Context

Percentage is a fundamental mathematical concept in everyday life. Every time we buy something in a store, make a bank transaction, or talk about interest rates, we are dealing with percentages. Therefore, mastering this concept is essential to understand the world around us.

Percentage literally means 'per cent' or 'per hundred.' When we say something is 50% of something, for example, we are saying it is half of it, as 50 is half of 100. Understanding this concept is vital for many aspects of life, from comparing prices to understanding news about the economy and politics.

With this project, you will have the opportunity to apply the theory of percentages to real-life situations. We will explore the concept of percentage increase and discount through the development and resolution of problems involving these two themes. The project goes beyond just applying formulas; it encourages logical reasoning, text interpretation, and teamwork.

In real life, knowing how to calculate percentages can help you understand if a discount in a store is really worth it, what it means when interest rates go up or down, or how profits and losses are calculated. In short, percentages are everywhere - in news, finances, sciences, sports, and even in how we evaluate our own performance.

Recommended study resources:

• Khan Academy's Mathematics Portal: Percentage

• Só Matemática website: Percentage

• Textbook: IMENES & LELLIS. Mathematics: It's within your reach. 8th grade. São Paulo: Scipione Publisher, 2010.

Practical Activity

Activity Title: 'Doing the Math: Shopping and Discounts'

Project Objective:

Students should simulate shopping in a supermarket, solving practical problems involving the application of discounts and percentage increases. Additionally, they should be able to create problems involving percentages and present solutions for them.

Detailed Project Description:

In the project, groups should research the prices of products in different supermarkets or stores and calculate the total cost of a shopping basket. With this data, students will calculate the discounts and percentage increases that can occur at each location according to promotions or surcharges.

Each group should create a shopping catalog containing the researched products and their respective prices, and from this catalog, they should develop at least 5 problems involving percentages (discounts or increases) to be solved by the group.

Students should use digital technologies (computers, tablets, calculators, or smartphone apps) to solve the formulated problems.

Required Materials:

• Internet access for price research;
• Pencils, pens, and notebooks for notes;
• Computer or calculator for calculations;
• Text editing program for the catalog and final report.

Detailed Step-by-Step for Activity Execution:

1. Form groups of 3 to 5 students.
2. Each group should research online the prices of at least 10 common products in different supermarkets or stores.
3. Record the prices of the researched products and calculate the total cost of the shopping basket at each location.
4. Based on the price research, calculate the possible discounts or increases that can occur at each location.
5. Develop 5 problems involving percentages and percentage discounts or increases to be solved by the group.
6. Solve the formulated problems using the acquired calculation skills.
7. Create a shopping catalog containing the researched products, their prices, the calculations performed, and the solution to the problems.
8. Write a detailed project report covering the following topics: Introduction, Development, Conclusions, and Bibliography used.
9. Submit the report and the shopping catalog for evaluation.

Project Deliverables:

At the end of the project, each group must submit a 'Shopping Catalog' containing all the researched products, their price variations, the calculations performed, and the solution to the created problems.

Additionally, the group must present a written report that includes the following points:

• Introduction: Provide context for the theme, its relevance and real-world application, as well as the objective of this project.
• Development: Explain the theory behind percentages, detail the activity, indicate the methodology used, and finally, present and discuss the results obtained.
• Conclusion: Summarize the main points, explain the learnings obtained, and draw conclusions about the project.
• Bibliography: Indicate the sources used to work on the project such as books, web pages, videos, etc.

Remember that each work will be evaluated not only for the theoretical content presented but also for teamwork, organization, writing clarity, and presentation of results.