Introduction

Fractions are mathematical concepts that express the idea of parts of a whole. They are formed by two natural numbers, where the top one is called the numerator and the bottom one is called the denominator. When two or more fractions represent the same quantity, when simplified, they are called equivalent fractions. For example, the fractions 1/2 and 2/4 are equivalent because they both represent half of a whole.

In this journey, you will explore the concept of equivalent fractions, learn to recognize and represent different fractions that refer to the same quantity, and understand how the same fraction can be represented in various ways. Additionally, you will delve into the important notion of irreducible fractions, which is the fraction in its simplest form possible and cannot be further simplified.

Contextualization

Fractions play an important role in the world around us. They are used to represent quantities that are not whole numbers, such as dividing a pizza, measuring ingredients for a recipe, or calculating the probability of an event happening. Mastering the concept of equivalent fractions is the key to a better understanding of more complex topics in mathematics, such as simplifying fractions and performing operations with fractions.

In the real world, understanding equivalent fractions is essential. If you are cooking and the recipe calls for 1/2 cup of flour, but you only have a measuring spoon of 1/4 cup, you need to know that two 1/4 cups are equivalent to 1/2 cup for the recipe to work. Similarly, if you are drawing and need to divide a line into three equal parts, but your ruler only has markings in quarters, you need to understand that three quarters and three thirds are equivalent for your drawing to be precise.

Practical Activity

Activity Title: "The Magic of Equivalent Fractions: A River of Discoveries"

Project Objective

To apply the concept of equivalent fractions in a playful way, understand the irreducibility of fractions, and relate them to the real world. Additionally, the project aims to enhance teamwork skills, time management, problem-solving, creative thinking, and proactivity.

Detailed Project Description

Students, organized in groups of 3 to 5, will be challenged to create a model of a river where equivalent fractions are represented in the division and marking of its course. Additionally, they will have to prepare a presentation to explain the work done, correlating it with real-world examples.

The river will be divided into several segments, each representing a fraction. Then, the students will select a set of equivalent fractions for each segment, for example, 1/2, 2/4, 3/6, and so on. The river model should also show the corresponding irreducible fraction for each set of equivalent fractions.

At the end of the project, students should present a detailed report and an oral presentation on the concept of equivalent fractions, the procedures used in the project, the discoveries, the difficulties encountered, and how they were overcome.

Required Materials

• Cardboard
• Paints and brushes
• Ruler and compass
• Glue
• Sand and small stones (for decoration)
• Cutouts of colored paper (to represent the fractions)

Detailed Step-by-Step for Activity Execution

1. Groups should start the project with research on the concept of equivalent fractions.
2. Next, they should sketch the shape and course of the river on cardboard, dividing it into various segments.
3. In each segment, students will represent a set of equivalent fractions using cutouts of colored paper. Each color will represent a numerator, and the total number of cutouts will represent the denominator.
4. After finishing the representation of equivalent fractions, students should identify and note down the corresponding irreducible fraction.
5. Once this is done, students will decorate the model with rocks, sand, and other elements to make it more realistic.
6. Alongside the construction of the model, students should work on preparing the presentation and writing the report.
7. The completed work should be presented to the class, where groups must explain how the fractions were represented and how they are used in daily life.

Final Product and Connection to Activities

The final product should be the model, an oral presentation, and a written report. The model and the presentation will allow students to apply practically and visually what they have learned about equivalent fractions.

The written report, in turn, should contain the theory behind the topic, the detailed procedure of the activity, representation of fractions in the model, examples of the application of fractions in everyday life, and the conclusions drawn. The report should also include the bibliography used for the project development.

Students should write this document clearly and organized, dividing it into the following sections:

• Introduction: It must contextualize the topic, its relevance and application in the real world, as well as the project's objective.
• Development: Should explain the theory behind the topic, detail the activity, indicate the methodology used, present and discuss the results obtained.
• Conclusion: Should conclude the work by summarizing the main points, explaining the learnings obtained, and the conclusions drawn about the project.
• Bibliography: Should indicate the sources they relied on to work on the project such as books, web pages, videos, etc.

The project as a whole presents a profound and inclusive way of understanding the topic of equivalent fractions and their application in the real world.