Objectives (5 minutes)

1. Introduce the concept of flat shapes, highlighting that they are formed by straight lines that do not intersect.

2. Teach students about the sides and vertices of flat shapes, explaining that the sides are the lines that form the shape and the vertices are the points where the sides meet.

3. Provide students with the opportunity to explore flat shapes through practical activities, such as counting sides and vertices in different geometric forms.

Secondary Objectives:

• Foster the development of students' logical reasoning as they identify and count the sides and vertices of flat shapes.

• Stimulate active participation of students through questions and discussions in the classroom, promoting collaborative learning and expression of ideas.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher starts the lesson by reminding students about what straight lines and points are and how to count them. Explains, in simple terms, that all objects around us are formed by combinations of points and lines.

2. Problem-solving situations:

   • The teacher can start with the following question: 'Have you ever observed how the sides and corners of a pencil box or a sheet of paper are? What do you think these sides and corners are?'
   • Then, can present a simple drawing containing some geometric shapes and ask: 'How many sides and corners can you count in this drawing? How did you count them?'

3. Contextualization: The teacher explains that the study of flat shapes and their sides and vertices is very important because it helps us better understand the world around us. He can cite examples such as:

   • 'When you draw a house, you need to know how many sides and vertices a square, a rectangle, a triangle have, to be able to represent the house correctly.'
   • 'When you play with a puzzle, the shape of the pieces, with their sides and vertices, is what allows them to fit perfectly.'

4. Introduction of the topic:

   • The teacher can show images of simple objects, such as a pencil box, a sheet of paper, a window, and ask: 'What do you think these objects have in common?'.
   • Then, explain that all these objects are examples of flat shapes, and that in today's class they will learn more about them, especially about their sides and vertices.

5. Engage students' attention:

   • The teacher can say: 'Today, you will become true shape detectives! You will learn to identify and count the sides and vertices of flat shapes!'.
   • To arouse students' curiosity, the teacher can show some images of more complex flat shapes, such as a hexagon or an octagon, and ask: 'Can you guess how many sides and vertices these shapes have?'.

Development (20 - 25 minutes)

1. Theoretical description of the concept of flat shapes: (5 minutes)

   • The teacher starts the explanation with the definition of flat shapes, saying that they are shapes that do not have volume, only length and width.
   • To facilitate understanding, the teacher can draw a square on the board and show that, even if he tries, he cannot give it depth.
   • He can show the same with a triangle and a circle, emphasizing that, no matter how hard he tries, he cannot make them look 3D.
   • The teacher must ensure that students understand that flat shapes are just drawings, without volume.

2. Theoretical description of sides and vertices: (5 minutes)

   • The teacher draws a square on the board and explains that the sides are the lines that form the shape. In the case of the square, there are 4 sides.
   • He shows that the sides are line segments that do not intersect.
   • Then, the teacher draws the vertices, which are the points where the sides meet.
   • In the example of the square, there are 4 vertices.
   • The teacher must emphasize that all sides have 2 vertices, one at each end.

3. Theoretical description of other shapes and their sides and vertices: (5 minutes)

   • The teacher should draw and explain the sides and vertices of other flat shapes, such as triangles, rectangles, circles, pentagons, and hexagons.
   • It is important for the teacher to have students count the sides and vertices as he draws, so they also practice.
   • The teacher should ask questions like 'How many sides does a triangle have? And a pentagon? And a circle?' so that students can answer and verify if they are following the lesson.

4. Initial verification: (5 minutes)

   • The teacher should hand out a sheet with drawings of various flat shapes to the students and ask them to count the sides and vertices and mark these quantities next to each shape.
   • The teacher should walk around the room, observing the students' progress and assisting those who have doubts.
   • This activity aims to consolidate students' understanding of the concept of sides and vertices and their quantities in different flat shapes.

5. Practical activity: (5 - 10 minutes)

   • The teacher can propose a playful activity in which students create their own flat shapes using toothpicks and modeling clay.
   • They should challenge themselves to create shapes with a specific number of sides and vertices, for example, a shape with 3 sides and 3 vertices (triangle) or a shape with 4 sides and 4 vertices (square).
   • This practical activity will help students visualize and manipulate flat shapes, reinforcing the theoretical concepts presented.

Return (10 - 15 minutes)

1. Group discussion: (5 minutes)

   • The teacher should gather all students and ask each of them to show the shape they built with the toothpicks and modeling clay.
   • Each student must explain how many sides and vertices their shape has and how they came to that conclusion.
   • The teacher should congratulate the students on their creations and correct answers. If any student made a mistake in counting, the teacher should help them correct the error, reinforcing the concept of sides and vertices.
   • The teacher should also emphasize the importance of teamwork and collaboration, as during the activity the students helped each other in assembling the shapes and counting the sides and vertices.

2. Connection to theory: (5 minutes)

   • The teacher should revisit the shapes from the practical activity and, using the board, reinforce the correct counting of the sides and vertices of each one.
   • The teacher should ask the students if the shape they created resembles any of the shapes they learned in class. For example, if a student created a shape with 3 sides and 3 vertices, the teacher can ask if this shape resembles the triangle they studied.
   • The teacher should explain that the shapes they created are called polygons and that polygons are flat shapes whose sides are line segments that do not intersect.
   • The teacher can then draw a polygon on the board and show that it is formed by sides and vertices, connecting the practical activity with the theory studied.

3. Final reflection: (5 minutes)

   • The teacher should ask students to reflect for a minute on what they learned in the lesson. He can ask two simple questions to guide the reflection:
     1. 'What was easier for you in today's lesson: counting the sides or the vertices? Why?'
     2. 'What was harder for you in today's lesson: counting the sides or the vertices? Why?'
   • After the minute of reflection, the teacher should invite some students to share their answers with the class. He should value all answers, reinforcing that everyone is learning and that it is normal to encounter difficulties on the learning path.
   • The teacher should end the lesson by reinforcing the most important concepts learned: what flat shapes are, what sides and vertices are, and how to count them. He can suggest that students continue to observe their surroundings and identify flat shapes, sides, and vertices as a homework activity.

Conclusion (5 - 10 minutes)

1. Lesson summary: (2 - 3 minutes)

   • The teacher should review the main points of the lesson, summarizing the concepts of flat shapes, sides, and vertices and how to count them.
   • He can quickly revisit the drawings that students made with the modeling clay, reinforcing the correct counting of the sides and vertices of each shape and how they fit into the concept of flat shapes.
   • The teacher should remind students to observe their surroundings carefully, as they can find many flat shapes, sides, and vertices in common objects.

2. Connection of theory with practice: (2 - 3 minutes)

   • The teacher should explain how the practical activity of building flat shapes with modeling clay helped reinforce students' understanding of the theoretical concepts of sides and vertices.
   • He can emphasize that, by creating their own shapes, students had to identify and count the sides and vertices, which consolidated the concept in a more playful and enjoyable way.

3. Extra materials: (1 - 2 minutes)

   • The teacher should suggest some extra materials for students who wish to deepen their knowledge on the subject.
   • He can recommend illustrated math books, educational websites with interactive games for counting sides and vertices, and even educational videos available on the internet.
   • The teacher should remind students that these materials are just a suggestion and that they are not required to use them, but they can be useful for those who want to continue learning and exploring the topic.

4. Importance of the subject: (1 - 2 minutes)

   • Finally, the teacher should explain to students the importance of what they learned in the lesson.
   • He can cite examples from everyday life, such as the use of flat shapes in the construction of objects, in art, in architecture, and even in solving more complex mathematical problems.
   • The teacher should emphasize that knowledge about flat shapes, sides, and vertices is a valuable skill that can help students better understand the world around them and solve problems more efficiently.