Contextualization

Mathematics is a fundamental discipline that permeates all aspects of our lives, from everyday problem solving to understanding the most complex phenomena in the universe. One of the essential topics in mathematics is factoring, a tool that allows us to simplify algebraic expressions and solve polynomial equations of the 2nd degree, which are the basis for many fields of science and technology.

In particular, we will pay special attention to the factoring process by grouping and factoring out common factors, two fundamental methods that allow us to understand the structure of an algebraic expression and simplify it effectively.

Factoring by grouping is a procedure used to factor algebraic expressions where it is observed that they can be divided into groups of terms that have a common factor. On the other hand, factoring by factoring out common factors consists of identifying and removing the common factor from all the terms of an algebraic expression.

Importance of Factoring

Factoring plays a crucial role in many aspects of our lives. Whether in the calculation of areas and volumes in geometry, in solving equations in physics and chemistry, or even in the optimization of algorithms in computer science. The ability to factor algebraic expressions is an invaluable tool for solving problems and understanding concepts in various fields of knowledge.

Furthermore, factoring is closely linked to the ability to solve problems. This becomes evident when we have problems that can be formulated as polynomial equations of the 2nd degree, where factoring is an essential part of the solution process. For example, factoring is key to solving optimization problems, which seek to maximize or minimize a given quantity, an important topic in economics and engineering.

To delve deeper into the topic, I suggest the following resources:

• Book: "Fundamentals of Elementary Mathematics" by Gelson Iezzi. This book has a chapter dedicated to factoring and is a classic reference in high school mathematics in Brazil.
• Website: Only Mathematics Factoring by Grouping
• Video: Khan Academy Factoring - factoring out

Practical Activity - "Factoring in Action: The Numbers Game"

Project Objectives

1. Understand and apply the factoring procedures by grouping and factoring out common factors.
2. Use factoring to solve practical problems.
3. Work in teams to solve problems and develop strategies.
4. Develop socio-emotional skills such as time management, communication, problem solving, creative thinking and proactivity.

Project Description

Students will work in groups of 3 to 5 for a period of two weeks. They will create and play a board game based on factoring by grouping and factoring out common factors. During this process, students will apply the concepts learned in the course, develop strategies, solve real problems, and work cooperatively.

Materials Required

1. Cardstock or other sturdy material to create the game board.
2. Blank cards to create the challenge cards.
3. Colored pens and other art supplies to decorate the game.
4. A dice.

Step-by-Step to Carry Out the Activity

1. Game Creation: The first step is to create the game board. It should have a winding path with several numbered spaces, where players will move their pieces according to the results of the dice rolls.
2. Challenge Cards: Each group must create at least 50 challenge cards. Each card should contain a factoring problem that the player must solve. The problems should vary in difficulty and should involve both factoring by grouping and factoring out common factors. In addition, students should provide the correct solution on the back of the card.
3. Game Rules: Students must develop the rules of the game. For example, each time a player lands on a numbered space, they must pick a challenge card and solve the factoring problem. If they solve it correctly, they advance the number of spaces equal to the number of the space they are on. If they fail, they must go back a number of spaces equal to the number of the space they are on.
4. Playing the Game: With the game created, students should play it. They should play the game at least 3 times, so that they can identify any problems or improvements that can be made.
5. Improving the Game: Based on the experience of playing the game, students should make adjustments to the game to make it more balanced, fun or challenging. They can also add new rules or challenge cards if they deem necessary.
6. Documenting the Game: Finally, students should document the entire process of creating the game, the rules, the strategies used, the problems encountered and how they overcame them in a written report.

Project Deliverables

1. Board Game: the finished game with all its pieces and cards.
2. Written Report: a detailed report containing the sections Introduction, Development, Conclusions and Bibliography used. The Introduction should contain a description of the project and its relevance, the Development should describe in detail the process of creating the game, the strategies used, the problems encountered and how they were overcome. The Conclusions should revisit the main points, the lessons learned and the conclusions about the project. The Bibliography should list the sources consulted during the project.

Remember, the key to a good report is clarity and accuracy. Be clear in your explanations and be precise in your descriptions. Do not forget to proofread your work to avoid any grammar or spelling errors.