Context

Percentage is a mathematical concept that has several applications in our daily lives. Whether when we are buying a product on sale or when we are investing our money in a venture that promises a percentage return, managing the knowledge of percentages is an essential skill in various situations, both personal and professional.

The term 'percentage' comes from the Latin per centum, which means 'per hundred' or 'for each hundred'. In our daily use, this concept helps us understand proportions and comparisons more directly. For example, we can say that 50% of people in a group like a certain flavor of ice cream, giving us a clear and direct idea of the proportion.

Studying percentages is important not only for the practical value this concept holds but also because it serves as the foundation for other more complex mathematical concepts. Therefore, having a solid understanding of this topic is crucial for successful progress in math studies.

In this project, we will explore and apply the concept of percentages in different contexts, allowing students a more practical approach and real-world topics. This way, learning will not only be theoretical but also applied, making teaching more engaging and effective.

For this project, we recommend reading the book 'Matemática Divertida e Curiosa' by Malba Tahan and visiting the Khan Academy website, which has a section dedicated to percentages that is easy to understand (www.khanacademy.org). Additionally, YouTube videos from the channels 'Matemática Rio' and 'Matemática Zup' can be a fun way to learn and review the content.

Practical Activity: The Cake Shop

Project Objective

The 'The Cake Shop' project aims to develop the understanding and application of percentage concepts, with the context being the operation of a fictional cake selling business. Additionally, it aims to promote the development of socio-emotional skills such as time management, communication, problem-solving, creative thinking, and proactivity.

Project Description

Students, in groups of 3 to 5, will have to manage a virtual cake shop. They will start with a fictional amount of $1000 for initial expenses, which include buying ingredients, paying rent, among others. Through a spreadsheet - which they will create themselves - they should calculate and manage the percentages of profit, taxes, discounts, losses, and other financial variables that can affect a business.

They will also need to conduct research to find average prices of ingredients, the cost of renting a space for the shop, among other expenses. This aspect of the project will involve the discipline of Geography, where they will learn about regional economic differences.

Required Materials

• Computer with internet access
• Spreadsheet program (Excel, Google Sheets, etc)
• Book 'Matemática Divertida e Curiosa' by Malba Tahan
• Access to the Khan Academy website and YouTube channels 'Matemática Rio' and 'Matemática Zup'

Project Step-by-Step

1. Divide the class into groups of 3 to 5 students.
2. Each group will receive an initial amount of $1000 to manage the cake shop.
3. Students must research prices of cake ingredients, shop space rental, cake selling prices, and other related expenses.
4. Using a spreadsheet program, students must create their own financial spreadsheet to track expenses, revenues, profits, losses, tax rates, discounts, and any other relevant financial variables they deem necessary.
5. Students must decide on a price for their cakes and calculate the profit percentage. They must also calculate tax percentages, discounts, and losses.
6. Over a set period (e.g., one month), they must keep track of their finances and adjust their strategies as needed.
7. At the end of the period, they must calculate their final finances and evaluate the effectiveness of their strategies.

Project Delivery and Document Writing

At the end of the project, groups must submit the completed spreadsheet and a report in which they explain the project's development, following the structure of Introduction, Development, Conclusions, and Bibliography used.

In the Introduction section, they must contextualize the work, explain the importance of understanding percentages, and the project's objective. In the Development section, they must explain the percentage theory, how the activity was carried out, the methodology used, and present the results. In the Conclusion section, they will assess what was learned and highlight the main discoveries made during the project execution. Finally, in the Bibliography section, they must list all sources used, whether for price research or content learning.

This document should complement the practical work and connect to it in a way that clarifies the learning, research, and application processes of the concepts that students undertook throughout the project.