Context

First-degree equations are an essential tool in mathematics, with various practical applications in the real world. They are used to solve practical problems in various disciplines, including economics, physics, engineering, and many others. The general form of a first-degree equation is ax + b = c, where a, b, and c are constants, and x is the variable we want to find.

The first-degree equation is named as such because the highest exponent of the unknown (x) is equal to 1. They are called linear equations because they represent a straight line when plotted on a graph. First-degree equations involve the process of finding the unknown value (or values) that satisfy the condition given in the equation. In other words, we are looking for the value of x that makes the equation true.

To solve a first-degree equation, there are several techniques that can be applied. One of the most common is the isolation technique, which involves rearranging the equation so that the unknown variable is on one side of the equation. Once the equation has been rearranged in this way, it is easy to find the value of the unknown variable simply by performing a calculation.

In practical terms, first-degree equations are everywhere. Imagine you are saving money to buy a new smartphone that costs R$ 1,200.00. You save R$ 100.00 every month. How long will it take to save enough money to buy the smartphone? This is a simple example of a real-world problem that can be solved with a first-degree equation.

We encounter first-degree equations in even more complex situations. From solving engineering problems to defining strategies in companies, these equations are fundamental tools for making data-driven decisions. Learning to solve and apply first-degree equations is a valuable skill that will be useful in a variety of careers and life situations.

Here are some useful resources to help you better understand first-degree equations:

• Khan Academy - First-Degree Equations
• Only Mathematics - First-Degree Equations
• World Education - First-Degree Equations

Practical Activity

Activity Title: "A Mathematical Mystery: The Hunt for Equations"

Project Objective:

The objective of this practical activity is to reinforce students' understanding of first-degree equations through an interactive and fun project, promoting teamwork, creative thinking, and problem-solving. Additionally, through integration with the Portuguese Language discipline, students will develop written communication skills by preparing a detailed project report.

Detailed Project Description:

Students will be divided into groups of 3 to 5 members. Each group will receive a set of riddles that lead to different first-degree equations they need to solve. Each solution will lead to a clue for the next riddle until they reach a final equation that will solve the "Mathematical Mystery".

The activity will be divided into three phases:

1. Discovery Phase (6 hours of work): Students will encounter various situations that need to be translated into first-degree equations. These situations may include stories, real-world problems, logic puzzles, etc.

2. Resolution Phase (4 hours of work): In this phase, students will work together to solve the equations that were formed in the Discovery Phase.

3. Documentation Phase (2 hours of work): Each group will write a detailed project report, aligned with the main topics: Introduction, Development, Conclusions, and Bibliography used.

Required Materials:

• Printed or digital riddles that lead to first-degree equations.
• Writing materials (pencils, pens, paper, etc.).
• Computers or tablets (For research and report preparation).

Detailed Step-by-Step for Activity Execution:

1. Discovery Phase
   • Groups receive the riddles and start deciphering them.
   • Each riddle translated into a first-degree equation marks the progression of the groups.
2. Resolution Phase
   • Groups use their equation-solving skills to find the solutions to each riddle.
   • Each solution leads to the next clue until the final equation.
3. Documentation Phase
   • Groups write a detailed project report, including an introduction with contextualization, the project's objective, and a summary of the activity.
   • The report's development should include an explanation of the first-degree equations and their resolution, the proposed riddles, and the solutions found.
   • The conclusion should highlight the learnings obtained and the conclusions drawn from the project.
   • The bibliography should contain the references of the sources used to understand and solve the first-degree equations.

Project Deliverables:

At the end of the project, groups must deliver the following:

• The resolution of all proposed first-degree equations in the riddles.
• The final solution to the "Mathematical Mystery".
• A written report detailing all project phases, from deciphering the riddles to solving the first-degree equations. The report should connect the theoretical aspects of first-degree equations with the practice of solving the riddles, exemplifying with the situations encountered in the challenges.

Students should be evaluated both for the accuracy and clarity of their mathematical resolution and for their ability to document and reflect on the process in their report. This report should be a formal written document in which students must practice technical writing and communication in an academic context.