Contextualization

Multiplication and division of fractions are recurring themes in mathematical studies and apply to various everyday situations. These fundamental operations are an important pillar for the construction of students' logical-mathematical reasoning.

Introduction

Mathematics is the universal language that connects a vast range of disciplines and topics. To deal with numbers and their processes, it is sometimes necessary to understand them in their fractional form. Therefore, the multiplication and division of fractions are crucial operations in understanding many concepts, from pure mathematics to natural sciences.

Fractions allow the representation of quantities that are not whole numbers, characterizing non-integer quantities. For example, when dividing a pizza into equal parts, each part is a fraction of the whole pizza. Multiplying and dividing fractions expand this concept to even more complex and useful situations.

Division of fractions, for example, is a topic that may seem complex at first glance, but when understood, it helps solve a variety of problems, especially in resolving everyday situations.

Importance and Connection to the Real World

The ability to deal with fractions also aids in the development of proportional thinking, which is essential for understanding concepts of probability, percentage, rule of three, and scales, which we encounter daily.

For example, in cooking, recipes often require specific measurements of ingredients that are frequently expressed in fractions. Or in a situation where a family needs to divide an inheritance equally among heirs, fractions can be an effective way to represent this division.

Thus, understanding how to multiply and divide fractions, students will have a solid foundation to rationally manipulate numbers, which is an essential skill in the current scenario, where critical and logical thinking is increasingly demanded.

Activity - The Festival of Fractions

Project Objective

This project aims to provide a practical experience on the topic of 'Multiplication and division of fractions', enhancing students' understanding of the subject through collaborative and creative work.

Project Description

In this project, students will create a 'Board Game: The Festival of Fractions', where the movement of pieces will be determined by correctly solving problems involving the multiplication and division of fractions. To connect mathematics to multidisciplinarity, the problem themes will be related to the Science discipline, for example, quantities in culinary recipes or proportions in ecosystems.

Required Materials

• Cardboard or wooden board for the board game;
• Colored cardboard or paper for the pieces and question cards;
• Pens or markers for drawing and writing on the board and cards;
• Dice;
• Ruler, scissors, and glue.

Step by Step

1. Creation of the Board and Pieces: The group must create the board and pieces of the game. The board should be divided into several spaces and the pieces should be of different sizes and shapes for each player.

2. Development of Questions: The group must develop questions about multiplication and division of fractions. The questions should be relevant to everyday situations and linked to the Science subject, in order to connect the two disciplines. Each question should have a correct answer along with a detailed solution. The questions and answers should be noted on separate cards.

3. Game Rules: Students must formulate the game rules, which should include how to move on the board, how the question cards are used, how to win the game, among others.

4. Game Testing: The group must play the game several times to ensure it is fun, educational, and with well-defined rules.

5. Report: Each group must write a report on the game creation, including the resolution of fraction problems, the connection with the Science discipline, and how this contributes to the understanding of multiplication and division of fractions.

Project Deliverables

At the end of the project, students must deliver:

1. The Board Game: Containing all pieces, question cards and solutions, and game rules.

2. The Report: The document should be divided into four parts: Introduction, where students will contextualize the theme and objective of the project; Development, where they will explain the theory, describe the practical activity, and discuss the results; Conclusion, where they will review the main points and explain the learnings obtained; and Bibliography, where they will indicate the research sources.

In the Introduction, students must report the relevance of multiplication and division of fractions in the real world and the objective of this project. In the Development, students must explain the theory behind the topic, describe the practical activity in detail, the methodology used, and present and discuss the results obtained. In the Conclusion, students must indicate the learnings obtained, the skills developed, and the conclusions about the project. In the Bibliography, students must indicate the sources used to work on the project, such as books, websites, videos, etc.

This practical activity will serve to enhance students' ability to collaborate in groups, manage project time, solve multiplication and division problems of fractions, and especially, connect mathematical concepts to real life and other disciplines.