Lesson plan of Linear Systems: Resolution

Objectives (5-7 minutes)

• Grasp Concept of System of Equations: Instructor ensures students understand what a system of equations is, its characteristics and how it pertains to solving problems in the real world.

• Develop Strategies to Solve Systems of Equations: The focus should be on developing the ability to solve systems of equations. Students will learn different methods, such as the elimination (addition/subtraction) method, substitution method, and matrix inverse method.

• Apply Systems of Equations to Real-World Problems: The ultimate goal should be for students to apply their newly acquired knowledge to real-world problems. The teacher will share real world examples and encourage the students to think of situations when solving systems of equations could be useful.

Additional Learning Objectives

• Foster Critical Thinking Skills: Instructor encourages students to think critically about problems presented, analyzing different methods for solving systems of equations and explaining their reasoning behind their chosen methods.

• Promote Collaboration: Solving system of equations problems can be collaborative. The teacher encourages students to work in teams, discussing their ideas and sharing their solutions.

Introduction (10-15 minutes)

• Review Prerequisites: Begin class by reviewing the concepts that are foundational to the study of systems of linear equations. This may include linear equations, coefficients and variables (3-5 minutes).

• Introduce Word Problem: Present learners with a real world example or scenario that can be represented by a system of linear equations - an example of how the concept can be applied. For instance: the need to determine the right combination of ingredients when baking different products or the calculation of how many study hours are needed for certain grades in multiple classes. Clearly state how solving the problem will be the main focus of the lesson (5-7 minutes).

• Make the Connection: Explain the many uses for system of linear equations in different aspects of real life such as engineering, chemistry and economics to name a few. Examples to share are how systems of linear equations can be used in predicting the weather, designing a building, optimizing manufacturing or in computer gaming (2-3 minutes).

• Spark Student Curiosity: Share an intriguing fact or demonstrate a creative application of systems of equations. This could be how a system of linear equation was utilized to break an encrypted code, or to create realistic movements of characters or objects within video games. Share the historical development of linear systems and their importance within modern mathematics (3-5 minutes).

Development (20-25 minutes)

Activity 1: “The Linear Bakery” (7-10 minutes)

- **Description**: In teams of five learners will be given a “recipe” of sorts that will lead them through a series of systems equations that they will solve in order to determine how much of each specific ingredient they need to make one batch of a particular baked good.

- **Implementation**: Students solve a system of equations in order to determine how much of each specific ingredient will be needed in order to make the requested amount of that particular recipe.

Activity 2: “Space Exploration” (7-10 minutes)

- **Description**: Presented with another system of equations students, still in groups of five, are given a “Space Exploration” scenario that will present them with two linear equations. The linear equation will describe a path of an object that is traveling through space in terms of the x,y and z axis.

• Implementation: Learners are then tasked to use either substitution, elimination, or matrix inverse method in order to solve for x, y, and z. This will allow them to map the path of their space object.

• Class Discussion & Debrief (6 -10 minutes)

  • Debrief: Once students have had the opportunity to work through both scenarios facilitate a classroom discussion in which they share their answers, methods and provide justification or reasoning behind their method selection such as:
  • Why they decided to eliminate a variable through the addition or subtraction method

• Provide Real World Examples of Systems Equations: Provide students with scenarios in which systems of linear equations are used to solve everyday problems. This can help them develop an understanding of why learning about systems of equations is relevant and important.

  • Facilitate Discussion: Provide purposeful prompts that get the students to elaborate and justify their answers and their methods such asking them to compare and contrast various approaches to solving the system or asking what alternative approaches they considered but choose not to use.
  • Summarize Concepts : Restate the important characteristics of systems equations that have been learned during this lesson. Review and define key vocabulary terms and restate how to apply what they learned about system of equations to the activities they will do during their independent practice time (6 -10 minutes).

Closure (10 - 12 minutes)

• Student Reflection (2-3 minutes)

  • Individually students take a moment to reflect on their own learning and growth over the course of the lesson.

  • Have each learner take a moment and answer on a sticky note or in a learning management system:

    • What is one strategy or concept that you learned today that was particularly valuable?
    • Are there any questions that you have about today’s topic that remain unanswered?

• Class Discussion (3-4 minutes)

  • Facilitate Discussion: Select 3 - 4 students to share their reflections with the class, be sure to include a variety of answers in the responses you choose.

• Relate Back to the Standards (2-3 minutes)

  • Review Objectives: Remind the students of the learning goals/objectives that were stated at the beginning of the class period.
  • Review Key Concepts: Revisit the main concepts, vocabulary and methods learned during this lesson, be certain to focus on any misconceptions that students may have had prior to today's lesson. - Upcoming Events/Assessments: Provide students with a preview into what they can expect for upcoming lessons or assessments

Conclusion (3 -5 minutes)

• Summarize Content: Summarize the major concepts covered including: a definition of system of equations, the various methods that were utilized in order to solve, and real-world connections that were discussed.

• Reiterate Theory/Practice Connection: Emphasize the connections between the activities that students participated in during the development portion of this lesson and the theoretical knowledge they gained from the introductory portion of this lesson.

• Offer Extension Opportunities: Provide students with additional materials that will allow for further learning of system of equations should they desire. These may include supplemental websites or an additional list of word problem examples for students to complete.

• Importance of the skill: Summarize the role of systems equations and their applications across different disciplines.

• Student Questions /Feedback : Open the floor to students for any unanswered questions, encourage students to comment on what helped and what needs improving for future lessons and ask what additional support is needed in order for them to be successful in learning how to solve systems equations.