Contextualization

Polynomials are mathematical expressions of fundamental importance in different areas of knowledge. They are composed of variables and coefficients, using the operations of addition, subtraction, and multiplication, in addition to the use of exponentiation with natural exponents. In our daily life, polynomials are present in ways that we do not always perceive, such as in weather forecasting, in physics when calculating trajectories, and even in economics, which are used to represent economic phenomena.

Polynomial operations are a basic concept that arises in high school and is widely used in all areas of mathematics. The study of polynomials and their operations includes the solution of polynomial equations, the implementation of polynomial functions, and the analysis of graphs generated by them. It is a crucial point in high school and higher mathematics, being necessary for the study of many other topics, such as calculus and algebra.

Polynomials are an essential tool for those who work with mathematics or exact sciences. It is with them that we develop a deeper understanding of how the world works. They are used to model various real-world situations such as the population of cities, the evolution of prices in markets, among others. For example, in physics, polynomials are used to represent the movement of objects with a very high degree of precision.

For a deeper understanding of the topic, I suggest the following resources in Portuguese:

• Book "Fundamentals of Elementary Mathematics - Volume 1: Sets, Functions", by Gelson Iezzi and Carlos Murakami. This material is a classic and offers a very complete approach to the topic we are dealing with.

• Article on "Polynomial Operations", on the Mundo Educação website: https://mundoeducacao.uol.com.br/matematica/operacoes-com-polinomios.htm. This text addresses the content in a simple and objective way, ideal for a first contact with the topic.

• Video "Polynomials - Operations and Properties", on the YouTube channel "Matemática Rio": https://www.youtube.com/watch?v=wSYWp3mHZP0. The video brings a visual and practical approach to the subject, which helps to understand in a more concrete way.

Practical Activity: Operating Polynomial Park

Project Objective

This project aims to allow students to improve their understanding of polynomials by learning to perform the fundamental operations: addition, subtraction, multiplication, and division.

Project Description

Each group of 3 to 5 students will be responsible for creating the "Polynomial Park". This park is made up of several attractions that are represented by polynomials, and the operations between attractions are represented by mathematical operations between polynomials.

The construction of the park will be done in a fun way, using basic materials such as paper, cardboard, pens, ruler, among others.

The attractions of the park, which are the polynomials, will be identified with plates containing the representation of the polynomial in question. Each member of the group must create at least one attraction.

The operations between attractions will be represented by paths in the park. A path that connects two attractions represents the operation between these two polynomials.

The work will be divided as follows:

1. Each student will develop a distinct polynomial.
2. The students will assemble the attractions (polynomials) in the park (map) together.
3. The students will draw the paths between the attractions, representing each mathematical operation between the polynomials.

Materials Required

• Cardboard sheet for making signs
• Colored pens
• Ruler
• Scissors
• Glue
• Graph paper to draw the map of the park

Step by Step

1. Discussion and elaboration of polynomials: each member must create a different polynomial, which will be the attraction he represents. This polynomial must be presented and discussed with the other members of the group.
2. Creation of plates: students should use cardboard to create plates for each attraction. The plates should have the name of the attraction (the polynomial) clearly written.
3. Assembly of the park: students should use a sheet of paper to draw the map of the park, placing the attraction plates in appropriate locations.
4. Creation of paths: students should, together, decide which operations they want to represent between the attractions and draw the paths between them.
5. Solving the operations: using the polynomials of the attractions and the paths traced, students must solve the represented operations and write down the results.

Regarding the report, each group must propose a written document that must contain:

1. Introduction: Contextualization of the theme of polynomials and its practical relevance. Project objective, description of "Polynomial Park", and the methodology used in the activity.
2. Development: Detailed discussion of the polynomials created, description of the operations performed, and justifications for the choice of attractions and their respective paths. The results of the operations should be presented here.
3. Conclusion: Reflection on the process of carrying out the project, what was learned from the activity, and the students' opinion on the applicability of the knowledge acquired.
4. Bibliography: List of all sources of information consulted, such as books, websites, videos, among others.

The activity should be carried out in one week, considering a total working time of two to four hours per student.