Contextualization

Introduction

Mathematics is a quite comprehensive subject and one of the most fundamental themes that it approaches is the concept of fraction. Fractions represent a division - the division of the whole in parts. This principle is of extreme importance for its use in several mathematical applications and in our daily lives.

Fractions are very useful in solving problems that involve the division of a unit or quantity in many equal parts. Through the use of fractions, we can solve complex problems that would be much more difficult and time-consuming if we had to use only whole numbers.

In addition to fractions, another important concept that we will explore is the composition of shapes. Shapes are part of our daily lives and they are essential for us to understand the world around us. When we talk about shapes, we are not only referring to the format of an object, but also to its structure and organization. For example, when we cut a pizza in 8 equal parts, we are working with shapes and fractions at the same time.

Contextualization

In the real world, we find the use of fractions and shapes in several situations. For example, a cut pizza, a cake that is divided among a number of people, the measurement of ingredients in a recipe, the division of tasks among team members, among many other situations.

These concepts are essential for several professional activities. For example, engineers use the concept of fractions and shapes to create complex projects, scientists use it to make precise calculations and teachers use it to teach these important mathematical concepts to students.

To deepen your studies, I suggest the following resources:

• Matemática Divertida - Frações A website that brings an interesting and fun approach to learning about fractions.
• Escola Games - Compondo formas This online game helps to understand the concept of composing shapes in a ludic and interesting way.
• Só Matemática - Frações This page offers a more detailed explanation about the concept of fractions, with fixation exercises.
• Youtube - "Matemática Zupi - Compondo formas" This video explains in a visual and interactive way the concept of composing shapes.

Remember, the best way to learn is by practicing! Therefore, when using these resources, do not forget to practice with exercises and activities.

Practical Activity

Activity Title: "Building Shapes with Fractions"

Project Goal

The goal of this activity is to provide students with a practical and visual understanding of the relationship between fractions and the composition of shapes. Through this activity, students will be able to represent whole quantities as fractions and understand how different shapes can be composed by fractions of a larger quantity.

Detailed Project Description

Students will work in groups of 3 to 5 people, and each group will be responsible for creating an artistic composition using shapes cut from colored paper. Each shape will represent a fraction of a larger shape. For example, a large circle can be composed of 4 quarters, a rectangle can be composed of 2 halves, and so on.

The groups will have to create several compositions, each one using different fractions. After completing the compositions, they will take pictures to document their work. Each group will then prepare a report detailing the process of creating the compositions, the relationship between fractions and shapes, and their conclusions about the activity.

Materials Needed

• Colored paper of different colors
• Scissors
• Glue
• Ruler or compass for measurements
• Camera or smartphone to take pictures

Detailed Step by Step to Perform the Activity

1. Begin by dividing the class into groups of 3 to 5 students.
2. Explain the concept of fraction and how it can be visually represented through the composition of shapes.
3. Provide students with the materials needed for the activity. Each group will need a variety of colored papers, scissors, glue, and a camera to document their work.
4. Each group will begin by choosing the shape they will create, such as a circle, square, or rectangle.
5. They will then decide on the fraction that this shape will represent and cut the chosen shape into parts that represent this fraction (for example, if the choice is a circle representing 1/2, then the circle must be cut into two equal parts).
6. After cutting the shapes, students will arrange and glue the parts together to create the larger shape.
7. The groups will repeat this process to create several different compositions using different fractions.
8. Once all the compositions are ready, students will document their work by taking pictures of each composition and noting which fractions were used in each one.
9. Each group will use the photos and notes to prepare a detailed report of the activity, explaining the process of creating the compositions, the relationship between fractions and shapes, and their conclusions about the activity.

Project Deliverables and Connection to the Activities

The final product of this practical activity will be a set of artistic compositions along with a written report. The report should be structured in four main parts:

1. Introduction: The group should contextualize the theme, highlighting the relevance and application of fractions and shape composition in the real world. The objective of the project should also be stated here.
2. Development: The group should explain the theory behind fractions and shape composition. They should detail the activity they carried out, explaining the methodology they used, and present the compositions created along with a discussion of the results obtained.
3. Conclusion: Students should conclude the work by summarizing their main points, explaining the lessons learned and the conclusions drawn about the project.
4. Bibliography: The group should indicate the sources on which they based their project, such as books, web pages, videos, etc.

The report must be delivered together with the photos of the compositions. The deadline for submission of the project will be one week from the introduction of the activity.

With this activity, students will be able to demonstrate their understanding of the concept of fractions and how shapes can be composed of fractions of a whole. In addition, they will have the opportunity to work on their socio-emotional skills, such as time management, communication, problem-solving, creative thinking and proactivity.