Contextualization

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. Algebraic expressions are mathematical statements that include variables, operations, and constants. They are essential for understanding many mathematical concepts and have broad applications in various areas such as science, engineering, economics, and many others.

In mathematics, algebraic expressions can represent unknown numbers or values that are subject to change. These expressions are written using numbers, arithmetic operations, letters (to represent variables), and some other operation symbols.

We can simplify an algebraic expression by combining similar terms, that is, terms that contain the same variables and powers. For example, in the expression 2x + 5x + 3y, we can combine them to get a result like 7x + 3y. Learning about algebraic expressions and simplifying expressions is a fundamental step in the study of mathematics and calculus.

Algebraic expressions are essential tools in various professions and daily activities. For example, engineers use them to describe physical relationships in complex systems, economists use them to model market behavior, computer scientists use them to describe algorithms and processes, and educators use them to teach problem-solving and critical thinking.

This project aims to develop essential skills in manipulating algebraic expressions and understanding their applications in problem-solving. The goal is that by the end of this project, students will be able to understand and manipulate algebraic expressions, formulate problems and solutions in algebraic terms, and understand the role of algebra in problem-solving.

To aid in the understanding and deepening of the topic, it is suggested to consult the following resources:

• Khan Academy: Offers video lessons on the topic of solving equations and algebraic expressions.
• SOS Professor: Excellent resource with detailed explanations and examples of algebraic expressions and equation solving.
• Mundo Educação: Explanatory article on algebraic expressions and how to manipulate them.

Practical Activity - "Algebraic Expressions in Real Life"

Activity Objective

The proposed activity aims to illustrate and solidify students' understanding of algebraic expressions, as well as to provide collaborative work practice.

Each group of 3 to 5 students should create a practical project where algebraic expressions are applied to solve everyday problems. The expected time for this activity is 2 to 4 hours, with a total duration of one week for completion.

Detailed Description

Students should choose a real-life situation (for example: calculating the household budget, planning a trip, organizing a birthday party, etc.) where it is possible to apply algebraic expressions to solve problems.

Students should mathematically model the chosen situation through algebraic expressions, creating and solving a series of problems/practices based on these expressions.

The final work should clearly demonstrate the application of algebraic expressions in practical life and the students' ability to use this mathematical tool in everyday situations.

Necessary Materials

• Paper and pencil for notes.
• Calculator.

Activity Step by Step

1. Formation of groups with 3 to 5 students.
2. Students choose a real-life situation where algebraic expressions can be applied.
3. Students discuss and define the algebraic expressions that represent the chosen situation.
4. Groups create a series of problems that can be solved by applying the defined algebraic expressions.
5. Students collaboratively solve these problems by applying the algebraic expressions.
6. Each group should prepare a project presentation explaining the process of creating algebraic expressions and solving the proposed problems.

To conclude the activity, each group must prepare a written report in which the following topics are presented:

1. Introduction: The group should present the chosen situation, its relevance in the real world, and the project's objectives.
2. Development: In this topic, the group should explain the algebraic expressions elaborated, describe the methodology used to create and solve the problems, and present the results obtained.
3. Conclusion: Students should summarize the main points of the activity, discuss the learnings obtained, and draw conclusions about the application of algebraic expressions in solving everyday problems.
4. Bibliography: The group should indicate the references and sources used in the project development, such as books, videos, websites, among others.

This practical activity, along with the report, aims not only at the application and understanding of algebraic expressions but also at the development of important socio-emotional skills, such as teamwork, time management, critical thinking, and problem-solving.