Contextualization

Introduction

Hello, class! We are about to embark on an exciting journey through the world of Reasons and Proportions. But you must be wondering: 'What are reasons and proportions? What are they used for?' Well, let's get started!

A reason is the comparison between two numbers. It is represented by a fraction, where the numerator is greater than the denominator. For example, if you have 5 cats and 3 dogs, the ratio of cats to dogs is 5/3. The ratio helps us understand the relationship between two sets of numbers.

Proportion, on the other hand, is the equality between two ratios. For example, if we have 5 cats to 3 dogs, and 10 cats to 6 dogs, we can say that these two ratios are proportional. Proportion is a very useful tool in various situations in our daily lives, such as in culinary recipes, for instance.

Contextualization

But why is it important to learn about reasons and proportions? Well, mathematics is everywhere, and reasons and proportions are fundamental tools to understand how the world around us works. Think about a cake recipe: if you want to make half the recipe, you need to reduce all quantities by half, right? That's a proportion.

Let's explore more examples of the use of reasons and proportions in our daily lives: if you are saving up to buy a toy, and you earn $5.00 per week, and the toy costs $20.00, how many weeks will it take to save up the money? In this case, the number of weeks it will take you to save up the money is a reason.

Reasons and proportions are also present in many other areas, such as music, art, science, and even sports. So, get ready to embark on this mathematical adventure with us!

Practical Activity: 'Reasons and Proportions in the Real World'

Project Objective

The objective of this project is to apply the concepts of reasons and proportions in the real world, in a practical and fun way. Students will conduct research, collect data, solve problems, and present their findings in a creative and collaborative manner.

Project Description

Each group of students will be responsible for choosing a specific theme (for example: sports, music, art, culinary, science, etc.) and investigate how reasons and proportions are applied in that theme. Students will collect data, solve real problems, and create a presentation to share their discoveries with the class.

Materials Needed

• Paper and pens for notes
• Internet access for research
• Various materials, depending on the chosen theme (for example, if the theme is culinary, students may need ingredients and kitchen utensils)

Step by Step

1. Theme Selection: Each group should choose a theme that is of interest to all group members. The theme should be related to an area of life where reasons and proportions are used.

2. Research: Students should research the chosen theme, seeking to understand how reasons and proportions are applied in that area. They can look for information on the internet, books, and magazines, as well as talk to experts, if possible.

3. Data Collection: After the research, students should collect data on the theme. For example, if the chosen theme is sports, they can collect data on the heights and weights of players from different teams.

4. Problem Solving: Using the collected data, students should create and solve problems of reasons and proportions related to the theme. For example, using the data of basketball players, they can create a problem about the proportion between height and weight.

5. Presentation Creation: After solving the problems, students should create a presentation to share their findings with the class. The presentation can be done in various ways: a poster, a play, a song, a video, etc. Creativity is very welcome!

6. Class Presentation: Finally, each group will present their project to the class. During the presentations, students should explain the chosen theme, how reasons and proportions are applied in that area, the problems they solved, and the conclusions they drew from the project.

Remember, mathematics is part of our daily lives, and understanding how reasons and proportions work can help us better understand the world around us. Have fun exploring and discovering!