Contextualization

Fractions are an essential part of the field of rational numbers. They represent a relationship between parts and the whole, such as half of a pizza or a quarter of an hour. Studying fractions is a fundamental pillar in building mathematical understanding and paves the way for exploring more complex concepts such as proportions, ratios, probability, among others.

Understanding fractions is fundamental for everyday life, as they are present in several routine activities, whether it is when dividing a pizza, calculating the change at the supermarket, or when visualizing the graphs of a report.

Studying fractions involves several subtopics, such as representation, comparison, equivalence, ordering, and operations with fractions. However, many students face difficulties in understanding the concept of fractions and their various operations. This project aims to facilitate this understanding through playful and collaborative learning.

Introduction

Comparing fractions is one of the first topics addressed when we begin to explore the concept of fractions. The objective of this stage is to understand which fraction is greater or smaller, or if two fractions are equal. Given that a fraction represents a part of the whole, comparing fractions means comparing parts of the same whole. For example, when comparing 1/2 and 3/5, we are interested in knowing which represents the greater part of the whole.

In a second moment, we explore the equivalence of fractions. Two fractions are equivalent when they represent the same quantity, even if their numerator and denominator are different. For example, 1/2 is equivalent to 2/4, 3/6, 4/8, and so on.

The third concept we will explore is the ordering of fractions. Just as we can order integers on a number line, we can also do the same with fractions. This concept is fundamental for understanding other operations with fractions such as addition and subtraction.

To delve deeper into these concepts, I would like to recommend the following resources:

1. Khan Academy: Comparing Fractions and Decimals
2. Zup Mathematics: Ordering Fractions
3. Only Mathematics: Fraction Equivalence

These materials will serve as a basis for understanding the theoretical concepts necessary for the development of this project.

Practical Activity

Activity Title: "Fractions Battle"

Project Objective:

The "Fractions Battle" project seeks to instigate the understanding, comparison, and ordering of fractions through a playful and collaborative activity. In addition, it promotes interdisciplinarity by incorporating elements of the Arts discipline, since the students will create a personalized card game.

Detailed Project Description:

Students will be divided into groups of 3 to 5 students. Their task will be to create an original card game called "Fractions Battle", where the goal is to compare fractions and conquer the opponent's deck.

Each game card should contain a fraction and an illustration corresponding to that fraction, which should be drawn by the students themselves. They will also create the rules for comparing fractions during the game. In addition to the basic rules for comparing fractions, students are free to add extra rules to make the game more challenging and fun.

During the project, in addition to deepening the knowledge in fractions, students will develop teamwork, communication, and creativity skills.

Materials Required:

• Colored cardstock
• Colored pens and markers
• Ruler
• Scissors
• Math textbooks for reference

Step by Step:

1. Each group receives the materials necessary to create the card game.
2. Next, the groups should discuss and decide which fractions will be used in their game.
3. After selecting the fractions, the students should draw the fraction on its corresponding card. For example, if the fraction is 1/2, they will draw a pizza with one half colored and the other half blank.
4. With all the cards ready, the groups should create and write down the rules of the game, which should include how the fractions will be compared during the battle.
5. After creating the game, the groups should play against each other to test the game and make the necessary adjustments.
6. Finally, each group will present their game to the class, explaining the rules and demonstrating a round of the game.

Project Deliverables:

After completing the practical project, each group must write a document in the format of a report according to the following topics:

1. Introduction: Here, the groups should contextualize the topic, mention the relevance and application of fractions in everyday life, state the objective of the project and the strategy chosen to achieve it.
2. Development: In this section, students should explain the theoretical concepts studied and how they were applied during the project. They should also describe the game in detail, including the fractions chosen, the corresponding illustrations, and the rules of the game. In addition, they should indicate the methodology used (how the game was created, tested, and adjusted) and present and discuss the results obtained (how the game contributed to the students' learning, what were the challenges encountered and how they were overcome).
3. Conclusion: The students should revisit the main points of the project, describe the lessons learned and conclude on the effectiveness of the project in facilitating the understanding of fractions and promoting teamwork and creativity.
4. Bibliography: Finally, the students should list all the sources consulted during the project, including books, websites, videos, etc.