Lesson Plan | Traditional Methodology | Geometric Constructions

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage is to provide students with a clear and detailed view of the specific objectives of the lesson, preparing them to understand the geometric constructions that will be addressed. This stage helps to contextualize the content, highlighting the skills that will be developed throughout the lesson.

Main Objectives

1. Understand the fundamental concepts of perpendicular bisectors and angle bisectors.

2. Learn to construct angles of 30º, 45º, and 60º using geometric methods.

3. Develop skills to construct regular polygons through algorithms and flowcharts.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage is to provide students with a clear and detailed view of the specific objectives of the lesson, preparing them to understand the geometric constructions that will be addressed. This stage helps to contextualize the content, highlighting the skills that will be developed throughout the lesson.

Context

To start the lesson on Geometric Constructions, it is important to situate students in the historical and practical context of geometry. Begin by explaining that geometry is one of the oldest mathematical sciences, with roots in ancient Greece, where mathematicians like Euclid developed many of the principles we use today. Geometric construction, in particular, is a technique that allows for the creation of precise figures and shapes using only a compass and a ruler. These constructions are fundamental not only in mathematics but also in various fields such as engineering, architecture, and graphic design.

Curiosities

Did you know that geometry is used in the creation of video game graphics? Angles and geometric shapes help create realistic 3D environments. Moreover, many of the patterns we find in nature, such as the symmetry of flowers and the formation of snow crystals, can be explained and replicated through geometric constructions.

Development

Duration: (50 - 60 minutes)

The purpose of this stage of the lesson plan is to provide students with an in-depth understanding of geometric constructions through detailed explanations and practical examples. This stage aims to ensure that students can apply the concepts learned to solve geometric problems independently and accurately.

Covered Topics

1. Definition and Construction of Perpendicular Bisectors: Explain the concept of the perpendicular bisector of a line segment. Detail the step-by-step process for constructing a perpendicular bisector using a ruler and compass. Show practical examples and draw on the board. 2. Definition and Construction of Angle Bisectors: Present the concept of the angle bisector. Demonstrate how to construct an angle bisector using a ruler and compass. Provide examples and draw on the board to illustrate. 3. Construction of Angles of 30º, 45º, and 60º: Teach the technique for constructing specific angles of 30º, 45º, and 60º. Use geometric methods, explaining each step in detail. Draw on the board and allow students to practice in their notebooks. 4. Construction of Regular Polygons: Explain how to construct regular polygons (triangles, squares, hexagons) using a ruler and compass. Provide algorithms or flowcharts that assist in understanding and executing these constructions. Draw examples on the board and allow students to practice.

Classroom Questions

1. Construct the perpendicular bisector of the line segment AB using a ruler and compass. Ensure that all steps are clearly indicated. 2. Construct the angle bisector of a 60º angle using a ruler and compass. Indicate each step of the process. 3. Using a ruler and compass, construct a regular hexagon. Explain each step of the construction process.

Questions Discussion

Duration: (15 - 20 minutes)

The purpose of this stage of the lesson plan is to promote reflection and discussion among students about the techniques and methods used in geometric constructions. This discussion allows students to reinforce learning, share their experiences and challenges, and deepen their understanding of the concepts addressed.

Discussion

•  Construction of Perpendicular Bisector of a Line Segment AB:

• Place the dry point of the compass at point A and draw an arc above and below the segment AB.

• Without changing the compass opening, repeat the process at point B, creating two intersection points of the arcs above and below AB.

• Using the ruler, draw a straight line connecting these two intersection points. This line is the perpendicular bisector of segment AB.

•  Construction of the Angle Bisector of a 60º Angle:

• Place the dry point of the compass at the vertex of the angle and draw an arc that intersects both sides of the angle.

• Without changing the compass opening, place the dry point at the intersection of the arc with one side of the angle and draw a small arc inside the angle.

• Repeat the process for the other side of the angle, creating an intersection point of the two arcs inside the angle.

• Using the ruler, connect the vertex of the angle to the intersection point of the arcs. This line is the angle bisector of the 60º angle.

•  Construction of a Regular Hexagon:

• Draw a circle with the compass.

• Without changing the compass opening, mark a point anywhere on the circumference of the circle and place the dry point of the compass at that point.

• Draw an arc that intersects the circumference of the circle. Mark this intersection point.

• Move the dry point of the compass to this new point and repeat the process until six points are marked on the circumference of the circle.

• Use the ruler to connect the adjacent points, forming a regular hexagon.

Student Engagement

1. ️ Questions for Student Engagement: 2. What difficulties did you encounter while constructing the perpendicular bisector of a line segment? How did you resolve these difficulties? 3. What is the importance of using a compass and ruler in constructing the angle bisector? Could you do this without these tools? 4. How can the construction of regular polygons, such as the hexagon, be applied in everyday situations or other subjects? 5. Did anyone manage to construct an angle of 30º, 45º, or 60º using different methods than those taught? If so, how did you do it? 6. How can you verify if the constructed bisector or perpendicular bisector is correct?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to recap the main points covered in the lesson, reinforcing student learning. Additionally, this stage highlights the connection between theory and practice, as well as the relevance of the content in everyday life, helping students understand the importance and application of geometric concepts.

Summary

• Definition and construction of perpendicular bisectors using a ruler and compass.
• Definition and construction of angle bisectors.
• Techniques for constructing angles of 30º, 45º, and 60º.
• Construction of regular polygons, such as triangles, squares, and hexagons, using algorithms and flowcharts.

The lesson connected theory with practice by demonstrating step-by-step, using a ruler and compass, how to perform precise geometric constructions. This allowed students to visualize and apply theoretical concepts in practical activities, consolidating learning through guided exercises and examples drawn on the board.

The importance of geometric constructions goes beyond the classroom, as they are fundamental in various fields such as engineering, architecture, and graphic design. The precision and skill in creating geometric figures are essential for project creation and solving real problems, from building construction to the development of video game graphics.