Contextualization

Multiplication and division are fundamental operations in mathematics. They are used in a multitude of everyday situations, such as calculating areas, dividing food portions, converting currencies, understanding proportions, among others. When it comes to decimal numbers, things get a bit more complex, but equally important. After all, many of the quantities we deal with on a daily basis have decimal places, such as distance measurements, volumes, weights, and money.

By learning to multiply and divide decimal numbers, you will be taking a big step in your mathematical journey, deepening your understanding of the numbering system and fundamental operations. Additionally, you will be developing valuable skills that will be used in various areas of knowledge and in everyday situations.

Introduction

To multiply and divide decimal numbers, we first need to understand well what these numbers are. Decimal numbers are those that have a comma separating the whole part from the decimal part. Understanding this is essential to correctly perform the operations and interpret the results obtained.

Multiplying decimal numbers is similar to multiplying integers. What changes is that, at the end of the operation, we count how many decimal places are in the numbers we are multiplying and place the same quantity in the result. In division, the process is a bit different. We divide normally, as if the numbers had no comma, and then place the comma in the right place in the result.

When working with decimal numbers, it is also important to understand the concept of rounding, which will be very useful, for example, when the division is not exact. If a division is not exact and we have to round the result, we need to do it conveniently so that the result is as accurate as possible.

Practical Activity

Activity Title: "Decimal City: Building Cities with Decimal Numbers"

Project Objective:

The main objective of this project is to have students apply the concepts of multiplication and division of decimal numbers in a practical and fun scenario. Additionally, it also aims to enhance teamwork skills, time management, problem-solving, and creative thinking.

Detailed Project Description:

Students will be divided into groups of 3 to 5 students, and each group will be responsible for creating a city, the "Decimal City." In this city, decimal numbers actively participate in the construction and maintenance of buildings, roads, parks, among other urban items. For this, the teams will have to plan, calculate, and analyze the costs and benefits of each construction using the operations of multiplication and division of decimal numbers.

Required Materials:

1. Graph paper or grid paper.
2. Pencils and erasers.
3. Colored pens.
4. Ruler.
5. Calculator.

Step by Step:

1. Start the project by introducing the concept of "Decimal City" to the students. Explain that they will work as a team to create their own city, using the concepts of multiplication and division with decimal numbers.

2. Divide the students into teams of 3 to 5 members. Each team will be responsible for designing and calculating the aspects of their city.

3. Provide each group with graph paper or grid paper. This paper will be the map where they will build the city. Explain that each square on the paper represents a unit in the city, and they will need to calculate the area and cost of each building based on the number of squares it occupies.

4. Instruct the students to start planning their city. Develop a list of possible constructions (houses, buildings, parks, roads, etc.) along with their respective costs in decimal numbers. For example, a house may cost 2.5 units, a building 7.8 units, and so on.

5. The students will design their city having to calculate the total cost of each chosen item through multiplication (quantity of items by unit cost) and division of decimal numbers (for example, to evenly distribute resources or spaces).

6. At the end of the activity, each group must present their city, explaining the methodology used to calculate the costs and the logic applied in the distribution of spaces in the city.

Project Deliverables:

After completing the practical part, students must write a document (report), which will contain the four main topics: Introduction, Development, Conclusions, and Bibliography.

• Introduction: In this part, the group will contextualize the theme, explain its relevance and practical application, as well as the project's objective.

• Development: Here, the group must explain the theory behind the multiplication and division of decimal numbers, detail the activity carried out, indicate the methodology used, and finally present and discuss the results obtained.

• Conclusions: In this section, students will review the main points, explain the learnings obtained, and draw conclusions about the project.

• Bibliography: The group will indicate the sources they relied on to work on the project, such as books, web pages, videos, etc.

Students must present the "Decimal City" along with the written report, which must be submitted one week after the start of the project. It is important to emphasize that the project aims not only for the correct results of the operations but mainly for the learning process, teamwork skills, and the creative application of mathematics in solving practical problems.