Contextualization

Mathematics is a universal language used for interpreting and describing real-world phenomena. Among the various fields it comprises, the study of arithmetic expressions is fundamental for understanding how we can synthesize and solve everyday problems in a condensed form.

Mathematical expressions include a variety of operations such as addition, subtraction, multiplication, division, exponentiation, and rooting. They are used in various areas of knowledge, such as physics, engineering, and economics. Therefore, understanding the resolution of mathematical expressions is an important step towards improving logical reasoning and abstract thinking.

Expressions are commonly used in problem situations where we need to express an unknown quantity in terms of known quantities. Moreover, they are essential in solving equations and interpreting functions, which are topics widely covered in high school mathematics and physics disciplines. Through this project, you will explore the world of expressions in a practical and engaging way!

Introduction

Knowing how to operate and solve mathematical expressions is a basic skill in mathematics. However, what seems to be a simple topic hides a complexity and beauty that go beyond calculation.

In this project, four key concepts will be explored: numerical expressions (additions, subtractions, multiplications, and divisions), exponentiation, exact root extraction, and algebraic expressions. A numerical expression is the representation of a calculation involving numbers and mathematical operations. In algebraic expressions, in addition to numbers and operations, we have variables that can take on various values.

The operations of exponentiation and rooting will also be explored in the context of expressions. Exponentiation is the operation that represents the product of equal factors, while rooting is the inverse operation of exponentiation. They are used in various practical situations, such as calculating areas and volumes, in physics, and in chemistry.

Practical Activity

Activity Title: "Real World Operations: Exploring Mathematical Expressions through Theme Park Design"

Project Objective:

To develop an understanding of mathematical expressions through the creation of a real project: the design of a theme park. Thus, students will be able to apply theoretical concepts related to numerical expressions, exponentiation, rooting, and algebraic expressions in a practical and playful context. In this sense, it is expected that this activity promotes the deepening of mathematical knowledge associated with the development of socio-emotional skills such as teamwork, time management, critical thinking, and problem-solving.

Detailed Project Description:

Students will be divided into groups of 3 to 5, and each group will have the task of designing a theme park. Each park must have a certain number of attractions (rides, restaurants, shops, etc.), green areas, and infrastructure. Students will have to use mathematical expressions to calculate construction costs, the area occupied by the park, the amount of staff needed, among other aspects.

Each group must complete the activity by delivering a blueprint of the park and a detailed report.

This project should take at least 12 hours per student to complete.

Required Materials:

• Graph paper to draw the park blueprint (a design software like AutoCad can also be used)
• Calculator
• Books and reference materials
• Computer with internet access
• Materials for creating a report (paper, pen, text editing software, etc)

Detailed Step-by-Step:

1. Group Formation and Research: Form groups of 3 to 5 people. Each group should choose a theme for the park and research existing theme parks, attractions, infrastructure, etc.

2. Park Planning: Think about what you want to include in your theme park and sketch an initial plan. Include at least 5 types of attractions (e.g., roller coaster, Ferris wheel, haunted house, etc.), shops, restaurants, and rest areas.

3. Calculations: Use mathematical expressions involving addition, subtraction, multiplication, division, exponentiation, and rooting to calculate various aspects of the park such as total area, construction costs of attractions, revenue potential based on ticket prices, operating costs, etc.

4. Drawing the Blueprint: Use graph paper to draw the park blueprint. Indicate where each attraction, shop, restaurant, and rest area will be located, as well as the infrastructure (restrooms, first aid stations, etc).

5. Report: Prepare a detailed report of the project, including the introduction, development, conclusion, and bibliography. In the introduction, contextualize the theme, explain the relevance of mathematical expressions in the real world, and the project's objectives. In the development, present the theory behind the concepts used, detail how the activity was carried out, the methodology used, and present and discuss the results obtained. In the conclusion, summarize the main points of the project, explain what was learned, and draw conclusions about the work. In the bibliography, list the sources used for the project.

6. Presentation: Prepare to present your project to the class, sharing all aspects of your theme park.

Project Deliverables:

At the end of the project, each group must deliver:

1. The blueprint of the theme park.
2. A written report that includes a detailed description of the project, the calculations performed, the expressions used, the difficulties encountered, the proposed solutions, and the lessons learned. This report should follow the topics: Introduction, Development, Conclusions, and Bibliography.
3. Oral presentation of the project to the class, explaining the main challenges and solutions found, as well as the lessons learned.

In this activity, students must apply the concepts of numerical expressions, rooting, exponentiation, and algebraic expressions in a practical and fun context. In addition, students will have the opportunity to develop teamwork, communication, and time management skills.