Contextualization

Mathematics is often seen as something abstract and difficult to connect with reality. However, upon closer inspection, we recognize its presence in various aspects of our lives. Factoring second-degree expressions is one of those areas of mathematics that not only frequently appears in everyday problems but is also fundamental to understanding and advancing in more advanced topics in many STEM disciplines (Science, Technology, Engineering, and Mathematics).

Factoring is the process of decomposing an algebraic expression into a product of other expressions. In particular, factoring second-degree expressions is a key concept used not only to solve quadratic equations but also to understand how these equations model various real-world phenomena, such as the movement of an object under the force of gravity, the optimization of functions in economics and engineering, and even the prediction of the behavior of subatomic particles in quantum physics.

By learning to factor second-degree expressions, you will be prepared to address a wide range of real problems, as well as to explore more challenging and interesting topics in mathematics and the sciences. The knowledge you gain here will serve as a powerful tool in your future academic explorations.

Introduction

In mathematics education, factoring is one of the most fundamental skills that students learn. It helps simplify complex problems, making them easier to solve and understand. In particular, factoring second-degree expressions is a practical application of this skill, which involves breaking down a second-degree expression into the form of a product of factors.

Second-degree expressions are polynomials that contain terms with a maximum degree of two. They are commonly written in the form ax² + bx + c, where a, b, and c are constants and x is the variable. Factoring second-degree expressions involves decomposing this expression into a form in which it is expressed as a product of two factors, usually in the form a(x-r1)(x-r2), where r1 and r2 are the roots of the polynomial.

These are crucial skills that provide a solid foundation for understanding a wide range of more advanced topics in mathematics and sciences, as they are used in many practical and theoretical applications. Therefore, mastering these skills is an important step in your academic journey.

Here are some reliable sources you can use to learn more about factoring second-degree expressions:

• Khan Academy: Factoring
• Mundo Educação: Factoring Second-Degree Expressions
• Só Matemática: Second-Degree Equations

Practical Activity: The Factoring Game

Project Objective

Develop a practical and applied understanding of factoring second-degree expressions and promote collaboration and teamwork among students through the creation and execution of an educational game.

Project Description

Students, organized in groups of 3 to 5 members, will create a game whose central theme is the factoring of second-degree expressions. The game should be designed to encourage players to apply and improve their understanding of factoring second-degree expressions. The game format (board game, cards, digital, etc.) is free and should be decided by the group.

The project will be developed over a month, with an estimated duration of 5 to 10 hours per student. At the end, the groups will present the game to their peers and the teacher, demonstrating its functionality and how it aids in understanding the topic.

Required Materials

• Paper, pencil, and eraser
• Materials for making the game (such as cardboard, markers, stickers, etc.)
• Research material (books, internet, videos, etc.)

Step by Step

1. Research and Planning: Understand the concept of factoring second-degree expressions through research and studies. After understanding the concept, plan your game. Decide on the format, create the rules, and determine how factoring second-degree expressions will be incorporated.

2. Game Development: Using the chosen materials, create your game. Remember, the game should be playable, engaging, and, above all, should help players understand and apply factoring second-degree expressions.

3. Testing and Revision: Play several rounds of the game within your group to test if it works as expected. Make necessary corrections to the rules or game design if needed.

4. Presentation: Present the game to the class and the teacher. Explain the concept of the game, the rules, and how it aids in understanding factoring second-degree expressions.

Project Deliverables

In addition to the game itself, each group must prepare a written report following the proposed template:

1. Introduction: In this section, students should contextualize the theme (factoring second-degree expressions), its relevance and real-world application, as well as the objective of this project.

2. Development: Here, students should explain the theory behind factoring second-degree expressions, detail the game, indicate the methodology used for creating the game, and discuss the results obtained through testing the game.

3. Conclusion: In this part, students should summarize the main points of the work, explaining the learnings obtained and the conclusions drawn about the project.

4. Bibliography: Finally, students should list all the sources they used to work on the project, such as books, web pages, videos, among others.

Each of these items should be clearly outlined and discussed in depth in the report. The writing of the report is an important part of the project and should be taken seriously as such.

For project evaluation, the quality and functionality of the game, the depth and understanding of the concept of factoring second-degree expressions presented in the report, and finally, the presentation of the project to the class and the teacher will be considered.