Context

In mathematics, an inequality is an order relation between algebraic expressions that can produce an infinity of solutions. First-degree inequalities are an important tool to understand various quantitative relationships that exist in our daily lives. The expressions obtained through these inequalities can be graphically represented on the Cartesian plane, thus facilitating the visualization of possible solutions.

Mathematics is a language that allows us to understand the world around us more deeply, and first-degree inequality is one of the fundamental components of this language. A good understanding of the subject will allow us to perceive everyday phenomena and situations from a new perspective.

The first-degree inequality is an extremely useful tool in solving practical problems. Whether in calculating profits for companies, analyzing performance, making important decisions, or simply planning the family budget. We can also find applications in other disciplines such as physics, chemistry, and engineering.

Understanding first-degree inequalities is then an essential skill for anyone who wants to be able to effectively deal with quantitative issues in any area of study. Mathematics is truly a universal language, and the better we are able to 'speak' this language, the better we will be able to understand and interact with the world around us.

Activity

Activity Title: 'Math in Action: Solving Real Life Problems with First Degree Inequalities'

Project Objective

Students, working in groups of 3 to 5, will be challenged to identify a practical everyday problem that can be solved with the application of first-degree inequalities. After identifying the problem, students should develop a mathematical solution for it, describe the step-by-step of their resolutions, and present their conclusions.

Detailed Project Description

This project aims to connect mathematics with real situations, using first-degree inequalities as a resolution tool. Students will have to work in teams to decide on which practical problem they will work on, develop the equation, and find the solution.

Required Materials

1. Notebook for notes.
2. Pencils, erasers, and pens.
3. Calculator (if necessary).
4. Internet access for research.

Step-by-Step Guide for the Activity

1. Form groups of 3 to 5 members.
2. Decide on a practical everyday problem that can be solved with the application of first-degree inequalities. This can be something like determining the minimum cost to keep a car running, finding the minimum number of study hours to ensure a certain grade in school, among others.
3. Research and discuss the chosen problem. Research may include checking prices, costs, study hours, expense cutting plans, among others. Use the internet to gather the necessary information.
4. Develop a first-degree inequality that represents the chosen problem.
5. Solve the inequality and interpret the result within the context of the problem.
6. Write a final report containing: the problem description, the research conducted, the development and solution of the inequality, and the interpretation of the result. The report should be written in clear and precise language and should contain all the steps taken to solve the problem.

Project Deliverables

Students must submit a written report containing all the project details, from the choice of the problem to the final resolution. The report should include:

1. Introduction: Description of the chosen problem, justification for the choice, relevance of the problem, and how the first-degree inequality can be applied to solve it.
2. Development: Description of the research conducted, detailed explanation of the developed inequality, and the steps taken for its resolution.
3. Conclusions: Interpretation of the results obtained, discussion of the learnings acquired during the process, suggestions on how the study could be improved or expanded.
4. Bibliography: References from where the information was obtained, books, web pages, videos, etc.

The participation of each group member should also be documented in the report. Students will be evaluated both individually and as a team, on the technical skills acquired and on collaboration and teamwork.