Background

The Rule of Three is based on an important property of proportion, the fundamental property of proportions, which states that the product of the means is equal to the product of the extremes. This property is, in fact, the foundation of the Rule of Three, which is nothing more than an application of proportionality between quantities. Quantities can be directly or inversely proportional, but in this project we will focus on directly proportional quantities.

The Direct Rule of Three is used when we have two quantities that are directly proportional, that is, when one increases, the other also increases in the same proportion. Similarly, when one decreases, the other also decreases in the same proportion. This rule is a powerful tool and one of the most used for solving everyday problems, both in the school environment and in everyday life.

Mathematics is a discipline present in all spheres of life, and the rule of three is a clear demonstration of this. It is used in countless everyday situations, whether domestic, professional or academic. For example, when calculating the time needed to complete a task, the amount of ingredients for a recipe, or the speed of a trip, you are applying the direct rule of three.

To learn more about the concepts covered here, you can refer to the following resources:

• Khan Academy: Section dedicated to the rule of three (https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratios-proportions)
• Only Mathematics: Complete article on direct rule of three (https://mundoeducacao.uol.com.br/matematica/regra-tres-simples.htm)
• Mathematics Rio with Prof. Rafael Procopio: Explanatory video about the rule of three (https://www.youtube.com/watch?v=H9HtOKyV2O0)

Practical Activity: "Building a Sustainable City with the Direct Rule of Three"

Project Objective

The main objective of this project is to apply the Direct Rule of Three to solve real problems related to urban sustainability and, at the same time, promote teamwork, creativity, and problem solving.

Project Description

The students, divided into groups of 3 to 5 members, will have to plan and describe the construction of a sustainable city on an A3 sheet of paper. They will have to apply the Direct Rule of Three to determine the amount of resources (such as energy, water, food, etc.) needed for the population of that city, taking into account the proportion of resource consumption.

Materials Needed

• A3 paper sheets;
• Pencils and colored pens;
• Ruler and compass;
• Calculator.

Step by step

1. Each group must define the population of their city. The group must justify why they chose this number of inhabitants.
2. Identify how many liters of water, kilowatts of electricity, kilos of food, among other resources, a person uses per day.
3. Using the Direct Rule of Three, calculate the total amount of each resource needed for the entire population of the city per day. The group must show all calculations performed.
4. Sketch the city on the A3 sheet of paper, indicating where the resources will be allocated (eg: water catchment site, power plant, farms, markets, etc.).
5. After the city is designed, the group must present the city to the class, explaining the calculations performed and how the Direct Rule of Three was applied.
6. At the end, all members of the group must participate in writing a report describing the project.

Project Deliverables

The group must deliver the A3 paper sheet containing the city drawing and a report that must contain:

• Introduction: Contextualization of the project, explaining the importance of the Rule of Three and its use in planning a sustainable city.
• Development: Detailed explanation of all the calculations used, together with the methodology used to arrive at them. Students should explain the direct relationship between the number of inhabitants and the consumption of resources. In addition, the report should contain a description of the planned city and how the resources were allocated.
• Conclusions: Discussion of the results obtained and the effectiveness of the Direct Rule of Three in city planning. Students should also reflect on the importance of teamwork and collaboration.
• Bibliography: References used for the development of the project, including links to websites, videos or books consulted.

This project must be completed and delivered within one week. Each member of the group must contribute equally to the research, calculations, drawing of the city and writing of the report.