Contextualization
A figure that is very present in our daily lives is the circle. It can be found in car wheels, clocks, bottle caps, among many other objects. But have you ever stopped to think about what a circle is, how to draw it, or what its properties are?
The circle is defined as a set of points in the plane equidistant from a central point, known as the center of the circle. The line segment that connects the center to any point on the circle is called the radius, and the line segment that connects two points on the circle passing through the center is known as the diameter.
To draw a circle with radius R, we take any point on the paper that will be the center of the circle, then we extend the compass to a length that will be the measure of radius R and rotate the compass 360° keeping the point fixed at the center. There you have a circle.
Importance of Circles in the Real World
Circles are not only relevant in the academic world but also in the real world. It is a shape that can be seen in various places. For example, the Earth orbits the Sun in an orbit that is approximately a circle. Car wheels are circles. Have you ever thought about what the world would be like without circles?
The concepts of circles are fundamental for engineering, architecture, astronomy, among other areas. Understanding circles and their properties helps in solving various practical problems, such as calculating the area of a circle or the distance a wheel travels in each rotation.
Practical Activity
Activity Title: "Circles in the Real World: Building and Understanding"
Project Objectives:
- Understand the concept of a circle.
- Understand the elements of a circle such as radius, diameter, and chord.
- Know how to use a compass to draw circles.
- Apply circle concepts to real-world problems.
- Develop teamwork and time management skills.
Detailed Project Description:
This project will be carried out in groups of 3 to 5 students and has an estimated duration of 12 hours. The project consists of two parts: a theoretical part and a practical part, which complement each other.
In the theoretical part, students should research the concept of a circle, its properties, and its elements (radius, diameter, chord). Students should include in the report the formal definition of a circle, as well as the application of circles in the real world.
In the practical part, students should carry out modeling and measurement activities of circles.
Required Materials:
- Paper
- Compass
- Ruler
- Pencil
- Colored pens
Detailed Step-by-Step for Activity Execution:
Step 1: Theoretical Research
Research the concept of a circle, its components (radius, diameter, chord), and its properties. Each group should prepare an oral presentation on the topic.
Step 2: Modeling Circles
Each group should find and bring to the classroom 5 objects that have a circular shape (e.g., bottle caps, CDs, etc.). Draw the circle of these objects on paper using the compass, marking the center, radius, and diameter.
Step 3: Measurement of Circles
Using the ruler, measure the radius and diameter of the drawn circles. Record the values and compare them with the actual measurements of the objects.
Step 4: Practical Applications of Circles
Research the use of circles in different real-world contexts (engineering, architecture, sciences, etc.). Write a short text about the importance of circles in these areas.
Step 5: Final Report
Prepare a final report that includes the following topics: Introduction, Development, Conclusions, and Bibliography used.
The Introduction should explain what a circle is, the relevance of circles in the real world, and the project's objective.
In the Development, bring the theory about circles and their elements, describe the activity carried out in detail, presenting the methodology and the results obtained.
In the Conclusion, it is necessary to summarize the main points of the report, explain the learnings, and draw conclusions about the project.
The Bibliography should list the research sources for the project work.
