Contextualization

Mathematics is a discipline that permeates diverse aspects of our lives, from the purchase and sale operations of everyday life to complex calculations that guide the construction of architectural structures and strategic actions in large companies. Within this scope, the study of divisibility criteria stands out for establishing division rules that facilitate the handling of numbers, without the need for long and laborious divisions.

The divisibility criteria are rules that allow us to determine, more quickly and simply, if a number is divisible by another, that is, if when dividing the number the result is an integer. Studying and understanding the divisibility criteria is fundamental for developing mathematical skills that will be used in various situations, from solving equations to simplifying fractions.

These criteria vary according to the number by which we wish to divide. For example, to verify if a number is divisible by 2, simply check if the last digit is even. To verify if a number is divisible by 3, add up the digits of the number and check if the result is divisible by 3. These rules are practical and help in the more agile handling of numbers.

Mathematics is not just a series of rules and theoretical concepts, it has a very important practical application in our lives. In our daily lives, we often come across situations that require quick and precise calculations, and knowing the divisibility criteria can make it much easier at these times. For example, when splitting a bill at a restaurant or when dividing tasks equally among a group of people.

In addition, mathematics plays a fundamental role in diverse areas of knowledge, such as physics, chemistry, economics, and engineering, among others. In these fields, the ability to perform calculations quickly and accurately is fundamental and, often, the divisibility criteria are a useful tool in this process.

To assist in the study of this topic, I suggest the following sources for consultation:

• Book "Mathematics: Context & Applications", by Luiz Roberto Dante. This book addresses, in a clear and didactic way, various topics in mathematics, including the divisibility criteria.

• Portal "Only Mathematics" (https://www.somatematica.com.br), which has a section dedicated to the divisibility criteria, with detailed explanations and practical examples.

• Channel "Rio Mathematics with Professor Rafael Procopio" on YouTube (https://www.youtube.com/user/matematicario), which has a series of didactic videos on diverse topics in mathematics, including the divisibility criteria.

Practical Activity: "The Divisibility Challenge - A Multidisciplinary Approach"

Project Objective

This project aims to deepen students' understanding of the divisibility criteria, through the development of practical and fun activities, encouraging teamwork, logical reasoning and interdisciplinarity.

Project Description

The project will be carried out in groups of 3 to 5 students, with a duration of more than twelve hours of work per student. It consists of the creation of an educational game, involving the divisibility criteria, where the students will apply the mathematical knowledge in a fun and interesting way, and an interdisciplinary research, relating the divisibility criteria with other disciplines, such as Physics and History.

Necessary Materials

• Paper and pencil for drafts and notes.
• Computer with Internet access for research and game development.
• Graphic design and programming software (such as Scratch or Microsoft PowerPoint) for game development.

Step by Step

1. Study of the divisibility criteria: each group must study the divisibility criteria for the numbers from 2 to 11. The objective is to understand how these criteria work and how they can be applied to determine if a number is divisible by another.

2. Game creation: the students must use the knowledge acquired to elaborate an original game that explores the divisibility criteria. The game can have a choice format: board, cards, video game, etc. This game must be well-structured, with clear rules and defined objectives.

3. Interdisciplinary Research: the students must research and prepare a report that relates the divisibility criteria with other disciplines. How are the criteria applied in Physics? And in History? How were they discovered? How have they evolved over time?

4. Work presentation: Each group will present their game and report to the class, explaining how they applied the divisibility criteria and the interdisciplinary relationships found.

Project Delivery

The project delivery will be composed of two main parts:

1. The Game: a physical or digital copy of the game developed by the group. The game should be sufficiently interesting and challenging for students to want to play again, and also educational enough for them to learn the divisibility criteria in a fun and engaging way.

2. Written Report: this must be presented according to the following sections:

   Introduction

   In this section, the students should contextualize the theme of the project, explain its relevance and application in the real world, and clearly define the objective of the project.

   Development

   Here, the students should explain in detail how they carried out the project. This should include:

   • The theory behind the divisibility criteria;
   • The methodology used to create the game and to carry out the interdisciplinary research;
   • The detailed description of the game, including its rules, objectives, and how the divisibility criteria were applied;
   • The discussion of the results of the interdisciplinary research, explaining how the divisibility criteria relate to other disciplines.

   Conclusions

   In this section, the students should revisit the main points of the work, express the learning obtained and the conclusions drawn about the project.

   Bibliography

   Finally, the students should list all the references they used to carry out the work, be they books, websites, videos, etc.