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Wentzville School District Algebra 1: Unit 6 Stage 1 – Desired Results Unit 6 Systems of Equations and Inequalities Unit Title: Systems of Equations/Inequalities Course: Algebra I Brief Summary of Unit: Students will be able to solve systems of equations by graphing, substitution, and elimination. Students will learn to interpret the point of intersection of two graphs as meaningful in a given real world situation. Students will graph and solve systems of linear inequalities to represent real world situations. Textbook Correlation: Glencoe Algebra I Chapter 6.1 - 6.6 (6.1 with technology) Time Frame: 3 weeks WSD Overarching Essential Question Students will consider… ● ● ● ● ● ● ● ● ● ● ● ● How do I use the language of math (i.e. symbols, words) to make sense of/solve a problem? How does the math I am learning in the classroom relate to the real-world? What does a good problem solver do? What should I do if I get stuck solving a problem? How do I effectively communicate about math with others in verbal form? In written form? How do I explain my thinking to others, in written form? In verbal form? How do I construct an effective (mathematical) argument? How reliable are predictions? Why are patterns important to discover, use, and generalize in math? How do I create a mathematical model? How do I decide which is the best mathematical tool to use to solve a problem? How do I effectively represent quantities and relationships through mathematical notation? WSD Overarching Enduring Understandings Students will understand that… ● ● ● ● ● ● ● ● ● Mathematical skills and understandings are used to solve real-world problems. Problem solvers examine and critique arguments of others to determine validity. Mathematical models can be used to interpret and predict the behavior of real world phenomena. Recognizing the predictable patterns in mathematics allows the creation of functional relationships. Varieties of mathematical tools are used to analyze and solve problems and explore concepts. Estimating the answer to a problem helps predict and evaluate the reasonableness of a solution. Clear and precise notation and mathematical vocabulary enables effective communication and comprehension. Level of accuracy is determined based on the context/situation. Using prior knowledge of mathematical ideas can help discover more efficient problem solving ● ● How accurate do I need to be? When is estimating the best solution to a problem? ● strategies. Concrete understandings in math lead to more abstract understanding of math. Transfer Students will be able to independently use their learning to… know that a system of equations or inequalities can be written to model a real world situation. Meaning Essential Questions Understandings Students will consider questions such as . . . Students will understand that . . . How many solutions does a system of equation have? Which method of solving a system of equations (graphing, substitution or elimination) would be most useful in different situations? What is the significance of the intersection point? In what real world situations is the intersection point meaningful? When a system of equations does not have a single solution, what does it mean? In a system of inequalities, what does the solution mean? How can technology aide in finding the solution to a system of equations? What is a viable solution to a system of inequalities? Acquisition The point of intersection or common solution is where the functions share the same outcome. In a real world situation this point of intersection is meaningful. Systems of equations can be used to model real world situations to determine real world solutions. When two different functions can model the same scenario, their point of intersection describes where the models coincide. Systems of equations can be solved by graphing, substitution and elimination. Each method has benefits and drawbacks. The number of solutions of a system of equations is dependent on the nature of the lines in the system. There is an infinitely number of solutions to a system of inequalities. Acquisition Key Knowledge Key Skills ● ● ● ● ● ● ● ● System of Equations Infinite number of solutions (same line, coincident) No solutions (parallel lines) One Solutions (intersecting lines) Substitution Linear combination (elimination) System of Inequalities ● ● ● ● ● ● ● Solve a system of equations using a graphing utility to include graphing and viewing a table. Determine the number of solutions of a system. Write and solve a system of equations that represents a real world situation. Use substitution to solve a system. Use elimination to solve a system. Show that regardless the method of solution, the result will be the same. Solve a system of inequalities. Apply system of linear inequalities in real world situations. Standards Alignment MISSOURI LEARNING STANDARDS A.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. A.CED 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★ A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. SHOW-ME STANDARDS Goals: 1.1, 1.4, 1.5, 1.6, 1.7, 1.8 2.2, 2.3, 2.7 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8 4.1, 4.4, 4.5, 4.6 Performance: Math 1, 4, 5