Lesson Plan | Technical Methodology | Perimeter: Circle

Objectives

Duration: 10 - 15 minutes

The purpose of this stage of the lesson plan is to introduce students to the fundamental concept of the ratio between the perimeter and the diameter of the circle, which results in the value of π, and empower them to calculate the perimeter of any circle. This promotes the development of practical and applicable mathematical skills, essential in various areas of the job market, such as engineering, architecture, and design, where accuracy in measurements is crucial.

Main Objectives

1. Verify that the ratio of the perimeter to the diameter of the circle is π.

2. Calculate the perimeter of the circle.

Side Objectives

1. Familiarize with the formula for the perimeter of a circle.
2. Develop the ability to measure and calculate using practical instruments.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage of the lesson plan is to introduce students to the fundamental concept of the ratio between the perimeter and the diameter of the circle, which results in the value of π, and empower them to calculate the perimeter of any circle. This promotes the development of practical and applicable mathematical skills, essential in various areas of the job market, such as engineering, architecture, and design, where accuracy in measurements is crucial.

Contextualization

Imagine you are drawing a circular racetrack. To ensure that the runners cover the correct distance, you need to calculate the length of this track. This length is what we call the perimeter of the circle. Knowing how to calculate the perimeter of a circle is essential in many practical situations, such as building roads, creating circular designs, and even in bridge and tunnel engineering.

Curiosities and Market Connection

️ Curiosities and Connection to the Market ️ History of π: The value of π (pi) is a mathematical constant that has been studied for over 4,000 years, starting with the ancient Babylonians and Egyptians. Applications in Engineering: Civil engineers and architects use the perimeter of circles to design circular structures, such as sports arenas and highways. Design and Art: Graphic designers often use circles and need to know how to calculate their perimeters to create patterns and symmetrical shapes. Technology and Robotics: In robotics, knowing the perimeter of circular wheels is crucial for calculating the distance traveled by mobile robots.

Initial Activity

 Initial Activity: Show a short video (2-3 minutes) demonstrating how π is used in different professions, such as engineering and design. After the video, ask the following provocative question: "How do you think the ancients discovered that the perimeter of a circle is always related to its diameter?" Encourage students to discuss their ideas in small groups and then share with the class.

Development

Duration: 50 - 60 minutes

The purpose of this stage of the lesson plan is to provide students with a practical and applied understanding of the concept of the perimeter of a circle, developing their skills in measurement, calculation, and comparative analysis. This prepares them to face real challenges in various areas of the job market where precision and the ability to perform calculations are essential.

Covered Topics

1. Definition of the perimeter of a circle
2. Formula for the perimeter of a circle (C = 2πr or C = πd)
3. Ratio between the perimeter and the diameter (π)
4. Practical applications of calculating the circumference of circles

Reflections on the Theme

Encourage students to reflect on the importance of calculating the perimeter in various fields of knowledge and the job market. Ask how understanding the perimeter can help in professions such as engineering, architecture, product design, and even in programming robots. Inspire them to think of specific examples, such as building a Ferris wheel or designing a sports stadium.

Mini Challenge

Building Circles and Calculating Perimeters

In this practical activity, students will build circles of different sizes using simple materials and calculate their perimeters. They can use strings, rulers, and calculators to measure and perform the necessary calculations.

Instructions

1. Divide the class into groups of 3 to 4 students.
2. Distribute strings, rulers, scissors, and calculators to each group.
3. Ask the students to choose three different sizes of circles to create (small, medium, and large).
4. Guide the students to form circles with the strings and measure the diameters of each circle using rulers.
5. With the measured diameters, students should calculate the perimeters of the circles using the formula C = πd. Remind them to use π ≈ 3.14.
6. Ask students to record the results in a table for comparison.
7. Guide the groups to discuss the differences and similarities found between the circles of different sizes.

Objective: Enable students to apply the formula for the perimeter of a circle in practice, developing measurement, calculation, and comparative analysis skills.

Duration: 35 - 40 minutes

Evaluation Exercises

1. Calculate the perimeter of a circle with a diameter of 10 cm.
2. A circle has a radius of 7 cm. What is its perimeter?
3. If the perimeter of a circle is 31.4 cm, what is its diameter?
4. Draw a circle with a radius of 5 cm and calculate its perimeter.

Conclusion

Duration: 10 - 15 minutes

The purpose of this stage of the lesson plan is to consolidate the students' learning by reinforcing the theoretical and practical concepts discussed throughout the lesson. This stage also aims to promote reflection on the application of the knowledge acquired in real situations and in various professions, encouraging students to recognize the relevance and importance of the content learned.

Discussion

 Discussion on the Topic: Foster a discussion about how the calculation of the perimeter of a circle can be applied in different professions and everyday situations. Question the students about what they found most challenging in the practical activity and how they overcame those challenges. Encourage them to reflect on the importance of precision in calculations in fields such as engineering, architecture, product design, and robotics. Ask: 'How can you use what you learned today in a real situation?'

Summary

 Summary: Recap the main concepts covered in the lesson, such as the definition of the perimeter of a circle, the formula for calculating the perimeter (C = 2πr or C = πd), and the constant ratio between the perimeter and the diameter (π). Reinforce the importance of knowing how to measure correctly and use the formula to solve practical problems.

Closing

 Closing: Explain how the lesson connected theory with practice and real applications. Emphasize that understanding the perimeter of circles is fundamental not only for mathematics but also for various fields of knowledge and the job market. Conclude by highlighting the importance of developing practical and applicable skills that are essential for solving everyday problems and facing professional challenges.