The purpose of this project is to deepen students' understanding of systems of equations by applying mathematical concepts to solve complex, real-world problems. Through this project, students will explore how systems of equations can model situations involving multiple variables and constraints, enhancing their problem-solving skills and critical thinking. By engaging in activities such as solving equations using substitution, elimination, and graphing, students will build a strong foundation in algebraic methods. This project also aims to foster students' ability to articulate their problem-solving processes and reflect on their learning journey, ultimately preparing them to apply these skills in diverse contexts. Through presentations and a gallery walk, students will communicate their solutions and insights, demonstrating their mastery of the standards and competencies required at the 11th-grade level.

In this project, students will deepen their understanding of systems of equations by exploring how they can be used to solve complex real-world problems involving multiple variables and constraints. They will learn to apply various methods such as substitution, elimination, and graphing to effectively solve these systems. Through this process, students will develop critical thinking and problem-solving skills, as they compare properties of functions represented in different forms, aligning with the CCSS.Math.Content.HSF-IF.C.9 standard. The project will also enhance students' ability to communicate mathematical concepts, as they prepare to present their findings and solutions in a real-world problem-solving presentation and participate in a 'Math in Action Gallery Walk'. This experience will encourage students to reflect on their learning journey, articulate their evolving understanding, and apply mathematical concepts to practical scenarios.

In this project, students will create a comprehensive presentation that addresses a real-world problem using systems of equations. They will develop a detailed problem-solving narrative that includes their chosen methods (such as substitution, elimination, or graphing) and demonstrate how these methods apply to the problem's variables and constraints. Additionally, students will produce a reflective journal entry that captures their learning journey and insights gained. Finally, students will prepare a visual display for the 'Math in Action Gallery Walk,' which will consist of posters or digital presentations showcasing their problem-solving process, solutions, and the evolution of their understanding. This project will culminate in a presentation where students articulate their approach and findings, demonstrating their mastery of solving systems of equations and their ability to apply mathematical concepts to complex, real-world situations.

To launch the project, begin with a real-world scenario that students can relate to, such as planning a school event with a budget. Present them with a scenario where they must allocate resources (e.g., food, decorations, entertainment) while adhering to specific constraints and budget limitations. Introduce the concept of systems of equations as a tool to optimize their plan. Encourage students to brainstorm initial strategies and discuss how they might use mathematical models to solve the problem. This activity will set the stage for understanding the practical application of systems of equations in addressing complex issues involving multiple variables and constraints.

To effectively showcase the students' learning and problem-solving skills in using systems of equations, organize a 'Math in Action Gallery Walk'. This exhibition will allow students to present their projects through posters and digital presentations. Each student or group will have a designated space to display their work, including detailed explanations of the real-world problems they tackled, the systems of equations they developed, and the methods they used to find solutions. Visitors, such as peers, teachers, and community members, can walk through the gallery, engaging with students by asking questions and discussing the problem-solving processes. This interactive format not only celebrates the students' achievements but also provides an opportunity for them to articulate their understanding and receive feedback from a broader audience.