Context
Mathematics is a discipline that provides tools to understand and interpret the world around us. Several phenomena and everyday situations are governed by rules and behaviors that can be described mathematically. One of these tools is the 'First Degree Inequality'.
The first degree inequality is a mathematical expression that establishes an inequality relationship between two quantities. In other words, it indicates that one quantity is less, greater, less than or equal, greater than or equal to another. This concept is fundamental for solving many practical problems in daily life, as well as in various areas of knowledge, such as economics, engineering, physics, etc.
Although it may seem like a simple concept, the first degree inequality involves a rich field of study and has a series of practical applications. In this project, you will learn how to manipulate and solve first degree inequalities, as well as apply them in real-world situations.
Introduction
The first degree inequality can be understood as an extension of the first degree equation: just like in the equation, the goal is to find the possible values for the unknown. However, instead of seeking an exact value (as in the equation), in the inequality, the aim is to find an interval of values that satisfy the inequality.
Solving a first degree inequality involves knowing and applying a series of properties of inequalities, as well as manipulating the inequality with mathematical operations to isolate the unknown. Thus, it is an excellent exercise to deepen your knowledge in algebra.
Now, imagine being able to use this knowledge to solve practical problems in daily life, such as determining an acceptable price range for a product, or predicting possible outcomes in a game, or even optimizing the allocation of resources in a project. This is the power of first degree inequalities!
Support Material
To better understand this topic, we suggest that you consult the following sources:
- Book 'Fundamentos de Matemática Elementar Vol. 3 - Trigonometria'. Gelson Iezzi, Osvaldo Dolce, Carlos Murakami. Publisher: Atual
- Website: Só Matemática (https://www.somatematica.com.br/emedio/inequacao1.php)
- Video: 'First degree inequalities' on the 'Me Salva!' channel on Youtube (https://www.youtube.com/watch?v=Zr2oG9I-8Xs)
These resources will provide a solid foundation for the development of the project and also for deepening the topic, if you are interested.
Practical Activity
Activity Title: 'InequaBowl' Challenge
Project Objective
The 'InequaBowl' activity aims to apply the knowledge about first degree inequalities in a playful and competitive context. The idea is for students to build and solve inequalities that represent strategies in an imaginary bowling game, the 'InequaBowl'.
Detailed Project Description
In this project, the class will be divided into groups of 3 to 5 members. Each group will be a 'team' in InequaBowl, an imaginary bowling tournament. Each team will have to develop a strategy based on first degree inequalities to maximize their points in the tournament.
InequaBowl works like this: each game has 10 rounds. In each round, you can knock down 0 to 10 pins. Knocking down 10 pins in a round is worth 20 points, but knocking down less than 10 pins is worth three times the number of pins knocked down. For example, knocking down 6 pins is worth 18 points.
Each team's strategy must be expressed in the form of a first degree inequality, representing the number of pins the team should try to knock down in each round to maximize their points.
Required Materials
- Notebooks or sheets for notes
- Pencils, pens
- Computer with internet access (for simulations and research)
Detailed Step-by-Step for Activity Execution
- Divide the class into teams of 3 to 5 members.
- Explain the rules of InequaBowl and the objective of the strategy.
- Each team should then start developing their strategy. They must express this strategy in the form of a first degree inequality.
- Each team must solve the inequality and interpret the result in terms of the game.
- The team must create a plan to implement the strategy in the game, discussing possible variations according to the result of each round.
- Finally, each team must prepare a presentation explaining their strategy, the inequality used, how they solved it, and how they plan to implement it in the game.
- The teams must present their strategies to the rest of the class, who can ask questions and pose challenges.
Project Deliverables
At the end of the activity, each team must produce a report detailing the process of creating and implementing the strategy. The report should include:
- Introduction: a summary of the activity and the project's objective.
- Development: a detailed description of the inequality used in the strategy, how it was solved, and how it was interpreted in terms of the game. They should also explain the methodology used to develop the strategy and discuss the results obtained.
- Conclusion: here, the students should summarize the main points of the work, discuss what they learned from the experience, and the conclusions drawn from the project.
- Bibliography: list of resources used for the project development.
The evaluation of this report will take into account not only the correct application and resolution of the inequality, but also the originality and ingenuity of the strategy, the clarity and quality of the strategy presentation, and the quality of teamwork demonstrated during the activity.
