Contextualization

Hello students, today we will start an exciting project about measuring angles, a fundamental concept in mathematics, but also present in various situations in our daily lives.

Introduction

In mathematics, angles are a measure of rotation between two intersecting lines, known as rays. The standard unit of angle measurement is the degree (°) and the instrument used to measure them is the protractor. However, do you know how this instrument works? Throughout this project, we will understand not only how to use it, but also the concepts behind this mathematical tool.

In angle measurement, there are some key concepts that we need to understand. The first one is the angle itself, which can be classified into several categories, such as right angle (90°), acute (less than 90°), or obtuse (more than 90°). Additionally, there are ways to calculate angles through triangles and other geometric figures.

In the second part of this project, we will address concepts related to analytical geometry, a branch of mathematics that studies the properties of geometric figures through their positions in a coordinate system. As part of this study, we will understand how angles are fundamental for defining the positions of points and studying the relationships between them.

Contextualization

But how can this knowledge be applied in real life? Well, the answer is simple: everywhere! Angle measurement is used in various areas, such as engineering for construction projects, in physics to understand the behavior of waves and light, in astronomy to measure the position of stars, and in many other situations.

In fact, sports like soccer and basketball use angle concepts to determine the best way to kick a ball or make a basket. Even in everyday activities, such as driving a car or playing video games, we use these concepts, often without realizing it. Therefore, understanding how to measure and interpret angles is an extremely useful skill.

Activity

Title: Navigating through Angles

Project Objective

This project aims to deepen the understanding of angle measurement and its application in practical situations through the design and construction of a navigation device. This project will combine knowledge of mathematics, specifically geometry, with physical science and art materials to create something tangible.

Detailed Project Description

Students will be divided into groups of 3 to 5, and each group will be tasked with creating an 'angular navigator,' a device that can be used to measure angles. This device will then be used in a series of navigation challenges that require precision in angle measurement.

The groups will have to research how angles are measured and related concepts, such as right, acute, and obtuse angles, analytical geometry, and their applications to make a project of their device. Once built, they will have to test their navigator in a series of challenges, documenting their results.

Finally, the groups will have to prepare a detailed report covering all the work done, including theoretical concepts, device design, testing and results obtained, as well as final conclusions. This process will require research, planning, construction time, testing, and report writing.

Required Materials

• Cardboard
• Pencils, pens, and/or markers
• Protractor
• Ruler
• Compass
• Adhesive material (Tape, Glue)
• Scissors

Step by Step

1. Research and Planning: Groups should start by researching angle measurement, types of angles, and their applications. They should understand how analytical geometry applies to angle measurement and how mathematics and physics interrelate in this context.

2. Project Creation: Based on their research, each group should propose a design for their angular navigator, which should be presented to the teacher for approval. The design should be detailed, with all parts clearly identified and their functions explained.

3. Device Construction: After project approval, groups should start building their angular navigator using the provided materials. They should ensure that the device is capable of measuring angles accurately.

4. Testing: Once the navigator is ready, groups should test it using a series of navigation challenges chosen by the teacher. They should document their results, including any issues encountered and how they solved them.

5. Final Report: Finally, each group should compile their findings and experiences into a detailed report. The report should include: introduction (project context), development (research, device design, construction, and testing) and conclusions (learnings, results, and how the experience contributed to their understanding of angles).

This project should take more than twelve hours to complete per student, considering the time spent on research, design, construction, testing, and report writing.

Project Deliverables

The project will have two deliverables:

• Device: The angular navigator built by the group.
• Report: A detailed report on the navigator's construction process, including: the research conducted, the device design, test results, and learnings.

The written document should be clear and objective. In it, students should compile all relevant information about the project development, from the research phase to the testing phase. The document should include an introduction explaining the context and relevance of the project, followed by a development section detailing the theory, activity, and methodology used, in addition to the results obtained. Finally, a conclusion should be drawn highlighting the learnings and experiences gained during the project. The report should also include the bibliography used.