Contextualization

Theoretical Introduction

First-degree equations, also known as linear equations, are mathematical expressions that relate two or more quantities, where the highest power of the exponents of the unknowns is 1. They are in the form ax + b = 0, where 'a' and 'b' are real numbers and 'a' cannot be equal to zero.

These types of equations are powerful tools often used in various areas of knowledge. They serve as a basis for understanding more complex concepts in mathematics and other disciplines, such as physics and engineering. Therefore, learning how to solve these equations is a crucial step in a student's educational journey.

Solving a first-degree equation means finding the value of the unknowns that satisfy the equation. To do this, we use the fundamental property of equality, which establishes that if the same quantity is added, subtracted, multiplied, or divided on both sides of an equation, the equality will still be maintained.

Contextualization

First-degree equations are useful for solving practical problems in various real-life situations. For example, they can help determine the amount of ingredients needed to make a certain number of servings of a recipe, find out the speed of a car if we know the distance traveled and the time spent, among other things.

Furthermore, understanding first-degree equations is essential for dealing with advanced technologies and effectively participating in modern society. They play an important role in computer programming, game design, economic modeling, and much more. It is worth noting that teaching students how to apply these equations in real contexts can make learning more interesting and motivating.

Practical Activity

Activity Title: Equations in Real Life

Project Objective

Enhance understanding of first-degree equations and their applicability in daily life. Develop the ability to work in a team, manage time, improve communication, and foster creative thinking.

Detailed Project Description

Students should form groups of 3 to 5 members, and each group must identify a daily life situation that can be represented by a first-degree equation. The group should then develop a problem based on this situation, which will be solved by applying the concepts of first-degree equations.

Required Materials

• Notebook or sheets of paper
• Various pens
• Calculator

Step-by-Step Guide for the Activity

1. Form groups of 3 to 5 students.

2. Each group should then choose a daily life situation that can be represented by a first-degree equation.

3. The group should then create a mathematical problem based on the chosen situation.

4. Next, the group should solve the created problem, explaining step by step the process used to reach the solution.

5. Each group should prepare a presentation for the class, where the problem will be presented, and the solution will be explained. Be creative, you can create slides, posters, or any other visual resource you find interesting to assist in the presentation.

Final Product and Delivery

Each group must submit a written report and make an oral presentation to the class regarding the created problem and its solution.

The report should include:

1. Introduction: In this part of the report, students should describe the chosen daily life situation and explain why they decided to represent it through a first-degree equation.

2. Development: Students should explain in detail the problem they created and the process used to solve it. This is the moment to explain the theory and practice of first-degree equations.

3. Conclusion: Students should talk about what they learned from the project, both regarding the mathematical content and teamwork.

4. Bibliography: Indicate the sources consulted for the project.

Each group has one week to complete the project. Remember, the goal is not only to solve the problem but also to learn how to collaborate and effectively communicate your ideas and understanding of the studied concept.