Contextualization

Angles are structures of utmost importance in the study of mathematics. They serve to measure the amplitude between two half-lines that depart from a common point, called the vertex of the angle. The most basic classification we have for angles is based on measurement. This classification divides angles into three categories: acute (less than 90°), right (equal to 90°), and obtuse (greater than 90° and less than 180°).

This classification of angles is one of the most basic concepts in Geometry, a subdiscipline of Mathematics that deals with shapes and their properties. Geometric shapes are described by their angle measurements, and therefore, recognizing and correctly calculating these measurements is a fundamental skill for those working with Geometry. The classification of angles is an essential part of this understanding.

The concept of angles is of extreme importance in many fields of everyday life. Whether in civil construction, where right angles are most commonly used because they provide stability to buildings, in navigation, where calculating the route requires taking angles into account, in physics, engineering, space research, sports, and many other areas.

Studying angles and their classification provides tools to understand and interpret the world around us. Through this study, students can better comprehend how the world is structured and how many of the objects and phenomena they see every day work.

Practical Activity

Title: Building and Classifying Angles

Project Objective:

• Provide students with a practical and interactive experience with angle classification.
• Promote a broader understanding of angle classifications through hands-on activities.
• Encourage teamwork, collaboration, and problem-solving skills.

Project Description:

In this project, students will work in groups of 3 to 5 members. Each group will be tasked with creating a series of geometric figures, measuring their angles, and classifying them according to the learned classification (acute, right, and obtuse). Additionally, students will have to research the application of each type of angle in the real world and present examples to their peers in a short presentation. The project will last one week.

Required Materials:

• Cardboard paper
• Protractor
• Pencil
• Ruler
• Scissors

Step by Step:

1. Each group should start the project by reviewing the theoretical concepts learned in class about angles and their classification.
2. Next, the groups should discuss and plan the geometric figures they want to create. At least five figures with different types of angles should be produced (triangles, quadrilaterals, etc.).
3. After the discussion, each group should draw the planned figures on the cardboard paper and cut them out.
4. With the help of a protractor, students should measure all the angles of the created figures and classify them.
5. Students should write down on a separate paper all the measurements and classifications of the angles they obtained.
6. Now, it's time to investigate: each group should research the use of different types of angles (acute, right, and obtuse) in the real world and prepare a brief presentation about their findings.
7. Finally, each group should present their findings to the class and submit the paper with the measurements, classifications, and their geometric figures.

Deliverables:

• The created geometric figures: to be evaluated regarding the correct construction and measurement of the angles.
• The paper with the notes of measurements and classifications: to verify the correct understanding and application of the theory.
• The presentation of the applications of angles in real life: to assess the ability to connect theory to practice.

After the practical part, the group should write a report detailing the project and present it to the teacher. The report should include:

• Introduction: Contextualization of the theme, justification of the relevance of studying angles, and the project's objective.

• Development: Explanation of the theory studied, detailed description of the activities carried out, the methodology used, and the results obtained.

• Conclusion: Reflection on the main points of the work, the learnings and conclusions drawn, and how this impacts the understanding of angles.

• Bibliography: Citation of the sources used for the study and project development.

Therefore, the final submission will consist of two parts: the practical product of the activity (geometric figures, notes, and presentation) and the written report.