and connects them with the hands-on activities carried out.

   • The teacher can, for example, ask students how they applied the formula for interior angles (n-2)*180 in the activity “Drawing the Treasure Map”. Or how they ensured that all the interior angles of the polygons they built in the activity “Building Polygons” were correct.

3. Individual reflection (2-3 minutes): The teacher suggests that students individually reflect on what they learned in the lesson. The teacher asks guiding questions, such as:

   1. What was the most important concept you learned today?

   2. What questions have not yet been answered?

   3. How can you apply what you learned in real-world situations?

   • Students have one minute to think about the answers to these questions. The teacher can ask some volunteers to share their reflections with the class, if they wish.

4. Teacher feedback (1 minute): The teacher ends the lesson by giving brief feedback on the class's performance. The teacher praises the students' efforts, highlights the positive points, and suggests areas for improvement. The teacher also answers any final questions that students may have.

   • The teacher can, for example, praise the students' active participation, the way they worked in teams, or the way they applied the theory in solving the hands-on activities. The teacher can suggest, on the other hand, that the students practice more calculating the interior angles of polygons at home to consolidate their learning.

Feedback is a fundamental stage of the lesson plan, as it allows the teacher to assess students' understanding of the topic, identify possible gaps in learning, and adjust the teaching approach if necessary. In addition, Feedback promotes reflection and metacognition in students, which are important skills for autonomous learning and self-regulation.

Conclusion (5-7 minutes)

1. Summary and Recapitulation (2-3 minutes): The teacher summarizes the main points covered during the lesson, recapitulating the concepts of interior angle, polygons, and the formula for calculating the sum of the interior angles of a polygon ((n-2) * 180). He reinforces the idea that all polygons, regardless of the number of sides, follow the same rule to calculate the sum of their interior angles. The teacher can also ask students to recap the main points, promoting active participation and checking students' understanding.

2. Connection between Theory, Practice, and Applications (1-2 minutes): The teacher highlights how the lesson connected theory, practice, and applications through the activities carried out. He reinforces that the construction of polygons and the resolution of the treasure map problem allowed students to apply the theoretical concepts in a practical and contextualized way. The teacher also reinforces the applications of calculating interior angles in various real-world situations and in different areas, such as architecture, engineering, cartography, and art.

3. Complementary Materials (1 minute): The teacher suggests complementary materials for students who wish to deepen their knowledge of the subject. These materials may include textbooks, mathematics websites, educational videos, mathematical games, and online exercises. The teacher can, for example, recommend the use of dynamic geometry software, such as Geogebra, to explore the interior angles of polygons interactively.

4. Importance of the Subject (1-2 minutes): Finally, the teacher highlights the importance of interior angles of polygons in everyday life and in various areas of knowledge. He reinforces that the understanding of this concept is fundamental for solving practical problems and for understanding many other mathematical concepts. The teacher can, for example, mention that the calculation of interior angles is used in architecture and engineering to design and build structures, in cartography to draw maps, and in art and design to create patterns and geometric shapes. The teacher concludes the lesson by encouraging students to continue exploring the fascinating world of mathematics and to realize the presence and importance of polygons and their interior angles in their daily lives.