Finite. U-46 Curriculum Scope and Sequence. Reporting Strand Instructional Focus Standards Semester. Represent linear equations in matrices.

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1 Finite U-46 Curriculum Scope and Sequence Repting Strand Instructional Focus Standards Semester Represent linear equations in matrices. A.REI.8, A.REI.9 Matrices Perfm operations on matrices and use matrices in s. N.VM.6, N.VM.7,N.VM.8, N.VM.9, N.VM.10, N.VM.11, N.VM.12 1 Linear Programing Use geometric linear programing s. A.REI.6, A.REI.12, A.CED.1, A.CED.3 1 Use simplex linear programing s. A.REI.8, A.REI.9 Applied Matrix They Evaluate and analyze Markov Chains Use Game They s. A.REI.8, S.MD.6, S.MD.7 S.MD.5, S.MD.6, S.MD.7 1 Financial Math Analyze and apply different types interest and rate A.SSE.1, A.CED.2, A.CED.4, F.BF.5, F.LE.3, F.IF.6 2 Probability Calculate expected values and use m s S.MD.1, S.MD.2, S.MD.3, S.MD.4 2 Statistics Analyze and use data s AP Stats Prep 2 1

2 Matrices Instructional Focus: Representing linear equations CCSS 4 Mastery 3 Pricient 2 - Basic 1 Below Basic (A-REI.8) (A REI.9) involve one Represent a system equations using matrices when variables are on both sides an equation, have missing variables. Find inverse a and use it solve systems linear equations with dimensions 2x2 without technology 3x3 with technology Represent a system equations using matrices when all variables are on one side each equation. Find inverse a and use it solve systems linear equations with dimensions 2x2 with technology 3x3 with technology Identify a system equations in a. Find inverse a (HSA REI.C.9)Find inverse a if it exists and use it systems linear equations. (HSA-REI.C.8)Represent a system linear equations as a single equation in a vect variable. 2

3 Matrices Instructional Focus: Perfm operations on matrices and use matrices in s. CCSS 4 Mastery 3 Pricient 2 - Basic 1 Below Basic N.VM.6, N.VM.7, N.VM.8, N.VM.11 N.VM.9, N.VM.10 involve one Extract a matrices from a situation (i.e. wd ) and use matrices s. Given matrices, do all following with and without solving technology: Multiply by scalars Add matrices Subtract matrices Multiply matrices Multiply by a vect Can explain all Lack Commutative property Matrix Associative property Matrix Distributive property Matrix Zero Matrix Identity Matrix Extract a matrices from a situation (i.e. wd ) Given matrices, do all following with solving technology: Multiply by scalars Add matrices Subtract matrices Multiply matrices Multiply by a vect Can explain four Lack Commutative property Matrix Associative property Matrix Distributive property Matrix Zero Matrix Identity Matrix Identify cresponding from a situation. Given matrices, do three following with solving technology : Multiply by scalars Add matrices Subtract matrices Multiply matrices Multiply by a vect Can explain three Lack Commutative property Matrix Associative property Matrix Distributive property Matrix Zero Matrix Identity Matrix N.VM.12 Find area by using determinant and absolute value a 2 x 2 as a transfmation on plane. Find determinant and absolute value a 2 x 2 as a transfmation on plane. Find determinant and absolute value a 2 x 2 (HSN-VM.C.6) Use matrices to represent and manipulate data. (HSN-VM.C.7) Multiply matrices by scalars to produce new matrices. (HSN-VM.C.8) Add, subtract, and multiply matrices appropriate dimensions. (HSN-VM.C. 11) Multiply a vect (regarded as a with one column) by a suitable dimensions to produce anor vect. Wk with matrices as transfmations vects. (HSN-VM.C.9) Understand that, unlike multiplication numbers, multiplication f square matrices is not a commutative operation, but still satisfies associative and distributive properties. (HSN-VM.C. 10) Understand that zero and identity matrices play a role in addition and multiplication similar to role 0 and 1 in real numbers. (HSN-VM.C. 12) Wk with 2 2 matrices as a transfmations plane, and interpret absolute value determinant in terms area. 3

4 Linear Programing Instructional Focus: Geometric Linear Programing CCSS 4 Mastery 3 Pricient 2 - Basic 1 Below Basic A.REI.6 Solve Systems Equations Graph Systems Equations and Inequalities (A.REI.6, A.REI.12) Create Equations Inequalities (A.CED.1*) Represent constraints and interpret solutions (A.CED.3*) involve one Graph feasible region based on constraints. Find each vertex feasible region by solving a system equations State feasible region as being bounded unbounded Create objective function with two me variables and use it in a linear programming to find optimal solution. Explain constraints with equations, inequalities and in a system equations and/ inequalities in contextual situations Interpret solutions as viable nonviable in context situation. Graph feasible region based on constraints. Find each vertex feasible region by solving a system equations Create objective function with two me variables and use it in a linear programming to find optimal solution. Represent constraints with equations, inequalities and in a system equations and/ inequalities in contextual situations Interpret solutions in context situation. Graph feasible region based on constraints. Create objective function with two me variables and use it in a linear programming to find optimal solution. Represent constraints with equations inequalities, and in part a system equations and/ inequalities in contextual situations Identify solutions A.REI.6 Solve systems linear equations exactly and approximately (e.g., with graphs), focusing on pairs linear equations in two variables. A.CED.1* Create equations and inequalities in one variable and use m s A.CED.3* Represent constraints by equations inequalities, and by systems equations and/ inequalities, and interpret solutions as viable nonviable options in a modeling context. 4

5 Linear Programing Instructional Focus: Simplex Linear Programing CCSS 4 Mastery 3 Pricient 2 - Basic 1 Below Basic (A-REI.8) (A REI.9) involve one Represent a system given constraints using a Identify an optimized Identify pivot Find solution (me than 1 pivot required) Interpret tableau in context situation Create a system optimized constraints from a context Represent a system given constraints using a 2x2 3x3 Identify an optimized Identify pivot Find solution using simplex method (1 pivot required) Interpret tableau in context situation Represent a system given constraints using a 2x2 Identify an optimized Identify pivot Find solution using simplex method (1 pivot required) Interpret parts tableau A-REI.C.8 Represent a system linear equations as a single equation in a vect variable A-REI.9 Find inverse a if it exists and use it systems linear equations (using technology f matrices dimension 3 3 greater). 5

6 Applied Matrix They Instructional Focus: Markov Chains CCSS 4 Mastery 3 Pricient 2 - Basic 1 Below Basic A.REI.8 involve one From context, create a transition distribution vect find and interpret: steady state distribution (regular) distribution after n transitions (regular absbing) probability being absbed Create a transition and vect from context, and find steady state distribution distribution after n transitions Create a transition from a diagram find steady state distribution distribution after n transitions (HSA-REI.C.8)Represent a system linear equations as a single equation in a vect variable. 6

7 Applied Matrix They Instructional Focus: Game They CCSS 4 Mastery 3 Pricient 2 - Basic 1 Below Basic S.MD.5, S.MD.6, S.MD.7 involve one F zero sum games including me than two options without a saddle point (simplex method) Create a payf Find mixed strategy (probability distributions) f each player Find expected value game F zero sum games including two options without a saddle point Create a payf Find mixed strategy (probability distributions) f each player Find expected value game F zero sum games including two options with a saddle point Create a payf Find strategy (probability distributions) f each player Find expected value game (HSS.MD.B.5)Weigh possible outcomes a decision by assigning to payf values and finding expected values. HSS.MD.B.6)Use to make fair decisions (e.g., drawing by lots, using a random number generat). HSS.MD.B.7)Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at end a game). 7

8 Financial Math Instructional Focus: Analyze and apply different types interest and rate CCSS 4 Mastery 3 Pricient 2 - Basic 1 Below Basic Interpret Expressions (A.SSE.1) involve one Interpret individual parts expressions (such as variables, coefficients, facts, etc.) and explain ir meaning in terms context in all Group parts an expression and interpret ir meaning in terms context in all Interpret individual parts expressions (such as variables, coefficients, facts, etc.) and explain ir meaning in terms context in two Group parts an expression and interpret ir meaning in terms context in two Interpret individual parts expressions (such as variables, coefficients, facts, etc.) in all Group parts an expression and interpret ir meaning in all a level 1 Create and solve equations (A.CED.2 A.CED.4) Create and solve equations to represent relationships in contextual situations, including all following situations: Create and solve equations to represent relationships in contextual situations, including two following situations: Create and solve equations to represent relationships in contextual situations, in one following situations: Exponential and Logarithmic inverses (F.BF.5) Recognize that exponential and logarithmic functions are inverses each or and use se functions real-wld s. Recognize that exponential and logarithmic functions are inverses each or and use se functions logarithmic and exponential equations. Recognize that exponential and logarithmic functions are inverses each or and convert from one fm into or. Compare Rate Change (F.LE.3) (F.IF.6) Calculate and compare rate change and value function presented in symbolic and table fm in context a situation and use it to make a decision Stated rate Effective rate Calculate and compare rate change and value function presented in symbolic and table fm in context a situation Stated rate Effective rate Calculate rate change and value a function presented in symbolic table fm Stated rate Effective rate A.CED.2 Create equations in two me variables to represent relationships between quantities; graph equations on codinate axes with labels and scales. A.CED.4 Rearrange fmulas to highlight a quantity interest, using same as in solving equations. F example, rearrange Ohm s law V =IR to highlight resistance R. A.SSE.1 Interpret expressions that represent a quantity in terms its context. a. Interpret parts an expression, such as terms, facts, and coefficients. b. Interpret complicated expressions by viewing one me ir parts as a single entity. F example, interpret P(1+r)n as product P and a fact not depending on P. F.BF5. (+) Understand inverse relationship between exponents and logarithms and use this relationship s involving logarithms and exponents. F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, (me generally) as a polynomial function. *(Modeling Standard) F.IF.6 Calculate and interpret average rate change a function (presented symbolically as a table) over a specified interval. Estimate rate change from a graph. 8

9 Probability Instructional Focus: Calculate expected values and use m s CCSS 4 Mastery 3 Pricient 2 - Basic 1 Below Basic S.MD.1 S.MD.2 S.MD.3, S.MD.4 involve one Define a random variable f a quantity interest Assign a numerical value to each event in a sample space Graph cresponding probability distribution using same graphical displays as f data distributions. Calculate and interpret expected value a random variable and use infmation to make a decision Develop a probability distribution f a random variable f a sample space etical experimental and find expected value Assign a numerical value to each event in a sample space Graph cresponding probability distribution using same graphical displays as f data distributions. Calculate expected value a random variable and use infmation to make a decision Develop a probability distribution f a random variable f a sample space etical experimental Graph a given probability distribution Calculate expected value a random variable Calculate f a sample space etical experimental (S.MD.1)Define a random variable f a quantity interest by assigning a numerical value to each event in a sample space; graph cresponding probability distribution using same graphical displays as f data distributions. (S.MD.2)Calculate expected value a random variable; interpret it as mean probability distribution. (S.MD.3)Develop a probability distribution f a random variable defined f a sample space in which etical can be calculated; find expected value (S.MD.4)Develop a probability distribution f a random variable defined f a sample space in which are assigned empirically; find expected value. 9

10 Statistics Instructional Focus: Analyze and use data s CCSS 4 Mastery 3 Pricient 2 - Basic 1 Below Basic involve one F random variables, calculate and interpret all Chebychev s Theem F binomial random variables, calculate and interpret all Determine binomial probability by using nmal approximation F random variables, calculate all Chebychev s Theem F binomial random variables, calculate all Determine probability nonstandard nmal distributions by calculating a z-sce F random variables, calculate three Chebychev s Theem F binomial random variables, calculate two Determine probability standard nmal distributions, given a z-sce 10