Practical Activity

'Proportionality in the Real World'

Project Objective

The objective of this project is to apply the concepts of direct and inverse proportionality in practical situations, exploring examples from our daily lives. The activity will involve research, discussion, problem-solving, and the preparation of a detailed report.

Detailed Project Description

Students will be grouped into teams of 3 to 5 members. Each team must choose two real-life situations that involve the concepts of direct and inverse proportionality. For example, the first situation may involve the relationship between a vehicle's speed and the time required to travel a certain distance (direct proportionality), while the second may address the relationship between the number of workers on a task and the time required to complete it (inverse proportionality).

After choosing the situations, teams must conduct detailed research to better understand each scenario, collect data, and develop mathematical problems based on this data. They must then solve the proposed problems, explain the approach used, and discuss the results.

The activity should be carried out over a month, with each student dedicating between five to ten hours to the project.

Required Materials

• Mathematics textbooks and/or online resources for research.
• Materials for note-taking and problem development (paper, pencils, erasers, etc.).
• Computer for research and report writing.

Detailed Step-by-Step Guide for the Activity

Step 1: Formation of groups of 3 to 5 students.

Step 2: Selection of two practical situations involving the concepts of direct and inverse proportionality.

Step 3: Detailed research on the chosen situations, collecting relevant data and information.

Step 4: Development of mathematical problems based on the collected data. Each problem should be well-structured to elucidate the concepts of direct and inverse proportionality.

Step 5: Resolution of the proposed problems, with a detailed explanation of the approach used.

Step 6: Discussion of the results, identifying the conclusions and insights obtained.

Step 7: Writing the project report, containing the following topics:

1. Introduction: Describe the relevance of proportionality in everyday life and the project's objective.

2. Development: Explain the theory of direct and inverse proportionality, describe the chosen situations and the research conducted, describe the problems and the methodology used in their resolution, and present and discuss the results.

3. Conclusion: Recap the main points of the work, explain what was learned, and draw conclusions about proportionality.

4. Bibliography: List the sources of information used.

Project Deliverables

The team must deliver:

1. Proposed Problems: Each team must submit the mathematical problems they developed, along with detailed solutions for each.

2. Project Report: The team must submit a report documenting their findings, analyses, and conclusions. The report should follow the four main topics: Introduction, Development, Conclusions, and Bibliography used.

By the end of the project, students should be able to relate theory to practice, applying mathematical concepts to everyday situations, and should also have improved their socio-emotional skills, such as time management, teamwork, problem-solving, and critical thinking.