HS Math - Common Core to ODE Crosswalk

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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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