Objectives (5 - 10 minutes)

1. Understand the concept of polygons: Students should be able to define what polygons are and identify them in different contexts. They should also be able to recognize the fundamental characteristics of a polygon, including the presence of closed lines and line segments.

2. Learn to classify polygons: Students should be able to classify polygons based on their characteristics. This includes classifying them according to the number of sides, angles, and angle measurements. Students should understand that, although all polygons have straight and closed sides, they can vary in terms of the number and size of angles.

3. Develop critical thinking and problem-solving skills: When working with polygons and their classification, students should be able to apply the information they have learned to solve problems and answer questions. This involves the ability to analyze a polygon, identify its characteristics, and classify it correctly.

   • Secondary objectives:
     1. Stimulate logical thinking and spatial visualization: Classifying polygons requires students to visualize shapes and their geometric characteristics. This helps develop spatial visualization skills and logical thinking.
     2. Promote collaboration and communication: Practical activities involving the classification of polygons can be done in groups, promoting collaboration among students. Sharing ideas and communicating solutions are also encouraged, contributing to the development of social skills.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher starts the lesson by reviewing the basic geometry concepts that serve as the foundation for the study of polygons. This may include defining lines, segments, angles, as well as the terms 'closed' and 'open'. The teacher may ask questions to verify students' understanding of these concepts and clarify any doubts that may arise.

2. Problem-solving situations: The teacher presents two situations that pique students' interest and introduce them to the topic of the lesson. For example:

   • 'Imagine you are designing a new board game and need to create different quadrilateral shapes. How could you ensure that all shapes created are quadrilaterals and not other types of polygons?'
   • 'Have you ever noticed the street signs in your city? Many of them have different shapes. How do you think engineers and architects decide on the shape of each sign? How do they ensure that all signs are of the same type of polygon?'

3. Contextualization: The teacher then contextualizes the importance of studying polygons, explaining how they are widely used in our daily lives. This may include examples of their application in architecture, engineering, game design, cartography, among others. The teacher may emphasize that by understanding and being able to classify polygons, students will be developing skills that are useful in many careers and areas of study.

4. Introduction to the topic: To introduce the topic of the lesson, the teacher may:

   • Curiosity 1: Mention that the study of polygons dates back to Ancient Greece, where mathematicians like Euclid and Archimedes dedicated much time to the study of these shapes.
   • Curiosity 2: Present the 'Polygon Challenge', a mathematical problem that involves the classification of polygons and is considered one of the oldest unsolved problems in mathematics.
   • Practical application 1: Show an image of a construction site and ask students what type of polygons they can see in the image.
   • Practical application 2: Show an image of a popular board game and ask students what type of polygons they can identify in the board's design.

Development (20 - 25 minutes)

1. Activity of Building Polygons with Toothpicks and Marshmallows:

   • Materials: Toothpicks and marshmallows.
   • Objective: Understand the structure and characteristics of polygons.
   • Step by step:
     1. Divide the class into groups of 3 to 4 students.
     2. Provide each group with toothpicks and marshmallows.
     3. Explain that the toothpicks represent the sides of the polygons and the marshmallows represent the vertices.
     4. Instruct the groups to build different polygons (triangles, squares, pentagons, hexagons, etc.) with the provided materials.
     5. As the groups build the polygons, the teacher should circulate around the room, assisting and asking questions that stimulate students' understanding of the polygons' characteristics.
     6. After the construction of the polygons, the teacher should lead a classroom discussion on the observed characteristics of each polygon and how they can be classified.

2. Polygon Classification Activity:

   • Materials: Cards with images of different polygons.
   • Objective: Develop the ability to classify polygons based on their characteristics.
   • Step by step:
     1. Prepare cards in advance with images of different polygons (triangles, quadrilaterals, pentagons, hexagons, etc.).
     2. Distribute the cards randomly to the student groups.
     3. Instruct the groups to classify the polygons according to the number of sides and angle measurements.
     4. Each group must justify their classification, explaining how they arrived at the conclusion.
     5. The teacher should circulate around the room, assisting groups that encounter difficulties and asking questions that stimulate critical thinking.
     6. After the activity, the teacher should lead a classroom discussion, reviewing the classifications made by the groups and clarifying any doubts that may have arisen.

3. Board Game Activity:

   • Materials: A printed board game with various polygon shapes and a die.
   • Objective: Reinforce the ability to classify polygons in a playful way.
   • Step by step:
     1. Prepare in advance a printed board game with various polygon shapes. Each square on the board represents a polygon.
     2. Divide the class into groups of 3 to 4 students and distribute the groups around the board.
     3. Each group receives a marker and a die.
     4. The player from each group rolls the die and moves the marker on the board according to the number rolled on the die.
     5. When a player lands on a square, the group must classify the polygon represented in that square.
     6. If the group classifies correctly, they stay on the square. If they classify incorrectly, they must go back to the previous square.
     7. The game continues until a group reaches the end of the board.
     8. During the game, the teacher should circulate around the room, monitoring the progress of the groups and clarifying doubts.
     9. After the game, the teacher should lead a classroom discussion on the classifications made by the groups and clarify any doubts that may have arisen.

These practical and playful activities allow students to explore the concept of polygons interactively and collaboratively, reinforcing their understanding and classification skills.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes): The teacher should gather all students and promote a collective discussion about the solutions or conclusions found by each group during the activities. At this moment, students will have the opportunity to share their experiences, listen to others' ideas, and learn from different approaches.

   • The teacher should start the discussion by asking each group about the main characteristics they identified in the polygons built in the first activity.
   • Next, the teacher can ask each group to share their classification of the polygons in the second activity, encouraging them to justify their decisions.
   • Finally, the teacher can ask students about the challenges they faced during the activities and how they managed to overcome them.

2. Connection to Theory (2 - 3 minutes): After the discussion, the teacher should summarize the main ideas discussed and make the connection to the theory. The teacher can:

   • Recall the definition of polygons and their fundamental characteristics.
   • Explain how students applied these characteristics to classify the polygons during the activities.
   • Highlight the importance of observation, analysis, and argumentation in the classification of polygons.

3. Individual Reflection (3 - 5 minutes): The teacher should propose that students reflect individually on what they learned during the lesson. To do this, the teacher can ask the following questions:

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

   2. What questions have not been answered yet?

   3. How can you apply what you learned today in everyday situations?

   • Students should be encouraged to write down their answers, as this can help them consolidate their learning and identify areas that need further study or clarification.

4. Feedback and Closure (1 - 2 minutes): To end the lesson, the teacher should:

   • Ask for feedback from students about the lesson, asking them what they liked, what they found difficult, and what they would like to learn more about.
   • Thank everyone for their participation and effort, emphasizing the importance of teamwork and collaboration.
   • Briefly inform about the topic of the next lesson and any necessary preparation.

This Return moment is crucial to consolidate students' learning, clarify any remaining doubts, and prepare students for the next topic. By promoting discussion, reflection, and feedback, the teacher helps students become active and autonomous learners.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes): The teacher should recap the main points covered during the lesson, reinforcing the concepts of polygons, their characteristics, and classification based on the number of sides and angle measurements. Some suggestions for the summary include:

   • Recall the definition of polygons as closed figures formed by line segments.
   • Recap the fundamental characteristics of polygons, such as the presence of straight and closed sides.
   • Review the classification of polygons based on the number of sides and angles, reinforcing the terms 'triangle', 'quadrilateral', 'pentagon', 'hexagon', and their respective characteristics.
   • Summarize the practical activities carried out during the lesson and how they helped reinforce students' understanding of polygon classification.

2. Theory-Practice Connection (1 - 2 minutes): The teacher should explain how the lesson connected theory to practice, highlighting how the practical activities allowed students to apply theoretical concepts concretely. Some suggestions for this connection include:

   • Recall the polygon construction and classification activities, explaining how they allowed students to see and manipulate the characteristics of polygons in practice.
   • Highlight how the group discussion after the activities allowed students to share their experiences and understandings, further enriching the learning.

3. Extra Materials (1 minute): The teacher can suggest additional materials for students who wish to deepen their knowledge of polygons and their classification. Some resources may include:

   • Mathematics textbooks, which often have sections dedicated to geometry and polygons.
   • Online educational videos, which can visually and interactively present polygon concepts and their classification.
   • Mathematics websites, which often have interactive activities and games to help students practice polygon classification.

4. Importance of the Subject (1 - 2 minutes): To conclude, the teacher should emphasize the importance of the subject presented for students' daily lives and for other areas of knowledge. Some suggestions for this explanation include:

   • Explain that the ability to classify polygons is useful in many fields, including architecture, engineering, game design, cartography, among others.
   • Highlight how understanding polygons and their classification can help students perceive the presence of these shapes in their everyday environment, from street signs to food packaging.
   • Finally, the teacher can encourage students to reflect on how what they learned in the lesson can be applied in their lives, encouraging them to see mathematics as a useful and relevant tool.

The output should be formatted as a JSON instance that conforms to the JSON schema below.

As an example, for the schema {"properties": {"foo": {"title": "Foo", "description": "a list of strings", "type": "array", "items": {"type": "string"}}}, "required": ["foo"]} the object {"foo": ["bar", "baz"]} is a well-formatted instance of the schema. The object {"properties": {"foo": ["bar", "baz"]}} is not well-formatted.

Here is the output schema:

{"properties": {"description": {"title": "Description", "description": "Translated Description.", "type": "string"}, "title": {"title": "Title", "description": "Translated Title", "type": "string"}, "markdown": {"title": "Markdown", "description": "Translated Markdown", "type": "string"}}, "required": ["description", "title", "markdown"]}