Contextualization

In this project, we will explore the fascinating world of Polynomials - Properties. A crucial part of mathematics, polynomials are mathematical expressions that help us to simplify complex problems into more manageable versions. They are composed of variables, coefficients, and exponents that, combined, form an algebraic expression. The properties of polynomials are essential rules that define how polynomials interact with each other and how they can be manipulated. They have great utility in various areas, from the foundations of algebra to theoretical physics.

Polynomials are characterized by terms with variables to integer and non-negative powers. The most important properties of polynomials include the Sum, Subtraction, and Multiplication Properties. Understanding these properties will be crucial for our project.

Importance

Mathematics plays a fundamental role in the world we live in, acting in almost every aspect of everyday life. Polynomials, in particular, have a myriad of practical applications. They are used in a variety of fields, from physics to economics. They allow scientists and mathematicians to describe curves, solve equations, and even predict behavioural trends. In physics, polynomials are used for describing movements, in geometry for calculating areas and volumes, and in economics for modelling growth and income.

In this sense, understanding the properties of polynomials and how to apply them is crucial for anyone who intends to delve into the scientific area, or simply wants to improve their thinking and problem-solving skills. Becoming proficient in polynomials and their properties opens up a myriad of learning and growth opportunities.

Practical Activity

Activity title: Polynomials in the Board

Project objective

The objective of this project is to help students understand the main properties of polynomials through a playful and interactive activity, in order to promote both mathematical competence and socio-emotional skills, such as teamwork, problem-solving, and creative thinking.

Detailed description of the project

Students should create a board game related to the properties of polynomials. The idea is that the game is fun and educational, aiming to apply and challenge the acquired knowledge about polynomials, their properties, and their applications.

Required materials

• Cardboard or paperboard for the base of the board.
• Colourful pens, crayons, or markers to draw the game.
• Paper for question/answer cards.
• Game pawns.

Detailed step-by-step to carry out the activity

1. Form groups of 3 to 5 people.
2. Each group should study the properties of polynomials and create a set of questions and answers related to these properties. Each question should be classified in terms of difficulty, so that they can be evenly distributed across the board.
3. Based on the questions created, draw the game board. Special houses should be included that add dynamics to the game, such as "go back two spaces", "skip your turn", etc.
4. The answers to the questions should be written on separate cards, which will be used during the game.
5. For the execution of the game, each player must answer a question upon arriving at a space. If the answer is correct, the player advances. If the answer is incorrect, the player remains in the same place.
6. The winner is the first player to reach the end of the board.

Project Deliverables

• Board game: The group must deliver the board game produced, which will be used in the classroom in a game session.
• Report: The group must write a report, preferably typed, containing the following sections:
  1. Introduction: Contextualize the theme and explain the relevance of polynomials and their properties, and present the objective of the project.
  2. Development:
     • Theory: Explain the theory behind the properties of polynomials.
     • Activity: Describe the activity performed in detail.
     • Methodology: Indicate the methodology used for the creation of the game.
     • Results: Present and discuss the results obtained, considering the application of the game in the classroom.
  3. Conclusion: Finalize the work, mentioning the main points of the project, the learnings acquired, and the conclusions about the project.
  4. Bibliography: Indicate the research sources for the work.

The report must have at least 10 pages, including images of the game made and bibliographic references. The group has one month to finalize and deliver the project and the report.

Students will be evaluated both for the board game they create and for the report they deliver.