Context

Angles are a fundamental part of mathematics and are deeply rooted in our everyday world. Whether it's designing a skate ramp, the architecture of a building, or even figuring out the best way to cut a pizza, angles are there.

But what is an angle? Simply put, an angle is formed by the meeting of two lines or line segments. The opening formed by these two lines is measured in degrees and can range from 0 to 360. Angles can be classified into various types, such as right (90 degrees), acute (less than 90 degrees), and obtuse (more than 90 degrees).

Angles are also the basis of Geometry, a branch of Mathematics that studies the shapes, sizes, and properties of space. As we advance in mathematics, the concepts of angles and geometry become increasingly complex and challenging, but also more fascinating and useful.

Now, let's explore the importance of angles. Imagine an engineer designing a bridge. They need to consider the angles of support to ensure that the bridge is strong and safe. Or think of an artist creating a sculpture. The artist needs to understand angles to give the artwork the correct shape. Even athletes must be concerned with angles. A basketball player, for example, needs to calculate the angle and force of their shot to make the basket.

In this project, we will explore the concept of angles in more depth. I recommend the following resources as a starting point for your studies:

1. The textbook "Geometry and Measurement" by Modern Publishing. You can find this book in your school library. It has an entire chapter dedicated to angles and their properties.
2. The Khan Academy website, which has several lessons on angles, including videos, exercises, and quizzes. Here is the link to the section on angles: Khan Academy - Angles.
3. YouTube also has a plethora of videos that teach about angles. I recommend the channel "Math Rio with Prof. Rafael Procopio". Here is the link to one of his lessons on angles: Angles - Math Rio.

Let's embark on this adventure and discover the beauty and relevance of angles together!

Hands-on Activity

Activity Title: "Angle Detectives"

Project Goal

The goal of this activity is to provide a hands-on and engaging way for students to learn how to identify and understand different types of angles.

Detailed Project Description

Students will be grouped (3-5 students per group) and transformed into "Angle Detectives". Their task will be to find, identify, and classify different types of angles in their immediate surroundings. This could be in the classroom, around the school, or even in their homes.

Each group will document their findings in an "Angle Detective Report", which will include pictures, drawings, and explanations of where they found the angles and how they identified and classified each one.

Required Materials

• Paper and pencils
• Ruler
• Protractor (an instrument for measuring angles)
• Camera or cell phone for taking pictures (optional)

Detailed Step-by-Step Activity

Step 1: Gather your group and discuss the different ways you can find angles in your surroundings. This could be an open door, the meeting of two walls, the corner of a piece of paper, etc.

Step 2: Distribute the necessary materials (paper, pencils, rulers, and protractors) among the group members.

Step 3: Begin your angle hunt. Whenever you find an angle, use the protractor to measure its opening and classify it (for example, a right angle has 90 degrees).

Step 4: Record your findings in the "Angle Detective Report". Include where the angle was found, a description or picture of the angle, its measurement with the protractor, and its classification.

Step 5: Repeat steps 3-4 until your group has identified and classified at least 10 different angles.

Step 6: Regroup with your team and discuss your findings. Each member should share one angle they found, describing where they found it, how they measured it, and how they classified it.

Step 7: As a final project, each group must prepare a final report. This report should include:

• Introduction: The student should contextualize the topic, its relevance and application in the real world, as well as the objective of this project.
• Development: The student should explain the theory behind angles, explain the activity in detail, indicate the methodology used and, finally, present and discuss the results obtained.
• Conclusion: The student should conclude the work, resuming their main points, explaining the lessons learned and the conclusions drawn about the project.
• Bibliography: The student should indicate the sources on which they relied to work on the project, such as books, web pages, videos, etc.

The total duration of the project is estimated at five to ten hours per student, and the deadline will be one month after the start date.