Contextualization

The study of fractions and decimals is a fundamental point in Mathematics. Many concepts from our daily lives, such as dividing a pizza into equal parts or understanding discount percentages in a product, are directly related to these subjects. Fractions and decimals are just different ways to represent values less than an integer, and choosing one depends on the context of the application.

Operations with fractions and decimals can a bit complex at first. Adding and subtracting fractions requires skills to find a common denominator. Multiplying and dividing fractions is more straightforward but requires understanding the rule of how to deal with numerators and denominators. Operations with decimals may be considered simpler because one can treat them as if they were whole numbers, just being careful to position the decimal point correctly.

In addition to this, having knowledge in these operations provides a solid base for more advanced study, such as solving problems related to scales, proportions, percentages, measures, and geometry. In this sense, understanding these concepts and knowing how to use them is an essential step for the development of mathematic studies.

In the real world, operations with fractions and decimals are everywhere, from dividing a cake at a birthday party to programming a computer. Decimals are widely used in situations involving money, metrics, growth rate, and many others. Fractions, besides being present in the kitchen while preparing recipes, are also utilized to represent chances and probability. Therefore, mastering these skills does not only improve our school performance but also prepares us to deal with everyday situations.

For more in-depth study of the subject, we suggest the following resources:

• Khan Academy has several videos explaining operations with decimals and fractions: Link Khan Academy
• Just Math, a complete website containing explanations and exercises: Link Just Math

Practical Activity: "Building the Fraction and Decimal Garden"

Project Objective

The goal of this project is to propose the building of a hypothetical garden (on paper or on a design software) where the areas of different parts of the garden are represented by fractions and decimals. This way, the students will have the opportunity to practice operations with fractions and decimals and understand how they are applied in the real world.

Project Description

Students will be divided into groups of 3 to 5, and each group must plan and design a garden. The garden's specifications (such as total area, flower areas, grass areas, pathways, etc.) must be represented by fractions and decimals. The challenge is juxtaposing the division of a limited space (the garden) into several parts (flowers, grass, paths), which requires operations with fractions and decimals.

Necessary Materials

• Graph paper or a design software (such as Google SketchUp, AutoCAD, or even more simple ones such as Paint);
• Ruler, pencil, and eraser (if the project is drawn on paper);
• Calculator.

Step-by-step

1. Each group must choose a total size for the garden (for example, 10m x 10m).
2. Then, they must decide how many different parts the garden will have and what they will be (for example, flowers, grass, paths, pond, etc.).
3. Each part of the garden must be represented by a fraction or a decimal of the total size of the garden. These values must be justified and documented by the group.
4. Then, students must draw the garden on the graph paper or on the design software, according to the percentages they decided on.
5. Throughout the process, students must document all the decisions, calculations, and project justifications that they did.

Project Delivery

At the end of the project, groups must deliver:

1. The plan for the garden designed, containing all the specifications (if done on paper, a good quality scan or photo must be delivered).
2. A written report containing:

• Introduction: Describing the importance and applications of operations with fractions and decimal and project's objective.
• Development: Detailing the theory of operations with fractions and decimals, detailed description of the activity, employed methodology, and calculations and obtained results.
• Conclusions: Summarizing the work done, obtained learnings and drawn conclusions about the project.
• Bibliography: Indicating the sources of information used during the work.

This project is multidisciplinary and includes skills in mathematics with the creativity and planning of visual arts. It will also improve students' teamwork skills, time management, and critical thinking.