Contextualization

Introduction

The Rule of Three is a fundamental concept in mathematics that is a practical process for solving problems involving four values directly or inversely proportional, of which we know three. Thus, the rule of three allows us to discover a fourth value from three others that are interrelated in a certain way.

To apply the Direct Rule of Three, we need to remember that quantities are directly proportional when the increase or decrease of one produces a proportional increase or decrease in the other. Thus, if we have two directly proportional quantities, the ratio between them is always constant.

Knowing the rule of three and having the perception to identify when quantities are directly or inversely proportional, it becomes possible to solve a multitude of problems we encounter in everyday life, from calculating distances on trips to financial management.

Contextualization

The Direct Rule of Three is an essential tool in many areas of practical application. It is frequently used in daily life, at school, at work, and in various professions. For example, in cooking, it is essential to adjust the proportions of ingredients in a recipe. In agriculture, it is used to calculate the amount of seeds or fertilizers needed for a specific area. In finance, it is used to calculate interest and yield rates.

Furthermore, the Direct Rule of Three is also fundamental for understanding and analyzing graphs and tables, which is essential for any area involving data interpretation, from economics to physics.

Practical Activity

Activity Title: "The Mathematics Behind Performance"

Project Objective

The objective of this activity is to create a clear and practical understanding of the Direct Rule of Three through the development of a project in which students will calculate and analyze the performance of a marathon runner.

Detailed Project Description

In groups of 3 to 5 people, students will collect data from marathon races (such as time, distance, and speed) and use the Direct Rule of Three to determine the relationship between these elements. Additionally, they will predict the runner's performance in different scenarios, such as running a longer or shorter distance, or running the same distance but in a different time.

Required Materials

• Internet access for data research.
• Calculator.
• Paper and pen for note-taking and calculations.
• Spreadsheet software (such as Microsoft Excel or Google Sheets) to analyze data and present results.

Detailed Step-by-Step for Activity Execution

1. Choose a famous marathon runner and research their race times and distances in different marathons.
2. Based on this data, calculate the runner's average speed in each marathon.
3. Use the Direct Rule of Three to predict the time the runner would take to run different distances (e.g., 5km, 10km, 21km, etc.).
4. Use the Direct Rule of Three to predict the distance the runner could run in different times (e.g., 30 minutes, 1 hour, 2 hours, etc.).
5. Present your calculations and results in a spreadsheet.
6. Prepare a detailed report following the guidelines below.

Project Deliverables and Report Guidelines

To demonstrate your understanding of the project and articulation of the subject, you will present a written report containing the following sections:

1. Introduction: Present the chosen runner, their performances in marathons, and discuss the importance of the direct rule of three in this scenario.
2. Development: This section should include the theory used, the project methodology, the calculations performed, the analysis of the results obtained, and relevant discussions. Use tables and graphs to make your findings visible and clear.
3. Conclusion: Summarize the main points and reflect on the skills acquired, such as the application of the direct rule of three in problem-solving, time management, teamwork, and effective communication.
4. Bibliography: List the sources consulted during the project, such as websites, books, videos, etc.

This project should take two to four hours to complete, and the deadline is one week. Reminder: The goal is not only to get the calculations right but also to demonstrate an understanding of the process and skills acquired during the completion of this activity.