Introduction

Operating with fractions is an important milestone in students' mathematical learning, as it paves the way for understanding various concepts and practical applications in everyday life. In this sense, the multiplication and division of fractions are operations that require a level of abstraction that can be challenging for many students.

In the case of multiplication, the operation is done by multiplying the numerators to obtain a new numerator and the denominators to obtain a new denominator. For example, multiplying 1/2 by 3/4 results in 3/8. On the other hand, dividing fractions requires multiplying the dividend by the reciprocal of the divisor. For example, dividing 1/2 by 3/4 results in 2/3.

These operations are fundamental for the development of mathematical thinking and are applied in various areas of knowledge, besides being used in everyday situations. Therefore, it is essential for students to master these concepts.

Contextualization

The study of fractions and their operations, including multiplication and division, is essential knowledge in mathematics. It allows solving problems that involve dividing a quantity into equal parts, comparing quantities, among other situations.

Furthermore, the ability to operate with fractions is fundamental in various everyday situations. For example, when dividing a pizza among friends, when calculating the proportion of ingredients in a recipe, when splitting expenses in a group, among others. Therefore, mastering these operations can facilitate the resolution of everyday problems and enhance students' understanding of how mathematics is present in their lives.

Practical Activity

Title: The Mathematics of Recipes

Project Objective

The objective of this project is for students to apply the multiplication and division of fractions in a practical and relevant context: preparing a culinary recipe. This will allow them to see the real-world application of this concept and develop their mathematical skills while enhancing abilities such as teamwork, time management, and problem-solving.

Detailed Project Description

Each group should choose a recipe of their liking that contains at least five ingredients in fractional quantities. The students must then adjust this recipe to feed a larger number of people, using fraction multiplication, and for a smaller number of people, using fraction division.

The project should be executed in four stages:

1. Choosing the recipe and adjusting the quantity of ingredients for more people.
2. Adjusting the quantity of ingredients for fewer people.
3. Presenting the work to the class.
4. Creating a detailed project report.

Required Materials

• Internet access for recipe research
• Textbooks or reference materials on fraction multiplication and division

Detailed Step-by-Step Guide for Activity Execution

1. Each group should research and choose a recipe that contains at least five ingredients with quantities expressed in fractions.

2. Each group should adjust the recipe for a larger number of people using fraction multiplication. The ingredients should be listed in a table, along with their original quantities and the adjusted quantities.

3. Next, the groups need to adjust the recipe for a smaller number of people, this time using fraction division. The new quantities should be added to the table.

4. Each group should make a presentation to the class, explaining the chosen recipe, showing their tables, and explaining how they made the adjustments using fraction multiplication and division.

5. Finally, the groups should create a detailed project report, including the introduction, development, conclusions, and bibliography used, as described in the introduction of this project.

Project Deliverables and Connection to Activities

At the end of the project, students must deliver:

1. The table with the original and adjusted quantities of ingredients for more and fewer people.
2. The detailed project report, with the required topics.

In the report, students should contextualize the theme (Introduction), detail the chosen recipe and the adjustments made (Development), comment on what they learned from the experience and how they applied the theory in practice (Conclusions), and list the resources they used to learn and apply fraction multiplication and division (Bibliography).

This project was designed to have a direct connection between the practical activity (adjusting ingredient quantities) and the report writing. The practical experience will allow students to understand the theory more deeply and apply it in a real context. This will help make the report more concrete and meaningful, rather than just being a writing exercise.