Context

Mathematics is a discipline that allows the development of various skills, such as logical reasoning, abstraction, concentration, and problem-solving. Within this discipline, there is a very interesting topic that is present in our daily lives in one way or another: rotations.

Rotations are transformations of the plane or space that move points around a fixed point, called the center of rotation. In this project, we will study this concept and see how it is applied in practice. To begin, let's delve into the basic concepts of rotations. A rotation can be defined as a circular movement around a fixed central point.

But why study rotations? The answer to this question is quite simple: they are present everywhere around us. If you look at any circular object, such as a clock or a wheel, there is rotation in action. They are in the gears of machines, in car engines, and even on Earth, which rotates around its own axis and around the Sun.

To learn more about the subject, some suggested resources that can be used are the book 'Mathematics: Context and Applications' by Luiz Roberto Dante; some videos from the 'Matemática Rio' channel on YouTube; and the Khan Academy platform, which has various exercises and explanations about rotations. Additionally, you can use the GeoGebra software, which allows you to build and visualize geometric figures and perform transformations with them, including rotations.

Our goal with this project is to explore, understand, and apply the concept of rotations in problem-solving, developing not only technical skills but also socio-emotional skills, such as time management, communication, creative thinking, proactivity, among others. How about joining us on this journey? Let's take on this challenge together!

Practical Activity

Activity Title: The Magic of Rotations

Project Objective:

The objective of this project is the understanding and application of the concept of rotations through the construction of a sundial and the preparation of a final report.

Detailed Project Description:

In this project, students will be challenged to create a sundial using rotation concepts. Additionally, it will be necessary to document the entire process in a report.

Groups of 3 to 5 students will be formed. The project will last for one month, with each student dedicating between five to ten hours to complete the work.

Required Materials:

• Cardboard
• Ruler
• Compass
• Pencil
• Scissors
• Barbecue stick
• Glue
• Wristwatch or cellphone (to check the time)
• Computer with internet access (for research)

Detailed Step-by-Step for Activity Execution:

1. Initial Research: The group should research the history and concept of sundials, how they work, and their relationship with the concept of rotations.

2. Sundial Planning: Based on the research, the group should create a sketch of the sundial, defining the dimensions and construction method. This sketch will be used to guide the construction phase.

3. Sundial Construction: Using the necessary materials, the group should build the sundial according to the sketch created.

4. Sundial Testing: The group should test the sundial, comparing the time indicated by the sundial with the time from a regular clock. In this stage, the group should record the results and adjust the sundial if necessary.

5. Report Preparation: Finally, the group should prepare a report documenting the entire process.

Students should describe in detail in the report how each step was executed, pointing out the challenges encountered and how they were overcome, as well as indicating the results obtained and how the concept of rotations was applied in the construction of the sundial.

Project Deliverables:

After completing each stage, students must document the activities carried out, the decisions made, and the results achieved in a final report that should include:

1. Introduction: Contextualization of the theme, relevance and real-world application of the concept of rotations, and project objective.
2. Development: Detailed explanation of the theory on rotations, description of the activity performed, methodology used, and discussion of the results obtained.
3. Conclusion: Recap of the main points of the project, lessons learned, and conclusions drawn.
4. Bibliography: Indication of the sources used for project development.

In addition to the report, the final project deliverable should be the sundial built by the students. Both will be used to evaluate the students' performance, both in understanding and applying the concept of rotations and in the socio-emotional skills developed during the project.