Context

Theoretical Introduction

Percentages are an important mathematical tool used in a variety of everyday contexts. From shopping and sales to taxes and interest, understanding how to calculate and interpret percentages is an essential skill. A particularly interesting topic is successive percentages, where we apply percentages in sequence.

For example, let's consider a discounted t-shirt in a store. First, it has a 20% discount, then another 30% discount. In this case, the total discount is not simply 50%, because the second discount is applied to the value already reduced by the first percentage. This is the concept of successive percentages.

The mathematics involved in applying successive percentages is both challenging and rewarding. It allows us to develop a deeper understanding of percentages and how they work.

Context

In real life, successive percentages are common. As mentioned, they can be found during a major retail sale, where discounts are applied successively to an item. Additionally, banks use the concept of compound interest, which also involves successive percentages, to calculate returns on their clients' investments.

Understanding how successive percentages work will not only help us interpret these situations correctly but also enable us to make better financial choices. Whether buying a discounted t-shirt or investing money in the bank, a solid understanding of successive percentages can save (or earn) money.

Practical Activity

Activity Title: "Saving with Successive Percentages"

Project Objective

Through a real or fictional case involving the purchase and sale of products or services, develop the understanding and ability to calculate successive percentages.

Detailed Project Description

Students will be divided into groups of 3 to 5 people to work together on this project. Each group will be responsible for investigating a scenario from everyday life where successive percentages are applied. It can be a store promotion, a bank investment plan, or any other relevant scenario.

In the chosen scenario, students must identify at least three moments where successive percentages are applied and calculate the final result. Then, they must create a presentation, using presentation software of their choice, to explain the scenario, the calculations performed, and the conclusions.

Required Materials

1. Internet access for research.
2. Presentation software (e.g., Google Slides, PowerPoint).
3. Writing materials for the report.

Detailed Step-by-Step for Activity Completion

1. Group formation and selection of the scenario to be investigated.
2. Detailed research of the chosen scenario, identifying instances where successive percentages are applied. Remember to note all explored sources of information.
3. Calculation of successive percentages and final result, step by step.
4. Preparation of a presentation explaining the scenario, the calculations, and the conclusions.
5. Preparation of a final report, as detailed below.

Project Delivery and Final Report

The project will have two main deliveries:

1. The PowerPoint presentation (or equivalent) that explains the chosen scenario, illustrates the calculations performed, and presents the conclusions. The presentation will be delivered to the teacher and the class.

2. The final report, with the following elements:

   a. Introduction: A contextualization of the theme, its relevance, and real-world application. Additionally, a description of the project's objective.

   b. Development: A detailed narrative of the theory behind successive percentages, an explanation of the chosen scenario and the methodology used. Then, a discussion of the calculations performed and the results obtained.

   c. Conclusions: An analysis of what was learned during the project, reiterating the main points raised in the development and the lessons learned.

   d. Bibliography: A list of sources used during the research and project development. Sources must be cited correctly according to ABNT standards.

By the end of this project, students will have developed technical skills in calculating successive percentages and practical applications of these calculations. Additionally, they will have developed socio-emotional skills such as time management, communication, problem-solving, creative thinking, and proactivity.