Contextualization

Rotation is one of the main geometric transformations that exist and it is widely used in our world as a whole. From the movement of planets around the sun to the operation of a bicycle wheel, rotation is present in many aspects of our daily lives.

In mathematics, rotation is a geometric transformation that involves spinning a shape around a fixed point, called the center of rotation. It is a very important operation in various areas of mathematics and physics, as it helps to understand how things move and change shape.

Introduction

In the context of geometry, rotation can be understood as a transformation that changes the position of a shape without changing its shape or size. Thus, rotation is a type of isometry, a class of transformations that preserve distances.

Rotation is defined by two elements: the center of rotation and the angle of rotation. The center of rotation is the fixed point around which the shape rotates, while the angle of rotation is the measurement of the rotation performed by the shape.

For example, if we have a square and rotate it 90 degrees around its center, we will obtain a new figure that is identical to the original square. Although the figure has changed position, its shape and size remained the same.

Practical Activity: "Spinning Through the World of Mathematics"

Project Objective

The objective of the project is to deeply and entertainingly understand the geometric transformation known as rotation and all its nuances, through the completion of a practical experiment and the production of a final report.

Detailed Project Description

In this project, students will create a stop motion animation using geometric shapes and applying the rotation transformation. The idea is that students can explore, visualize and concretely understand the concept of rotation and its properties.

Stop motion animation consists of capturing several static images and compiling them into a video. The geometric shapes must be moved slowly and in small increments to create the illusion of movement.

Students will need to develop a script for the animation, which must contain at least three different scenes in which the rotation is applied. In addition, the angles of rotation for each scene must be different.

Materials Needed

• Sheets of bond paper
• Color pencils
• Ruler, set square, compass
• Scissors
• Smartphone or digital camera
• Software for creating stop motion videos (can be free and online, such as Stop Motion Studio or JellyCam)

Method - Step by Step

1. Group Formation: Students should form groups of 3 to 5 people.
2. Previous Study: Students should study the concept of rotation and its properties. They can use the resources indicated in the project introduction.
3. Planning: Students should develop the animation script, defining the shapes that will be used, the angles of rotation and the sequence of scenes.
4. Execution: Students should draw and cut the geometric shapes, execute the rotation as planned and photograph each step. Afterwards, they should compile the images using the stop motion software.
5. Report: Finally, students should write a detailed report about the project, contemplating the Introduction, Development, Conclusions and Bibliography.

Project Deliverables

At the end of the project, students must deliver:

1. Stop Motion Animation: A stop motion video that shows the application of rotation in different geometric figures.
2. Report: A written report that includes:
   1. Introduction: The student should contextualize the concept of rotation and its application in real life and in the project.
   2. Development: The student should explain the theory of rotation, describe the activity in detail, indicate the methodology used and discuss the results obtained.
   3. Conclusion: The student should summarize the main points of the work, explain the lessons learned and the conclusions drawn on the project.
   4. Bibliography: The student should indicate the sources used in the project.

This report is essential for students to reflect on the learning process and the application of the concept of rotation in practice. In addition, the report is also an opportunity for students to practice writing, argumentation and information synthesis skills.