Contextualization

Introduction

Algebraic expressions are combinations of numbers and letters related to each other by the fundamental operations of addition, subtraction, multiplication, division, and exponentiation. In other words, they represent calculations that have not yet been performed. The letters are called variables and serve to represent unknown values.

Algebraic expressions are powerful tools in solving mathematical, physical, and other scientific problems. They allow modeling reality, creating formulas and equations that can be solved to find solutions to concrete problems.

To work with algebraic expressions, it is crucial to understand and apply the properties of operations, such as the commutative property (the order of terms does not change the result), the associative property (the way terms are grouped does not change the result), and the distributive property (multiplying a term by a sum is the same as multiplying the term by each of the terms of the sum and adding the results).

Contextualization

Algebra, and by extension algebraic expressions, are used in a variety of contexts in our daily lives. For example, if you want to calculate the distance you can travel with a certain amount of fuel in your car, you can use an algebraic expression. Or, if you are trying to figure out how much you will pay for an item with a discount, you are also using algebra.

Moreover, algebra is an important tool in various professions, including engineering, medicine, economics, graphic design, computer programming, and many others. Therefore, having a solid understanding of algebraic expressions is not only useful for your academic success but also for your professional life.

Practical Activity

Activity Title: The Mathematics of Art - Creating and Deciphering Algebraic Codes

Project Objective

The objective of this activity is to apply algebraic expressions creatively to create and solve problems. In the process, students will explore the connection between mathematics and art by creating algebraic codes that translate into images or drawings. This will allow them to actively engage with the subject while learning about the application of these concepts in different areas of knowledge.

Detailed Project Description

The activity will be carried out in groups of three to five students. Each group should develop an "Algebraic Code" that represents an image or drawing and should be able to decipher the "Algebraic Code" developed by another group.

The "Algebraic Code" must be composed of several algebraic expressions, each of which corresponds to a specific component of the image or drawing. The algebraic expressions should vary in complexity, involving at least four algebraic concepts or properties chosen by the group, such as multiplication, division, exponentiation, distributive properties, among others.

In parallel, the images or drawings should be related to a topic from another discipline chosen by the group, such as history, geography, science, art, etc. This will allow students to see how different topics and disciplines can be interconnected.

Necessary Materials

• Paper and pencil for developing algebraic expressions and drawings
• Computers with internet access for research

Detailed Step-by-Step for the Activity

1. Each group should choose a topic from another discipline that will be the theme of the drawing.
2. Next, the group should develop the "Algebraic Code," a set of algebraic expressions that represent the image or drawing related to the chosen topic.
3. The group should also prepare a solution for their "Algebraic Code," which will be used to check the solution of other groups.
4. After finalizing the creation of the "Algebraic Code," each group will exchange their code with another group. They should then decipher the "Algebraic Code," that is, solve the algebraic expressions to discover and draw the image or graphic representation hidden behind them.
5. Finally, each group should present the drawing they deciphered and the reasoning followed to decipher the associated "Algebraic Code."

Project Deliverables

Each group should produce:

1. The "Algebraic Code," a list of algebraic expressions that represent their image, including an explanation of how each expression is linked to the image.
2. The solution to their own list of algebraic expressions, which will be used to check the answers of other groups.
3. The deciphered image from another group's "Algebraic Code."
4. A written report containing a detailed discussion of the algebraic concepts and properties used, the methodology followed to solve the algebraic expressions of the "Algebraic Code," the graphic representation of the deciphered image, and the sources used to research information.

In the report, the group should provide a contextualization of the chosen theme, explain how the "Algebraic Code" was created, which properties of operations were used and why, and how the process of solving another group's "Algebraic Code" took place. Additionally, they should discuss the results obtained and the conclusions drawn from the project.