Objectives (5 - 7 minutes)

1. Understand the concept of geometric constructions: Students should be able to understand what geometric constructions are and how they relate to the real world. They should understand that constructions are made using only a ruler and a compass and that they follow certain rules and limitations.

2. Develop drawing and visualization skills: Students should be able to draw basic geometric constructions, such as bisecting a segment, constructing a 60-degree angle, and constructing triangles. They should be able to visualize and understand how these constructions are made and why they are important.

3. Apply geometric constructions to practical problems: Students should be able to apply the geometric constructions they have learned to solve practical problems. They should be able to use the constructions to solve geometry problems and understand how they can be useful in real-world situations.

Secondary Objectives:

• Stimulate logical and critical thinking: By performing geometric constructions, students will be exposed to a series of challenges that will require them to think logically and critically to find solutions. This will help develop their problem-solving skills and logical thinking.

• Promote collaboration in the classroom: By working in groups to perform the constructions, students will have the opportunity to collaborate with each other, sharing ideas and strategies, which can help promote a collaborative and supportive learning environment.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher should start the lesson by briefly reviewing the concepts of geometry and drawing tools, such as the ruler and compass. This review is essential for students to understand and correctly apply geometric constructions. (2 - 3 minutes)

2. Problem situation 1: The teacher can propose the following challenge: "Imagine you are engineers and need to build a bridge over a river. You need to calculate the height the bridge should have so that boats can pass underneath it. But the problem is that you cannot directly measure the height of the river. How could you use the geometric constructions you have learned to solve this problem?" (3 - 4 minutes)

3. Problem situation 2: Next, the teacher can present another challenge: "Now, imagine you are architects and are designing a new building. You want the building's shadow not to fall on a neighboring park for most of the day. How could you use geometric constructions to determine the maximum height the building can have?" (3 - 4 minutes)

4. Contextualization: The teacher should then explain that geometric constructions are not just abstract concepts, but have practical applications in the real world. They are used by engineers, architects, cartographers, and even artists to solve problems and create drawings and projects. (2 - 3 minutes)

5. Introduction to the topic: Finally, the teacher should introduce the topic of geometric constructions, explaining that they are a set of rules that allow us to create precise geometric figures using only a ruler and a compass. The teacher can also mention that geometric constructions are an important part of Euclidean geometry, which is the basis of the geometry we study in school. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Triangle Construction Activity (10 - 12 minutes):

   • The teacher should divide the class into groups of 4 or 5 students, distributing a ruler and a compass to each group.
   • Next, the teacher should propose that the students, in their respective groups, construct an equilateral triangle on the paper.
   • The teacher should guide the students to perform the activity step by step: (a) Mark a point A in one corner of the paper. (b) Use the compass to mark two points B and C, one on each side of the paper, so that the distance between A and each of these points is the same. (c) Draw the line segments AB, AC, and BC, forming the equilateral triangle. (d) Name the vertices of the triangle as A, B, and C.
   • The teacher should circulate around the room, assisting groups that encounter difficulties and clarifying doubts.
   • Finally, each group should present their triangle to the class, explaining the construction process.

2. Bisector Construction Activity (5 - 7 minutes):

   • Still in their groups, students should construct the bisector of the angle formed by two sides of the equilateral triangle they built in the previous activity.
   • The teacher should guide the students to perform the activity step by step: (a) Choose one of the angles of the triangle and mark a point D inside that angle. (b) Use the compass to draw two arcs, one with center at D and radius to one side of the angle, and the other with center at D and radius to the other side of the angle. (c) Where these arcs intersect, mark a point E. (d) Draw the line segment DE, which will be the bisector of the angle.
   • The teacher should again circulate around the room, assisting groups and clarifying doubts.
   • Each group should then present their bisector to the class, explaining the construction process.

3. Hexagon Construction Activity (5 - 6 minutes):

   • Finally, students, still in their groups, should construct a regular hexagon on the paper.
   • The teacher should guide the students to perform the activity step by step: (a) Mark a point F in the center of the paper. (b) Use the compass to mark six points, one on each side of point F, so that the distance between F and each of these points is the same. (c) Draw the line segments that connect point F to each of the points they marked, forming the regular hexagon.
   • The teacher should circulate