Contextualization

Theoretical Introduction

Mathematics, as a discipline, presents in its contents diverse elements that are essential for the understanding of the world around us. One of these elements is angles. In geometry, an angle is the figure formed by two lines that start from a common point, the vertex. The angle measure is the amount of rotation required for one of the lines to coincide with the other.

The classification of angles is an essential part of the study of angles. There are four main types of angles which are: acute, right, obtuse, and straight. An acute angle is one whose measure is less than 90 degrees. A right angle has exactly 90 degrees. An obtuse angle is greater than 90 degrees and less than 180 degrees. And finally, a straight angle is exactly 180 degrees.

Understanding this classification of angles and knowing how to identify them is one of the pillars of geometry. This ability is crucial for solving problems and situations that involve the use of geometry, whether in other mathematical disciplines or in real-world applications.

Contextualization

Angles are constantly present in our daily lives, whether in architectural and engineering constructions, in art, in drawings, and even in the bodily movements of humans and other species. The ability to recognize and work with different types of angles is, therefore, an extremely useful skill to be developed.

Moreover, when studying the classification of angles, students are not only learning a mathematical concept but also developing critical thinking and problem-solving skills. They learn to look more closely at the world around them, to question, analyze, and synthesize information. These are skills that are extremely valuable in life beyond the classroom.

Practical Activity

Activity Title: Discovering Angles in the World Around Us

Project Objective

Students should be able to identify and classify the four main types of angles (acute, right, obtuse, and straight) from everyday objects or geometric figures present in the environment in which they live. In addition, the project aims to develop socio-emotional skills such as time management, communication, problem solving, and creative thinking.

Detailed Project Description

The students, divided into groups of 3 to 5, will have to carry out an "angle safari", which consists of identifying, cataloging, and classifying the different angles found in everyday objects or in the architecture around them.

As a final deliverable of the project, the groups will have to produce an Angle Safari Report, which includes photographs of the angles found, as well as a description and classification of each angle and an account of the exploration and discovery process.

Required Materials

1. Camera or cell phone with a camera.
2. Paper and Pen.
3. Protractor (to check the angle measurement).
4. Computer with a text editor to create the report (optional).

Detailed Step-by-Step for the Activity

1. Division of students into groups of 3 to 5 people.
2. Explanation and discussion of the rules and objectives of the "angle safari".
3. Carrying out of the "angle safari" by the groups, each group must photograph at least 10 different angles found in everyday life. Students should note where the angle was found and why it is interesting.
4. After the "safari", students should classify each photographed angle as acute, right, obtuse, or straight.
5. Students will write an "angle safari" report mentioning where each angle was found, what type of angle it is, and why it is interesting.
6. The report should also include a discussion of the exploration and discovery process, highlighting teamwork and time management.

Regarding the final document, students should pay attention to the following aspects:

1. Introduction: Contextualize the theme, its relevance, and application in the real world as well as the objective of this project.
2. Development: Explain the theory behind angles and their classification, describe each angle found during the activity and justify its classification, include the images taken during the "angle safari" and comment on the methodology used. Present and discuss the results obtained.
3. Conclusion: Summarize the main points, presenting the lessons learned and the conclusions drawn about the project.
4. Bibliography: Indicate the sources on which you relied to work on the project such as books, web pages, videos, etc.

For the realization of this project, each group of students has one month, from the beginning of the project, to prepare and submit the final report. The work should be carried out consistently throughout the available period rather than being left until the last minute.