Contextualization
Introduction to Equations and Inequalities
Equations and inequalities are fundamental concepts in algebra. They help us describe and solve problems by using mathematical expressions and symbols to represent unknowns and operations. An equation is a statement that two expressions are equal. We often use a variable, a letter that represents an unknown value, to write an equation. The process of finding the value(s) of the variable that make the equation true is called solving the equation.
On the other hand, an inequality is a statement that two expressions are not necessarily equal. Instead, they can be greater than, less than, greater than or equal to, or less than or equal to each other. Like an equation, we often use a variable to write an inequality. However, the difference is that there are often many possible values for the variable that make the inequality true. The solution to an inequality is often expressed as a solution set, which is a range of values that satisfy the inequality.
Relevance of Equations and Inequalities
The concepts of equations and inequalities are not only limited to the realm of mathematics, but they also have wide applications in realworld scenarios. For instance, they are extensively used in physics to model and solve problems related to motion, force, and energy. In economics, equations and inequalities are used to represent and solve problems related to supply and demand, cost and revenue, and profit and loss.
In the digital age, where data is abundant and powerful, equations and inequalities are the language of data analysis. They are used in statistics and machine learning to formulate models, make predictions, and solve optimization problems. In short, understanding equations and inequalities is not only crucial for academic success but also for problemsolving, decisionmaking, and critical thinking in various fields.
Resources
To enhance your understanding of equations and inequalities, you may refer to the following resources:
 Khan Academy: Introduction to equations
 Khan Academy: Introduction to inequalities
 Math is Fun: Equations and Inequalities
 Book: Elementary Algebra by Harold R. Jacobs
These resources provide a solid foundation on the topic and will be useful references throughout the project.
Practical Activity
Activity Title: "Math Detectives: Solving Equations and Inequalities"
Objective of the Project:
The main objective of this project is to deepen your understanding of equations and inequalities and their realworld applications. You will work as a team of 35 students to solve a series of math problems involving equations and inequalities. Your solutions will be presented in a creative way, such as a video or a poster, and accompanied by a detailed report explaining your methodology and findings.
Detailed Description of the Project:
The project will involve the following major steps:

Step 1: Problem Selection and Research: Your team will select a realworld problem that can be solved using equations and inequalities. This could be a problem from physics, economics, or any other field that interests you. Your team will then research the problem, its context, and how equations and inequalities can be used to solve it.

Step 2: Problem Formulation: Based on your research, your team will formulate an equation or an inequality that represents the problem. You will also identify the variable(s) and the type of solution(s) that the equation or inequality should yield.

Step 3: Problem Solution: Your team will solve the equation or inequality using appropriate mathematical methods. You will also determine the solution set(s) and interpret them in the context of the problem.

Step 4: Presentation and Report Writing: Finally, your team will create a presentation summarizing your findings and solutions. You will also write a detailed report, following the guidelines provided.
Necessary Materials:
 Access to a computer and the internet for research and report writing.
 A mathematical software or calculator for equation and inequality solving.
 Craft materials, if you choose to create a poster.
 A camera or smartphone, if you choose to create a video.
Detailed Stepbystep for Carrying out the Activity:

Form a Team: Form a team of 35 students.

Select a Problem: Choose a realworld problem that can be solved using equations and inequalities. It is advisable to choose a problem that is challenging but manageable.

Conduct Research: Research the problem and how it can be solved using equations and inequalities. Use the resources provided and any other credible sources you find.

Formulate the Problem: Formulate an equation or an inequality that represents the problem. Identify the variable(s) and the type of solution(s) that the equation or inequality should yield.

Solve the Problem: Solve the equation or inequality using appropriate mathematical methods. Determine the solution set(s) and interpret them in the context of the problem.

Create a Presentation: Create a presentation summarizing your findings and solutions. Be creative and use visual aids, such as diagrams or graphs, where appropriate.

Write a Report: Write a detailed report based on your project. The report should be divided into four main sections: Introduction, Development, Conclusions, and Used Bibliography.
 Introduction: Contextualize the chosen problem, its realworld application, and the objective of your project.
 Development: Detail the theory behind equations and inequalities, explain the problem you chose and how you formulated it, present and discuss your findings and solutions.
 Conclusion: Revisit the main points of your project, state the learnings obtained, and the conclusions drawn about the project.
 Used Bibliography: List all the resources you used to work on the project such as books, web pages, videos, etc.

Submit the Project: Submit your presentation and report to the teacher by the specified due date.
Project Deliverables:
 A presentation summarizing your findings and solutions.
 A detailed report following the format: Introduction, Development, Conclusion, Used Bibliography.
Remember, the project is not just about solving a math problem, but also about understanding the process of problemsolving, collaborating as a team, and communicating your solutions effectively. Good luck, Math Detectives!