(Allow approximately 3.5 weeks for instruction, review, and assessment) Conceptual Category: Number and Quantity Domain: Matrix Operations .1 Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. .2 Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. .3 Add, subtract, and multiply matrices of appropriate dimensions. Enduring Understanding(s): Tennessee Finite Math Textbook 6-1 Matrix Notation and Algebra Additional Resources Khan Academy Video –Precalculus - Matrices (Lessons 1-3) Engageny Precalculus Module 2 Topic B (select from Lessons 4-13) Task(s) Important Terms & Concepts (Chapter 6) Addition of matrices, column vector, coordinates of a vector, demand vector, dimension of a matrix, equality of matrices, external demand vector, input-output matrix, inverse of a matrix, Leontief model, matrix, matrix addition, matrix multiplication, method of determining invertibility and computing the inverse of a square matrix A, production schedule, row-by-column multiplication, row vector, scalar multiplication, technology matrix, the (I, j) entry in a matrix Writing in Math Summarize how to perform matrix operations on matrices. Explain how to find 4D 3C for two given matrices C and D with the same dimensions.
Conceptual Category: Algebra Domain: Linear systems, matrices, and their applications A-LM.1 Find and use the inverse of a matrix to solve a contextual problem. Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3x3 or greater). A-LM.3 Use matrices to solve systems of linear equations, including the echelon method and the Gauss-Jordan method. Objectives: Students will: Determine the Inverse of a Matrix Solve Systems of Equations using the Inverse of a Matrix Tennessee Finite Math Textbook 6-2 Matrix Inverses Additional Resources Khan Academy Video –Intro to Matrix Inverses FiniteHelp Lecture Video- 6.2 Task(s) SCS Finite Math Task- How Do You Beat the System (Graphing Calculator) Conceptual Category: Algebra Domain: Linear systems, matrices, and their applications Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3x3 or greater). Conceptual Category: Algebra Domain: Linear programming Objectives: Students will: Solve a Linear Economic Problem using the Leontief input-output model. Tennessee Finite Math Textbook 6-3 A Linear Economic Model Additional Resources Video: Input-Output Model Part 3 Video: Input-Output Model Part 4 Writing in Math Research the Russian-born American economist, Wassily Leontief (1906-1999) and describe his work with input-output analysis. Chapter 7 Linear Programming: Modeling and Graphical Solution (Allow approximately 3.5 weeks for instruction, review, and assessment) Conceptual Category: Algebra Domain: Linear programming Enduring Understanding(s): A linear model can be used to represent Tennessee Finite Math Textbook 7-1 Formulation of Linear Programming Important Terms & Concepts (Chapter 7) Bounded (unbounded) set, constraint, corner point, decision variables, feasible set,
(CCSS) Conceptual Category: Reasoning with Equations and Inequalities Domain: Represent and solve equations and inequalities graphically. Graph the solutions to a linear inequality in two variables Objectives: Students will: Solve linear programming problems in two variables Tennessee Finite Math Textbook 7-3 Graphical Solution of Linear Programming Additional Resources Task(s) Writing in Math Determine whether the following is sometimes, always, or never true. Explain your reasoning. An unbounded region will not have both a maximum and a minimum value. Chapter 10 Linear Programming: The Simplex Method (Allow approximately 2 weeks for instruction, review, and assessment) Conceptual Category: Algebra Domain: Linear programming Use linear programming to solve optimization problems. Interpret the meaning of the maximum or minimum value in terms of the objective function. Enduring Understanding(s): A linear model can be used to represent relationships between data. Essential Question(s): What are some real-world situations that can be solved using linear programming? Objectives: Students will learn: Solve linear programming problems using the simplex method. Tennessee Finite Math Textbook 10-1 Standard Maximum Problems, Slack Variables, and Basic Solutions 10-2 Tableaus and Pirot Operation 10-3 Optimal Vectors via the Simplex Method (OPTIONAL) 10-4 Dual Programming Problems and Minimum Problems (OPTIONAL) Additional Resources Simplex Method Video Important Terms & Concepts (Chapter 10) Basic solution, decision variables, departing variable, dual of an SMP, Dual Linear Programming Problems, entering variable, feasible vector, initial tableau, linear function, optimal vector, pivot element, pivot operation, simplex method, slack variables, standard maximum problem (SMP), tableau, vector inequalities, vector transpose Writing in Math Research the simplex algorithm, which was invented by George Dantzig in the late 1940s. RESOURCE TOOLBOX The Resource Toolbox provides additional support for comprehension and mastery of subject-level skills and concepts. While some of these resources are embedded in the map, the use of these categorized materials can assist educators with maximizing their instructional practices to meet the needs of all students.