Contextualization
Theoretical Introduction
Mathematics is a science dedicated to the study of properties and relationships of abstract entities (such as numbers, geometric figures, among others) and is used as an essential tool in many sciences and disciplines. Within the wide range of topics that mathematics covers, there is one that is particularly relevant to 9th-grade students: Second Degree Equations.
Second Degree Equations are those that can be written in the form ax² + bx + c = 0, where a, b, and c are real constants and a ≠ 0. These equations have one variable and are characterized by the degree of the polynomial, in this case, of degree 2. The presence of this unknown of degree two gives a series of particular properties to these equations that will be explored during this project.
Solving these equations involves some fundamental mathematical skills, including factoring, equation manipulation, and the use of the quadratic formula. The latter, derived from the method of completing the squares, gives us the solutions (or roots) of the second-degree equation.
Importance and Applications
Second-degree equations are extremely useful in various real-life situations. For example, in Physics, quadratic equations are often used to analyze the motion of objects under the action of gravity. In Economics, they can be used to maximize profits or minimize costs. In Geometry, they are applicable in the calculation of areas, volumes, and in solving problems involving properties of flat and spatial figures.
The ability to solve these equations is, therefore, a valuable skill that applies in many fields and studies. Furthermore, understanding the theory behind them helps us better understand how mathematics works and develop logical thinking and problems solving skills.
Practical Activity
Activity Title: "Deciphering Quadratic Equations"
Project Objective:
Enhance skills in solving second-degree equations while exercising creativity, teamwork, and effective communication.
Project Description:
Students will form groups of 3 to 5 members. Each group will be tasked with creating and solving a "quadratic equation challenge," which must be presented in a playful and creative way, such as within a plot or story, a treasure hunt, an interactive game, etc. After creating the challenge, they will exchange their projects between groups and will have to unravel each other's challenges.
Required Materials:
- Paper and pencil
- Textbooks related to the content
- Internet access for additional research
- Materials to create the challenge in a playful way (depending on the chosen format, cardboards, printed images, drawing materials, etc., may be used)
Activity Step by Step:
- Formation of work groups and assignment of the task.
- Research and study on second-degree equations.
- Development and solution of a challenge based on quadratic equations.
- Creation of the "scenario" for the challenge in a playful and creative way.
- Exchange of challenges between groups.
- Resolution of the challenge proposed by the other group.
- Presentation of solutions and discussion in the classroom.
Project Deliverables:
Students will deliver a written document with the following topics:
1. Introduction
It should contextualize the theme of second-degree equations, their relevance and application in the real world, and explain the objective of the project carried out.
2. Development
Students should elaborate on the theory of second-degree equations, explain the developed challenge and the methodology adopted. They should then detail the process of solving the challenge proposed by the other group and discuss the results obtained.
3. Conclusion
Students should summarize the main points, what they learned throughout the project, and the conclusions drawn about the activity.
4. Bibliography
Indicate the sources of information and references used for the work, which may include books, web pages, videos, etc. A reference model, such as ABNT or APA, should be adopted.
The report must be submitted within one week after the end of the classroom activity.
