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OR standard CC standard Task Analysis OR.12.adv.A.5.1 Find equivalent CC.9-12.N.RN.1 Explain how the Distinguish between rational and expressions using the properties of definition of the meaning of rational irrational numbers. Convert rational exponents. exponents follows from extending between radical and rational the properties of integer exponents exponent form of expressions. to those values, allowing for a notation for radicals in terms of rational exponents. OR.12.adv.A.5.4 Graph and analyze radical functions. OR.9-12.1A.3 Express square CC.9-12.N.RN.2 Rewrite Convert between equivalent roots in equivalent radical form and expressions involving radicals and forms of expressions using their decimal approximations when rational exponents using the rational exponents and radical appropriate. properties of exponents. forms OR.9-12.1A.4 Develop, identify, and/or justify equivalent algebraic expressions, equations, and inequalities using the properties of exponents, equality and inequality, as well as the commutative, associative, inverse, identity, and distributive propertie OR.12.adv.A.5.1 Find equivalent expressions using the properties of rational exponents. OR.12.adv.A.5.2 Perform arithmetic operations to simplify radical expressions. CC.9-12.N.RN.3 . Explain why the Distinguish between rational and sum or product of rational numbers irrational numbers. is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. CC.9-12.N.Q.1 Use units as a way Use unit conversion between to understand problems and to various units. Perform unit guide the solution of multi-step conversion on multi-step problems; choose and interpret conversions. Use formulas to units consistently in formulas; convert between units. choose and interpret the scale and the origin in graphs and data displays. CC.9-12.N.Q.2 Define appropriate Choose appropriate units or quantities for the purpose of convet to appropriate units for a descriptive modeling. problem. CC.9-12.N.Q.3 Choose a level of Use percent uncertainty and accuracy appropriate to limitations absolute uncertainty when on measurement when reporting reporting error and accuracy. quantities. OR.12.adv.A.3.1 Perform CC.9-12.N.CN.1 Know there is a operations on complex numbers complex number i such that i^2 = and represent, apply and discuss −1, and every complex number has the properties of complex numbers. the form a + bi with a and b real. OR.12.adv.A.3.1 Perform CC.9-12.N.CN.2 Use the relation operations on complex numbers i^2 = –1 and the commutative, and represent, apply and discuss associative, and distributive the properties of complex numbers. properties to add, subtract, and multiply complex numbers. CC.9-12.N.CN.3 (+) Find the Write the conjugate of pure conjugate of a complex number; imaginary and complex use conjugates to find moduli and numbers. Calculate the quotients of complex numbers. modulus of a complex number and its conjugate. Calculate quotients of complex numbers. OR.12.T.5.1 Define polar CC.9-12.N.CN.4 (+) Represent coordinates, relate them to complex numbers on the complex rectangular coordinates, and plane in rectangular and polar form fluently convert between the two. (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. OR.12.T.5.2 Represent equations given in rectangular coordinates in terms of polar coordinates. OR.12.T.5.3 Graph equations in the polar coordinate plane. OR.12.T.5.4 Define complex CC.9-12.N.CN.5 (+) Represent numbers, convert complex addition, subtraction, multiplication, numbers to trigonometric form, and and conjugation of complex multiply complex numbers in numbers geometrically on the trigonometric form. complex plane; use properties of this representation for computation. CC.9-12.N.CN.6 (+) Calculate the Calculate distances in the distance between numbers in the complex plane. Determine complex plane as the modulus of midpoints between complex the difference, and the midpoint of a numbers. segment as the average of the numbers at its endpoints. CC.9-12.N.CN.7 Solve quadratic Factor and/or use completing equations with real coefficients that the square or the quadratic have complex solutions. formula to solve quadratic formulas with complex solutions. CC.9-12.N.CN.8 (+) Extend Perform calculations with polynomial identities to the complex polynomials with complex numbers. coefficients. OR.12.adv.A.4.4 Apply long (or CC.9-12.N.CN.9 (+) Know the synthetic) division, the Fundamental Theorem of Algebra; Fundamental Theorem of Algebra, show that it is true for quadratic Descartes Rule of Signs, the polynomials. Intermediate Value Theorem and the Rational Root Theorem to analyze and/or determine the roots of a polynomial. CC.9-12.N.VM.1 (+) Recognize Recognize vectors in various vector quantities as having both situations (e.g. velocity, force, magnitude and direction. Represent etc). Use vectors and their vector quantities by directed line various representations. segments, and use appropriate symbols for vectors and their magnitudes (e.g., v(bold), |v|, ||v||, v(not bold)). CC.9-12.N.VM.2 (+) Find the Define initial and terminal points components of a vector by for vectors. Calculate vector subtracting the coordinates of an components by subtracting the initial point from the coordinates of coordinates of an initial point a terminal point. from the coordinates of a terminal point. OR.12.T.2.6 Solve problems using CC.9-12.N.VM.3 (+) Solve linear and angular velocity. problems involving velocity and other quantities that can be represented by vectors. OR.12.T.4.2 Use vectors to model situations and solve problems. OR.12.T.4.1 Perform operations on CC.9-12.N.VM.4 (+) Add and vectors. subtract vectors. CC.9-12.N.VM.4a (+) Add vectors Add vectors end-to-end, end-to-end, component-wise, and component-wise, and by the by the parallelogram rule. parallelogram rule. Understand that the magnitude of a Demonstrate that the sum of two sum of two vectors is typically not vectors is not generally equal to the sum of the magnitudes. the sum of the vectors. CC.9-12.N.VM.4b (+) Given two Convert from magnitude and vectors in magnitude and direction direction form of a vector to form, determine the magnitude and component form. Sum vectors direction of their sum. in component form and then convert the sums to magnitude and direction form. CC.9-12.N.VM.4c (+) Understand Determine the negative of a vector subtraction v – w as v + (–w), vector in both component and where (–w) is the additive inverse of magnitude and direction form. w, with the same magnitude as w Draw vectors and their negative. and pointing in the opposite Perform vector subtraction. direction. Represent vector subtraction graphically by connecting the tips in the appro OR.12.T.4.1 Perform operations on CC.9-12.N.VM.5 (+) Multiply a Differentiate between scalar vectors. vector by a scalar. multiplication on components as well as magnitude and direction form of vectors. CC.9-12.N.VM.5a (+) Represent Use the result of scalar scalar multiplication graphically by multiplication to redraw vectors. scaling vectors and possibly reversing their direction; perform scalar multiplication component- wise, e.g., as c(v(sub x), v(sub y)) = (cv(sub x), cv(sub y)). CC.9-12.N.VM.5b (+) Compute the Compute the magnitude of a magnitude of a scalar multiple cv scalar multiple of a vector. using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0). OR.12.adv.A.8.5 Interpret, analyze, CC.9-12.N.VM.6 (+) Use matrices and solve linear programming to represent and manipulate data, problems. e.g., to represent payoffs or incidence relationships in a network. OR.12.adv.A.8.1 Use matrix CC.9-12.N.VM.7 (+) Multiply operations and properties of matrices by scalars to produce new matrices to solve problems. matrices, e.g., as when all of the payoffs in a game are doubled. OR.12.adv.A.8.1 Use matrix CC.9-12.N.VM.8 (+) Add, subtract, operations and properties of and multiply matrices of appropriate matrices to solve problems. dimensions. CC.9-12.N.VM.9 (+) Understand Show that in general matrix that, unlike multiplication of multiplication is not commutative numbers, matrix multiplication for by multiplying matrices which do square matrices is not a not commute and matrices commutative operation, but still which do commute. satisfies the associative and distributive properties. OR.12.adv.A.8.3 Analyze an CC.9-12.N.VM.10 (+) Understand Calculate the determinant of inconsistent system of equations. that the zero and identity matrices marix to determine whether the play a role in matrix addition and corresponding system of multiplication similar to the role of 0 equations has a solution. and 1 in the real numbers. The Understand the connection determinant of a square matrix is between the determinant nonzero if and only if the matrix has equalling zero and the matrix a multipli being singular. OR.12.T.4.1 Perform operations on CC.9-12.N.VM.11 (+) Multiply a vectors. vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. CC.9-12.N.VM.12 (+) Work with 2 X Use 2 x 2 matrices to transform 2 matrices as transformations of the equations in the plane. Use plane, and interpret the absolute them to also calculate areas. value of the determinant in terms of area. CC.9-12.A.SSE.1 Interpret Convert between written expressions that represent a problems and expressions used quantity in terms of its context. to mathematically define the problems. CC.9-12.A.SSE.1a Interpret parts of Define parts of an expression, an expression, such as terms, such as terms, factors, and factors, and coefficients.* coefficients. CC.9-12.A.SSE.1b Interpret Correspond individual parts of complicated expressions by viewing an expression to a context. one or more of their parts as a single entity. CC.9-12.A.SSE.2 Use the structure Use the associative, of an expression to identify ways to commutative, distributive and rewrite it. other properties to rewrite expressions. OR.9-12.1A.2 Evaluate, compute CC.9-12.A.SSE.3 Choose and with, and determine equivalent produce an equivalent form of an numeric and algebraic expressions expression to reveal and explain with real numbers and variables properties of the quantity that may also include absolute represented by the expression. value, integer exponents, square roots, pi, and/or scientific notation. OR.9-12.3A.5 Given a quadratic CC.9-12.A.SSE.3a Factor a equation of the form x^2+ bx + c = quadratic expression to reveal the 0 with integral roots, determine and zeros of the function it defines. interpret the roots, the vertex of the parabola that is the graph of y = x^2 + bx +c, and an equation of its axis of symmetry graphically and algebraic OR.12.adv.A.3.3 Solve quadratic CC.9-12.A.SSE.3b Complete the equations using the zero product square in a quadratic expression to property, completing the square, reveal the maximum or minimum the quadratic formula, and graphing. value of the function it defines.* CC.9-12.A.SSE.3c Use the Transform expressions using the properties of exponents to properties of exponents. transform expressions for exponential functions. OR.12.adv.A.9.3 Convert between CC.9-12.A.SSE.4 Derive the a series and its sigma notation formula for the sum of a finite representation. geometric series (when the common ratio is not 1), and use the formula to solve problems. OR.12.D.7.6 Use understanding of relationship of finite and infinite geometric series, including how the concept of limits connects them. OR.12.adv.A.4.1 Perform CC.9-12.A.APR.1 . Understand that operations on polynomial polynomials form a system expressions. analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. OR.12.adv.A.1.11 Connect the CC.9-12.A.APR.2Know and apply relationships among the solution of the Remainder Theorem: For a an equation, zero of a function, x- polynomial p(x) and a number a, the intercept of a graph and the factors remainder on division by x – a is of a polynomial expression. p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). OR.12.adv.A.1.11 Connect the CC.9-12.A.APR.3 Identify zeros of relationships among the solution of polynomials when suitable an equation, zero of a function, x- factorizations are available, and use intercept of a graph and the factors the zeros to construct a rough of a polynomial expression. graph of the function defined by the polynomial. OR.12.adv.A.4.6 Write a polynomial equation given its real and/or complex solutions. CC.9-12.A.APR.4 Prove Use the associative, polynomial identities and use them commutative, distributive and to describe numerical relationships. other properties to rewrite For example, the polynomial identity polynomials in equivalent forms. (x^2 + y^2)^2 = (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples. OR.12.adv.A.4.3 Understand and CC.9-12.A.APR.5 (+) Know and apply the binomial theorem and/or apply that the Binomial Theorem Pascal's triangle to expand gives the expansion of (x + y)^n in binomial expressions. powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. OR.12.D.5.3 Apply basic fundamental counting principles such as The Pigeonhole Principle, Multiplication Principle, Addition Principle, and Binomial Theorem to practical problems. OR.12.adv.A.4.4 Apply long (or CC.9-12.A.APR.6 Rewrite rational synthetic) division, the expressions. Rewrite simple Fundamental Theorem of Algebra, rational expressions in different Descartes Rule of Signs, the forms; write a(x)/b(x) in the form Intermediate Value Theorem and q(x) + r(x)/b(x), where a(x), b(x), the Rational Root Theorem to q(x), and r(x) are polynomials with analyze and/or determine the roots the degree of r(x) less than the of a polynomial. degree of b(x), usin OR.12.adv.A.6.1 Find equivalent representations for rational expressions and identify restrictions. OR.12.adv.A.6.2 Perform CC.9-12.A.APR.7 (+) Understand operations on rational expressions. that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expr OR.9-12.1A.4 Develop, identify, CC.9-12.A.CED.1 Create and/or justify equivalent algebraic equations and inequalities in one expressions, equations, and variable and use them to solve inequalities using the properties of problems. exponents, equality and inequality, as well as the commutative, associative, inverse, identity, and distributive propertie OR.9-12.2A.7 Write, use, and solve linear equations and inequalities using graphical and symbolic methods with one or two variables. Represent solutions on a coordinate graph or number line. OR.9-12.3A.1 Given a quadratic or exponential function, identify or determine a corresponding table or graph. OR.9-12.3A.2 Given a table or graph that represents a quadratic or exponential function, extend the pattern to make predictions. OR.9-12.2A.3 Determine the CC.9-12.A.CED.2 Create equation of a line given any of the equations in two or more variables following information: two points on to represent relationships between the line, its slope and one point on quantities; graph equations on the line, or its graph. Also, coordinate axes with labels and determine an equation of a new scales. line, parallel or perpendicular to a given line, through OR.12.D.4.1 Use graphs to model and solve problems such as shortest paths, vertex coloring, critical paths, routing, and scheduling problems. OR.12.adv.A.8.4 Solve systems of CC.9-12.A.CED.3 Represent linear inequalities by graphing. constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non- viable options in a modeling context. CC.9-12.A.CED.4 Rearrange Use the rules of algebra to solve formulas to highlight a quantity of a formula for a specific variable. interest, using the same reasoning as in solving equations. CC.9-12.A.REI.1 Explain each Use the rules of algebra to justify step in solving a simple equation as steps in problem solving. following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solu OR.12.adv.A.5.3 Solve radical CC.9-12.A.REI.2 Solve simple equations. rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. OR.12.adv.A.6.3 Solve algebraic proportions and rational equations. OR.12.adv.A.2.1 Graph, solve, and CC.9-12.A.REI.3 Solve linear analyze inequalities in two variables. equations and inequalities in one variable, including equations with coefficients represented by letters. OR.9-12.1A.5 Factor quadratic CC.9-12.A.REI.4 Solve quadratic expressions limited to factoring equations in one variable. common monomial terms, perfect- square trinomials, differences of squares, and quadratics of the form x^2 + bx + c that factor over the integers. OR.9-12.3A.5 Given a quadratic CC.9-12.A.REI.4a Use the method equation of the form x^2+ bx + c = of completing the square to 0 with integral roots, determine and transform any quadratic equation in interpret the roots, the vertex of the x into an equation of the form (x – parabola that is the graph of y = x^2 p)^2 = q that has the same + bx +c, and an equation of its axis solutions. Derive the quadratic of symmetry graphically and formula from this form. algebraic OR.12.adv.A.3.2 Derive the quadratic formula. OR.9-12.1A.5 Factor quadratic CC.9-12.A.REI.4b Solve quadratic expressions limited to factoring equations by inspection (e.g., for common monomial terms, perfect- x^2 = 49), taking square roots, square trinomials, differences of completing the square, the squares, and quadratics of the form quadratic formula and factoring, as x^2 + bx + c that factor over the appropriate to the initial form of the integers. equation. Recognize when the quadratic formula gives OR.9-12.3A.5 Given a quadratic equation of the form x^2+ bx + c = 0 with integral roots, determine and interpret the roots, the vertex of the parabola that is the graph of y = x^2 + bx +c, and an equation of its axis of symmetry graphically and algebraic OR.12.adv.A.3.3 Solve quadratic CC.9-12.A.REI.4b Solve quadratic equations using the zero product equations by inspection (e.g., for property, completing the square, x^2 = 49), taking square roots, the quadratic formula, and graphing. completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives CC.9-12.A.REI.5 Prove that, given Prove that, given a system of a system of two equations in two two equations in two variables, variables, replacing one equation by replacing one equation by the the sum of that equation and a sum of that equation and a multiple of the other produces a multiple of the other produces a system with the same solutions. system with the same solutions. OR.12.adv.A.8.2 Solve systems of CC.9-12.A.REI.6 Solve systems of linear equations in two or three linear equations exactly and variables algebraically, graphically, approximately (e.g., with graphs), and/or with matrix algebra. focusing on pairs of linear equations in two variables. OR.12.adv.A.8.6 Solve nonlinear CC.9-12.A.REI.7 . Solve a simple systems of equations algebraically system consisting of a linear and graphically, including linear- equation and a quadratic equation quadratic and quadratic-quadratic. in two variables algebraically and graphically. OR.12.adv.A.8.2 Solve systems of CC.9-12.A.REI.8 (+) Represent a linear equations in two or three system of linear equations as a variables algebraically, graphically, single matrix equation in a vector and/or with matrix algebra. variable. OR.12.adv.A.8.1 Use matrix CC.9-12.A.REI.9 (+) Find the operations and properties of inverse of a matrix if it exists and matrices to solve problems. use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). OR.9-12.2A.7 Write, use, and solve CC.9-12.A.REI.10 Understand that linear equations and inequalities the graph of an equation in two using graphical and symbolic variables is the set of all its methods with one or two variables. solutions plotted in the coordinate Represent solutions on a plane, often forming a curve (which coordinate graph or number line. could be a line). OR.12.adv.A.4.7 Graph and analyze polynomial functions. OR.12.D.4.1 Use graphs to model and solve problems such as shortest paths, vertex coloring, critical paths, routing, and scheduling problems. OR.12.adv.A.2.3 Graph, solve, and CC.9-12.A.REI.11 Explain why the analyze absolute value equations x-coordinates of the points where and inequalities. 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, OR.12.adv.A.3.5 Construct and solve quadratic inequalities in one and two variables. OR.12.adv.A.4.5 Find approximate CC.9-12.A.REI.11 Explain why the solutions for polynomial equations x-coordinates of the points where using graphing technology. 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, OR.12.adv.A.4.7 Graph and analyze polynomial functions. OR.12.adv.A.7.3 Solve exponential and logarithmic equations. OR.9-12.2A.7 Write, use, and solve CC.9-12.A.REI.12 Graph the linear equations and inequalities solutions to a linear inequality in two using graphical and symbolic variables as a half-plane (excluding methods with one or two variables. the boundary in the case of a strict Represent solutions on a inequality), and graph the solution coordinate graph or number line. set to a system of linear inequalities in two variables as the intersection o OR.9-12.2A.8 Solve systems of two linear equations graphically and algebraically, and solve systems of two linear inequalities graphically. OR.12.adv.A.2.1 Graph, solve, and analyze inequalities in two variables. OR.12.adv.A.8.4 Solve systems of linear inequalities by graphing. OR.9-12.2A.5 Given a linear CC.9-12.F.IF.1 Understand that a function, interpret and analyze the function from one set (called the relationship between the domain) to another set (called the independent and dependent range) assigns to each element of variables. Solve for x given f(x) or the domain exactly one element of solve for f(x) given x. the range. If f is a function and x is an element of its domain, then f(x) denotes th OR.9-12.3A.3 Compare the characteristics of and distinguish among linear, quadratic, and exponential functions that are expressed in a table of values, a sequence, a context, algebraically, and/or graphically, and interpret the domain and range of each as OR.9-12.3A.4 Given a quadratic or exponential function, interpret and analyze the relationship between the independent and dependent variables, and evaluate the function for specific values of the domain. OR.12.adv.A.1.1 Demonstrate an understanding of the concept of a function, use function notation, evaluate a function, determine whether or not a given relation is a function and determine whether or not a given function is one-to-one. OR.12.adv.A.1.2 Determine the CC.9-12.F.IF.1 Understand that a domain and range of a relation function from one set (called the including those with restricted domain) to another set (called the domains. range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes th OR.9-12.2A.5 Given a linear CC.9-12.F.IF.2 Use function function, interpret and analyze the notation, evaluate functions for relationship between the inputs in their domains, and independent and dependent interpret statements that use variables. Solve for x given f(x) or function notation in terms of a solve for f(x) given x. context. OR.9-12.3A.4 Given a quadratic or exponential function, interpret and analyze the relationship between the independent and dependent variables, and evaluate the function for specific values of the domain. OR.12.adv.A.9.5 Generate and CC.9-12.F.IF.3 . Recognize that describe other recursive sequences sequences are functions, such as factorials and the sometimes defined recursively, Fibonacci sequence. whose domain is a subset of the integers. OR.8.1.3 Identify and interpret the CC.9-12.F.IF.4 For a function that properties (i.e. slope, intercepts, models a relationship between two continuity, and discreteness) of quantities, interpret key features of linear relationships as they are graphs and tables in terms of the shown in the different quantities, and sketch graphs representations and recognize showing key features given a verbal proportional relationships (y/x = k or description of the relationship. y = kx) as a special case OR.12.adv.A.1.11 Connect the CC.9-12.F.IF.4 For a function that relationships among the solution of models a relationship between two an equation, zero of a function, x- quantities, interpret key features of intercept of a graph and the factors graphs and tables in terms of the of a polynomial expression. quantities, and sketch graphs showing key features given a verbal description of the relationship. OR.12.adv.A.1.12 Find the x and y- intercepts of a function if they exist. OR.12.adv.A.1.2 Determine the CC.9-12.F.IF.5 Relate the domain domain and range of a relation of a function to its graph and, where including those with restricted applicable, to the quantitative domains. relationship it describes. CC.9-12.F.IF.6 Calculate and Calculate and interpret the interpret the average rate of change average rate of change of a of a function (presented function (presented symbolically symbolically or as a table) over a or as a table) over a specified specified interval. Estimate the rate interval. Estimate the rate of of change from a graph. change from a graph. OR.9-12.3A.1 Given a quadratic or CC.9-12.F.IF.7 Graph functions exponential function, identify or expressed symbolically and show determine a corresponding table or key features of the graph, by hand graph. in simple cases and using technology for more complicated cases. OR.12.adv.A.1.3 Represent a given relation in multiple ways and convert between each representation. OR.12.adv.A.3.7 Graph and analyze equations of conic sections. OR.12.adv.A.5.4 Graph and CC.9-12.F.IF.7 Graph functions analyze radical functions. expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. OR.12.adv.A.1.12 Find the x and y- CC.9-12.F.IF.7a Graph linear and intercepts of a function if they exist. quadratic functions and show intercepts, maxima, and minima. OR.12.adv.A.3.4 Graph and analyze quadratic functions and relate the zeros to the discriminant. OR.12.adv.A.1.13 Identify, CC.9-12.F.IF.7b Graph square root, distinguish between, and describe cube root, and piecewise-defined the characteristics of the following functions, including step functions functions in tabular, verbal, and absolute value functions. graphical or symbolic form: polynomial, power, absolute value, rational, radical, logarithmic, exponential, algebraic, piece-wi OR.12.adv.A.2.2 Graph and analyze piece-wise functions. OR.12.adv.A.2.3 Graph, solve, and analyze absolute value equations and inequalities. OR.12.C.1.2 Investigate asymptotic CC.9-12.F.IF.7c Graph polynomial and unbounded behavior in functions, identifying zeros when functions. suitable factorizations are available, and showing end behavior. OR.12.adv.A.4.7 Graph and CC.9-12.F.IF.7d (+) Graph rational analyze polynomial functions. functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. OR.12.adv.A.6.1 Find equivalent CC.9-12.F.IF.7d (+) Graph rational representations for rational functions, identifying zeros and expressions and identify restrictions. asymptotes when suitable factorizations are available, and showing end behavior. OR.12.adv.A.6.4 Graph and analyze rational functions. OR.12.C.1.2 Investigate asymptotic and unbounded behavior in functions. OR.12.adv.A.7.4 Graph and CC.9-12.F.IF.7e Graph exponential analyze exponential and logarithmic and logarithmic functions, showing functions. intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. OR.12.T.2.4 Construct and analyze graphs of the six trigonometric functions and inverse trigonometric functions. OR.9-12.2A.4 Fluently convert CC.9-12.F.IF.8 Write a function among representations of linear defined by an expression in relationships given in the form of a different but equivalent forms to graph of a line, a table of values, or reveal and explain different an equation of a line in slope- properties of the function. intercept and standard form. OR.12.adv.A.1.3 Represent a given relation in multiple ways and convert between each representation. OR.9-12.3A.5 Given a quadratic CC.9-12.F.IF.8a Use the process of equation of the form x^2+ bx + c = factoring and completing the square 0 with integral roots, determine and in a quadratic function to show interpret the roots, the vertex of the zeros, extreme values, and parabola that is the graph of y = x^2 symmetry of the graph, and + bx +c, and an equation of its axis interpret these in terms of a context. of symmetry graphically and algebraic OR.12.D.7.1 Use recursive and CC.9-12.F.IF.8b Use the properties iterative thinking to solve problems of exponents to interpret such as population growth and expressions for exponential decline, exponential functions, functions. problems involving sequential change and compound interest. OR.12.adv.A.1.3 Represent a given CC.9-12.F.IF.9 Compare properties relation in multiple ways and of two functions each represented convert between each in a different way (algebraically, representation. graphically, numerically in tables, or by verbal descriptions). CC.9-12.F.BF.1 Write a function Write a function that describes a that describes a relationship relationship between two between two quantities. quantities. OR.12.D.7.1 Use recursive and CC.9-12.F.BF.1a Determine an iterative thinking to solve problems explicit expression, a recursive such as population growth and process, or steps for calculation decline, exponential functions, from a context. problems involving sequential change and compound interest. OR.12.adv.A.1.8 Perform CC.9-12.F.BF.1b Combine arithmetic operations on functions standard function types using and determine the composition of arithmetic operations. functions. OR.12.adv.A.5.2 Perform arithmetic operations to simplify radical expressions. OR.12.adv.A.1.8 Perform CC.9-12.F.BF.1c (+) Compose arithmetic operations on functions functions. and determine the composition of functions. OR.12.adv.A.10.1 Write and CC.9-12.F.BF.1c (+) Compose evaluate parametric equations. functions. OR.12.adv.A.9.2 Find the explicit CC.9-12.F.BF.2 Build a function and recursive formulas for that models a relationship between arithmetic and geometric two quantities. Write arithmetic and sequences and use these formulas geometric sequences both to determine a specific term or term recursively and with an explicit number. formula, use them to model situations, and translate between the two forms. OR.12.D.7.2 Use finite differences to solve problems and to find explicit formulas for recurrence relations. OR.12.D.7.5 Describe arithmetic and geometric sequences recursively. OR.12.adv.A.1.4 Determine CC.9-12.F.BF.3 Build new functions whether a given relation is even, from existing functions. Identify the odd or neither and what this means effect on the graph of replacing f(x) in predicting behaviors. by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment OR.12.adv.A.1.5 Analyze the effect CC.9-12.F.BF.3 Build new functions on the graph of a relation by from existing functions. Identify the changing its parameters and effect on the graph of replacing f(x) perform a given transformation. by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment OR.12.adv.A.1.6 Determine, verify, CC.9-12.F.BF.4 Find inverse and graph the inverse of a function functions. or relation (if it exists) and understand the reversing roles of domain and range. OR.12.adv.A.1.6 Determine, verify, CC.9-12.F.BF.4a Solve an equation and graph the inverse of a function of the form f(x) = c for a simple or relation (if it exists) and function f that has an inverse and understand the reversing roles of write an expression for the inverse. domain and range. OR.12.adv.A.1.6 Determine, verify, CC.9-12.F.BF.4b (+) Verify by and graph the inverse of a function composition that one function is the or relation (if it exists) and inverse of another. understand the reversing roles of domain and range. OR.12.adv.A.1.7 Determine the composition of inverse functions and whether or not it is one-to-one. CC.9-12.F.BF.4c (+) Read values of Recognize that points on the an inverse function from a graph or inverse of a function are the a table, given that the function has reversal of the x and y values of an inverse. the original function. OR.12.adv.A.1.6 Determine, verify, CC.9-12.F.BF.4d (+) Produce an and graph the inverse of a function invertible function from a non- or relation (if it exists) and invertible function by restricting the understand the reversing roles of domain. domain and range. OR.12.adv.A.7.1 Establish the CC.9-12.F.BF.5 (+) Understand the inverse relationship between inverse relationship between exponential and logarithmic exponents and logarithms and use functions. this relationship to solve problems involving logarithms and exponents. OR.9-12.3A.3 Compare the CC.9-12.F.LE.1 Distinguish characteristics of and distinguish between situations that can be among linear, quadratic, and modeled with linear functions and exponential functions that are with exponential functions. expressed in a table of values, a sequence, a context, algebraically, and/or graphically, and interpret the domain and range of each as CC.9-12.F.LE.1a Prove that linear Prove that linear functions grow functions grow by equal differences by equal differences over equal over equal intervals and that intervals and that exponential exponential functions grow by equal functions grow by equal factors factors over equal intervals. over equal intervals. CC.9-12.F.LE.1b. Recognize Recognize situations in which situations in which one quantity one quantity changes at a changes at a constant rate per unit constant rate per unit interval interval relative to another. relative to another. CC.9-12.F.LE.1c Recognize Recognize situations in which a situations in which a quantity grows quantity grows or decays by a or decays by a constant percent constant percent rate per unit rate per unit interval relative to interval relative to another. another. OR.9-12.3A.1 Given a quadratic or CC.9-12.F.LE.2 Construct linear exponential function, identify or and exponential functions, including determine a corresponding table or arithmetic and geometric graph. sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). OR.12.adv.A.4.6 Write a polynomial equation given its real and/or complex solutions. OR.12.adv.A.9.1 Define, recognize, and discriminate among arithmetic, geometric and other sequences and series. OR.9-12.3A.3 Compare the CC.9-12.F.LE.3 Observe using characteristics of and distinguish graphs and tables that a quantity among linear, quadratic, and increasing exponentially eventually exponential functions that are exceeds a quantity increasing expressed in a table of values, a linearly, quadratically, or (more sequence, a context, algebraically, generally) as a polynomial function. and/or graphically, and interpret the domain and range of each as OR.12.adv.A.7.1 Establish the CC.9-12.F.LE.4 For exponential inverse relationship between models, express as a logarithm the exponential and logarithmic solution to ab^(ct) = d where a, c, functions. and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. OR.9-12.2A.6 Analyze how CC.9-12.F.LE.5 Interpret the changing the parameters parameters in a linear or transforms the graph of f(x)=mx + exponential function in terms of a b. context. OR.9-12.3A.3 Compare the characteristics of and distinguish among linear, quadratic, and exponential functions that are expressed in a table of values, a sequence, a context, algebraically, and/or graphically, and interpret the domain and range of each as CC.9-12.F.TF.1 Understand radian Use the formula s = r x θ and measure of an angle as the length the unit circle to demonstrate of the arc on the unit circle that radian measure of an angle subtended by the angle. is the length of the arc subtended by the angle. OR.12.T.2.1 Define the six CC.9-12.F.TF.2 Explain how the trigonometric functions, construct unit circle in the coordinate plane the unit circle, and use the unit enables the extension of circle to calculate the exact values trigonometric functions to all real of these functions for special numbers, interpreted as radian angles. measures of angles traversed counterclockwise around the unit circle. OR.12.T.1.1 Develop and apply the CC.9-12.F.TF.3 (+) Use special properties of special right triangles. triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values OR.12.T.2.1 Define the six CC.9-12.F.TF.3 (+) Use special trigonometric functions, construct triangles to determine geometrically the unit circle, and use the unit the values of sine, cosine, tangent circle to calculate the exact values for π/3, π/4 and π/6, and use the of these functions for special unit circle to express the values of angles. sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values CC.9-12.F.TF.4 (+) Use the unit Show properties of symmetry circle to explain symmetry (odd and with trionometric funstions using even) and periodicity of the unit circle. trigonometric functions. OR.12.T.2.5 Perform translations of CC.9-12.F.TF.5 Choose trigonometric functions and inverse trigonometric functions to model trigonometric functions. periodic phenomena with specified amplitude, frequency, and midline. CC.9-12.F.TF.6 (+) Understand Sketch the inverse of that restricting a trigonometric trigonometric functions which function to a domain on which it is have restricted domains so that always increasing or always thiey have inverses. decreasing allows its inverse to be constructed. OR.12.T.2.3 Evaluate trigonometric CC.9-12.F.TF.7 (+) Use inverse functions and inverse trigonometric functions to solve trigonometric functions. equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.* OR.12.T.3.1 Prove the CC.9-12.F.TF.8 Prove the Pythagorean Identities and other Pythagorean identity (sin A)^2 + trigonometric identities and apply (cos A)^2 = 1 and use it to find sin them to verify other identities and A, cos A, or tan A, given sin A, cos simplify trigonometric expressions. A, or tan A, and the quadrant of the angle. OR.12.T.3.3 Solve trigonometric CC.9-12.F.TF.9 (+) Prove the equations. addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. CC.9-12.G.CO.1 Know precise Know and use precise definitions of angle, circle, definitions of angle, circle, perpendicular line, parallel line, and perpendicular line, parallel line, line segment, based on the and line segment, based on the undefined notions of point, line, undefined notions of point, line, distance along a line, and distance distance along a line, and around a circular arc. distance around a circular arc to solve related problems. OR.9-12.3G.2 Identify and perform CC.9-12.G.CO.2 . Represent single and composite transformations in the plane using, transformations of geometric e.g., transparencies and geometry figures in a plane, including software; describe transformations translations, origin-centered as functions that take points in the dilations, reflections across either plane as inputs and give other axis or y = ±x, and rotations about points as outputs. Compare the origin in multiples of 90°. transformations that preserv OR.9-12.3G.1 Recognize and CC.9-12.G.CO.3 Given a identify line and rotational rectangle, parallelogram, trapezoid, symmetry of two-dimensional or regular polygon, describe the figures. rotations and reflections that carry it onto itself. CC.9-12.G.CO.4 Develop Develop and use definitions of definitions of rotations, reflections, rotations, reflections, and and translations in terms of angles, translations in terms of angles, circles, perpendicular lines, parallel circles, perpendicular lines, lines, and line segments. parallel lines, and line segments to solve problems. OR.9-12.3G.2 Identify and perform CC.9-12.G.CO.5 Given a single and composite geometric figure and a rotation, transformations of geometric reflection, or translation, draw the figures in a plane, including transformed figure using, e.g., translations, origin-centered graph paper, tracing paper, or dilations, reflections across either geometry software. Specify a axis or y = ±x, and rotations about sequence of transformations that the origin in multiples of 90°. will carry a given figure onto anoth OR.9-12.1G.2 Apply theorems, CC.9-12.G.CO.6 Use geometric properties, and definitions to descriptions of rigid motions to determine, identify, and justify transform figures and to predict the congruency or similarity of triangles effect of a given rigid motion on a and to classify quadrilaterals. given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congr OR.9-12.1G.3 Apply theorems of CC.9-12.G.CO.7Use the definition corresponding parts of congruent of congruence in terms of rigid and similar figures to determine motions to show that two triangles missing sides and angles of are congruent if and only if polygons. corresponding pairs of sides and corresponding pairs of angles are congruent. OR.9-12.1G.2 Apply theorems, CC.9-12.G.CO.8 Explain how the properties, and definitions to criteria for triangle congruence determine, identify, and justify (ASA, SAS, and SSS) follow from congruency or similarity of triangles the definition of congruence in and to classify quadrilaterals. terms of rigid motions. OR.9-12.1G.1 Identify, apply, and CC.9-12.G.CO.9 Prove theorems analyze angle relationships among about lines and angles. two or more lines and a transversal to determine if lines are parallel, perpendicular, or neither. CC.9-12.G.CO.10 Prove theorems Prove theorems about triangles. about triangles. CC.9-12.G.CO.11 Prove theorems Prove theorems about about parallelograms. parallelograms. CC.9-12.G.CO.12. Make formal Make formal geometric geometric constructions with a constructions with a variety of variety of tools and methods tools and methods (compass (compass and straightedge, string, and straightedge, string, reflective devices, paper folding, reflective devices, paper folding, dynamic geometric software, etc.). dynamic geometric software, etc.). CC.9-12.G.CO.13 Construct an Construct an equilateral triangle, equilateral triangle, a square, and a a square, and a regular hexagon regular hexagon inscribed in a circle. inscribed in a circle. OR.9-12.3G.3 Apply a scale factor CC.9-12.G.SRT.1 Verify to determine similar two- and three- experimentally the properties of dimensional figures, are similar. dilations given by a center and a Compare and compute their scale factor: respective areas and volumes of -- a. A dilation takes a line not similar figures. passing through the center of the dilation to a parallel line, and leaves a line passing through the center uncha OR.9-12.1G.2 Apply theorems, CC.9-12.G.SRT.2 Given two properties, and definitions to figures, use the definition of determine, identify, and justify similarity in terms of similarity congruency or similarity of triangles transformations to decide if they are and to classify quadrilaterals. similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding OR.9-12.1G.3 Apply theorems of CC.9-12.G.SRT.2 Given two corresponding parts of congruent figures, use the definition of and similar figures to determine similarity in terms of similarity missing sides and angles of transformations to decide if they are polygons. similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding OR.9-12.3G.3 Apply a scale factor to determine similar two- and three- dimensional figures, are similar. Compare and compute their respective areas and volumes of similar figures. CC.9-12.G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. OR.9-12.1G.2 Apply theorems, CC.9-12.G.SRT.4 Prove theorems properties, and definitions to about triangles. determine, identify, and justify congruency or similarity of triangles and to classify quadrilaterals. OR.9-12.1G.2 Apply theorems, CC.9-12.G.SRT.5 Use congruence properties, and definitions to and similarity criteria for triangles to determine, identify, and justify solve problems and to prove congruency or similarity of triangles relationships in geometric figures. and to classify quadrilaterals. OR.9-12.1G.3 Apply theorems of corresponding parts of congruent and similar figures to determine missing sides and angles of polygons. OR.12.T.1.2 Develop, define, and CC.9-12.G.SRT.6 Understand that apply right triangle trigonometric by similarity, side ratios in right ratios. triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. OR.12.T.2.1 Define the six trigonometric functions, construct the unit circle, and use the unit circle to calculate the exact values of these functions for special angles. CC.9-12.G.SRT.7 Explain and use Demonstrate the equivalency of the relationship between the sine the cosine and sine of and cosine of complementary complementary angles. angles. OR.9-12.1G.4 Use trigonometric CC.9-12.G.SRT.8 . Use ratios (sine, cosine and tangent) trigonometric ratios and the and the Pythagorean Theorem to Pythagorean Theorem to solve right solve for unknown lengths in right triangles in applied problems. triangles. OR.12.T.1.4 Develop and apply the CC.9-12.G.SRT.9 (+) Derive the area formulas of a triangle. formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. OR.12.T.1.3 Develop and apply the CC.9-12.G.SRT.10 (+) Prove the Law of Sines and the Law of Laws of Sines and Cosines and use Cosines. them to solve problems. OR.12.T.1.3 Develop and apply the CC.9-12.G.SRT.11 (+) Understand Law of Sines and the Law of and apply the Law of Sines and the Cosines. Law of Cosines to find unknown measurements in right and non- right triangles (e.g., surveying problems, resultant forces). CC.9-12.G.C.1 Prove that all Prove that all circles are similar. circles are similar. OR.9-12.1G.7 In problems CC.9-12.G.C.2 Identify and involving circles, apply theorems describe relationships among and properties of chords, tangents, inscribed angles, radii, and chords. and angles; and theorems and formulas of arcs and sectors. CC.9-12.G.C.3 Construct the Construct the inscribed and inscribed and circumscribed circles circumscribed circles of a of a triangle, and prove properties triangle, and prove properties of of angles for a quadrilateral angles for a quadrilateral inscribed in a circle. inscribed in a circle. CC.9-12.G.C.4 (+) Construct a Construct a tangent line from a tangent line from a point outside a point outside a given circle to the given circle to the circle. circle. OR.9-12.1G.7 In problems CC.9-12.G.C.5 Derive using involving circles, apply theorems similarity the fact that the length of and properties of chords, tangents, the arc intercepted by an angle is and angles; and theorems and proportional to the radius, and formulas of arcs and sectors. define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. OR.12.adv.A.3.6 Solve problems CC.9-12.G.GPE.1 Derive the relating to conic sections including equation of a circle of given center systems of equations and and radius using the Pythagorean inequalities involving conics. Theorem; complete the square to find the center and radius of a circle given by an equation. OR.12.adv.A.3.8 Determine conic CC.9-12.G.GPE.1 Derive the equations from graphs or data. equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. OR.12.adv.A.3.6 Solve problems CC.9-12.G.GPE.2 Derive the relating to conic sections including equation of a parabola given a systems of equations and focus and directrix. inequalities involving conics. OR.12.adv.A.3.8 Determine conic equations from graphs or data. OR.12.adv.A.3.6 Solve problems CC.9-12.G.GPE.3 (+) Derive the relating to conic sections including equations of ellipses and systems of equations and hyperbolas given the foci, using the inequalities involving conics. fact that the sum or difference of distances from the foci is constant. OR.12.adv.A.3.8 Determine conic equations from graphs or data. CC.9-12.G.GPE.4 Use coordinates Use coordinates to prove simple to prove simple geometric theorems geometric theorems algebraically. algebraically. OR.9-12.2A.3 Determine the CC.9-12.G.GPE.5 Prove the slope equation of a line given any of the criteria for parallel and following information: two points on perpendicular lines and use them to the line, its slope and one point on solve geometric problems (e.g., find the line, or its graph. Also, the equation of a line parallel or determine an equation of a new perpendicular to a given line that line, parallel or perpendicular to a passes through a given point). given line, through OR.9-12.3G.4 Apply slope, CC.9-12.G.GPE.5 Prove the slope distance, and midpoint formulas to criteria for parallel and solve problems in a coordinate perpendicular lines and use them to plane. solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). OR.12.D.9.2 Use fair division CC.9-12.G.GPE.6 Find the point on techniques to divide continuous a directed line segment between objects. two given points that partitions the segment in a given ratio. OR.12.D.9.3 Use fair division techniques to solve apportionment problems. OR.9-12.3G.4 Apply slope, CC.9-12.G.GPE.7 Use coordinates distance, and midpoint formulas to to compute perimeters of polygons solve problems in a coordinate and areas of triangles and plane. rectangles, e.g., using the distance formula. OR.7.3.4 Use models to explain the CC.9-12.G.GMD.1 Give an informal reasonableness of formulas for the argument for the formulas for the surface area of pyramids and circumference of a circle, area of a cylinders, and volume of pyramids, circle, volume of a cylinder, cylinders, and cones. pyramid, and cone. CC.9-12.G.GMD.2 (+) Give an Give an informal argument using informal argument using Cavalieri’s Cavalieri’s principle for the principle for the formulas for the formulas for the volume of a volume of a sphere and other solid sphere and other solid figures. figures. OR.9-12.2G.2 Identify and apply CC.9-12.G.GMD.3 Use volume formulas for surface area and formulas for cylinders, pyramids, volume of spheres; right solids, cones, and spheres to solve including rectangular prisms and problems. pyramids; cones; and cylinders; and compositions thereof. Solve related context-based problems. OR.9-12.2G.3 Identify and apply formulas to solve for the missing dimensions of spheres and right solids, including rectangular prisms and pyramids, cones, and cylinders, both numerically and symbolically. CC.9-12.G.GMD.4 Identify the Identify the shapes of two- shapes of two-dimensional cross- dimensional cross-sections of sections of three-dimensional three-dimensional objects, and objects, and identify three- identify three-dimensional dimensional objects generated by objects generated by rotations of rotations of two-dimensional objects. two-dimensional objects. CC.9-12.G.MG.1 Use geometric Use geometric shapes, their shapes, their measures, and their measures, and their properties properties to describe objects (e.g., to model objects. modeling a tree trunk or a human torso as a cylinder). CC.9-12.G.MG.2 Apply concepts of Apply concepts of density based density based on area and volume on area and volume in modeling in modeling situations (e.g., situations. persons per square mile, BTUs per cubic foot). CC.9-12.G.MG.3 Apply geometric Apply geometric methods to methods to solve design problems solve design problems. (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). OR.8.2.1 Organize and display data CC.9-12.S.ID.1 Represent data (e.g., histograms, box-and-whisker with plots on the real number line plots, scatter plots) to pose and (dot plots, histograms, and box answer questions; and justify the plots). reasonableness of the choice of display. OR.9-12.1S.5 Construct, analyze, and interpret tables, scatter plots, frequency distributions, and histograms of data sets. OR.8.2.2 Use measures of center CC.9-12.S.ID.2 Use statistics and spread to summarize and appropriate to the shape of the data compare data sets. distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. OR.9-12.1S.3 Compare and draw conclusions about two or more data sets using graphical displays or central tendencies and range. OR.12.adv.S.1.1 Construct, interpret, and summarize numerical characteristics of univariate data sets to describe patterns and departure from patterns, using measures of center, spread, and position. OR.12.adv.S.3.2 Explore the CC.9-12.S.ID.2 Use statistics independence versus dependence appropriate to the shape of the data of two random variables. Determine distribution to compare center the mean and standard deviation (median, mean) and spread for sum or difference of (interquartile range, standard independent random variables. deviation) of two or more different data sets. OR.12.adv.S.3.4 Explore sampling distributions to include: sampling distribution of a sample of proportion and mean; Binomial Distribution and Geometric Distribution; applying the Central Limit Theorem; investigating sampling distributions of a difference OR.12.adv.S.1.2 Compare CC.9-12.S.ID.3 Interpret differences distributions of univariate data by in shape, center, and spread in the comparing center and spread, context of the data sets, accounting clusters and gaps, outliers, and for possible effects of extreme data other unusual features and points (outliers). comparing shapes. OR.12.adv.S.3.2 Explore the CC.9-12.S.ID.4 Use the mean and independence versus dependence standard deviation of a data set to of two random variables. Determine fit it to a normal distribution and to the mean and standard deviation estimate population percentages. for sum or difference of Recognize that there are data sets independent random variables. for which such a procedure is not appropriate. Use calculators, spreadsheets, a OR.12.adv.S.3.3 Analyze the CC.9-12.S.ID.4 Use the mean and properties of the normal standard deviation of a data set to distribution; use tables of the fit it to a normal distribution and to normal distribution; and explore a estimate population percentages. normal distribution as a model for Recognize that there are data sets measurements. for which such a procedure is not appropriate. Use calculators, spreadsheets, a OR.12.adv.S.1.4 Explore CC.9-12.S.ID.5 Summarize categorical data using frequency categorical data for two categories tables and bar charts; investigating in two-way frequency tables. marginal, joint and conditional Interpret relative frequencies in the relative frequencies; and by context of the data (including joint, comparing distributions. marginal, and conditional relative frequencies). Recognize possible associations and tren OR.9-12.1S.5 Construct, analyze, CC.9-12.S.ID.6 Represent data on and interpret tables, scatter plots, two quantitative variables on a frequency distributions, and scatter plot, and describe how the histograms of data sets. variables are related. OR.12.adv.S.4.5 Understand how to read the results of a regression, and use this to make predictions of future events with a stated confidence. OR.9-12.1S.4 Use or construct a CC.9-12.S.ID.6a Fit a function to scatter plot for a given data set, the data; use functions fitted to data determine whether there is a (n) to solve problems in the context of linear, quadratic, exponential, or no the data. trend. If linear, determine if there is a positive or negative correlation among the data; and, if appropriate, sket OR.12.adv.A.1.10 Collect and analyze data to make predictions and to investigate scatterplots and to determine the equation for a curve of best fit including linear, power, exponential, and logarithmic functions. OR.12.adv.S.4.5 Understand how to read the results of a regression, and use this to make predictions of future events with a stated confidence. OR.12.adv.A.1.10 Collect and CC.9-12.S.ID.6b Informally assess analyze data to make predictions the fit of a function by plotting and and to investigate scatterplots and analyzing residuals. to determine the equation for a curve of best fit including linear, power, exponential, and logarithmic functions. OR.12.adv.S.1.3 Explore bivariate data by analyzing patterns, correlation, linearity, least-squares regression line, residual plots, outliers, influential points, and transformations to achieve linearity. OR.12.adv.S.4.5 Understand how CC.9-12.S.ID.6b Informally assess to read the results of a regression, the fit of a function by plotting and and use this to make predictions of analyzing residuals. future events with a stated confidence. OR.12.adv.A.1.10 Collect and CC.9-12.S.ID.6c Fit a linear function analyze data to make predictions for a scatter plot that suggests a and to investigate scatterplots and linear association. to determine the equation for a curve of best fit including linear, power, exponential, and logarithmic functions. OR.12.adv.S.1.3 Explore bivariate data by analyzing patterns, correlation, linearity, least-squares regression line, residual plots, outliers, influential points, and transformations to achieve linearity. OR.12.adv.S.4.5 Understand how to read the results of a regression, and use this to make predictions of future events with a stated confidence. OR.12.adv.S.4.4 Apply various CC.9-12.S.ID.7 Interpret the slope large sample tests for a proportion - (rate of change) and the intercept i.e. difference between two (constant term) of a linear model in proportions, mean, difference the context of the data. between two means, Chi-square test, and slope of a least squares regression line. OR.9-12.1S.4 Use or construct a CC.9-12.S.ID.8 Compute (using scatter plot for a given data set, technology) and interpret the determine whether there is a (n) correlation coefficient of a linear fit. linear, quadratic, exponential, or no trend. If linear, determine if there is a positive or negative correlation among the data; and, if appropriate, sket OR.12.adv.S.1.3 Explore bivariate data by analyzing patterns, correlation, linearity, least-squares regression line, residual plots, outliers, influential points, and transformations to achieve linearity. CC.9-12.S.ID.9 Distinguish Distinguish between correlation between correlation and causation. and causation. OR.12.adv.S.4.3 Explain the logic CC.9-12.S.IC.1 Understand of significance testing, null and statistics as a process for making alternative hypotheses; p-values; inferences about population one-and two-sided tests; concepts parameters based on a random of Type I and Type II errors; sample from that population. concept of power. OR.9-12.1S.1 Given a context, CC.9-12.S.IC.2 . Decide if a determine appropriate survey specified model is consistent with methods, analyze the strengths and results from a given data- limitations of a particular survey, generating process, e.g., using observational study, experiment, or simulation. simulation, and the display of its data. OR.9-12.1S.1 Given a context, CC.9-12.S.IC.3 Recognize the determine appropriate survey purposes of and differences among methods, analyze the strengths and sample surveys, experiments, and limitations of a particular survey, observational studies; explain how observational study, experiment, or randomization relates to each. simulation, and the display of its data. OR.12.adv.S.2.1 Describe the methods of data collection. Evaluate how appropriate each method is relative to the purposes of various types of inquires and hypotheses under investigation given various population distributions. OR.12.adv.S.2.2 Plan, analyze, and conduct a survey, and/or observational study; describe characteristics of a well-designed and well-conducted survey; explore various sampling methods including investigating sources of bias. OR.12.adv.S.2.3 Plan, analyze, and conduct an experiment; describe characteristics and components of a well-designed and well-conducted experiment; explore various methods of experimental designs; and associated sources of bias and confounding. OR.12.adv.S.2.2 Plan, analyze, and CC.9-12.S.IC.4 Use data from a conduct a survey, and/or sample survey to estimate a observational study; describe population mean or proportion; characteristics of a well-designed develop a margin of error through and well-conducted survey; explore the use of simulation models for various sampling methods random sampling. including investigating sources of bias. OR.12.adv.S.4.1 Investigate the following: estimating population parameters, margins of error, confidence intervals, and properties of point estimators. OR.12.adv.S.2.3 Plan, analyze, and CC.9-12.S.IC.5 Use data from a conduct an experiment; describe randomized experiment to compare characteristics and components of two treatments; use simulations to a well-designed and well-conducted decide if differences between experiment; explore various parameters are significant. methods of experimental designs; and associated sources of bias and confounding. OR.12.adv.S.4.3 Explain the logic of significance testing, null and alternative hypotheses; p-values; one-and two-sided tests; concepts of Type I and Type II errors; concept of power. OR.8.2.7 Identify claims based on CC.9-12.S.IC.6 Evaluate reports statistical data and evaluate the based on data. reasonableness of those claims. OR.8.2.8 Use data to estimate the likelihood of future events and evaluate the reasonableness of predictions. OR.9-12.1S.2 Evaluate data-based CC.9-12.S.IC.6 Evaluate reports reports by considering the source based on data. of the data, the design of the study, and the way the data was analyzed and displayed. OR.12.adv.S.2.4 Explore the generalizability of results and types of conclusions that can be drawn from observational studies, experiments, and surveys. Understand when each method is most appropriate, and explain the differences between the three methods OR.9-12.2S.3 Compute and CC.9-12.S.CP.1 Describe events as interpret probabilities for subsets of a sample space (the set independent, dependent, of outcomes) using characteristics complementary, and compound (or categories) of the outcomes, or events using various methods (e.g., as unions, intersections, or diagrams, tables, area models, and complements of other events (“or,” counting techniques). “and,” “not”). OR.12.D.1.2 Perform set operations such as union and intersection, difference, and complement. OR.9-12.2S.3 Compute and CC.9-12.S.CP.2 Understand that interpret probabilities for two events A and B are independent, dependent, independent if the probability of A complementary, and compound and B occurring together is the events using various methods (e.g., product of their probabilities, and diagrams, tables, area models, and use this characterization to counting techniques). determine if they are independent. OR.12.D.5.4 Solve probability CC.9-12.S.CP.2 Understand that problems such as conditional two events A and B are probability, probability of simple independent if the probability of A events, mutually exclusive events, and B occurring together is the and independent events. product of their probabilities, and use this characterization to determine if they are independent. OR.12.adv.S.3.2 Explore the independence versus dependence of two random variables. Determine the mean and standard deviation for sum or difference of independent random variables. OR.9-12.2S.3 Compute and CC.9-12.S.CP.3 Understand the interpret probabilities for conditional probability of A given B independent, dependent, as P(A and B)/P(B), and interpret complementary, and compound independence of A and B as saying events using various methods (e.g., that the conditional probability of A diagrams, tables, area models, and given B is the same as the counting techniques). probability of A, and the conditional probability of B OR.12.D.5.4 Solve probability problems such as conditional probability, probability of simple events, mutually exclusive events, and independent events. OR.12.adv.S.3.1 Analyze CC.9-12.S.CP.3 Understand the probability by exploring such topics conditional probability of A given B as "Law of Large Numbers," as P(A and B)/P(B), and interpret addition and multiplication rule, independence of A and B as saying conditional probability and that the conditional probability of A independence, discrete random given B is the same as the variables and their probability probability of A, and the conditional distributions, simulations of random probability of B behavi CC.9-12.S.CP.4 Construct and Construct and interpret two-way interpret two-way frequency tables frequency tables of data when of data when two categories are two categories are associated associated with each object being with each object being classified. classified. Use the two-way table as Use the two-way table as a a sample space to decide if events sample space to decide if events are independent and to are independent and to approximate conditional proba approximate conditional probabilities. OR.12.D.5.4 Solve probability CC.9-12.S.CP.5 Recognize and problems such as conditional explain the concepts of conditional probability, probability of simple probability and independence in events, mutually exclusive events, everyday language and everyday and independent events. situations. OR.12.D.5.4 Solve probability CC.9-12.S.CP.6 Find the problems such as conditional conditional probability of A given B probability, probability of simple as the fraction of B’s outcomes that events, mutually exclusive events, also belong to A, and interpret the and independent events. answer in terms of the model. OR.12.adv.S.3.1 Analyze CC.9-12.S.CP.6 Find the probability by exploring such topics conditional probability of A given B as "Law of Large Numbers," as the fraction of B’s outcomes that addition and multiplication rule, also belong to A, and interpret the conditional probability and answer in terms of the model. independence, discrete random variables and their probability distributions, simulations of random behavi OR.12.D.5.3 Apply basic CC.9-12.S.CP.7 Apply the Addition fundamental counting principles Rule, P(A or B) = P(A) + P(B) – P(A such as The Pigeonhole Principle, and B), and interpret the answer in Multiplication Principle, Addition terms of the model. Principle, and Binomial Theorem to practical problems. OR.12.adv.S.3.1 Analyze probability by exploring such topics as "Law of Large Numbers," addition and multiplication rule, conditional probability and independence, discrete random variables and their probability distributions, simulations of random behavi OR.12.D.5.3 Apply basic CC.9-12.S.CP.8 (+) Apply the fundamental counting principles general Multiplication Rule in a such as The Pigeonhole Principle, uniform probability model, P(A and Multiplication Principle, Addition B) = [P(A)]x[P(B|A)] Principle, and Binomial Theorem to =[P(B)]x[P(A|B)], and interpret the practical problems. answer in terms of the model. OR.12.adv.S.3.1 Analyze CC.9-12.S.CP.8 (+) Apply the probability by exploring such topics general Multiplication Rule in a as "Law of Large Numbers," uniform probability model, P(A and addition and multiplication rule, B) = [P(A)]x[P(B|A)] conditional probability and =[P(B)]x[P(A|B)], and interpret the independence, discrete random answer in terms of the model. variables and their probability distributions, simulations of random behavi OR.12.adv.A.4.2 Analyze and CC.9-12.S.CP.9 (+) Use calculate permutations, permutations and combinations to combinations, and other systematic compute probabilities of compound counting methods. events and solve problems. OR.12.D.5.1 Produce all combinations and permutations of sets. OR.12.D.5.2 Calculate the number of combinations and permutations of sets of m items taken n at a time. CC.9-12.S.MD.1 (+) Define a Define a random variable for a random variable for a quantity of quantity of interest by assigning interest by assigning a numerical a numerical value to each event value to each event in a sample in a sample space; graph the space; graph the corresponding corresponding probability probability distribution using the distribution using histograms, same graphical displays as for data box-and-whisker plots, and distributions. scatter plots. CC.9-12.S.MD.2 (+) Calculate the Calculate the expected value of expected value of a random a random variable; interpret it as variable; interpret it as the mean of the mean of the probability the probability distribution. distribution. CC.9-12.S.MD.3 (+) Develop a Develop a probability distribution probability distribution for a random for a random variable defined for variable defined for a sample space a sample space in which in which theoretical probabilities can theoretical probabilities can be be calculated; find the expected calculated; find the expected value. value. CC.9-12.S.MD.4 (+) Develop a Develop a probability distribution probability distribution for a random for a random variable defined for variable defined for a sample space a sample space in which in which probabilities are assigned probabilities are assigned empirically; find the expected value. empirically; find the expected value. CC.9-12.S.MD.5 (+) Weigh the Weigh the possible outcomes of possible outcomes of a decision by a decision by assigning assigning probabilities to payoff probabilities to payoff values and values and finding expected values. finding expected values. CC.9-12.S.MD.5a (+) Find the Find the expected payoff for a expected payoff for a game of game of chance. chance. CC.9-12.S.MD.5b (+) Evaluate and Evaluate and compare compare strategies on the basis of strategies on the basis of expected values. expected values. CC.9-12.S.MD.6 (+) Use Use probabilities to make fair probabilities to make fair decisions decisions (e.g., drawing by lots, (e.g., drawing by lots, using a using a random number random number generator). generator). OR.12.D.10.1 Use game theory to CC.9-12.S.MD.7 (+) Analyze solve strictly determined games. decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). OR.12.D.10.2 Use game theory to solve non-strictly determined games. OR.12.D.10.3 Use game theory to create models for games. OR.12.D.10.4 Use game theory to CC.9-12.S.MD.7 (+) Analyze find optimal mixed strategies such decisions and strategies using as expected values or payoff probability concepts (e.g., product values. testing, medical testing, pulling a hockey goalie at the end of a game). OR Grade OR OR OR Standard Grade Alignment Partial Type Partial Type2 Index Strand ID Δ 12adv.A5.1 12 adv.A -3 2 OR>CCSS OR>CCSS 12adv.A5.4 12 adv.A -3 1 91A3 9 1A MTH.HS.1A.3 0 2 Both Both 91A4 9 1A MTH.HS.1A.4 0 2 OR>CCSS OR>CCSS 12adv.A5.1 12 adv.A -3 3 12adv.A5.2 12 adv.A -3 1 0 0 0 0.NC 0 0 0 0.NC 0 0 0 0.NC 0 0 0 0.NC 12adv.A3.1 12 adv.A -3 2 OR>CCSS OR>CCSS 12adv.A3.1 12 adv.A -3 2 OR>CCSS OR>CCSS 0 0 0 0.NC 12T5.1 12 T 0 2 CCSS>OR CCSS>OR 12T5.2 12 T 0 2 CCSS>OR CCSS>OR 12T5.3 12 T 0 1 12T5.4 12 T 0 1 0 0 0 0.NC 0 0 0 0.OR(-) 0 0 0 0.NC 12adv.A4.4 12 adv.A 0 2 OR>CCSS OR>CCSS 0 0 0 0.OR(+) 0 0 0 0.OR(+) 12T2.6 12 T 0 1 12T4.2 12 T 0 3 12T4.1 12 T 0 2 CCSS>OR CCSS>OR 0 0 2.SS SS 0 0 2.SS SS 0 0 2.SS SS 12T4.1 12 T 0 2 CCSS>OR CCSS>OR 0 0 2.SS SS 0 0 2.SS SS 12adv.A8.5 12 adv.A 0 2 OR>CCSS OR>CCSS 12adv.A8.1 12 adv.A 0 2 OR>CCSS OR>CCSS 12adv.A8.1 12 adv.A 0 3 0 0 0 0.OR(+) 12adv.A8.3 12 adv.A 0 2 CCSS>OR CCSS>OR 12T4.1 12 T 0 2 CCSS>OR CCSS>OR 0 0 0 0.NC 0 0 0 0.OR(+) 0 0 0.SS SS 0 0 0.SS SS 0 0 0 0.NC 91A2 9 1A MTH.HS.1A.2 0 2 Both Both 93A5 9 3A MTH.HS.3A.5 0 2.SS Both Both 12adv.A3.3 12 adv.A -3 1.SS 0 0 2.SS SS 12adv.A9.3 12 adv.A -3 1 12D7.6 12 D -3 2 OR>CCSS OR>CCSS 12adv.A4.1 12 adv.A -3 2 CCSS>OR CCSS>OR 12adv.A1.11 12 adv.A -3 2 CCSS>OR CCSS>OR 12adv.A1.11 12 adv.A -3 2 CCSS>OR CCSS>OR 12adv.A4.6 12 adv.A -3 2 Both Both 0 0 0 0.NC 12adv.A4.3 12 adv.A 0 2 CCSS>OR CCSS>OR 12D5.3 12 D 0 2 OR>CCSS OR>CCSS 12adv.A4.4 12 adv.A -3 1 12adv.A6.1 12 adv.A -3 2 CCSS>OR CCSS>OR 12adv.A6.2 12 adv.A 0 2 CCSS>OR CCSS>OR 91A4 9 1A MTH.HS.1A.4 0 1 Both Both 92A7 9 2A MTH.HS.2A.7 0 2 Both Both 93A1 9 3A MTH.HS.3A.1 0 1 93A2 9 3A MTH.HS.3A.2 0 1 92A3 9 2A MTH.HS.2A.3 0 2 CCSS>OR CCSS>OR 12D4.1 12 D -3 1 12adv.A8.4 12 adv.A -3 2 OR>CCSS OR>CCSS 0 0 0 0.OR(+) 0 0 0 0.OR(+) 12adv.A5.3 12 adv.A -3 2 CCSS>OR CCSS>OR 12adv.A6.3 12 adv.A -3 2 CCSS>OR CCSS>OR 12adv.A2.1 12 adv.A -3 2 Both Both 91A5 9 1A MTH.HS.1A.5 0 2 CCSS>OR CCSS>OR 93A5 9 3A MTH.HS.3A.5 0 1.SS Both Both 12adv.A3.2 12 adv.A -3 2.SS CCSS>OR CCSS>OR 91A5 9 1A MTH.HS.1A.5 0 2.SS CCSS>OR CCSS>OR 93A5 9 3A MTH.HS.3A.5 0 2.SS CCSS>OR CCSS>OR 12adv.A3.3 12 adv.A -3 2.SS OR>CCSS OR>CCSS 0 0 0 0.OR(+) 12adv.A8.2 12 adv.A -3 2 OR>CCSS OR>CCSS 12adv.A8.6 12 adv.A -3 3 12adv.A8.2 12 adv.A 0 2 OR>CCSS OR>CCSS 12adv.A8.1 12 adv.A 0 2 OR>CCSS OR>CCSS 92A7 9 2A MTH.HS.2A.7 0 2 Both Both 12adv.A4.7 12 adv.A -3 2 OR>CCSS OR>CCSS 12D4.1 12 D -3 1 12adv.A2.3 12 adv.A -3 2 Both Both 12adv.A3.5 12 adv.A -3 2 CCSS>OR CCSS>OR 12adv.A4.5 12 adv.A -3 1 12adv.A4.7 12 adv.A -3 1 12adv.A7.3 12 adv.A -3 1 92A7 9 2A MTH.HS.2A.7 0 2 OR>CCSS OR>CCSS 92A8 9 2A MTH.HS.2A.8 0 2 OR>CCSS OR>CCSS 12adv.A2.1 12 adv.A -3 2 OR>CCSS OR>CCSS 12adv.A8.4 12 adv.A -3 3 92A5 9 2A MTH.HS.2A.5 0 2 OR>CCSS OR>CCSS 93A3 9 3A MTH.HS.3A.3 0 2 OR>CCSS OR>CCSS 93A4 9 3A MTH.HS.3A.4 0 2 Both Both 12adv.A1.1 12 adv.A -3 2 Both Both 12adv.A1.2 12 adv.A -3 2 OR>CCSS OR>CCSS 92A5 9 2A MTH.HS.2A.5 0 2 OR>CCSS OR>CCSS 93A4 9 3A MTH.HS.3A.4 0 3 OR>CCSS OR>CCSS 12adv.A9.5 12 adv.A -3 3 81(A)3 8 1(A) MTH.8.1.3 1 2 CCSS>OR CCSS>OR 12adv.A1.11 12 adv.A -3 1 12adv.A1.12 12 adv.A -3 2 CCSS>OR CCSS>OR 12adv.A1.2 12 adv.A -3 2 OR>CCSS OR>CCSS 0 0 0 0.OR(+) 93A1 9 3A MTH.HS.3A.1 0 1 Both Both 12adv.A1.3 12 adv.A -3 2 OR>CCSS OR>CCSS 12adv.A3.7 12 adv.A -3 1 12adv.A5.4 12 adv.A -3 2 CCSS>OR CCSS>OR 12adv.A1.12 12 adv.A -3 1.SS SS 12adv.A3.4 12 adv.A -3 2.SS OR>CCSS OR>CCSS 12adv.A1.13 12 adv.A -3 2.SS OR>CCSS OR>CCSS 12adv.A2.2 12 adv.A -3 2.SS CCSS>OR CCSS>OR 12adv.A2.3 12 adv.A -3 1.SS 12C1.2 12 C -3 2.SS OR>CCSS OR>CCSS 12adv.A4.7 12 adv.A 0 2.SS OR>CCSS OR>CCSS 12adv.A6.1 12 adv.A 0 2.SS OR>CCSS OR>CCSS 12adv.A6.4 12 adv.A 0 3.SS 12C1.2 12 C 0 2.SS OR>CCSS OR>CCSS 12adv.A7.4 12 adv.A -3 3.SS 12T2.4 12 T -3 2.SS CCSS>OR CCSS>OR 92A4 9 2A MTH.HS.2A.4 0 2 Both Both 12adv.A1.3 12 adv.A -3 2 OR>CCSS OR>CCSS 93A5 9 3A MTH.HS.3A.5 0 2.SS Both Both 12D7.1 12 D -3 2.SS OR>CCSS OR>CCSS 12adv.A1.3 12 adv.A -3 2 OR>CCSS OR>CCSS 0 0 2 Both 12D7.1 12 D -3 2.SS OR>CCSS OR>CCSS 12adv.A1.8 12 adv.A -3 2.SS OR>CCSS OR>CCSS 12adv.A5.2 12 adv.A -3 2.SS CCSS>OR CCSS>OR 12adv.A1.8 12 adv.A 0 2.SS OR>CCSS OR>CCSS 12adv.A10.1 12 adv.A 0 1.SS 12adv.A9.2 12 adv.A -3 3 12D7.2 12 D -3 1 12D7.5 12 D -3 2 CCSS>OR CCSS>OR 12adv.A1.4 12 adv.A -3 1 12adv.A1.5 12 adv.A -3 3 12adv.A1.6 12 adv.A -3 2 OR>CCSS OR>CCSS 12adv.A1.6 12 adv.A -3 2.SS OR>CCSS OR>CCSS 12adv.A1.6 12 adv.A 0 2.SS OR>CCSS OR>CCSS 12adv.A1.7 12 adv.A 0 3.SS 0 0 2.SS SS 12adv.A1.6 12 adv.A 0 2 CCSS>OR CCSS>OR 12adv.A7.1 12 adv.A 0 3 93A3 9 3A MTH.HS.3A.3 0 2 OR>CCSS OR>CCSS 0 0 2.SS SS 0 0 2.SS SS 0 0 2.SS SS 93A1 9 3A MTH.HS.3A.1 0 2 Both Both 12adv.A4.6 12 adv.A -3 2 CCSS>OR CCSS>OR 12adv.A9.1 12 adv.A -3 2 Both Both 93A3 9 3A MTH.HS.3A.3 0 2 Both Both 12adv.A7.1 12 adv.A -3 2 OR>CCSS OR>CCSS 92A6 9 2A MTH.HS.2A.6 0 2 CCSS>OR CCSS>OR 93A3 9 3A MTH.HS.3A.3 0 1 OR>CCSS OR>CCSS 0 0 0 0.OR(-) 12T2.1 12 T -3 2 OR>CCSS OR>CCSS 12T1.1 12 T 0 2 Both Both 12T2.1 12 T 0 2 OR>CCSS OR>CCSS 0 0 0 0.OR(+) 12T2.5 12 T -3 2 Both Both 0 0 0 0.OR(+) 12T2.3 12 T 0 2 Both Both 12T3.1 12 T -3 3 12T3.3 12 T 0 1 0 0 0 0.OR(+) 93G2 9 3G MTH.HS.3G.2 0 2 CCSS>OR CCSS>OR 93G1 9 3G MTH.HS.3G.1 0 2 OR>CCSS OR>CCSS 0 0 0 0.OR(+) 93G2 9 3G MTH.HS.3G.2 0 2 Both Both 91G2 9 1G MTH.HS.1G.2 0 2 Both Both 91G3 9 1G MTH.HS.1G.3 0 2 OR>CCSS OR>CCSS 91G2 9 1G MTH.HS.1G.2 0 2 Both Both 91G1 9 1G MTH.HS.1G.1 0 2 Both Both 0 0 0 0.OR(+) 0 0 0 0.OR(+) 0 0 0 0.NC 0 0 0 0.NC 93G3 9 3G MTH.HS.3G.3 0 2 OR>CCSS OR>CCSS 91G2 9 1G MTH.HS.1G.2 0 2 OR>CCSS OR>CCSS 91G3 9 1G MTH.HS.1G.3 0 2 OR>CCSS OR>CCSS 93G3 9 3G MTH.HS.3G.3 0 3 OR>CCSS OR>CCSS 0 0 0 0.OR(+) 91G2 9 1G MTH.HS.1G.2 0 1 Both Both 91G2 9 1G MTH.HS.1G.2 0 2 OR>CCSS OR>CCSS 91G3 9 1G MTH.HS.1G.3 0 2 CCSS>OR CCSS>OR 12T1.2 12 T -3 2 OR>CCSS OR>CCSS 12T2.1 12 T -3 2 OR>CCSS OR>CCSS 0 0 0 0.OR(-) 91G4 9 1G MTH.HS.1G.4 0 2 CCSS>OR CCSS>OR 12T1.4 12 T 0 3 12T1.3 12 T 0 2 CCSS>OR CCSS>OR 12T1.3 12 T 0 2 CCSS>OR CCSS>OR 0 0 0 0.NC 91G7 9 1G MTH.HS.1G.7 0 2 OR>CCSS OR>CCSS 0 0 0 0.NC 0 0 0 0.NC 91G7 9 1G MTH.HS.1G.7 0 2 Both Both 12adv.A3.6 12 adv.A -3 2 OR>CCSS OR>CCSS 12adv.A3.8 12 adv.A -3 2 OR>CCSS OR>CCSS 12adv.A3.6 12 adv.A -3 2 OR>CCSS OR>CCSS 12adv.A3.8 12 adv.A -3 2 OR>CCSS OR>CCSS 12adv.A3.6 12 adv.A 0 2 OR>CCSS OR>CCSS 12adv.A3.8 12 adv.A 0 2 OR>CCSS OR>CCSS 0 0 0 0.OR(+) 92A3 9 2A MTH.HS.2A.3 0 2 Both Both 93G4 9 3G MTH.HS.3G.4 0 1 OR>CCSS OR>CCSS 12D9.2 12 D -3 1 12D9.3 12 D -3 1 93G4 9 3G MTH.HS.3G.4 0 2 OR>CCSS OR>CCSS 73(MG)4 7 3(MG) MTH.7.3.4 2 2 Both Both 0 0 0 0.NC 92G2 9 2G MTH.HS.2G.2 0 2 OR>CCSS OR>CCSS 92G3 9 2G MTH.HS.2G.3 0 2 OR>CCSS OR>CCSS 0 0 0 0.OR(+) 0 0 0 0.OR(+) 0 0 0 0.NC 0 0 0 0.NC 82(DA)1 8 2(DA) MTH.8.2.1 1 2 OR>CCSS OR>CCSS 91S5 9 1S MTH.HS.1S.5 0 2 OR>CCSS OR>CCSS 82(DA)2 8 2(DA) MTH.8.2.2 1 2 CCSS>OR CCSS>OR 91S3 9 1S MTH.HS.1S.3 0 2 Both Both 12adv.S1.1 12 adv.S -3 2 OR>CCSS OR>CCSS 12adv.S3.2 12 adv.S -3 2 12adv.S3.4 12 adv.S -3 2 OR>CCSS OR>CCSS 12adv.S1.2 12 adv.S -3 3 12adv.S3.2 12 adv.S -3 1 12adv.S3.3 12 adv.S -3 2 Both Both 12adv.S1.4 12 adv.S -3 3 91S5 9 1S MTH.HS.1S.5 0 2 OR>CCSS OR>CCSS 12adv.S4.5 12 adv.S -3 2 OR>CCSS OR>CCSS 91S4 9 1S MTH.HS.1S.4 0 2.SS Both Both 12adv.A1.10 12 adv.A -3 2.SS OR>CCSS OR>CCSS 12adv.S4.5 12 adv.S -3 2.SS OR>CCSS OR>CCSS 12adv.A1.10 12 adv.A -3 2.SS OR>CCSS OR>CCSS 12adv.S1.3 12 adv.S -3 2.SS OR>CCSS OR>CCSS 12adv.S4.5 12 adv.S -3 2.SS OR>CCSS OR>CCSS 12adv.A1.10 12 adv.A -3 2.SS OR>CCSS OR>CCSS 12adv.S1.3 12 adv.S -3 2.SS OR>CCSS OR>CCSS 12adv.S4.5 12 adv.S -3 2.SS OR>CCSS OR>CCSS 12adv.S4.4 12 adv.S -3 1 91S4 9 1S MTH.HS.1S.4 0 2 OR>CCSS OR>CCSS 12adv.S1.3 12 adv.S -3 2 OR>CCSS OR>CCSS 0 0 0 0.NC 12adv.S4.3 12 adv.S -3 1 91S1 9 1S MTH.HS.1S.1 0 2 OR>CCSS OR>CCSS 91S1 9 1S MTH.HS.1S.1 0 2 Both Both 12adv.S2.1 12 adv.S -3 2 OR>CCSS OR>CCSS 12adv.S2.2 12 adv.S -3 1 12adv.S2.3 12 adv.S -3 1 12adv.S2.2 12 adv.S -3 2 OR>CCSS OR>CCSS 12adv.S4.1 12 adv.S -3 2 Both Both 12adv.S2.3 12 adv.S -3 2 OR>CCSS OR>CCSS 12adv.S4.3 12 adv.S -3 2 OR>CCSS OR>CCSS 82(DA)7 8 2(DA) MTH.8.2.7 1 2 OR>CCSS OR>CCSS 82(DA)8 8 2(DA) MTH.8.2.8 1 1 91S2 9 1S MTH.HS.1S.2 0 2 OR>CCSS OR>CCSS 12adv.S2.4 12 adv.S -3 2 OR>CCSS OR>CCSS 92S3 9 2S MTH.HS.2S.3 0 1 OR>CCSS OR>CCSS 12D1.2 12 D -3 1 92S3 9 2S MTH.HS.2S.3 0 2 OR>CCSS OR>CCSS 12D5.4 12 D -3 2 OR>CCSS OR>CCSS 12adv.S3.2 12 adv.S -3 2 OR>CCSS OR>CCSS 92S3 9 2S MTH.HS.2S.3 0 2 Both Both 12D5.4 12 D -3 2 OR>CCSS OR>CCSS 12adv.S3.1 12 adv.S -3 2 OR>CCSS OR>CCSS 0 0 0 0.NC 12D5.4 12 D -3 1 12D5.4 12 D -3 2 OR>CCSS OR>CCSS 12adv.S3.1 12 adv.S -3 2 OR>CCSS OR>CCSS 12D5.3 12 D -3 2 OR>CCSS OR>CCSS 12adv.S3.1 12 adv.S -3 2 OR>CCSS OR>CCSS 12D5.3 12 D 0 2 OR>CCSS OR>CCSS 12adv.S3.1 12 adv.S 0 2 OR>CCSS OR>CCSS 12adv.A4.2 12 adv.A 0 2 OR>CCSS OR>CCSS 12D5.1 12 D 0 1 12D5.2 12 D 0 2 CCSS>OR CCSS>OR 0 0 0 0.NC 0 0 0 0.NC 0 0 0 0.NC 0 0 0 0.NC 0 0 0 0.NC 0 0 0.SS SS 0 0 0.SS SS 0 0 0 0.NC 12D10.1 12 D 0 1 12D10.2 12 D 0 1 12D10.3 12 D 0 1 12D10.4 12 D 0 1 Comment CCSS standard identifies information needed to understand the meaning of rational expressions. OR standard also includes finding equivalent expressions. Weak match on analyzing radical functions. CCSS more specific to using rational exponents and does not specify graphing radical functions. Match on rewriting equivalent radical forms. CCSS identifies using all irrational numbers which includes more than square roots. OR also does decimal approximations found which are found in other CC standards. Match on rewriting algebraic expressions. CCSS specific to expressions with radicals or rational exponents. OR includes justification and inequalities. Both standards identify the ability to use properties of exponents to rewrite equivalent expressions Match on rewriting radical expressions, but CCSS does not specify performing arithmetic operations with radical expressions New content found in the CCSS. New content found in the CCSS. New content found in the CCSS. New content found in the CCSS. Match on representing complex numbers. OR standard also includes performing operations on complex numbers. Partial match on the operation properties of complex numbers. OR standard also includes representing complex numbers and more cognitive demand levels. (Advanced Standard) New content found in the CCSS. Finding conjugates is typically taught in advanced algebra or precalculus, but moduli & quotients may not be taught. Match on representing polar coordinates, but CCSS also includes operations on complex numbers. CCSS standard identifies conversion of coordinates on the complex plane, but also includes an expectation to explain this connection. CCSS does not specify graphing equations in their polar form OR standard only specifies multiplication in trigonometric form, and not addition and subtraction operations (Advanced Standard) New content fount in the CCSS. Connecting operations of complex numbers to the complex plane may not be taught in all advanced algebra or precalculus courses. No exact match, but this content would likely be taught in an advanced algebra (e.g. OR.12.adv.A.3.3.) (Advanced Standard) New content found in the CCSS. Match on knowing the Fundamental Theorem of Algebra. This OR standard includes more theorems to know and apply. (Advanced standard) No exact match, but content would likely be taught in an advanced algebra or precalculus course. (e.g. OR.12.T.4.1). (Advanced standard) No exact match, but content would likely be taught in an advanced algebra or precalculus course. (e.g. OR.12.T.4.2). Only CCSS standard that identifies velocity, which does not include problems of angular velocity. Match on solving problems using vectors. Only CCSS standard that identifies using velocity. CCSS standard (including sub-standards) match on adding and subtracting vectors. Content within CC.9-12.N.VM.4 generally matches to OR.12.T.4.1, OR.12.T.4.2, &OR.12.T.2.6 Content within CC.9-12.N.VM.4 generally matches to OR.12.T.4.1, OR.12.T.4.2, &OR.12.T.2.6 Content within CC.9-12.N.VM.4 generally matches to OR.12.T.4.1, OR.12.T.4.2, &OR.12.T.2.6 CCSS standard (including sub-standards) match on multiplying vectors. Content within CC.9-12.N.VM.5 generally matches to OR.12.T.4.1 Content within CC.9-12.N.VM.5 generally matches to OR.12.T.4.1 CCSS standard does not specify linear programming. CCSS standard only identifies multiplying matrices by scalars. Both standards specify matrix operation skills (Advanced standard) No exact match, but content is typically taught in an advanced algebra or precalculus course (e.g. OR.12.T.4.1) The OR standard does not specify the use of the determinant. CCSS standard identifies multiplication of a vector by a matrix. (Advanced standard) New content found within the CCSS. No exact match, but content is similar to OR.9-12.1A.2, OR.9-12.1A.4, OR.6.3.2, & OR.6.3.6 No exact match, but content is similar to OR.9-12.1A.2, OR.9-12.1A.4, OR.6.3.2, & OR.6.3.6 No exact match, but content is similar to OR.9-12.1A.2, OR.9-12.1A.4, OR.6.3.2, & OR.6.3.6 New content found in the CCSS. Match on determining equivalent algebraic expressions. CCSS does not include evidence of manipulation of algebraic expressions with absolute value or roots. OR includes more which can be found in other CC standards. Match on factoring to find zeros (roots) of quadratic functions. OR is limited to leading coefficients of 1 (e.g. a=1) and integral (integer) roots; CCSS does not include any limitations on they type of quadratic function. Weak match on completing the square, but CCSS standard is more focused on maximum and minimum values than finding roots Content generally matches to OR.9-12.3A.5, OR.9- 12.1A.2, & OR.12.adv.A.15 Only CCSS standard that specifically identifies any type of series. CCSS does not specify using sigma notation. Match on deriving the formulas of finite geometric series. OR standard also includes infinite geometric series and connecting the concept of limits. Possible match to the mathematical practices (CC.MP.8) CCSS identifies operations on polynomials, but also asks students to draw comparisons to integer operations. Match on understanding the relationship of zeros, but CCSS also identifies remainder theorem and polynomial division Match on understanding the zeros of a polynomial, but CCSS standard also includes constructing graphs from factors Match on using zeros to construct a function. CCSS asks for a rough graph, and OR asks for an equation. New content found in the CCSS. Both standards identify binomial expansion and Pascal's triangle, but CCSS extends this understand to proving the theorem. Match on understanding the binomial theorem. OR standard also identifies the addition and multiplication principals. No CCSS standard identifies the Pigeonhole Principal. Weak match on applying polynomial long division, but the CC standard itself is more about operations on rational expressions than polynomial long division. This OR standard includes more theorems to know and apply. CCSS is more specific with the type of form that rational expressions can be converted into. CCSS identifies more specific skills to perform operations on rational expressions. Match on developing equations and inequalities. CCSS does not include properties of inequalities. CCSS identifies quadratic, rational and exponential functions. Match on solving equations and inequalities. OR identifies linear equations only. CCSS also includes quadratics, rational and exponentials. Oregon is using tables to graphs for comparison. CCSS identifies creating and solving equations and inequalities. Weak match on creating equations. CCSS also includes simple rational functions. Does not specify extending patterns but could be implied. OR is restricted to linear equations. CCSS is much more broad by including equations in two or more variables. Weak match to the ability of graphing equations. CCSS does not identify critical-path task mapping or networking modeling to solve problems. CCSS standard identifies representing system of inequalities, but not solving or graphing them. No exact match, but content is similar to OR.9-12.1A.4, OR.7.1.4, & OR.6.3.4 No exact match, but content is similar to OR.9-12.2A.7, & OR.6.3.6 Both standards address solving radical equations. CCSS also includes rational equations and specifically identifies extraneous solutions. CCSS identifies both rational and radical equations. Match on solving inequalities, but CCSS standard also include equations. OR standard includes graphing inequalities. CCSS includes using quadratic formula, completing the square, and recognizing complex solutions and specifies solving; not just factoring. OR standard is specific to quadratics with a leading coefficient of 1 (e.g. a =1). CCSS does not limit the types of CCSS specifies using completing the square and deriving the quadratic formula. CCSS is more specific in understanding transformations. OR is limited to leading coefficients of 1 (e.g. a=1) and integral (integer) roots; CCSS does not include any limitat Match on deriving the quadratic formula, but CCSS standard also includes completing the square and transforming quadratic equations. Match on factoring quadratics. OR standard is specific to quadratics with a leading coefficient of 1 (e.g. a =1). CCSS does not limit the types of quadratics used. CCSS specifically identifies completing the square and quadratic formula, and includes co CCSS includes complex solutions. OR is limited to leading coefficients of 1 (e.g. a=1) and integral (integer) roots. Match on solving quadratic equations using completing the square, but CCSS standard does not include graphing No exact match. Proof aspect of the standard may not be typically taught. Likely would be taught as part of solving systems of linear equations in OR high school standards (OR.9-12.2A.8 - substitution method). Other function types may not be taught. OR standard specifies two and three variable equations. CCSS is specific to linear equations. Both standards specify solving systems of non- linear equations algebraically and graphically OR standard specifies two and three variable equations. CCSS is specific to linear equations. CCSS specifies the ability to use an inverse matrix to solve linear equations. CC standard identifies solving equations graphically only. OR also includes symbolic methods. OR standard is specific to linear equations, and CCSS is more broad in identifying curves. OR also identifies inequalities. CCSS asks to understand the meaning of the function graph. OR standard also includes analyzing the graph of the function. Weak connection between what the graph represents and how it can represent a solution. CCSS does not identify critical-path task mapping or networking modeling to solve problems. Match on representing and solving absolute value equations. OR standard also includes inequalities. CC standard also includes solving linear, rational, exponential, and logarithmic functions. Match on solving quadratic inequalities, but CCSS standard also includes solving equations and more functions Weak match on using technology to approximate solutions to functions graphically. This CC standard is more focused on finding solutions of equating two functions than using graphing technology. CCSS references graphing, but the standard is more about finding solutions to polynomial expressions CCSS identifies solving equations and references exponential and logarithmic functions Match on graphing linear inequalities. CCSS identifies graphic methods only; OR standard also includes symbolic methods. Match on solving systems of linear equations graphically. OR standard also includes algebraic methods. Match on solving inequalities graphically. OR standard also includes solving inequalities algebraically. Both standards identify solving systems of linear inequalities graphically Match on using f(x) notation. CCSS uses more precise language in defining a function. OR includes the terms independent and dependent, CCSS identifies the domain and range of a function. Partial match on understanding the meaning of the domain and range of a function CCSS specifies understanding the concept of a function but does not necessarily include evaluating the function. OR specifies only quadratic and exponential functions, CCSS identifies functions in general. Match on understanding the concept of a function and using function notation. CCSS is more specific in its language describing a function. OR standard includes evaluating a function and determining one- to-one functions. OR standard only specifies determining the domain and range, but not the level of understanding outlined in CCSS Match on solving functions for given elements of the domain (e.g. solve for f(x) given x). OR also includes solving for a domain value given an element of the range (e.g. solve for x given f(x)). Good match to CCSS for evaluating functions, and implies analyzing relationships between variables. Oregon is analyzing relationship between domain/range. Both standards identify recursive sequences - including Fibonacci Match on identifying key features of a graph. CCSS addresses functions in general whereas OR addresses only linear functions.. Weak match in that CCSS standard identifies recognizing function intercepts. OR standard is limited to x-intercepts. Partial match to finding intercepts of a function. CCSS identifies understanding any key feature of a function graph and also includes using tables. Match on identifying appropriate domain of a function. OR standard also includes the range and restricted domains. No exact match. Generally address in terms of linear functions (slope), but not necessarily in context of non-linear functions. (e.g. OR.9-12.2A.2, OR.9-12.2A.3, OR.9-12.2A.4) Weak match on graphing functions. OR standard is limited to quadratic and exponential functions. Match on multiple representations (graphing). CCSS is more specific to functions. OR standard includes any given relation, which could also include non-functional relationships. CCSS identifies a number of functions to graph, but does not specifically identify graphing non-functions such as conics Match on graphing functions. OR standard is specific to graphing radical functions only. CCSS standard identifies only linear and quadratic functions. OR standard does not limit the type of function used. Match on graphing quadratics to identify zeros (intercepts), but CCSS does not specify the discriminant Match on graphing absolute value, radical, piece- wise, and step functions. OR standard also includes graphing polynomials, power, rational, logarithmic, and exponential functions. Match on graphing piece-wise functions. CCSS also includes graphing square root, cube root, step, and absolute value functions. Weak match on graphing absolute value functions, but CCSS does not ask students to solve these equations at this grade level Match on end behavior of polynomial functions. CCSS identifies skills needed than the OR standard, but the CC standard is specific to rational functions. Match on graphing rational expressions, which is one type of equivalent representation. Both standards identify solving rational functions graphically Match on end behavior of rational functions. Good match on graphing and analyzing exponential and logarithmic functions CCSS specifies graphing exponential and logarithmic functions in addition to trigonometric functions. CC standard is more focused on algebraic representations. OR standard is open to more types of representations. OR standard is limited of linear functions, and CCSS identifies functions in general. Match on equivalent expressions and converting between forms. CCSS is specific to symbolic expressions. CCSS specifies factoring and completing the square, which both can be used to find the zeros (roots) and the vertex. OR standard also includes graphical methods. OR is limited to leading coefficients of 1 (e.g. a=1) and integral (integer) roots; CCSS d Match on interpreting exponential growth functions only. Match on multiple representations. OR standard includes conversions between different representations. This is typically done with linear functions at the high school level (e.g. OR.9-12.2A.3, OR.9-12.2A.4, & OR.9-12.2A.5). Doing this with non-linear functions is typically not done until advanced algebra or precalculus. Match on being able to determine and explicit expression of a recursive process only. Match on performing arithmetic operations on functions. OR standard also includes the composition of functions. Match on performing arithmetic operations on functions. OR standard is specific to radical expressions. Match on composition of functions. OR standard also includes arithmetic operations on functions. No CCSS standard specifically identifies parametric equations. The CCSS standard on composition of function makes reference to the height of the balloon as a function of time, e.g. h(t). Both standards identify recursive formulas for arithmetic and geometric sequences. CCSS does not specify finite differences, but does ask students to write expressions for sequences. OR standard only asks students to describe, where CCSS asks students to write and translate between models. CCSS includes recognizing odd and even functions, but the standard is more focused on transformations of functions. Better match to OR.12.adv.A.1.5. Good match on analyzing the effect of transformations on functions General match on the ability to find an inverse function. OR standard includes more cognitive demands and when inverse functions exist. Match on writing an expression for the inverse function. OR standard also includes verifying the relationship. Match on verifying inverse functions by composition. OR standard also includes determining the inverse of the function. Good match on verifying inverse functions by composition Content within CC.9-12.F.BF.4 generally matches to OR.12.adv.A.1.6 & OR.12.adv.A.1.7 CCSS is specific to non-invertible functions by restricting the domain, which is not identified in the OR standard. Good match on understanding the inverse relationship between exponential and logarithmic functions. OR standard is implied if a student can do CCSS standard. Does not include quadratic in CCSS. Oregon includes domain and range and multiple representations Content within CC.9-12.F.LE.1 generally matches to OR.9-12.3A.3 Content within CC.9-12.F.LE.1 generally matches to OR.9-12.3A.3 Content within CC.9-12.F.LE.1 generally matches to OR.9-12.3A.3 Match on using exponential functions. CCSS also includes linear functions, and OR includes quadratic functions. CCSS goes from various representations to constructing the function, OR starts with the function and goes to a table or graph. CCSS identifies the ability to construct functions but expands the type of information that functions can be constructed from beyond using the function roots. CCSS more generally identifies the ability to construct linear and exponential functions, not just sequences. CCSS does not specify series. OR has domain and range, CCSS has polynomial functions. A student would have to do OR standard to complete the CCSS standard CCSS identifies the ability to construct logarithmic functions from exponential functions only. The OR standard is general enough to also include constructing exponential functions from logarithmic functions. OR standard is limited to linear functions. CCSS also includes exponential functions. Match on understanding the parameters of linear and exponential functions. OR also includes quadratic functions and more types of representations. No exact match in the OR standards. Content is typically taught in an advanced algebra or precalculus course. Match on using the unit circle to extend trig functions to all real numbers. OR standard also includes using the unit circle to calculate exact values of trigonometric ratios. CCSS is more specific by what is meant by the term "special triangles". OR standard does not specify how many special right triangles students should know, so potentially there could be more triangles than those identified in the CCSS. Match on using the unit circle to express exact values of trigonometric functions. OR standard also includes defining the six trigonometric ratios. (Advanced standard) Content is typically taught in an advanced algebra or precalculus course (e.g. OR.12.T.2.1) OR standard specifies translations; CCSS specifies modeling periodic phenomena. Different ways of expressing a similar concept. (Advanced standard) Content is typically taught in an advanced algebra or precalculus course. Match on the use of inverse trigonometric functions. OR standard also identifies evaluating trigonometric functions. CCSS also identifies applying modeling contexts and using technology. Both standards identify proving Pythagorean identities. General match between the standards on solving equations using trigonometric functions. No exact match. OR standards do not directly address these definitions, but they would likely be taught at some way in high school geometry. Match on representing transformations. CCSS also includes comparing transformations. OR is more specific about the types of transformations. CC standard does not specifically identify using dilations. Match on rotation and reflection symmetry of polygons. OR standard includes all two dimensional figures for transformations. No exact match, but content is similar to OR.9- 12.1G.7 (properties of circles), OR.9-12.3G.2 (transformations), OR.8.3.1 &OR.9-12.1G.1 (lines & transversals). Match on perfuming rotations, reflections, and translations. CC standard does not identify dilations. Oregon restricts the lines of reflection and angles of rotation, and CC standard does not. Match on congruency of two shapes. The OR standard is specific to triangles and quadrilaterals, and CCSS does not identify specific figures. CCSS includes transformation and Oregon includes similarity. Match on using congruence definitions. OR standard includes similar figures and determining the missing sides and angles of polygons. Match on congruency of triangles. CCSS includes transformations and Oregon includes similarity. Match on analyzing line and angle relationships. CCSS identifies proofs and the OR standards is focused on applying and analyzing these concepts. Proofs are not specifically identified in the OR content standards, but should be covered as part of "reasoning and proof" at this level. Proofs are not specifically identified in the OR content standards, but should be covered as part of "reasoning and proof" at this level. OR standards do not identify constructions. OR standards do not identify constructions. Match on using scale factors. Oregon addresses volume and area of similar figures. Match on using the similarity of triangles. Oregon includes classifying quadrilaterals. Match on using similarity definitions. OR standard includes congruence and determining the missing sides and angles of polygons. Match on determining the similarity of 2D figures. CCSS does not include comparing and computing areas and volumes No exact match, but content would likely be covered as part of "justifying similarity of triangles" found in OR.9-12.1G.2 CCSS includes proof for triangle theorems and Oregon includes identify, justify and apply for the concept. Match on using congruency and similarity of triangles. CCSS includes proving the concept and Oregon includes apply, identify and justify the concept. CCSS is specific to triangles, doesn't specifically say determine missing sides and angles but could be implied in "solve problems". CCSS also includes proving the theorems. OR standard specifies the ability to develop, define, and apply. CCSS only identifies the understanding of similarity. Match on defining trigonometric ratios. OR standard also includes constructing the unit circle and using the unit circle to calculate exact values of trigonometric ratios. Content would likely be taught in an advanced algebra or precalculus course. Match on using trigonometric ratios and Pythagorean Theorem to solve problems. OR specific to finding the lengths in right triangles. CCSS includes solving for missing angles. CCSS more specifically identifies the area formula using sine CCSS identifies the ability to prove the Laws, rather than "develop". Match on application of the Law of Sines and Cosines. CCSS also specifies using these laws to find unknown measurements. New content found in the CCSS. Match on using the relationships of angles and chords in a circle. CC standard does not identify tangents, arcs, or sectors. OR standards do not identify constructions. OR standards do not identify constructions. Match on using arcs and formulas for the area of a sector. CC standard does not include chords, tangents, and angles. CCSS includes derivation of the formula as well as defining radian measure. Match on solving equations relating to conic sections. CCSS standard includes more specific language to circles. This OR standard includes solving problems involving any conic section. Match on solving equations relating to conic sections. CCSS standard includes more specific language to circles. This OR standard includes determining the equation of any conic section. CCSS standard more specific to properties of parabolic behavior. This OR standard includes solving problems involving any conic section. CCSS standard more specific to parabola equations. This OR standard includes determining the equation of any conic section. CCSS standard more specific to ellipses and hyperbolas. This OR standard includes solving problems involving any conic section. CCSS standard more specific to equations of ellipses and hyperbolas. This OR standard includes determining the equation of any conic section. No exact match, content could be taught as part of "reasoning and proof" at the high school level (e.g. OR.9-12.3G.4) CCSS requires a proof of the slope criteria for parallel and perpendicular lines. OR includes more properties of lines that are covered in other CCSS. Weak match on applying the slope formula. CCSS standard focuses on proving parallel and perpendicular lines using slope, whereas the OR standard focuses more on using slope, distance & midpoint formulas to solve problems. Weak match on dividing finite segments. CCSS is written as a geometric concept. OR standard also identifies dividing continuous objects. Weak match on using division techniques. CCSS is written as a geometric concept. OR standard also identifies apportionment problems. Match on using distance formula and the coordinate plane. CCSS is missing slope and midpoint formulas. Match on explaining the reasonableness of the formulas. Both standards identify the surface area and volume of cylinders and cones. OR also includes pyramids, and CCSS specifies the circumference and area of circles. (Advanced standard) Not specifically identified in the OR standards. Match on finding volume of cylinders, pyramids, cones, and spheres. OR standard also includes volume and surface area of right solids. CCSS does not identify finding the surface area of spheres, pyramids, cones and cylinders. Surface area of pyramids c Match on using volume formulas for 3D shapes. Oregon also includes right solids. CCSS is specific about finding missing dimensions of the solid, but could be implied as part of "using formulas". No exact match, content could be taught as part of OR.9-12.2G.1 (nets/perspectives) or OR.9-12.3G.2 (transformations). No exact match, content could be taught as part of OR.9-12.2G.1 New content found in the CCSS. New content found in the CCSS. OR includes justifying the reasonableness of choice of display. Match on constructing histograms and frequency distributions. OR standard also includes scatter plots, tables, and more cognitive demands (e.g. analyze & interpret). Match on comparing the center and spread of a data set. CCSS addresses shape of the data and identifies comparing more than 2 data sets. Match on comparing measures of central tendencies. CCSS includes more measures of variability (e.g. IQR & standard deviation). Using graphical displays (OR) and the shape of data distribution (CCSS) are similar concepts. Match on using appropriate descriptive statistics (center & variation) to describe data distributions. OR standard also includes interpretation and summary of these values. Partial match on determining the mean and standard deviation of a data set. CCSS does not address exploring the meaning of independent and dependent events. Partial match on comparing sampling distributions. OR standard includes simulating sampling distributions, applying t-distributions and chi- squared distributions. Match on comparing the distribution of data sets using distribution shape, spread, and outliers. Partial match on using the standard deviation. CCSS does not address exploring the meaning of independent and dependent events. Partial match on analyzing normal distributions. CCSS also includes using technology to estimate the area under the normal curve, which could be inferred as part of using "tables of the normal distribution". CCSS also includes that there are data sets w Match on key concepts including frequency tables (marginal, joint, and conditional). Match on representing quantities using scatter plots (CCSS identifies construction of scatter plots in CC.8.SP.1). OR also includes histograms, tables, frequency distributions, and more cognitive demands (e.g. analyze and interpret). Overall the standard matches reasonably well to CCSS standards 6a, 6b, and 6c. OR standard also includes making predictions of future events. Match on creating a function of best fit. OR standard is specific to linear regressions only. Making predictions (OR) could be inferred as part of solving problems in contexts (CCSS). Good match on fitting linear and non-linear functions to scatterplots, but CCSS does not identity the predictive qualities of regression curves. Partial match on understanding how to read regression line data. OR standard also includes making predictions of future events. CCSS standard identifies the ability to informally assess the line of best fit. This OR standard includes non-linear regressions. Match on analyzing residual plots only. Partial match on understanding how to read regression line data. OR standard also includes making predictions of future events. CCSS specifically identifies linear regressions. This OR standard includes non-linear regressions. Match using linear regressions only. Partial match on understanding how to read regression line data. OR standard also includes making predictions of future events. Weak match on interpreting the slope of a regression line. CCSS does not identify chi- squared and least squared regression lines. Match on computing the correlation coefficient of linear regressions. CC standard does not identify using data displays. Match on calculating the correlation coefficient. OR standard also includes understanding how outliers and influential points affect the data analysis. New content found in the CCSS. Weak match on understanding inferential statistics (e.g. p-values & power). CCSS does not identify understanding different types of error (type I & II). Match on understanding simulations. OR standard also includes survey methods, experiments and data displays. Match on recognizing differences among survey methods, experiments, and observational studies. CCSS includes explaining how randomization relates to each type of sampling method. OR standard includes understanding data displays. Match on evaluating the appropriateness of various data collection methods. OR standard also includes understanding the appropriateness of inquires within various populations. Weak match on understanding the purposes of different types of surveys. The OR standard is focused more on the ability to carry out the survey itself. Weak match on designing various types of experiments. OR standard also planning and understanding elements of a well conducted experiment. Match on conducting and analyzing survey results, as well as identifying sources of error. OR standard also planning and understanding elements of a well conducted study. Match on developing a margin of error. OR standard includes confidence intervals and point estimates. CCSS includes using simulation models. Match on conducting a experiment and identify sources of error. OR standard also planning and understanding elements of a well conducted experiment. Partial match on significance testing. CCSS does not identify understanding different types of error (type I & II). OR includes an explanation of reasonableness. Must assume that a claim is a report for match to be valid. Match is based on the process of evaluating involves estimating reasonableness. Match on evaluating data-based reports. OR standard also includes more specifics how to evaluate this information. Match on evaluating the generalizability of reports. OR standard specifies understanding conclusions from observational studies, experiments, and surveys. Weak match on complementary events. CCSS does not clearly identify determining the probability for independent and dependent events. Only reference to set operations is found in a statistics context in the CCSS. Weak match on understanding independent events. CCSS uses products of probabilities to deterring the independence of events. OR standard identifies multiple representations, or methods, to determine independent events. CCSS does not clearly identify de CCSS match to understanding independent events. OR standard also identifies conditional probability and the probability of simple events. No CCSS standard identifies finding the probability of mutually exclusive events. Partial match on determining the independence of two events. CCSS does not address exploring the meaning of independent and dependent events. Weak match on compound events, but OR also identifies dependent and complementary events. CCSS is more specific in its language in finding conditional probability. CCSS does not clearly identify determining the probability for independent and dependent CCSS match to understanding conditional probability. OR standard also identifies probability of simple events and independent events. No CCSS standard identifies finding the probability of mutually exclusive events. Partial match on understanding conditional probability. CCSS does not specifically identify analyzing independence and discrete random variables. New content found in the CCSS. This is not typically taught at the high school level other than an AP Statistics course. Weak match on using conditional probability and independent events. CC standard is more focused on using these concepts in everyday language, and OR standard is more focused on solving probability problems using these concepts. Match on using conditional probability to solve problems. OR standard also identifies calculating the probability of simple and independent events. No CCSS standard identifies finding the probability of mutually exclusive events. Partial match on computing conditional probability. CCSS does not specifically identify analyzing independence and discrete random variables. CCSS match to applying the addition rule. OR standard also identifies applying the multiplication principal and binomial theorem. No CCSS standard identifies the Pigeonhole Principal. Partial match on applying the Addition Rule. CCSS does not specifically identify analyzing independence and discrete random variables. CCSS match to applying the multiplication rule. OR standard also identifies applying the addition principal and binomial theorem. No CCSS standard identifies the Pigeonhole Principal. Partial match on applying the Multiplication Rule. CCSS does not specifically identify analyzing independence and discrete random variables. Both standards identify calculating and using permutations and combinations. CCSS is more specific to compound events. This OR standard does not restrict the type of event used. CCSS refers to calculating permutations and combinations. OR standard also identifies producing the resulting sets. CCSS refers to compound events and solving problems as well. (Advanced standard) New content found within the CCSS. (Advanced standard) New content found within the CCSS. (Advanced standard) New content found within the CCSS. (Advanced standard) New content found within the CCSS. (Advanced standard) New content found within the CCSS. (Advanced standard) New content found within the CCSS. (Advanced standard) New content found within the CCSS. (Advanced standard) New content found within the CCSS. Weak match on analyzing decisions and strategies using probability. No CCSS standard specifically identifies game theory. Weak match on analyzing decisions and strategies using probability. No CCSS standard specifically identifies game theory. Weak match on analyzing decisions and strategies using probability. No CCSS standard specifically identifies game theory. Weak match on analyzing decisions and strategies using probability. No CCSS standard specifically identifies game theory.

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