Context

To understand our daily lives, we often turn to Mathematics. And one of the most versatile tools that Mathematics offers us is the 'Rule of 3', especially its variation 'Indirect'. Do you know what this is and how it helps us make decisions and understand the world around us?

The Rule of 3 is a systematic way to solve problems involving the proportionality between quantities. When these quantities are inversely proportional, we have the so-called Indirect Rule of Three. But what does that mean? When we talk about indirect or inverse proportion, we mean that when one value increases, the other decreases in the same proportion, and vice versa. Still seems complicated? Don't worry, let's dissect this concept together with a lot of practice!

Imagine you have a corn plantation and that the watering time directly influences the growth of these plants. If you increase the watering time, the plants grow more. But if you decrease it, the plants grow less. This is an example of a direct rule of three. However, if we think about the time needed for the plantation to be harvested, we see an inverse relationship. If the plants are watered for a longer time and, therefore, grow faster, the time until harvest is reduced. And if the plants are watered for a shorter time and grow more slowly, the time until harvest is increased. This is the essence of the indirect rule of three!

The application of the indirect rule of three is vast and essential for our daily lives. To cite just a few examples: it is used to calculate travel time considering the vehicle's speed, to understand how the quantity of ingredients in a recipe affects the number of servings we can make, to calculate the relationship between study hours and performance on a test, and many others. The indirect rule of three is a powerful tool that allows us to model and predict the behavior of inversely proportional quantities.

But how can we truly learn to apply this rule? The most efficient way to learn Mathematics is by getting hands-on, applying the concepts in real situations. For this, we propose an interesting project that will involve not only Mathematics but also the discipline of Portuguese.

For further exploration on the topic, here are reliable resources:

• Book: 'Mathematics: context & applications' by Luiz Roberto Dante. Ática Publisher.
• Website: Khan Academy. You can find various exercises on the indirect rule of three.

Practical Activity

Activity Title: The Show of the Indirect Rule of Three

Project Objective:

This activity aims to help you understand and apply the indirect rule of three in a playful and meaningful way. Additionally, we seek to stimulate group collaboration, written communication, and time management. Finally, this project also aims to develop your ability to solve problems and think creatively.

Project Description:

Each group must create a script for a short film that illustrates the application of the indirect rule of three in the real world. You will have total freedom to choose the context, but remember that it must be relevant and realistic.

The short film's story should involve at least four different types of situations where the use of the indirect rule of three is necessary. In addition, the script should be well elaborated, containing dialogues, descriptions of the characters and scenarios, and the actions that will take place during the story.

After creating the script, you will need to produce the short film. For this, you can use cell phones to film and basic video editing programs, such as Windows Movie Maker or iMovie. The video should be at least 10 minutes long.

The last part of the project consists of writing and delivering a report detailing the process of creating, producing, and analyzing the short film. The report should have at least 1500 words and follow the structure of: Introduction, Development, Conclusion, and Bibliography.

Required Materials:

• Paper and pen to develop the script.
• Cell phones or cameras for filming.
• Computer with video editing software.
• Books and online resources for consultation and research.

Step by Step:

1. Form groups of three to five members.
2. Among all, choose a realistic context for the story and start thinking about the situations where the indirect rule of three can be applied.
3. Develop the story and write the script for the short film. If necessary, consult books and online resources to ensure that the application of the indirect rule of three is correct in the created situations.
4. Plan and produce the short film. Be creative when filming and editing the video.
5. After finishing the video, start writing the report. Remember to describe in detail the entire process of creating and producing the short film, the applications of the indirect rule of three in the story, and the conclusions drawn from this project.
6. Submit the report and the video to the teacher on the agreed date.

Project Deliverables and Connection with the Activity:

In the end, each group must deliver the produced short film and the written report. In the report, students should describe how they applied the indirect rule of three in the situations created for the short film and how this tool helped solve problems in the context of the story. Additionally, they should reflect on the process of creating and producing the video, discussing the difficulties encountered and how they managed to overcome them.

The report should follow the format of Introduction (contextualizing the theme and the project's objective), Development (explaining the theory of the indirect rule of three, detailing the activity, the methodology used, and presenting and discussing the results obtained), Conclusion (summarizing the main points, explaining the learnings obtained, and drawing conclusions about the project), and Bibliography used.

This project offers students the opportunity to explore the application of the indirect rule of three in a practical and playful way, while developing important skills such as teamwork, research, problem-solving, written and oral communication, creativity, and time management.