Contextualization

Mathematics, often seen as a tough and complex discipline, is more present in our daily lives than we imagine. From simple situations like calculating change or splitting the dinner bill with friends, to more complex calculations with the aim of launching a rocket into space, mathematics is an indispensable tool.

Among the various topics studied in mathematics, the topic of Factoring stands out for its frequency of use in different areas of knowledge. Factoring an algebraic expression means rewriting that expression as the product of several other simpler expressions. This allows us to simplify complex equations and make the study of mathematics more palatable.

Introduction

The study of factoring is fundamental and can be applied in various areas such as engineering, computer science, physics, economics, among others. Whether in optimizing functions in a computer program, breaking codes in cryptography, or solving quadratic equations in physics, factoring is one of the pillars for the development of these areas.

The factoring process can be done in various ways, but in this project, we will focus on two specific methods: Factoring by Grouping and Factoring by Evidence. Factoring by Grouping is a method that groups similar terms to simplify the expression, while in Factoring by Evidence, a common term is removed from all terms of the expression.

In this project, you will actively work on this topic of mathematics through a project that will mix theory and practice in an engaging way. It will not only be an opportunity to learn and improve your understanding of factoring but also to develop teamwork skills, time management, and creative thinking.

Practical Activity

Activity Title: Factoring the World Around Us

Project Objective

This project aims to help students understand the practice and application of factoring by grouping and factoring by evidence concepts in everyday life.

Detailed Project Description

Each group of 3 to 5 students should investigate and present everyday situations that involve the direct or indirect application of factoring by grouping and factoring by evidence. The explanation should be done through a presentation, using visual resources (such as a slideshow, a poster, a video, etc.) and relevant materials that illustrate the chosen everyday situation.

Required Materials

• Research and study notes.
• Visual resources for the presentation (slides, posters, videos, etc).
• Equipment for video recording and editing (optional).

Detailed Step-by-Step for Activity Execution

1. Formation of groups of 3 to 5 students.
2. Research and study of factoring by grouping and factoring by evidence methods.
3. Group brainstorming to identify everyday situations where these methods can be applied (Ex: Economics, Engineering, Physics, etc).
4. Elaboration of the presentation concept: How the situation will be presented (slides, posters, videos, etc) and what materials will be needed for the explanation.
5. Development of the presentation and material.
6. Rehearsals for the presentation.
7. Presentation to the class.

Project Deliverables and Connection with Activities

Included in this project, each group should prepare a written document reporting each stage of the project and how these stages helped understand the taught concepts. The report should follow the following structure:

• Introduction: Provide context for the factoring theme, its relevance, and how it applies in real life. Present the project's objective.

• Development: Explain the theory of factoring by grouping and factoring by evidence. Describe in detail the activity carried out, the methodology followed, and present the chosen everyday situation by the group. Show, based on the chosen everyday situation, how factoring concepts can be applied in real life. Include all the bibliography used.

• Conclusion: Reflecting on the key points of the project, show what the group learned about factoring and its application in real life. Include what difficulties were faced in the project and how the group overcame these difficulties.

• Bibliography: List all study sources and materials used to carry out the project.

This practical project and the written document should be delivered within one month from the start of the project.