Context

The "Rule of 3" in mathematics is a simple and effective method used to solve problems involving the direct relationship between two different quantities. When the value of one quantity increases, the value of the other also increases in the same proportion, and vice versa. This direct relationship is known as direct proportion.

For example, if we are traveling by car and we know that the average speed will be 80 km/h, we can use the Rule of 3 to calculate how many hours it will take to cover a certain distance. The dimension of time (hours) and distance (kilometers) are directly proportional: the more hours we drive, the more kilometers we can cover.

The Rule of 3 is a relevant topic not only inside but also outside the classroom. It is widely used in various areas of knowledge, such as in Physics to solve speed problems, in Chemistry to calculate solution proportions, in Biology to understand population densities, in Economics to understand price and quantity variations, and many others. In everyday life, we can use the Rule of 3 to plan trips, calculate the amount of ingredients needed for a recipe, or even to understand the relationship between study time and learning a new subject.

Practical Activity: Ship's Log - Traveling with the Rule of Three

Project Objective

Integrate the disciplines of Mathematics and Geography through a detailed planning of trips, using the Rule of Three to calculate distances, times, and costs. Students will be able to apply theory in practice and develop teamwork, communication, and planning skills.

Detailed Project Description

Students will be divided into groups of 3 to 5 members. Each group will have to plan a virtual trip to two Brazilian cities. They will need to research distances, tourist attractions, lodging, and food.

The groups will use direct proportion to calculate:

• The total distance to be traveled on the trip.
• The travel time based on the average vehicle speed.
• The cost of fuel for the trip, knowing the average vehicle consumption and fuel price.
• The total cost of the trip, including food and lodging.

Required Materials

• Internet access for information research.
• Notebook or digital medium for notes and calculations.
• Calculator.

Step by Step

1. Divide the class into groups of 3 to 5 students.
2. Each group must choose two Brazilian cities to plan a virtual trip.
3. Conduct research on the distance between cities, tourist attractions, possible stops along the way, lodging, and food locations.
4. Use the Rule of Three to calculate the travel time, considering the average speed of a common vehicle.
5. Use the Rule of Three to calculate the cost of fuel, considering the average vehicle consumption and current fuel price.
6. Calculate the total cost of the trip, adding expenses such as food, lodging, and any tickets for tourist attractions.
7. Prepare a detailed report of the trip, containing all researched information, calculations made, and results obtained.

Project Deliverables

• A detailed travel planning report, including all calculations made, researched information, and results obtained.

Students should write a report, containing:

1. Introduction: Presenting the chosen cities, the relevance and application of the Rule of Three in trip planning.
2. Development: Detailing all calculations made and explaining the methodology used.
3. Conclusion: Concluding with their teamwork experience, what they learned from the practical use of the Rule of Three in planning a trip, and the difficulties encountered.
4. Bibliography: References to the places where the information was collected.

It is expected that, at the end of this project, students will have improved their technical skills in mathematics and geographical research, as well as important socio-emotional skills such as teamwork, planning, and time management.