Contextualization

Introduction

Mathematics is a universal language that permeates society in numerous ways. In the context of mathematics, the study of equations is fundamental for the understanding of more complex concepts and is present in our daily lives in not so obvious ways. One of the most basic types of equations, and the starting point for understanding this vast field, are first-degree equations.

First-degree equations, also known as linear equations, represent mathematical relationships that have the variable raised to the exponent 1. The most common way to represent a first-degree equation is: ax + b = 0, where 'a' and 'b' are real numbers and 'a' is different from zero. The study of these equations is the basis for understanding more advanced concepts in mathematics, such as functions, graphs, systems of equations, among others.

These equations are extremely important for the development of logical reasoning and for solving practical problems. The ability to set up and solve these equations is fundamental for understanding other areas of knowledge, such as physics and economics.

Contextualization

First-degree equations can be found in various everyday situations. For example, when making a purchase and needing to calculate the change, when planning a trip and needing to calculate the distance to be traveled or the time spent, when preparing a recipe and needing to calculate the proportions of the ingredients, and many other situations.

In the financial world, first-degree equations are used to calculate simple interest, discounts, rates, among others. In engineering and physics, they are used to describe the behavior of various systems, such as the speed of a car over time, the resistance of a material to applied force, etc.

Thus, mastering first-degree equations is essential not only for learning mathematics but also for practical life and the formation of a critical and active citizen in society.

Practical Activity

Activity Title: "Equations in Everyday Life"

Project Objective

This project aims to teach students to identify everyday situations that involve first-degree equations, to set up these equations, and to solve them.

Project Description

In groups of 3 to 5 students, each group must research situations experienced in daily life where first-degree equations can be applied. These situations should be represented by mathematical problems that can be solved using first-degree equations.

After the research, each group must create a script for a short video (5 to 10 minutes) in which these situations are represented and the respective first-degree equations are set up and solved.

Each group must create a slide presentation to demonstrate the theory used, the process of creating the video, the equations generated, and the resolution of the problems. The presentation should include a discussion of the results obtained and the conclusions drawn.

Required Materials

• Internet for research
• Video editing software (can be any of the students' choice)
• Presentation software (such as Microsoft PowerPoint or Google Slides)

Step by Step

1. Formation of groups of 3 to 5 students.
2. Research and list of everyday situations where first-degree equations are applicable.
3. Creation of mathematical problems corresponding to these situations.
4. Setting up and solving the corresponding first-degree equations.
5. Creation of the video script, including the situations, the equations, and their resolutions.
6. Filming and editing the video.
7. Creation of the slide presentation, including the theory, the process of creating the video, the equations and their resolutions, the discussion of the results, and the conclusions drawn.
8. Presentation of the activity to the class.

Project Deliverables

Students must deliver the video, the slide presentation, and a written report containing the following topics:

1. Introduction: Description of the chosen situations and their relevance in everyday life, presentation of the project's objective.
2. Development: Explanation of the theory of first-degree equations, detailed description of the process of creating the video and the presentation, presentation and discussion of the generated equations and their resolutions.
3. Conclusions: Review of what was learned, discussion of the difficulties encountered and how they were overcome, explanation of the conclusions drawn about the application of first-degree equations in everyday life.
4. Bibliography: Indication of the sources used in the research and project development.

The materials should be delivered both in digital format and in physical format, if possible. The deadline for delivery is one month from the start of the project.

The written report should be a document that proves and details the entire process experienced during the project. It should therefore complement and enrich what was dealt with and presented in the video and slides.

As a learning strategy, the report also aims to develop students' writing, synthesis, argumentation, and presentation skills. In addition, the written report will help develop research skills, as the bibliography used must be meticulously referenced.