Contextualization

Second degree equations are a vital part of mathematics and represent one of the first complex forms of equations that students learn. A second degree equation is a polynomial equation of the second degree, which can be represented by the general formula ax² + bx + c = 0. Here, a, b, and c are constants with a ≠ 0. Understanding how to solve these equations opens doors to learning more advanced concepts.

To understand second degree equations, it is crucial to first grasp the concept of an equation. An equation is a statement of equality that contains one or more variables. Solving the equation involves discovering which values (if any) satisfy the equality. In the case of second degree equations, this usually involves manipulating the equation into a form that allows us to apply the quadratic formula.

Importance of Second Degree Equations

Second degree equations have many practical applications in the real world, from physical calculations, such as the trajectory of a falling object, to financial problems, such as calculating compound interest. Furthermore, they form the basis for many topics in advanced mathematics, such as calculus, and also have applications in fields like engineering, physics, economics, among others.

Understanding second degree equations is an important step towards becoming proficient in mathematics. By mastering the resolution of these equations, students will also develop problem-solving skills and critical thinking, which are crucial for many academic and professional areas. The experience of working in groups to solve second degree equations can also help students develop communication and collaboration skills.

Practical Activity

Title: "The Parabola Journey: Exploring Second Degree Equations"

Project Objective

Apply and understand the theory behind second degree equations through the creation of an educational game involving the resolution of real-world problems that will be represented through second degree equations.

The game will consist of three phases, each addressing a key concept of second degree equations, namely: the roots of the equation, the vertex of the parabola, and the analysis of the discriminant. To progress through the phases, groups must correctly solve the problems presented.

Groups should consist of 3 to 5 students, and the project will last for about a month to be completed.

Detailed Project Description

The project will be divided into two main parts. In the first part, students must study and understand the theoretical concepts of second degree equations. Using the recommended resources, each group should delve into the theory and learn to identify and solve second degree equations.

In the second part of the project, groups will apply their knowledge to develop an educational game that deals with the concepts learned. The game must have three phases, each designed to address a specific aspect of second degree equations: roots, vertex of the parabola, and discriminant analysis.

Required Materials

• Paper and colored pens for sketching the game.
• Computer with internet access for research and digital creation of the game.
• Platform for creating online games (we recommend using Scratch or similar, but the choice is up to the students).

Detailed Step-by-Step

1. Form groups with 3 to 5 students.
2. Each group should study the concepts of second degree equations. We recommend using the materials listed in the "Recommended Resources" section.
3. After studying, the group should meet to discuss and sketch the game on paper, thinking about how the three phases of the game can address the concepts of equation roots, parabola vertex, and discriminant analysis. Each phase should contain real-world practical problems that can be modeled by second degree equations.
4. With the game sketch ready, the group should then start the digital creation of the game on the chosen platform.
5. After finishing the game, the group should test it to ensure it works correctly and addresses the concepts appropriately.
6. Finally, students should write a project report, covering the introduction, development, conclusions, and bibliography used.

Project Deliverables

1. Educational game on second degree equations: The final game file (or the link to the game if done online) must be delivered within the established deadline.

2. Written report: It must be delivered along with the game. The report should include:

• Introduction: Here, students should contextualize the theme, its relevance, and its real-world application. Also, explain the project's objective of creating a game to learn about second degree equations.

• Development: Document the entire creation process, from studying the concepts, choosing and sketching the game, to digital creation. All decision-making processes, challenges encountered, how they were overcome, and the results obtained should be discussed here.

• Conclusion: Students should summarize the main points of the project and reflect on the learning obtained, both in terms of technical knowledge and socio-emotional skills.

• Bibliography: Indicate the sources used to work on the project. This includes books, web pages, videos, etc.