Contextualization

Multiplication and division are fundamental mathematical operations used daily, from simple tasks such as dividing a cake into equal pieces to complex calculations involved in quantum physics. To understand the concepts behind these operations, it is necessary to enter a world of numbers, rules, and, most importantly, apply them correctly.

Our first key concept is multiplication. This operation can be understood as the sum of equal parts. That is, 4 x 3 means adding the number 4 three times, resulting in 12. On the other hand, division is an inverse operation of multiplication. When we say that 12 divided by 3 is equal to 4, we are saying that the number 12 can be divided into 3 equal parts, where each part is equal to 4. Division can also be understood as a way to find how many times one number is contained in another.

Regarding the importance of multiplication and division, we can say that these operations are fundamental to a series of daily activities. In the workplace, for example, it is common to use these operations to calculate salaries, working hours, earnings, and expenses. In household activities, they are used to divide food, calculate meal preparation time, among others. Even in our hobbies, such as watching a soccer game, we use multiplication and division to calculate the average number of goals, see the remaining time of the game, and so on.

Understanding these concepts is essential, not only for mathematics but also for other subjects such as Physics, Chemistry, Economics, and even Arts. Thus, it becomes crucial to learn how to apply multiplication and division correctly and to be able to solve various problems that require the use of these skills.

To this end, I suggest that you explore the following resources:

1. Khan Academy - On this platform, you will find theoretical lessons, practical exercises, and many other activities to delve deeper into the subject.

2. Só Matemática - This website addresses the main mathematical operations, including multiplication and division, through explanations and examples.

3. Book "Matemática: uma nova abordagem" by Bandeira, Gelson Iezzi, and Carlos Murakami (Editora Moderna). This textbook offers a solid theoretical foundation with worked examples and exercises of varying levels of difficulty.

Practical Activity

Title of the activity: "Mathematics in Artworks"

Objective of the Project:

The main objective of this project is to deepen students' understanding of the basic concepts of multiplication and division, applying them in a practical and relevant scenario. In addition, the project aims to develop collaborative, analytical, creative, and research skills.

Project Description:

Students will be divided into groups of 3 to 5 members and will be challenged to create an artwork using only a dot matrix (such as pixel art), where the number of dots, the colors used, the positioning of the dots, and their distribution will be determined by mathematical calculations using multiplication and division.

Through this practical work, students will be able to explore the presence of mathematical concepts in art, as well as the importance of mathematics for artistic forms of expression.

Required Materials:

• Cardboard or large, thick paper
• Colored pens or markers
• Ruler
• Calculators

Step by Step:

1. Research and Planning:

Each group should research the use of multiplication and division operations in artworks, especially in pixel art. They should plan what kind of pattern or image they would like to represent in their own artwork.

2. Creation of the Artwork:

Each group should divide the cardboard or paper into equal squares, which will serve as the "pixels" of the artwork. They can decide the size of the squares based on the total size of the paper and the desired level of detail.

Students should then fill in the "pixels" with different colors, according to the mathematical calculations they have made. They should use multiplication or division to decide things like: how many pixels of a certain color to use, where to position them, and so on.

3. Record and Analysis:

Each group should document the process of creating the artwork, recording the multiplication and division operations used as well as the reasoning behind their artistic and mathematical choices.

4. Presentation:

Each group will present their artwork and their creation process to the class, explaining the mathematical calculations involved and how they contributed to the final result. At this stage, they should also be able to connect their practical work to the theories studied in class.

Project Delivery:

In addition to the artwork created, each group will be evaluated based on a written report that must include the following items:

Introduction: Description of the chosen art, importance of multiplication and division in this context, and objectives of the project.

Development: Theory of multiplication and division; detailed description of the project, including decision-making process, calculations performed, and team experience during project execution; methodology used to carry out the work and results obtained.

Conclusion: The lessons learned, the difficulties encountered and how they were overcome, the impact of team collaboration on the project, and the conclusions drawn about the project.

Bibliography: References of the resources used, including books, websites, videos, and any other sources that assisted in the execution of the project.

The groups should also prepare an oral presentation, explaining the project done, the mathematical theory used, the methodology, and the conclusions.

The project is estimated to last over twelve hours, including research, planning, project execution, report writing, and presentation preparation.