Contextualization

Mathematics is a fascinating science full of curiosities, one of which is the study of cylinders and their metric relationships. A cylinder is a geometric solid that has two identical parallel bases, called the cylinder bases, and a single lateral surface, called the lateral area. Moreover, the cylinder is a geometric figure that frequently appears in various contexts of our daily lives.

From a mathematical point of view, the cylinder is relevant because it is an object that possesses unique properties and metric relationships. Studying these relationships allows us to better understand the shape of the cylinder and its structure, enabling us to use this information in various everyday situations. For example, we can use the metric relationships to calculate the amount of material needed to build a cylindrical can or the amount of water a cylindrical reservoir can hold.

In the real world, cylinders are present in various objects and structures around us, such as soda cans, PVC pipes, light poles, and observation towers. Furthermore, the metric relationships of the cylinder are used in various fields of knowledge, such as engineering, architecture, and physics. Therefore, understanding these relationships and knowing how to apply them is an important and useful skill.

You can use the following resources to delve into the study of cylinders and their metric relationships, as well as to assist in the development of the project:

• Book "Geometria Espacial: métrica" by Manoel Jairo Bezerra.
• Website "Mundo Educação" Cylinders – Mundo Educação
• Website "Só Matemática" Cylinders – Só Matemática
• Videos from the channel "Matemática Rio", such as How to calculate the area of a cylinder in less than three minutes?

Practical Activity

Activity Title:

"Cylinders: From Theory to Practice"

Project Objective:

Analyze, understand, and apply the metric relationships related to cylinders.

Detailed Project Description:

Students will build a cylinder with recycled materials, apply the learned concepts of metric relationships in class to calculate the properties of their cylinder, and finally, produce a detailed report on the process.

Required Materials:

1. Cardboard or cardstock
2. Adhesive tape
3. Ruler
4. Calculator
5. Pen and paper for notes
6. Camera or cellphone to document the process

Detailed Step-by-Step for Activity Execution:

Step 1: Form groups of 3 to 5 students.

Step 2: In your group, choose a real cylindrical object and measure it. Examples: a soda can or a PVC pipe. Take note of the measurements.

Step 3: Using cardboard or cardstock and adhesive tape, build a cylinder model that reproduces the dimensions of the chosen object.

Step 4: Calculate the properties of the cylinder (base area, lateral area, total area, and volume) using the metric relationships learned in class.

Step 5: Document the entire process, recording each step with photos and notes.

Step 6: Prepare a report on the project. It should include:

1. Introduction: Provide context on the theme, its relevance and real-world application, as well as the objective of this project.

2. Development: Explain the theory behind the central theme of the project, detail the activity, indicate the methodology used, and finally, present and discuss the results obtained.

3. Conclusion: Conclude the work by summarizing its main points, explaining the learnings acquired, and drawing conclusions about the project.

4. Bibliography: List the sources you relied on to work on the project such as books, web pages, videos, etc.

The project must be submitted within a week from the project start date. The expected hourly workload per student is two to four hours.

By the end of the project, it is expected that students have acquired the technical knowledge to calculate metric relationships in cylinders and socio-emotional skills such as time management, communication, problem-solving, creative thinking, and proactivity.

The project evaluation will be based on the accuracy of the calculations, the quality of the constructed cylinder model, the clarity and depth of the report, and collaboration and teamwork.

Remember, mathematics is a language that allows us to describe the world around us in a precise and complete way, and this project is an opportunity to experience that in practice.

Good luck and have fun!