Contextualization

Mathematics is a discipline extremely related to our daily lives. Whether it's deciding the fastest route to work, calculating the best angle to throw a ball, or even identifying how many slices of pizza we still have on the table. All of this leads us to the importance of a specific topic in mathematics: angles.

Angles are geometric structures formed by two half-lines that meet at a point. Depending on the angle formed, it can be acute, right, or obtuse. Furthermore, in some situations, angles can be supplementary or complementary. But don't worry! We will explore each of these concepts during the execution of our project.

The study of angles is important in various areas of knowledge, such as architecture, engineering, sports, among others. In architecture, for example, angles are used for the construction of safe and well-designed structures. In sports, the angle at which a player throws a ball can be the difference between scoring a goal or not. Therefore, understanding these concepts and knowing how to apply them is very important.

Introduction

In geometry, an angle is the figure formed by two half-lines that have the same origin. The measure of angles is the way to quantify the opening between these half-lines and is expressed in units of degrees (°) or radians (rad). There are several types of angles based on their measure, including acute, right, obtuse, and straight angles.

Learning about angles and their properties is fundamental for understanding various other areas of mathematics and even sciences, such as physics. From solving problems involving triangles to understanding the rotation of objects in space, the concept of an angle is crucial.

Angles are also used in solving everyday problems. For example, architects and engineers use angles to design safe and aesthetic structures. Additionally, even athletes use the notion of angles to improve their performance in games and sports.

Suggested resources for further exploration on the topic:

• Khan Academy: Khan Academy has a section in Portuguese and completely free dedicated to geometry, available at this link.

• Book 'Math Topics for Elementary School': This book, authored by Antônio Caminha Muniz Neto and Manfredo Perdigão do Carmo, can be found in online stores and brings a series of exercises and explanations about angles and other topics.

• Just Mathematics: This site has several explanations about the concept of angles, their types, and applications.

Practical Activity

Activity Title: 'Angles Journey'

Project Objective

The objective of this activity is to explore the concept and properties of angles in a practical and playful way, applying this knowledge in a real context. Students should combine knowledge of Mathematics and Arts, creating a 'Shadow Theater' that will represent scenarios with different situations involving angles.

Detailed Project Description

This project will be carried out in groups of 3 to 5 students. Detailed planning and good time management will be necessary to ensure that all tasks are completed within the proposed time.

Students will create a Shadow Theater representing different situations involving angles. Each group must invent a story where the characters face challenges involving the use of angle knowledge (angle measurement, complementary and supplementary angles, types of angles, etc.). When presenting the shadow theater, students must demonstrate how the angle concepts were applied in the challenge presented in each scene.

In addition, each group must prepare a detailed report on the project, including:

• The introduction and relevance of angles in real life and in the story created for the theater.
• The theoretical concepts used during the activity.
• The relationship between the use of angles in the story and their representation in practice.
• The conclusions drawn from the activity.

Required Materials

• Black cardboard paper
• Wooden sticks (can be barbecue sticks)
• Tape
• Scissors
• Pencils and erasers
• Protractor to measure angles
• Lamp or flashlight
• A4 paper sheets for the report
• Computer with internet access for research

Detailed Step-by-Step for Activity Execution

1. Activity Start: After forming the groups, each one should start planning their story. Remember that different angle concepts must be applied in the story situations, meaning that the characters must face and solve problems involving angles.

2. Story Planning: Each group must outline the story that will be represented in the Shadow Theater. In addition, students must list and describe each situation involving angles.

3. Creation of Characters and Scenarios: Using black cardboard paper, each group must create the characters and elements of the scenario that will be used in the shadow theater.

4. Assembly of the Shadow Theater: With all elements ready, the group must assemble the Shadow Theater. It is important that the lamp or flashlight is positioned in a way to project the shadows of the characters and scenarios on the wall.

5. General Rehearsal: The group must rehearse the presentation of the Shadow Theater several times, becoming familiar with the narrative and scene transitions.

6. Shadow Theater Presentation: Each group will present their play to the class. During the presentation, students must explain how the angle concepts were applied in each situation.

7. Writing the Report: After the presentation, each group must prepare a detailed report on the project.

Project Deliverables

In addition to the Shadow Theater presentation, each group must deliver a report containing:

1. Introduction: Explain what angles are and their importance in our daily lives and how they apply to the created story.

2. Development: Include a detailed description of the story created, and explain how angle concepts were applied in each situation. Report on the methodology used for the creation and presentation of the Shadow Theater and discuss the results obtained.

3. Conclusion: Here, recap the main points of the story, and explain what was learned and what conclusions could be drawn throughout the project.

4. Bibliography: Include all sources of information used to support the work. This includes books, web pages, videos, etc.

Remember that the report must be written clearly and in detail, ensuring that all angle concepts and applications used are well explained and supported with references.