Contextualization

Theoretical Introduction

The rule of three is a method for solving problems that involve the proportionality between three or more values. In particular, we will focus on the rule of three direct. It is used in situations where the quantities are directly proportional, meaning that the increase or decrease of one results in the increase or decrease of the other in the same proportion. To solve this situation, the product of the means is made equal to the product of the extremes.

In more accessible terms, the rule of three direct is used to discover a value from three others, provided that two of these values are directly proportional to two others. For example, if we know that 4 apples cost 8 reais, with the rule of three direct, we can find out how much 10 apples cost.

Another classic example occurs when a car travels a certain distance at a constant speed. If we know how long the car takes to travel a certain distance, we can predict the time needed to travel a different distance while maintaining the same speed. These examples demonstrate the usefulness of the rule of three in solving simple everyday problems.

Contextualization

The rule of three direct occupies a fundamental place in mathematics and its applications in exact and natural sciences. It is the basis for understanding various concepts in physics, chemistry, biology, geography, among others, where the relationship between different quantities is analyzed.

Furthermore, the rule of three direct has a wide application in the real world, ranging from solving everyday problems as presented earlier, to solving more complicated problems in the professional field. Engineers, architects, programmers, data analysts, economists, among many other professionals, frequently use it in their work. Knowing how to use the rule of three direct is therefore an essential skill not only for school subjects but also for personal and professional life.

Practical Activity

Activity Title: Planning a Trip with the Rule of Three Direct

Project Objective:

This project aims to apply and consolidate the knowledge of the rule of three direct in solving everyday problems. Students will plan a fictional trip, considering the main expenses and using the rule of three to calculate costs and distances. Time management, communication, problem-solving, and creative thinking skills will be necessary and developed during the project.

Project Description:

Groups of three to five members will plan a fictional 7-day trip to a location of their choice. They should consider:

1. The distance between the city of origin and the destination
2. Transportation costs
3. Accommodation expenses
4. Food
5. Sightseeing

Students should calculate transportation expenses (based on distance and vehicle consumption), accommodation (cost per night), food (average cost of a meal multiplied by the number of meals per day and number of days), and sightseeing (cost per activity).

The rule of three will be essential for these calculations. Students should present all calculation steps and justify the choices made. It is important for students to seek real information for the project development, such as current fuel prices, airfare costs, hotel and inn rates, among others.

Required Materials:

1. Internet access for price and distance research
2. Paper and pen for notes and calculations
3. Text editing software for writing the report

Project Step-by-Step:

1. Form groups of 3 to 5 students.

2. Choose the destination of the trip.

3. Research the distance between the city of origin and the destination, the cost of transportation, the cost of accommodation per night at the chosen location, the average cost of food, and the cost of the planned tourist activities during the trip.

4. Use the rule of three direct to calculate all trip expenses.

5. Each group must produce a detailed report of all calculations and choices made.

Project Deliverables:

At the end of the project, each group must deliver:

1. A detailed report containing all calculations performed, justification of the choices made (destination, means of transportation, accommodation, etc.), and the relationship between the calculations and the rule of three direct used. The report should be divided into Introduction, Development, Conclusions, and Bibliography.

• In the Introduction, students should contextualize the project, explain its relevance and real-world application, as well as the objective of the activity carried out.

• In the Development, students should explain the theory of the rule of three direct, detail the activity, indicate the methodology used, and finally present and discuss the calculations and results obtained.

• In the Conclusions, students should conclude the work by summarizing its main points, explaining the learnings obtained, and drawing conclusions about the project.

• In the Bibliography, students should indicate the sources they relied on to work on the project, such as price and distance research websites, videos, books, among others.

2. Oral presentation to the class about the developed project, highlighting the knowledge acquired about the rule of three direct, the challenges encountered during the project, and the decisions made in trip planning.

The project will last approximately 12 hours per student and will be evaluated not only for the understanding and correct application of the rule of three direct but also for the collaboration among group members and effective time management.