Contextualization

Polynomials are very powerful mathematical expressions and are present in various areas of knowledge. They play a fundamental role in disciplines such as physics, engineering, economics, statistics, among others. Polynomials are algebraic expressions that combine numbers and variables following certain rules and are characterized by their degree, which is determined by the highest exponent of the variable.

Polynomials appear in a variety of everyday situations, from determining the trajectories of objects in physics to modeling population growth in biology, as well as calculating yields and interest rates in economics. Therefore, the study of polynomials is not only a matter of mastering a mathematical skill, but also a way to better understand the world around us.

Regarding the calculation of the numerical value of a polynomial, this is a central point in the study of polynomials, as it allows, for example, evaluating the behavior of a polynomial function at a specific point, assisting in understanding the behavior of the function as a whole.

Practical Activity

Activity Title:

"Polynomial Festival: Creating and Exploring Polynomials in Real Life"

Project Objective:

This project aims to allow students to deeply understand the concept of polynomials and how to calculate numerical values of polynomials, as well as apply these concepts to the real world.

Detailed Project Description:

Students will be divided into groups of 3 to 5 people. Each group will be responsible for creating a realistic application for polynomials and presenting in a simple and clear way how to calculate the numerical value of these polynomials. Students should choose an area of interest (such as physics, economics, engineering, etc) and research where and how polynomials are applied. Then, they should create a polynomial based on their research and explain step by step how to calculate the numerical value of this polynomial.

Required Materials:

Students will need research materials, internet access to search for information, paper and pen for notes and drafts, a text editing software for the final report (Microsoft Word, Google Docs, etc). Additionally, materials for the project presentation may be necessary, such as cardboard, markers, etc.

Detailed Step-by-Step for Activity Execution:

1. Divide students into groups of 3 to 5.
2. Ask each group to choose an application area for polynomials.
3. Each group should research where and how polynomials are applied in this chosen area.
4. Based on the research, each group should then create a polynomial that is relevant to the chosen area.
5. Students should explain step by step how to calculate the numerical value of this polynomial.
6. Each group should prepare a presentation of their results.
7. Finally, each group should write a detailed report on the project, explaining the context of the problem, the polynomial created, how to calculate the numerical value of the polynomial, and the relevance of their work.

Project Deliverables

Students should deliver:

1. An oral presentation of their results, including a demonstration of how to calculate the numerical value of a polynomial invented by them.
2. A written report in article format, containing:
   • Introduction: Should include the project context, the relevance of polynomials in the chosen area, and a brief description of the polynomial created by the group.
   • Development: Should explain in detail the creation of the polynomial and how to calculate the numerical value of this polynomial. It should also discuss the research methodology and the project construction itself.
   • Conclusion: The group should talk about the learning throughout the project and the significance of the results obtained.
   • Bibliography: Include all sources consulted throughout the project.

Remember, this project is not only about getting the right answers. It is also about learning to work in a team, effectively communicate your ideas and thoughts, manage your time, and solve problems creatively.