Contextualization

Introduction

The 'Direct Rule of Three' is a very useful mechanism not only in mathematical problems, but in various everyday situations that require quick and direct calculations. It is a simple and effective way to find an unknown in a proportion.

The rule of three is a practical process to solve problems that involve four values, where we know three of them and need to find the fourth value. In direct rule of three, the increase of one quantity implies the increase of the other quantity in the same proportion.

We can apply the direct rule of three to problems involving direct variation between two quantities. That is, the increase or decrease of one quantity results in the proportional increase or decrease of the other quantity. To help you understand better, we will address this in a more detailed and practical way.

Contextualization

The 'Direct Rule of Three' can be seen in various aspects of real life. For example, when planning a trip, we use the direct rule of three to calculate the necessary time based on the average speed and the distance to be traveled; when cooking, the rule of three helps us adjust recipes according to the number of people to be served.

Another example of the application of the 'Direct Rule of Three' can be observed in sports. In soccer, for instance, the direct rule of three can be used to calculate the proportion of goals scored by a player in relation to the number of games played. In this case, if a player scored 5 goals in 10 games, how many goals would he score if he played 20 games?

Practical Activity

Activity Title: 'Direct Rule of Three: a Journey through Everyday Life'

Project Objective

The objective of this project is to apply the direct rule of three in everyday situations to reinforce students' understanding of this important mathematical concept. Additionally, the project will encourage collaboration among students, improve their research and report production skills, and develop socio-emotional skills such as time management and problem-solving.

Detailed Project Description

Students must form groups of 3 to 5 members, and each group must identify 3 everyday situations where the direct rule of three can be applied. The groups should study each of the situations, apply the direct rule of three to solve problems associated with these situations, and prepare a detailed report.

Each group will present their research to the class, explaining the chosen situations, how the direct rule of three was applied, and what the results were.

Required Materials

• Notebook for brainstorming ideas and project development.
• Computer or tablet with internet access for research.
• Various materials, depending on the chosen situations for demonstration (e.g., kitchen utensils for a culinary-related situation, or sports equipment for a sports-related situation).

Detailed Step-by-Step for Activity Execution

1. Form groups and discuss the project objective.
2. Brainstorm to identify everyday situations where the direct rule of three can be applied.
3. Select the 3 most promising situations to proceed with in the project.
4. Investigate each situation, applying the direct rule of three to solve associated problems.
5. Document the work of each step, including the identification of situations, the application of the direct rule of three, and the results.
6. Review and organize notes into a formal report.
7. Prepare a presentation to share the research and results with the class.

In the report, students should include an introduction section contextualizing the subject and detailing the project objective. The development should clearly explain the theory of the direct rule of three, the selected situations, the methodology used, and the results obtained. The conclusion should summarize the main points, explain the learnings obtained, and draw conclusions about the project. Finally, the bibliography where they based their work on the project.

Project Submission

The project submission will be in two parts: a written report and an oral presentation. The report must follow the structure mentioned above and must be submitted in digital format. The oral presentation will be done in the classroom, where each group will explain the chosen situations, how the direct rule of three was applied, and what the results were.

Through the completion of this project, students will have a practical understanding of the direct rule of three and how it can be applied in everyday situations. Additionally, they will learn to work collaboratively, conduct research, and present their findings effectively.