Introduction

In our daily lives, we are constantly using mathematics, even without realizing it. One of these applications is the conversion of decimal fractions into percentages, a fundamental skill for understanding various situations.

In mathematics, a decimal fraction is a fraction whose denominator is a power of 10 (including 10 raised to the power of 0 = 1). Normally, these are fractions that can be expressed with a finite number of decimal digits. Decimal fractions are widely used because they allow us to work with systems of units more easily and practically.

Percentage, on the other hand, is a way of expressing a proportion or a relationship based on 100. In general terms, percentage is a way of expressing a number as a fraction of 100. This allows us to make comparisons more intuitively, as we are used to thinking in terms of hundreds.

Contextualization

In our daily lives, we encounter examples of the use of decimal fractions and percentages in various contexts. Prices in stores, for example, often use decimal fractions (e.g. $19.99). Similarly, in many everyday situations, we come across percentages, such as in store discounts, loan interest rates, statistics in news, among others.

Furthermore, the ability to convert decimal fractions into percentages and vice versa is useful in various professions, such as engineering, accounting, marketing, and medicine. This skill is also essential for performance in standardized tests and exams, being a common part of mathematics subjects in elementary and high school.

Practical Activity

Activity Title: "Mathematics at the Supermarket: Understanding the Conversion of Decimal Fractions and Percentages"

Project Objective:

The objective of this project is to provide students with the opportunity to explore the topic of converting decimal fractions into percentages in a practical and engaging way. The activity aims to allow students to apply the theoretical concept in everyday situations, where this skill is often required, such as in supermarket shopping.

Detailed Project Description:

In this activity, students will be divided into groups of 3 to 5 people. Each group will receive a list of supermarket items with prices and discounts given in decimal fractions, percentages, and even mixed numbers (a combination of an integer and a fraction). The students will have to work together to convert the decimal fractions into percentages, and vice versa, to compare prices and discounts, and decide which are the best deals.

Required Materials:

1. Lists of supermarket items with prices and discounts.
2. Paper and pens.
3. Calculators, to confirm the calculations.

Detailed Step-by-Step:

1. The teacher will prepare lists of supermarket items, where prices and discounts will be given in different forms: decimal fractions, percentages, and mixed numbers.
2. The students will be divided into groups and will receive a list of supermarket items.
3. The groups will have to work together to convert the decimal fractions and mixed numbers into percentages and vice versa, and calculate the final prices of the products after the discounts.
4. The answers will be noted and shared with the other groups for comparison and discussion.
5. Each group should present a detailed explanation of how they performed the calculations and decided on the best deals.

Project Deliverables and Connection with Activities:

After completing the practical part of the project, each group should prepare a report documenting their work. This report should include:

1. Introduction: Students should contextualize the problem, explain the relevance of the conversion between decimal fractions and percentages, and mention the project's objectives.
2. Development: Here, students should explain the theory behind the conversion between decimal fractions and percentages, describe in detail the activity carried out, discuss the methodology used, including any specific strategies or techniques they used for the conversions and calculations, and present their results. The notes taken during the practical activity should be part of this topic.
3. Conclusions: Students should conclude the work by summarizing their main points, stating the learnings obtained, and drawing conclusions.
4. Bibliography: They should indicate the sources they relied on to carry out the project, including books, web pages, videos, etc.

It is worth mentioning that the writing of this document should be a collaborative activity, where all group members contribute to the writing and review of the report.