Context

Rational numbers form a set of numbers expressed in the form of a fraction, where the numerator is an integer and the denominator is a non-zero natural number. Examples include the number 2/3 (two thirds), 4 (which can be expressed as 4/1), and even 0 (zero over one).

Now, you might be wondering, why do we need to incorporate another set of numbers? Why not just stick with natural numbers or integers? Well, rational numbers are extremely useful and necessary for expressing quantities that are not whole numbers. Imagine if you wanted to divide a pizza with your friends and someone asked for 1/2 of a pizza, or if someone offered you 3/4 of an apple. Without rational numbers, we couldn't express these quantities accurately.

Rational numbers can be expressed as exact decimal numbers or recurring decimals. For example, the number 1/2 can be written as 0.5 and the number 1/3 as 0.3333..., which is a recurring decimal. This makes rational numbers essential in various fields, such as science and engineering or in finance, where they are used, for example, to calculate interest or exchange rates.

To delve deeper into the subject and have access to more practical experiences of how rational numbers are used, I suggest the following reliable sources:

1. Support material and exercises with solutions on the Escola Kids website - Rational Numbers
2. Theoretical and practical explanations on the YouTube channel Matemática Rio with Prof. Rafael Procopio - Rational Numbers

Practical Activity: "Dividing Cake Slices"

Project Objective

This project aims to introduce the concept of rational numbers through dividing a paper cake. By the end, students should be able to understand the representation of a fraction as a rational number.

Detailed Project Description

Students will be divided into groups of 3 to 5 people, and each group will receive a paper "cake" (which can be a cardboard circle or card paper). This cake will have to be divided into parts (slices) representing different fractions. The fractions must then be converted into decimal numbers and vice versa.

Required Materials

• Cardboard paper or cardboard to make the cake.
• Scissors.
• Colored pens or pencils.
• Ruler.
• Calculator.

Detailed Step-by-Step

1. Each group receives a paper cake.
2. The students decide among themselves how they will divide the cake. They can decide, for example, to divide it into 2, 3, 4, 5, etc. equal parts.
3. After deciding, they must divide the cake into equal parts using scissors.
4. Now, each slice of cake represents a fraction of the total cake. For example, if they divided the cake into 4 parts, each slice represents 1/4 of the total cake.
5. The students then write the corresponding fraction for each slice of cake.
6. Next, they must convert this fraction to a decimal number using the calculator and write this conversion next to the fraction on each slice of cake.
7. Exchange the cake slices between groups and ask each group to convert the fractions and decimals back to their originals.
8. After completing this activity, each group should prepare a report on the project.

Project Deliverables and Connection with Activities

Students should deliver, as the final result of this project, a paper "cake" divided into fractions and decimal numbers, as well as a written report.

The report should contain an Introduction about the concept of rational numbers, a detailed description of the activity carried out in the Development section, including the discussion of results such as the correspondence between fractions and decimal numbers. In the Conclusion section, students should reflect on what they learned from the practical activity and how it helped in understanding the concept of rational numbers. Finally, in the Bibliography section, they should list the sources of information used throughout the project.

This practical activity aims to connect theoretical knowledge about rational numbers with a daily situation that is dividing a pizza or cake, allowing mathematical concepts to gain meaning and become more tangible for students.