Context

Mathematics is present in all aspects of our lives. Whether it's sharing a pizza with friends, planning vacations considering the division of expenses, or even in the school environment when materials are equally divided among students. The concept of sharing, or dividing into equal parts, is essential to understand many everyday situations and, therefore, is an important topic to learn in math classes.

We can find examples of sharing in various everyday situations. When we receive a chocolate bar and have to share it with our friends, when we have a liter of juice and want everyone at home to receive the same amount, or even when we have a group task at school and need to divide it equally among the members. Understanding the concept of sharing helps us deal fairly and equitably with all these situations.

Division is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication. Although it may seem simple, dividing into equal parts is a concept that requires an understanding of other mathematical concepts, such as integers and fractions, and the ability to work with them. Furthermore, understanding division allows us to better comprehend the concepts of proportion and ratio, which are fundamental in various areas of mathematics.

To delve deeper into this topic, we recommend the following resources:

• The book 'Elementary Mathematics: Numbers and Operations' by Maria Teresa Carneiro Soares, which is an excellent source to study and understand the concepts of sharing and division.
• The website Escola Kids, which offers a wide range of explanatory material on division, showing in a playful and interesting way how this concept can be applied in everyday life.

Practical Activity

Activity Title: The Great Sharing

Project Objective:

Practice the concept of dividing into equal parts (sharing) and apply it to real-life situations through a playful and collaborative game.

Detailed Project Description:

In the game 'The Great Sharing,' groups of 3 to 5 students will have the task of 'managing' an orchard of various fruits, dividing them equally among themselves according to the quantity of fruits they produce and the specific requirements of each 'phase' of the game.

Materials Needed:

1. Paper and pencil for calculations and notes.
2. Paper fruits or symbolic objects to represent the fruits (can be any small and easy-to-handle object).
3. Board with rules and game phases, provided by the teacher.

Step-by-Step Guide for the Activity:

1. Preparation: Students form groups of 3 to 5 people, and each group receives a set of 'fruits' and a copy of the game rules, which include descriptions of the different 'phases' the group must overcome.

2. Game: Each round, the group receives a certain quantity of fruits and the rules to divide these fruits equally among them. The rules vary each round, so students have to solve different problems each time.

3. Problem Solving: Students must work together to figure out how to divide the fruits equally. They can help each other and discuss different strategies, but everyone must understand and agree on the final solution.

4. Documentation: At the end of each round, students must write down the solution they found, how they arrived at it, which strategies were effective or not. They should also note any questions or difficulties that arose during the process.

5. Presenting the Results: After completing all rounds, students will present their results to the class, explaining how they divided the fruits in each situation and what they learned from the experience.

Project Deliverables:

At the end of the project, each group must deliver:

1. Written Report: Students must produce a detailed report on the project. The Introduction should present the project's motivation and explain why sharing is an important skill. In the Development section, they should explain the game rules, how they divided the fruits in each round, which strategies they used, and the challenges they faced. In the Conclusion, they should summarize what they learned and reflect on the importance of knowing how to divide into equal parts. The Bibliography should list the sources they consulted to help them understand and solve the game's problems.

2. Oral Presentation: Each group must present their results to the class, explaining their thought process and the strategies they used to solve the problems. This will help students develop their communication and reflection skills.

Students should equally divide the task of writing the report and preparing the presentation among themselves. This way, everyone contributes to all parts of the project and has the opportunity to practice different skills.

Finally, the connection between the practical activity and the written report is of fundamental importance for the project. The report allows students to present their ideas, explain the process, and consolidate learning. Additionally, by writing about the experience, students will have the opportunity to reflect on the project, better understand the concept of sharing, and analyze their own problem-solving skills.