Contextualization

First-degree equations are the "golden key" to enter the world of algebra. With them, you have the ability to translate real-world situations into mathematical language and vice versa. It is a powerful tool that, when fully understood, can open the door to more advanced topics.

A first-degree equation is a mathematical sentence that expresses the equality between two algebraic expressions formed by additions or subtractions of products of real numbers by symbols. This usually follows the form ax + b = 0, where a ≠ 0. In first-degree equations, the variable x is always to the first degree. Mastering these equations prepares us to understand the principles of problem-solving, mathematical modeling, and also helps us understand more advanced concepts.

In the real world, first-degree equations are generally used to solve problems that require a solution to an uncertain situation. For example, we can use these equations to determine the amount of money needed to buy a specific number of items at a certain price. It can also be used to calculate the distance an object travels given a certain time and speed.

Mastering first-degree equations provides a solid foundation for solving more complex problems in mathematics and, more broadly, in exact sciences. Having a clear understanding of first-degree equations can make learning more advanced topics less intimidating and more accessible.

Students can use the following resources to delve deeper into the subject:

• Khan Academy: First-Degree Equations
• Brasil Escola: First-Degree Equation
• Youtube - Matemática Rio with Prof. Rafael Procopio: First-Degree Equations - Part 1
• Youtube - O Matemático: First-Degree Equation: complete summary
• Free Enem Course: First-Degree Equation

Dedicate yourselves, study hard, and don't hesitate to ask whenever doubts arise. Mathematics is a universal language, and you are completely capable of mastering it!

Practical Activity: "Equating the World"

Project Objective

In this project, students will divide into groups of 3 to 5 members and will have the challenge of creating a story that involves first-degree equations in the context of real problems. The idea is for students to apply the theory of first-degree equations in a practical and playful way.

Detailed Project Description

The story should be rich in details and should contain five problems, each being an example of a situation that can be solved using a first-degree equation. Students must provide the solution to each problem within the story itself, clearly indicating how the equation was formulated from the described scenario, showing the process of solving it, and interpreting the solution in the context of the story.

Materials Needed

• Notebook and pencil for notes during the discussion and creation of the story.
• Computer or tablet with text processing software (such as Google Docs, Word) for the elaboration and final presentation of the story.
• Textbooks, internet for research and references.

Detailed Step-by-Step for Carrying Out the Activity

1. The first step is to form the groups. Each group of students should have between 3 to 5 participants.

2. Next, the groups must choose a theme for the story. The theme is free, as long as it is possible to create situations that can be translated into first-degree equations.

3. After the theme is chosen, the groups must create five distinct problems that will involve first-degree equations and insert these problems into the story.

4. Each problem must be clearly described, and after its description, the students must present the transcription of the problem into a first-degree equation, show step by step how to solve this equation, and finally, interpret the solution in the context of the story.

5. The activity should be developed during the week, and the presentation of the story should be made in the next math class.

6. Finally, the groups must write a report describing the process of creating the story and the resolution of the problems. In the report, students should address the theme of the story, the problems created and how they were solved, and what were the most significant learnings of the group in the face of the activity. The report should follow the structure of: Introduction, Development, Conclusions, and Bibliography.

Project Deliverables

• Creative story containing five problems involving first-degree equations, with the solution and interpretation for each one described in detail.
• Written report explaining the process of creating the project and its results.

The report should be structured as follows:

1. Introduction: Students must contextualize the chosen theme for the story, the relevance and application of first-degree equations in the real world, and the objective of the activity.

2. Development: Students must explain the theory of first-degree equations, detail the problems created, indicate the methodology that was used to solve the problems, and the results obtained.

3. Conclusion: Students must explain the learnings obtained and the conclusions drawn about the project.

4. Bibliography: Students must indicate the sources they relied on to work on the project such as books, web pages, videos, etc.

This project was designed to fit a working time of two to four hours per participating student, therefore, it is ideal to be carried out during one week.