Contextualization

Theoretical Introduction

Learning mathematics is an essential part of every child's education. Among the various branches of this field of knowledge, the study of fractions and shapes is very important for the development of reasoning.

Fractions are numbers that represent parts of a whole. They are composed of a numerator, which indicates how many parts we have, and a denominator, which shows in how many parts the whole was divided. Understanding fractions is crucial for many practical applications, from dividing a cake to calculating percentages.

Geometric shapes, on the other hand, are the cornerstone of geometry. They are images that represent spaces or figures, such as circles, squares, and rectangles. Knowing them and understanding how they relate is a crucial step to grasp other more advanced mathematical concepts.

Contextualization

Fractions and shapes are present in various aspects of our daily lives. When we slice a pizza into pieces, we are dividing a circle into equal parts. Each slice can be represented by a fraction of the whole.

Similarly, when we cut a chocolate bar and share it with friends or family, we are dividing that unit into equal parts, and each part can be represented by a fraction.

These concepts are also used in cartography, architecture, engineering, design, and even in digital games. Therefore, mastering the understanding of fractions and shapes is essential for anyone wishing to pursue careers in these areas.

Practical Activity

Activity Title: Fraction in Art Form

Project Objective

Use art to understand the concept of fractions and shapes through the creation of a representative image. Students will divide a shape into different fractions and assign different colors to each fraction, creating a work of art. By the end of the project, students should be able to:

1. Divide shapes into several equal parts.
2. Represent these divisions as fractions.
3. Understand the relationship between fractions and shapes.
4. Work in a team and communicate effectively.

Detailed Project Description

This project involves students working in groups of 3 to 5 people, with an expected total working time of 5 to 10 hours per student.

The groups will choose an initial shape (rectangle, circle, square, etc.) and divide this shape into equal parts, each representing a fraction of the whole. Each part should be colored with a different color.

They will then artistically represent this image using craft materials. Students will have to work together to divide the shape, decide which colors to use for each division, and how to compose the final image.

Additionally, the groups should explain in writing, through a report, their division process, the representation in fractions, and the relationship of these fractions with the final image.

Required Materials

• Cardboard or cardstock
• Rulers
• Pencils and erasers
• Colored pens
• Craft materials (glue, scissors, colored paper, etc.)

Detailed Step-by-Step for Activity Execution

1. Group Formation: Students will be divided into groups of 3 to 5 people by the teacher.
2. Shape Selection: Each group must choose a basic geometric shape (circle, square, rectangle, etc.).
3. Shape Division: The group will divide the chosen shape into several equal parts, representing fractions of the whole.
4. Coloring the Shape: Each fraction of the shape will be colored with a different color.
5. Shape Representation: Each group will artistically represent the shape and fractions using craft materials.
6. Report Elaboration: Each group will prepare a report describing the division process, the representation in fractions, and the relationship of these fractions with the final image.

Project Deliverables

This activity has two main deliverables: The art image divided into fractions and the written report.

Art Image: Each group will deliver a handmade illustration of a shape divided into fractions, with each fraction colored differently. The goal is for this image to be the practical application of the concepts worked on.

Written Report: In parallel with the illustration, students must produce a written document reporting on the project. This document should be organized into four sections: Introduction, Development, Conclusions, and Bibliography.

In the introduction, students should contextualize the theme, explain its relevance and real-world application, as well as the project's objective. In the development, students should explain the theory behind fractions and shapes, describe the activity in detail, indicate the methodology used, and finally present and discuss the results obtained.

In the conclusion, students should highlight the main points learned, explicitly stating the lessons learned and the conclusions drawn about the project. In the bibliography, students should indicate the sources they relied on to work on the project, such as books, web pages, videos, etc.