Contextualization

Theoretical Introduction

A ratio, in Mathematics, is a fundamental tool that allows us to compare quantities in different ways. We can use it to understand proportions, rates, and several other things. In essence, ratio is the relationship between two quantities.

For example, when comparing the number of men and women in a room, we can use the ratio. If there are 5 men for every 3 women, we would say that the ratio is 5 to 3, or 5:3. This is the first part of the work, understanding what a ratio is and how it can be used.

In addition, ratio is also an important requirement for understanding other mathematical concepts, such as proportions, percentages, and probabilities, which are the basis for understanding complex subjects like Statistics.

Contextualization

Ratio is a key concept not only in Mathematics, but it is also crucial in several areas of knowledge and everyday life. Ratio is present in the kitchen, when we follow a recipe that says "one part sugar for every three parts flour", it is in the economy, for example, when we compare exchange rates between two countries, and it is in the sciences, where ratios are used to analyze experiment results.

Understanding ratios allow us to do things like evaluate the cost/benefit of a purchase, calculate the probability of an event occurring or even interpret statistical data about population growth.

Practical Activity: "Unveiling Ratios in the Real World"

Project Goal

To deepen the knowledge of Mathematics around the concept of ratio and its application in everyday scenarios, while working on research, critical analysis, writing and teamwork skills.

Detailed Project Description

The groups, composed of 3 to 5 students, will have the mission of producing a case study in which the concept of ratio is applied. This case study should be chosen from the fields of Economics, Statistics, Sciences, Engineering, among others, and must be relevant and applicable to real life. Students will have to delve into this case study and explain:

1. How is the ratio used in this context?
2. What are the implications of applying the ratio in this case study?
3. How could the concept of ratio be applied differently in the same case study?

An estimated duration of at least 12 hours of work per student is expected, including research, group discussion, analysis, report writing and review.

Required Materials

• Math books.
• Internet access for research.

Detailed Step-by-Step to Carry Out the Activity

1. Group formation: Form groups of 3 to 5 students.
2. Choice of case study: Each group should choose a case study where the concept of ratio is applied.
3. Research: Students should seek information about the chosen case study, focusing on how the ratio is used.
4. Analysis and Discussion: The group should meet to discuss the information collected, highlighting the importance of the ratio in the case study.
5. Report writing: Each group must write a report, following the proposed format: Introduction, Development, Conclusions and Bibliography.
6. Review: The group finalizes the project with a review of the report, checking if all topics were addressed correctly and clearly.

Project Deliverables

The groups must deliver:

1. Written report: The report must contain four sections: a. "Introduction", which explains the chosen case study and the importance of the ratio in this context; b. "Development", where they detail how the ratio is used in the case study, the implications of this application and suggestions of how the ratio could be applied differently; c. "Conclusion", where they should reflect on the lessons learned and the importance of the ratio in the chosen area; d. "Bibliography", citing all sources of information used.

2. Oral Presentation: Each group must prepare a 15-20 minute presentation for the class, explaining their case study and the importance of the ratio in this context. This presentation helps develop communication and information synthesis skills.