Lesson Plan | Technical Methodology | Angles: Clocks

Objectives

Duration: 10 - 15 minutes

The aim of this stage of the lesson plan is to ensure that students understand the importance of the angles formed by the clock hands, applying mathematical concepts in practical situations. Developing these skills is essential to prepare students for real challenges in the job market, such as in engineering, design, and technology, where precision and geometric analysis are critical.

Main Objectives

1. Understand the relationship between hours and angles, applying mathematical concepts to calculate the angle formed by the clock hands.

2. Develop practical skills in calculation and geometric analysis, using clocks as a learning tool.

Side Objectives

1. Stimulate critical thinking and problem-solving through mini practical challenges.
2. Promote collaboration among students in maker activities that involve building clock models.

Introduction

Duration: 15 - 20 minutes

The aim of this stage of the lesson plan is to introduce students to the topic in an engaging manner, showing the practical relevance and applications in the job market. This approach aims to spark students' interest and curiosity, preparing them to deepen their knowledge in the upcoming activities.

Contextualization

Clocks are fundamental instruments in our daily lives, used to measure and organize time. The mathematics behind clocks, specifically the relationship between the angles formed by the hands, is a clear example of how mathematical concepts are applied in practical situations. Understanding how to calculate these angles helps us develop analytical and precision skills, essential in various professions.

Curiosities and Market Connection

Did you know that the concept of angles in clocks is widely used in fields such as engineering and aeronautics? For example, in mechanical engineering, the precision of angles is crucial for the functioning of gears and engines. In aviation, accurate angle measurements are vital for navigation and aircraft control. These examples show how understanding the angles formed by clock hands can be applied in advanced technological fields.

Initial Activity

To start the class, present a short video (1-2 minutes) that shows the application of angles in clocks in mechanical engineering and aviation. After the video, pose a provocative question: 'How do you think precision in angle calculations can impact safety in different professional fields?' Encourage students to reflect and quickly share their ideas.

Development

Duration: 60 - 70 minutes

The aim of this stage of the lesson plan is to deepen students' understanding of the angles formed by clock hands through practical and collaborative activities. This aims to develop their analytical and problem-solving skills, preparing them for real situations in the job market.

Covered Topics

1. Concept of angles in clocks.
2. Calculation of the angle formed between the hour and minute hands.
3. Practical applications of angle calculations in different professional areas.

Reflections on the Theme

Guide students to reflect on how precision in angle calculations can influence efficiency and safety in various professions, such as engineering, design, and aviation. Question how understanding these concepts can be useful in their future careers and everyday life.

Mini Challenge

Building an Analog Clock

Students will build a model of an analog clock using simple materials such as paper, cardboard, ruler, and compass. The goal is for them to visualize and physically manipulate the hands, facilitating the understanding of the angles formed between them.

Instructions

1. Divide the students into groups of 3-4 people.
2. Distribute the necessary materials: paper, cardboard, scissors, ruler, compass, pencil, and glue.
3. Guide each group to draw a large circle on the cardboard, representing the clock face.
4. Ask them to mark and number the hours from 1 to 12 around the circle.
5. Using the paper, guide the students to create two hands: one for the hour and another for the minute. The hands should be attached to the center of the clock with a pin, allowing them to rotate freely.
6. Challenge the groups to position the hands at different times and calculate the angles formed. For example, 08:15, 12:34, etc.
7. Ask them to record their calculations and discuss the differences and similarities in the angles at different times.

Objective: Facilitate the practical understanding of the angles formed by the clock hands, encouraging collaboration and the application of mathematical concepts in a maker project.

Duration: 30 - 35 minutes

Evaluation Exercises

1. Calculate the angle formed between the hands at 03:00.
2. What is the angle between the hands at 06:30?
3. Determine the angle at 09:45 and explain your reasoning.
4. Calculate the angle formed at 02:20.
5. What is the smallest angle formed between the hands at 11:15?

Conclusion

Duration: 10 - 15 minutes

The aim of this stage of the lesson plan is to consolidate the knowledge acquired by students, ensuring they understand the importance and practical application of the studied concepts. By promoting reflection and discussion on the topic, the goal is to strengthen learning and stimulate ongoing interest in mathematics and its applications in the job market.

Discussion

Promote an open discussion about the concepts addressed in the lesson, encouraging students to reflect on the importance of precision in angle calculations and how this applies in different professional fields. Ask students how they felt while performing the practical activities and what difficulties they encountered. Encourage them to share their experiences and insights about the mini challenge of clock construction and the fixation exercises.

Summary

Recap the main topics covered, such as the concept of angles in clocks, the formula for calculating the angle between the hands and the practical applications of these calculations in fields like engineering and aviation. Emphasize the importance of understanding the mathematics behind angles to develop analytical and precision skills.

Closing

Explain to the students how the lesson connected theory, practice, and applications, showing the relevance of the knowledge acquired for the job market. Highlight the importance of continuing to develop these skills and how they can be useful in everyday life and in their future careers. Encourage students to continue exploring the topic and applying the concepts learned in different contexts.