Contextualization

The use of ratios and proportions is a vital and versatile mathematical tool that we encounter in various everyday situations. This concept allows us to compare the relationship or relative quantity of two quantities and, through this, solve several everyday problems.

Operating with ratios plays an essential role in many areas, including sciences, engineering, economics, and many other fields. For example, in our daily lives, when we compare the prices of products in different stores, we usually use proportions to determine which store offers the best value. Similarly, in cooking, ratios are used to maintain the correct proportions of ingredients. If you double all the ingredients in a cake recipe, you will end up with the same cake flavor, just in a larger quantity. Ratios are also used in maps to represent a real scale.

In this project, we want to present this important concept in a playful and engaging way, associating mathematics with real situations through a group project that challenges you to bring the concepts of ratio and proportion to life.

Introduction

A ratio is a mathematical concept used to express the relationship between two numbers or two quantities. Ratios can be expressed in various ways, such as a fraction, with two numbers separated by a colon (for example, 3:2) or as a verbal statement (for example, '3 to 2'). Ratios are often used to compare parts of a whole or to compare a value to a total.

Operations with ratios, such as addition, subtraction, multiplication, and division, follow the same rules as operations with fractions. In essence, a ratio is a way to express a fraction, and therefore, any operation we can perform with a fraction, we can perform with a ratio.

The concept of proportion is closely related to the ratio. A proportion is an equation that states that two ratios are equal. This allows us to make comparisons between two pairs of numbers and solve a wide range of practical problems.

In this project, you will work in groups to explore these concepts and apply them to concrete situations. Additionally, the project will have an interdisciplinary component, allowing you to apply your new skills in operations with ratios to problems from other disciplines, such as Sciences and Geography.

Practical Activity

Title: 'Cooking with Ratios'

Project Objective

Apply the concept of ratios and proportions in a real culinary activity, transforming a recipe for different portion sizes. This will not only help in understanding these mathematical concepts but also strengthen the interconnection between mathematics and everyday life.

Detailed Project Description

Students will be divided into groups of 3 to 5, and each group will choose a recipe as the basis for their project. The group will then be challenged to adjust this recipe for a different quantity of people, using ratios and proportions to increase or decrease the amount of each ingredient. The group should also apply the concept of ratios in other disciplines. For example, they can calculate the ratio of different nutrients present in their recipe to understand its nutritional value (Sciences) or even calculate the ratio of the recipe's cost per portion (Mathematics and Economics).

Necessary Materials

• A recipe chosen by the group.
• Ingredients for the recipe.
• Kitchen appliances needed to prepare the recipe.
• Calculator.
• Paper and pen to write down observations and calculations.
• Internet access for research.

Detailed Step-by-Step for Carrying Out the Activity

1. Each group should choose a recipe they would like to prepare.
2. Check the number of servings the original recipe yields.
3. The group must now decide how many people they would like to adjust the recipe for.
4. Each group uses the ratio to adjust the quantity of each ingredient according to the desired number of servings.
5. Write down the adjusted recipe.
6. Prepare the recipe following the new ingredient quantities.
7. Discuss the result: did the adjusted recipe produce the expected number of servings? How does the taste compare to the original recipe?
8. RESEARCH to discover the nutritional value of the ingredients used and calculate the ratio of the different nutrients present in one serving of your recipe (interdisciplinary application of Sciences).
9. Calculate the total cost of the recipe and the cost per portion. How does the ratio of the cost per portion compare between the original recipe and the adjusted recipe?

After completing the practical activity, each group should produce a detailed written report on the project. The report should include the following topics:

• Introduction: Contextualization of the theme, highlighting the relevance and application of the theme in the real world, and the project's objective.
• Development: The theory behind the main theme of the project, detailed explanation of the activity, the methodology used, and the results obtained. Detail how ratios were used to adjust the recipe and what the results were. Also discuss how ratios were applied in other disciplines, such as Sciences and Economics.
• Conclusions: Summarize the main points, highlighting the learnings obtained and the conclusions drawn about the project. Reflect on how the understanding of the concept of ratios was enhanced through the project.
• Bibliography: Indicate the sources you relied on to work on the project such as books, web pages, videos, etc.

This written report is an important document that will demonstrate how the group applied the concepts of ratio and proportion in a real-world context and how they managed to connect these mathematical concepts with other disciplines.