Introduction

Welcome, dear students, to the fantastic journey through the universe of Decimals! We embark on a challenge to explore and understand the workings of four fundamental operations (addition, subtraction, multiplication, and division) and powers when applied to decimal numbers. For some of you, this topic might initially seem complicated; however, with effort, dedication, and, most importantly, collaborative work, I am sure we will have a fun and enriching experience.

Decimal numbers are an essential part of our numeral system. They are used to denote quantities that are not whole numbers. Just think of a chocolate bar that you want to split among your friends. How can you represent the division fairly, if the bar can’t be divided into an equal number of whole parts? Or, how is it possible to express the distance that an athlete covers during a 100-meter race, if they do not reach the 100-meter mark, exactly but a bit ahead or behind it? We use decimal numbers for these and many other cases.

To become proficient in decimal operations, it is crucial to grasp the importance of decimal point alignment, strategies for performing addition and subtraction, techniques for multiplication and division, and rules of exponentiation. We will address these aspects and more, preparing you not just to solve mathematical problems, but also to apply such skills in real-world situations.

Contextualization

Decimal numbers are all around us. We use them for measurements of length, weight, volume, temperature, currency, percentages, and many more. Proficiency with decimals enables us to understand our surroundings better, to take informed decisions, and to resolve complex problems.

For instance, when we go shopping, we come across products tagged with decimal prices, such as $2.99 for a kilo of apples. If we plan to buy 2.5 kilograms, how do we calculate the total cost? The field of science relies heavily on decimals as well. A scientist may measure the acidity of a solution to be 5.6 in pH value or record a temperature of a chemical reaction to be 37.2 degrees Celsius. Decimal operations are essential in all these situations.

To delve deeper into the topic, I recommend you refer to the following resources:

• Khan Academy (www.khanacademy.org): Provides an array of videos, practice exercises, and quizzes for decimal operations.
• OBMEP Math Portal (https://portaldaobmep.impa.br/) : Offers in-depth explanations and problem sets on decimals along with tips and tricks.
• Only Math (www.somatematica.com.br): Features lessons and exercises on decimal numbers and their operations.
• Book: “Matemática Divertida e Curiosa” by Malba Tahan: An engaging way to learn mathematics, including decimal operations, through this classic of mathematical literature.

Hands-on Activity: Constructing a Decimal City

Project Goal

The aim of this project is to apply mathematical concepts, particularly decimal operations, in a practical context, as well as to hone skills like teamwork, time management, and problem-solving. During this activity, students will create a fictional “Decimal City,” based on a provided budget and measurements.

Project Description

Students will divide into groups of 3–5, with each group becoming responsible for constructing a part of “Decimal City.” Every group will have a fictitious budget to spend on different types of constructions (residential, commercial, schools, hospitals, etc.), each type having its cost per square meter. The groups must collaborate to decide the number and types of buildings they will construct, taking into account their costs and the available capital. They also have to calculate the necessary space for the buildings on the city map.

This project will also incorporate elements of Geography as the students must consider principles of urban planning, including the positioning of buildings and essential infrastructure (roads, avenues, etc.).

Required Materials

• Graph paper
• Color pencils or pens
• Calculator
• Rulers and set squares
• List of costs per square meter for each type of building

Step-by-Step Process

1. Each group receives graph paper representing their city plot, as well as the cost list per square meter for each building type.

2. Now, the group must discuss and decide on the number and types of constructions they will build, considering the budget available to them. This is a critical step in the project, for it will require them to perform several decimal operations to compute costs and measurements.

3. The group draws the buildings on graph paper, while adhering to the specified measurements for each structure.

4. After drawing all their buildings, the group should compute the total cost of these structures and verify if the total cost stays within the budget provided. Should the total cost exceed their budget, they must redesign their city plans.

5. Finally, the group needs to plan the city’s layout: Where will each building be located and how will people navigate through the city? For that purpose, they must design roads and avenues while considering public services (hospitals, schools, etc.).

Students must document each stage of this process in a report that comprises the following sections:

• Introduction: Explain the project, its objectives, and the relevance of decimal operations.
• Development: Describe in detail the work done, including the decimal operations performed, any challenges faced, and how they overcame them. In this section, present the methodology they adopted for carrying out the operations and calculations, along with the data considered for every decision taken throughout the project.
• Results and Discussion: Present and discuss all the results obtained, such as the total cost of constructions, number and type of buildings, and so on.
• Conclusion: Reflect on the learning that occurred, the nature of teamwork, and the difficulties and conveniences encountered.
• References: List the sources consulted for the project implementation.

Project Deliverables

At the end of the project, every group must submit a drawing of their “Decimal City” on graph paper, with each building adhering to the prescribed measurements. In addition, they should provide a structured written report, as outlined above, detailing the city's construction process, the performed calculations, problems and their resolutions, decisions taken, and the total construction cost.

During this project, students will develop proficiency in decimal operations, estimations, rounding off numbers, and the appropriate use of calculators. They will also strengthen social and emotional skills such as time management, communication, problem-solving, creative thinking, and proactiveness.

I hope you will enjoy this fantastic voyage into the realm of Decimals and seize this opportunity to learn through a fun and collaborative activity. Best wishes, budding urban architects!