Grades 9, 10, 11, 12

Other Wyoming Mathematics sets

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• Grade 8

Explain how the meaning of the definition of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.N.RN.A.1

Prove, use, and explain the properties of rational exponents (which are an extension of the properties of integer exponents) and extend to real-world context.N.RN.A.1.Ad

Explain and use the meaning of rational exponents in terms of properties of integer exponents and use proper notation for radicals in terms of rational exponents.N.RN.A.1.P

Use proper notation for radicals in terms of rational exponents, but is unable to explain the meaning.N.RN.A.1.Ba

May be able to use proper notation and use structure for integer exponents only.N.RN.A.1.BeB

Rewrite expressions involving radicals and rational exponents using the properties of exponents.N.RN.A.2

Compare contexts where radical form is preferable to rational exponents, and vice versa.N.RN.A.2.Ad

Rewrite expressions involving radicals and rational exponents, using the properties of exponents.N.RN.A.2.P

Identify equivalent forms of expressions involving rational exponents (but is not able to rewrite or find the product of multiple radical expressions).N.RN.A.2.Ba

May be able to convert radical notation to rational exponent notation.N.RN.A.2.BeB

Explain why the sum or product of rational 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.N.RN.B.3

Generalize the rules for sum and product properties of rational and irrational numbers.N.RN.B.3.Ad

Explain why the sum or product of rational 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.N.RN.B.3.P

The Basic student is able to:<ul><li>Explain why the sum or product of rational numbers is rational. OR</li><li>That the sum of a rational number and an irrational number is irrational. OR</li><li>That the product of a nonzero rational number and an irrational number is irrational.</li></ul>N.RN.B.3.Ba

May be able to explain why adding and multiplying two rational numbers results in a rational number.N.RN.B.3.BeB

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; and choose and interpret the scale and the origin in graphs and data displays.N.Q.C.1

Explain or defend their use of units as a way to understand problems and to guide the solution of multi-step problems; to explain and/or defend their choice of units consistently in formulas; and/or to explain and/or defend their choice of the scale and the origin in graphs and data displays.N.Q.C.1.Ad

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; and choose and interpret the scale and the origin in graphs and data displays.N.Q.C.1.P

Inconsistently uses units as a way to understand problems and/or to guide the solution of problems; chooses and/or interprets units inconsistently in formulas; and/or inconsistently chooses and/or interprets the scale and the origin in graphs and data displays.N.Q.C.1.Ba

May need guidance to use units as a way to understand problems and to guide the solution of problems; to choose and interpret units in formulas; and/or to choose and interpret the scale and the origin in graphs and data displays.N.Q.C.1.BeB

Define appropriate quantities for the purpose of descriptive modeling.N.Q.C.2

Explain or defend their choice of quantities for the purpose of descriptive modeling.N.Q.C.2.Ad

Define appropriate quantities for the purpose of descriptive modeling.N.Q.C.2.P

Inconsistently defines quantities for the purpose of descriptive modeling.N.Q.C.2.Ba

May need guidance to define quantities for the purpose of descriptive modeling.N.Q.C.2.BeB

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.N.Q.C.3

Explain or defend their choice of level of accuracy appropriate to limitations on measurement when reporting quantities.N.Q.C.3.Ad

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.N.Q.C.3.P

Inconsistently chooses a level of accuracy appropriate to limitations on measurement when reporting quantities.N.Q.C.3.Ba

Needs guidance to choose a level of accuracy appropriate to limitations on measurement when reporting quantities.N.Q.C.3.BeB

Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real.N.CN.D.1

Make generalizations about the powers of i to write complex numbers in the form a + b with a and b being real numbers.N.CN.D.1.Ad

Know there is a complex number i such that i² = -1, and every complex number has the form a + b with a and b real.N.CN.D.1.P

Incorrectly and/or inconsistently applies −1 for i and/or i².N.CN.D.1.Ba

Limited understanding of i² = −1 and needs guidance to correctly use i and/or i².N.CN.D.1.BeB

Use the relation i² = -1 and the Commutative, Associative, and Distributive Properties to add, subtract, and multiply complex numbers.N.CN.D.2

Perform arithmetic operations (add, subtract, multiply, divide) with complex numbers to include other powers of i and a + bi.N.CN.D.2.Ad

Uses the relation i² = -1 and the Commutative, Associative, and Distributive Properties to add, subtract, and multiply complex numbers.N.CN.D.2.P

Inconsistently uses the relation i² = -1 and the Commutative, Associative, and Distributive Properties to add, subtract, and multiply complex numbers.N.CN.D.2.Ba

Inconsistently uses the relation i² = -1 and the Commutative and Associative Properties to add and subtract complex numbers.N.CN.D.2.BeB

(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.N.CN.D.3

(+) Simplify complex number expressions that involve a quotient and at least one other operation.N.CN.D.3.Ad

(+)Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.N.CN.D.3.P

(+) Given the conjugate of a complex number, find the quotients of complex numbers.N.CN.D.3.Ba

(+) Does not meet the basic performance level.N.CN.D.3.BeB

(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.N.CN.E.4

(+) The Advanced student is able to:<ul><li>Given a complex number in rectangular form, convert it to polar form. AND</li><li>Given a complex number in polar form, convert it to rectangular form.</li></ul>N.CN.E.4.Ad

(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.N.CN.E.4.P

(+) Represent complex numbers on the complex plane in rectangular form.N.CN.E.4.Ba

(+) Does not meet the basic performance level.N.CN.E.4.BeB

(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.N.CN.E.5

(+) Compare and contrast the algebraic and geometric approaches to finding the nth root of all real numbers.N.CN.E.5.Ad

(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.N.CN.E.5.P

(+) Represent addition and subtraction of complex numbers geometrically on the complex plane; use properties of this representation for computation.N.CN.E.5.Ba

(+) Does not meet the basic performance level.N.CN.E.5.BeB

(+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.N.CN.E.6

(+) Compare and contrast how distance and midpoint between two numbers are represented on the Cartesian plane versus the complex plane.N.CN.E.6.Ad

(+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.N.CN.E.6.P

(+) Calculate the distance between numbers in the complex plane as the modulus of the difference.N.CN.E.6.Ba

(+) Does not meet the basic performance level.N.CN.E.6.BeB

Solve quadratic equations with real coefficients that have complex solutions.N.CN.F.7

The Advanced student is able to:<ul><li>Write a quadratic equation with real coefficients in standard form, when given a complex solution (recognizing that complex solutions to quadratic equations come in conjugate pairs). OR</li><li>Determine the relationship between the solutions, the discriminant, and the graph of a quadratic equation with real coefficients.</li></ul>N.CN.F.7.Ad

Solve quadratic equations with real coefficients that have complex solutions.N.CN.F.7.P

Solve quadratic equations with real coefficients that have pure imaginary solutions.N.CN.F.7.Ba

May be able to determine which graphs have real solutions and which graphs have complex solutions when given a series of graphical representations of quadratic equations with real coefficients.N.CN.F.7.BeB

(+) Extend polynomial identities to the complex numbers.N.CN.F.8

(+) The Advanced student is able to:<ul><li>Explore patterns in polynomial identities that are expressed with complex numbers. OR</li><li>Compare and contrast how polynomial identities are expressed in the real and the complex number system.</li></ul>N.CN.F.8.Ad

(+) Extend polynomial identities to the complex numbers.N.CN.F.8.P

(+) Match equivalent forms of polynomial identities expressed with complex numbers.N.CN.F.8.Ba

(+) Does not meet the basic performance level.N.CN.F.8.BeB

(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.N.CN.F.9

(+) Explore the solutions to quadratic polynomials with complex coefficients to identify patterns supporting the Fundamental Theorem of Algebra.N.CN.F.9.Ad

(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.N.CN.F.9.P

(+) Solve a given quadratic polynomial with real coefficients and discuss how the Fundamental Theorem of Algebra is validated.N.CN.F.9.Ba

(+) Does not meet the basic performance level.N.CN.F.9.BeB

(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).N.VM.G.1

(+) Create real-world examples in different units that are represented as vectors. [This is identified as having a cross-curricular connection to physics.]N.VM.G.1.Ad

(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g. v, |v|, ||v||, v).N.VM.G.1.P

(+) Identify quantities that could be represented with a vector when given a real-world example (e.g., I drove 10 mph versus I drove west at 10 mph).N.VM.G.1.Ba

(+) Does not meet the basic performance level.N.VM.G.1.BeB

(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.N.VM.G.2

(+) Model a real-world situation where subtracting the initial and terminal points of a vector would be applied.N.VM.G.2.Ad

(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.N.VM.G.2.P

(+) Identify the initial and terminal points when a vector is represented graphically.N.VM.G.2.Ba

(+) Does not meet the basic performance level.N.VM.G.2.BeB

(+) Solve problems involving velocity and other quantities that can be represented by vectors.N.VM.G.3

(+) Create and solve real-world problems involving velocity and other quantities that can be represented by vectors.N.VM.G.3.Ad

(+) Solve problems involving velocity and other quantities that can be represented by vectors.N.VM.G.3.P

(+) Solve problems involving velocity that can be represented by vectors.N.VM.G.3.Ba

(+) Does not meet the basic performance level.N.VM.G.3.BeB

(+) Add and subtract vectors.N.VM.H.4

(+) Create a real-world problem that requires addition or subtraction of two or more vectors, find the resultant vector, and interpret the magnitude and direction of the resultant vector.N.VM.H.4.Ad

(+) Add and subtract vectors.N.VM.H.4.P

(+) Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.N.VM.H.4.Ba

(+) Does not meet the basic performance level.N.VM.H.4.BeB

(+) Multiply a vector by a scalar.N.VM.H.5

(+) Create a real-world problem that requires scalar multiplication, find the resultant vector, and interpret the magnitude and direction of the resultant vector.N.VM.H.5.Ad

(+) Multiply a vector by a scalar.N.VM.H.5.P

(+) Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise.N.VM.H.5.Ba

(+) Does not meet the basic performance level.N.VM.H.5.BeB

(+) Use matrices to represent and manipulate data.N.VM.I.6

(+) Using data from a real-world situation, create a matrix, analyze the situation, and make decisions.N.VM.I.6.Ad

(+) Use matrices to represent and manipulate data.N.VM.I.6.P

(+) State what the data represents for elements in a given matrix.N.VM.I.6.Ba

(+) Does not meet the basic performance level.N.VM.I.6.BeB

(+) Multiply matrices by scalars to produce new matrices.N.VM.I.7

(+) In a real-world situation involving scalar multiplication, place data in a matrix, identify and interpret the scalar, and interpret the results.N.VM.I.7.Ad

(+) Multiply matrices by scalars to produce new matrices.N.VM.I.7.P

(+) Multiply matrices by integer scalars to produce new matrices.N.VM.I.7.Ba

(+) Does not meet the basic performance level.N.VM.I.7.BeB

(+) Add, subtract, and multiply matrices of appropriate dimensions.N.VM.I.8

(+) Apply addition, subtraction, and/or multiplication of matrices to real-world situations.N.VM.I.8.Ad

(+) Add, subtract, and multiply matrices of appropriate dimensions.N.VM.I.8.P

(+) Add and subtract matrices of dimensions limited to m and n less than or equal to 3.N.VM.I.8.Ba

(+) Does not meet the basic performance level.N.VM.I.8.BeB

(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the Associative and Distributive Properties.N.VM.I.9

(+) Compare and contrast the Commutative, Associative, and Distributive Properties for the addition, subtraction, and multiplication of non-square matrices versus the addition, subtraction, and multiplication of real-numbers.N.VM.I.9.Ad

(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the Associative and Distributive Properties.N.VM.I.9.P

(+) Calculate AB, BA, (AB)C, A(BC), A(B + C), AB + AC and determine which expressions are equivalent when given 2 × 2 matrices A, B, and C.N.VM.I.9.Ba

(+) Does not meet the basic performance level.N.VM.I.9.BeB

(+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.N.VM.I.10

(+) In addition to Proficient, the Advanced student is able to calculate the determinant,|A|, of a square matrix. Find the inverse, A^-1, using the determinant, |A|. Show that A(A^-1 is equal to the identity matrix (I).N.VM.I.10.Ad

(+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.N.VM.I.10.P

(+)Calculate AI, IA, A + 0, 0 + A, and determine which expressions are equivalent to A when given 2×2 matrices A, the zero matrix (0), and the identity matrix (I).N.VM.I.10.Ba

(+) Does not meet the basic performance level.N.VM.I.10.BeB

(+) Multiply a 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.N.VM.I.11

(+) Create a polygon on a coordinate grid, develop the appropriate matrix to represent the polygon, use vectors to translate the shape, and graph the translated polygon on the same coordinate grid.N.VM.I.11.Ad

(+) Multiply a 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.N.VM.I.11.P

(+) Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector.N.VM.I.11.Ba

(+) Does not meet the basic performance level.N.VM.I.11.BeB

(+) Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.N.VM.I.12

(+) Create a polygon on a coordinate grid, develop the appropriate matrix to represent the polygon, use vectors to transform the shape, graph the transformed polygon on the same coordinate grid, find the area for each polygon, and compare the areas.N.VM.I.12.Ad

(+) Work with 2×2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.N.VM.I.12.P

(+) Identify the transformation that is created by a given 2×2 transformation matrix.N.VM.I.12.Ba

(+) Does not meet the basic performance level.N.VM.I.12.BeB

Interpret expressions that represent a quantity in terms of its context.A.SSE.A.1

The Advanced student is able to:<ul><li>Interpret the effect of changes made to a term, a factor, or a coefficient in an expression. OR</li><li>Compose complicated expressions from simpler ones and decompose complicated expressions into simpler ones.</li></ul>A.SSE.A.1.Ad

Interpret expressions that represent a quantity in terms of its context.A.SSE.A.1.P

Interpret expressions that represent a quantity in terms of its context by interpreting parts of an expression, such as terms, factors, and coefficients.A.SSE.A.1.Ba

Interpret expressions that represent a quantity in terms of its context by interpreting parts of an expression, such as terms, factors, or coefficients.A.SSE.A.1.BeB

Use the structure of an expression to identify ways to rewrite it.A.SSE.A.2

Explain why various forms of equivalent expressions are more advantageous in a given situation.A.SSE.A.2.Ad

Use the structure of an expression to identify ways to rewrite it.A.SSE.A.2.P

Rewrite an expression into another equivalent form.A.SSE.A.2.Ba

May be able to determine if two given expressions are equivalent.A.SSE.A.2.BeB

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.A.SSE.B.3

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.A.SSE.B.3.Ad

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.A.SSE.B.3.P

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.<ul><li>Factor a quadratic expression to reveal the zeros of the function it defines. AND</li><li>Use the properties of exponents to transform expressions for exponential functions.</li></ul>A.SSE.B.3.Ba

May be able to choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.<ul><li>Factor a quadratic expression to reveal the zeros of the function it defines. OR</li><li>Use the properties of exponents to transform expressions for exponential functions.</li></ul>A.SSE.B.3.BeB

Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.A.SSE.B.4

The Advanced student is able to:<ul><li>Use the formula for the sum of a finite geometric series (when the common ratio is not 1) to solve real-world problems. OR</li><li>Write the series in proper summation notation.</li></ul>A.SSE.B.4.Ad

Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.A.SSE.B.4.P

Use the given formula for the sum of a finite geometric series (when the common ratio is not 1) to solve problems.A.SSE.B.4.Ba

May be able to:<ul><li>Write a geometric sequence as a finite geometric series and calculate its sum. AND</li><li>Identify the common ratio and initial term of a finite geometric series (when the common ratio is not 1).</li></ul>A.SSE.B.4.BeB

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.A.APR.C.1

The Advanced student is able to:<ul><li>Rewrite a polynomial expression involving multiplication, and addition or subtraction, into an equivalent polynomial expression in standard form. OR</li><li>Generalize a pattern when adding, subtracting, and multiplying polynomials of a varying number of terms.</li></ul>A.APR.C.1.Ad

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.A.APR.C.1.P

Add, subtract, and multiply polynomials.A.APR.C.1.Ba

May be able to add, subtract, and multiply binomials.A.APR.C.1.BeB

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by (a - x) is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).A.APR.D.2

Find a missing coefficient m, where m is a real number, of a polynomial p(x), when given (x - a) is a factor of p(x) or when given p(a).A.APR.D.2.Ad

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by (x - a) is p(a) = 0 if and only if (x - a) is a factor of p(x).A.APR.D.2.P

Evaluate p(a) and compare it to the remainder of p(x)/(x - a). Explain the significance of the remainder.A.APR.D.2.Ba

May be able to evaluate p(a) and compare it to the remainder of p(x)/(x - a). Explain the significance of the remainder.A.APR.D.2.BeB

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.A.APR.D.3

Given a graph of a polynomial function with integer x-intercepts, write the general form of the polynomial in standard form, understanding that the polynomial could have a stretch or compression.A.APR.D.3.Ad

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.A.APR.D.3.P

Identify zeros of polynomials when suitable factorizations are available, and locate the zeros on a coordinate plane.A.APR.D.3.Ba

May be able to match the polynomial to its factored form and its graph.A.APR.D.3.BeB

Prove polynomial identities and use them to describe numerical relationships.A.APR.E.4

Use the structure of a polynomial identity to give real-world contextual meaning to the identity (e.g., completing the square of a quadratic function to highlight the maximum or minimum, factoring a polynomial to highlight the zeros, or factoring a trinomial to highlight base times width).A.APR.E.4.Ad

Prove polynomial identities and use them to describe numerical relationships.A.APR.E.4.P

Evaluate each polynomial expression for given values, compare the results, and make a general statement concerning the polynomials as identities.A.APR.E.4.Ba

May be able to given two polynomial identities, evaluate the polynomials at a given value to demonstrate that the polynomials are identities.A.APR.E.4.BeB

(+) Know and apply the Binomial Theorem for the expansion of (x + y)ⁿ in 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.A.APR.E.5

(+) Find specified terms in the expansion of (x + y)ⁿ by applying properties of the binomial theorem.A.APR.E.5.Ad

(+) Know and apply the Binomial Theorem for the expansion of (x + y)ⁿ in 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.A.APR.E.5.P

(+) Expand (x + y)ⁿ in powers of x and y for a positive integer n, where x and y are any numbers, using Pascal's Triangle.A.APR.E.5.Ba

(+) Does not meet the basic performance level.A.APR.E.5.BeB

Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x) using inspection, long division, or, for the more complicated examples, a computer algebra system. (i.e. rewriting a rational expression as the quotient plus the remainder over divisor).A.APR.F.6

Given a(x)/b(x) = q(x) + r(x)/b(x):<ul><li>Identify the missing coefficient from a polynomial a(x) when given b(x), q(x), and r(x). OR</li><li>Generalize the patterns obtained by dividing various degrees of polynomials.</li></ul>A.APR.F.6.Ad

Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x) using inspection, long division, or, for the more complicated examples, a computer algebra system. (i.e. rewriting a rational expression as the quotient plus the remainder over divisor).A.APR.F.6.P

Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x) using inspection or long division where a(x) is a quadratic and b(x) is linear.A.APR.F.6.Ba

May be able to:<ul><li>Match a rational expression in the form a(x)/b(x) to its equivalent form q(x) + r(x)/b(x). OR</li><li>Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x) using inspection or long division where a(x) is a quadratic and b(x) is linear with assistance.</li></ul>A.APR.F.6.BeB

(+) Understand 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 expressions.A.APR.F.7

(+) Justify that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.A.APR.F.7.Ad

(+) Understand 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 expressions.A.APR.F.7.P

(+) Add, subtract, multiply, and divide rational expressions.A.APR.F.7.Ba

(+) Does not meet the basic performance level.A.APR.F.7.BeB

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.A.CED.G.1

Create equations and inequalities in one variable and use them to solve problems. Include compound inequalities arising from problems. Use interval notation to represent inequalities.A.CED.G.1.Ad

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.A.CED.G.1.P

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and simple exponential functions.A.CED.G.1.Ba

May be able to create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions.A.CED.G.1.BeB

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.A.CED.G.2

The Advanced student is able to:<ul><li>Interpret the relationships between the graph and its corresponding equation in real-world contexts. OR</li><li>Graph equations of the form x + y + z = c or ordered triples on the xyz-plane. OR</li><li>Graph equations from a real-world context of the form y = ab^x where a is a real number and b is greater than 0.</li></ul>A.CED.G.2.Ad

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.A.CED.G.2.P

The Basic student is able to:<ul><li>Create equations in two or more variables to represent relationships between quantities. OR</li><li>Graph equations on coordinate axes with labels and scales.</li></ul>A.CED.G.2.Ba

May be able to match a graph to its equation in two or more variables.A.CED.G.2.BeB

Represent 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.A.CED.G.3

Examine and explain constraints and solutions to systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.A.CED.G.3.Ad

Represent 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.A.CED.G.3.P

The Basic student is able to:<ul><li>Interpret solutions as viable or non-viable options in a modeling context. AND</li><li>Represent constraints by equations or inequalities, or by systems of equations and/or inequalities.</li></ul>A.CED.G.3.Ba

May be able to:<ul><li>Interpret solutions as viable or non-viable options in a modeling context. AND</li><li>Represent constraints by equations or inequalities.</li></ul>A.CED.G.3.BeB

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.A.CED.G.4

Choose and explain reasoning for highlighting the quantity of interest, rearrange the formula, use the rearranged formula to evaluate, and interpret the answer in a real-world context.A.CED.G.4.Ad

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.A.CED.G.4.P

Rearrange formulas to highlight a quantity of interest in two steps, using the same reasoning as in solving equations.A.CED.G.4.Ba

May be able to rearrange formulas to highlight a quantity of interest in one step, using the same reasoning as in solving equations.A.CED.G.4.BeB

Explain each step in solving a simple equation as 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 solution method.A.REI.H.1

Critique the solution and justification of self and others in the steps in solving linear equations.A.REI.H.1.Ad

Explain each step in solving a simple equation as 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 solution method.A.REI.H.1.P

Informally describe the steps in solving multi-step linear equations.A.REI.H.1.Ba

May be able to match steps to justifications when provided with the steps for solving multi-step linear equations.A.REI.H.1.BeB

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.A.REI.H.2

Critique the solutions of self and others for simple rational and radical equations in one variable.A.REI.H.2.Ad

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.A.REI.H.2.P

Solve simple rational and radical equations in one variable with no extraneous solutions, and when given equations with extraneous solution(s) demonstrate why the given solution(s) is/are not viable.A.REI.H.2.Ba

May be able to solve simple rational and radical equations in one variable with no extraneous solutions.A.REI.H.2.BeB

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.A.REI.I.3

The Advanced student is able to:<ul><li>Critique the solutions of self and others for linear inequalities in one variable, including equations with coefficients represented by letters. OR</li><li>Demonstrate the solution of a linear equation or inequality in multiple ways (e.g., graphically, set notation, interval notation). OR</li><li>Create and solve a real-world linear equation or inequality in one variable, determine its viable domain and solution set.</li></ul>A.REI.I.3.Ad

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.A.REI.I.3.P

Solve linear equations and inequalities in one variable, limited to numerical coefficients.A.REI.I.3.Ba

May be able to solve linear equations and inequalities in one variable, limited to numerical coefficients, where the variable is on only one side of the equal or inequality sign.A.REI.I.3.BeB

Solve quadratic equations in one variable.A.REI.I.4

The Advanced student is able to:<ul><li>Critique different methods used by self and others for solving quadratic equations in one variable. OR</li><li>Create and solve a real-world quadratic equation in one variable, determine its viable domain and solution. OR</li><li>Explain the purpose for the method chosen to solve the quadratic equation in a real-world situation.</li></ul>A.REI.I.4.Ad

Solve quadratic equations in one variable.A.REI.I.4.P

Solve quadratic equations in one variable by inspection (e.g., for x² = 49), taking square roots, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.A.REI.I.4.Ba

May be able to solve quadratic equations in one variable, using the quadratic formula. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.A.REI.I.4.BeB

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other, produces a system with the same solutions.A.REI.J.5

In addition to Proficient, the Advanced student is able to:<ul><li>Write a different system of two equations in two variables with the same solution as a given system of two equations in two variables. OR</li><li>Create and solve, if possible, a system of two equations in two variables for a real-world context (include systems with one solution, infinitely many solutions, or no solution).</li></ul>A.REI.J.5.Ad

Prove that given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other, produces a system with the same solutions.A.REI.J.5.P

Solve a system of two equations in two variables with different coefficients resulting in one solution using the elimination method.A.REI.J.5.Ba

Solve a system of two equations in two variables with equal or opposite coefficients resulting in one solution using the elimination method.A.REI.J.5.BeB

Estimate solutions graphically and determine algebraic solutions to linear systems, focusing on pairs of linear equations in two variables.A.REI.J.6

Approximate solutions to a system of linear equations for a real-world situation using a table and graph, then verify the solution algebraically and discuss the viability of the solution in the context of the problem.A.REI.J.6.Ad

Estimate solutions graphically and determine algebraic solutions to linear systems, focusing on pairs of linear equations in two variables.A.REI.J.6.P

Estimate solutions to linear systems graphically or determine algebraic solutions to linear systems, focusing on pairs of linear equations in two variables.A.REI.J.6.Ba

May be able to test a solution to the system in both original equations (graphically or algebraically).A.REI.J.6.BeB

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.A.REI.J.7

Explore algebraically, graphically, and tabularly the number and type of the solutions of one linear and one quadratic or two quadratics and describe findings.A.REI.J.7.Ad

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.A.REI.J.7.P

Solve a simple system consisting of a linear equation written in slope-intercept form and a quadratic equation written in standard form in two variables algebraically.A.REI.J.7.Ba

May be able to solve a simple system consisting of a linear equation written in slope-intercept form and a quadratic equation written in standard form in two variables graphically.A.REI.J.7.BeB

(+) Represent a system of linear equations as a single matrix equation in a vector variable.A.REI.J.8

(+) Represent a real-world situation using a system of linear equations as a single matrix equation in a vector variable.A.REI.J.8.Ad

(+) Represent a system of linear equations as a single matrix equation in a vector variable.A.REI.J.8.P

(+) Identify a system of linear equations given a matrix equation in a vector variable.A.REI.J.8.Ba

(+) Does not meet the basic performance level.A.REI.J.8.BeB

(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).A.REI.J.9

(+) Find the inverse of a matrix if it exists and use it to solve a real-world problem involving systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).A.REI.J.9.Ad

(+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).A.REI.J.9.P

(+) Solve systems of linear equations written as a single matrix equation in a vector variable when given the inverse of a matrix (using technology for matrices of dimension 3 × 3 or greater).A.REI.J.9.Ba

(+) Does not meet the basic performance level.A.REI.J.9.BeB

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.A.REI.K.10

Create and graph two equations of different degrees that pass through the same two specific points. Describe the relationship between the solution sets for each equation and the solution for the system.A.REI.K.10.Ad

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane (i.e., connect algebraic and graphical representations of an equation in two variables).A.REI.K.10.P

Create and verify a set of ordered pairs that lie on the graph when given an equation.A.REI.K.10.Ba

May be able to determine which ordered pairs do or do not lie on the graph of the equation when given an equation and a set of ordered pairs.A.REI.K.10.BeB

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.A.REI.K.11

Given a table of ordered pairs and graph for both a linear y = f(x) and quadratic y = g(x) where the intersection is a non-integer coordinate pair, describe a method to find the equations and solutions matching the depicted graphs and tables. Find the solutions using the generated equations. Describe the accuracy of the solution algebraically and graphically. Describe how to improve the method.A.REI.K.11.Ad

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.A.REI.K.11.P

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions or make tables of values. Include cases where f(x) and/or g(x) are linear, quadratic, absolute value, and exponential.A.REI.K.11.Ba

May be able to explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions or make tables of values. Include cases where f(x) and/or g(x) are linear, quadratic, and exponential.A.REI.K.11.BeB

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.A.REI.K.12

The Advanced student is able to:<ul><li>Write a system of linear inequalities that includes a set of specified points in a region and explain the choice of strict inequality or non-strict inequality notation. OR</li><li>Create a system of linear inequalities that will optimize the solution when given a real-life scenario. OR</li><li>Write the inequalities that describe the boundaries of that scenario and discuss the optimal solution when given a graphical representation of a real-life scenario.</li></ul>A.REI.K.12.Ad

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.A.REI.K.12.P

Graph the solution to a linear inequality in two variables as a half-plane (excluding the boundary in the case of strict inequality).A.REI.K.12.Ba

The Below Basic student may be able to match the solution to a linear inequality in two variables to its graph half-plane (excluding the boundary in the case of strict inequality).A.REI.K.12.BeB

Understand that a function from one set (called the domain) to another set (called the 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 the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).F.IF.A.1

Use multiple representations to generalize ways to define functions and non-functions.F.IF.A.1.Ad

Demonstrate that a function's domain is assigned to exactly one element of the range in equations, tables, graphs, and context.F.IF.A.1.P

Demonstrate that a function's domain is assigned to exactly one element of the range in equations, tables, and graphs.F.IF.A.1.Ba

May be able to demonstrate that a function's domain is assigned to exactly one element of the range in tables and graphs.F.IF.A.1.BeB

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.F.IF.A.2

Create context from a given domain and range and use function notation to write an equation, graph the function, and draw a picture that models the context.F.IF.A.2.Ad

Use function notation, evaluate functions for inputs in their domain, and interpret statements that use function notation in terms of a context.F.IF.A.2.P

Use function notation and evaluate functions for inputs in their domain.F.IF.A.2.Ba

May be able to evaluate equations for specific values and match the equation to function notation.F.IF.A.2.BeB

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.F.IF.A.3

Write the explicit and recursive forms of a sequence describing linear and exponential situations. Express the sequence graphically and in a table.F.IF.A.3.Ad

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.F.IF.A.3.P

Write an informal recursive description of a sequence.F.IF.A.3.Ba

May be able to write the first n terms when given an informal recursive description of a sequence.F.IF.A.3.BeB

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.F.IF.B.4

Graph and label the key features of the function and write the function in function notation when given key features from a linear, exponential, or quadratic context.F.IF.B.4.Ad

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.F.IF.B.4.P

The Basic student is able to, for linear, quadratic, and exponential functions that model a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, maximums and minimums; symmetries; end behavior.F.IF.B.4.Ba

The Below Basic student may be able to, for linear, quadratic, and exponential functions that model a relationship between two quantities, interpret key features of graphs in terms of the quantities, and sketch graphs showing key features given the function. Key features include: intercepts; intervals where the function is increasing, decreasing, maximums and minimums; symmetries; end behavior.F.IF.B.4.BeB

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.F.IF.B.5

In addition to Proficient, the Advanced student is able to:<ul><li>Write and graph a function for a given context where the domain meets given parameters. Express the domain of the function using interval and/or set notation as appropriate. OR</li><li>Given the graph of a function, write its domain and range using interval and/or set notation as appropriate.</li></ul>F.IF.B.5.Ad

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.F.IF.B.5.P

Match the domain of a function to its graph and explain why the selected domain is applicable to the situation.F.IF.B.5.Ba

May be able to match the domain of a function to its graph.F.IF.B.5.BeB

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.F.IF.B.6

The Advanced student is able to:<ul><li>Analyze the difference between the rates of change of different types of functions. OR</li><li>Compare average rates of change over different intervals of the same function. OR</li><li>Generalize how the average rate of change differs between different function types.</li></ul>F.IF.B.6.Ad

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.F.IF.B.6.P

Calculate and interpret the average rate of change of a linear, exponential, or quadratic function over a specified interval presented as a graph, an equation, or a table.F.IF.B.6.Ba

May be able to calculate and interpret the average rate of change of a linear, exponential, or quadratic function over a specified interval presented as a graph.F.IF.B.6.BeB

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.F.IF.C.7

Create different representations of linear, quadratic, and exponential functions when given one of the following representations: graphical, tabular, or algebraic. Compare and contrast all three function types identifying key features while referencing the representations.F.IF.C.7.Ad

Graph linear, quadratic, and exponential functions expressed symbolically and show appropriate key features of the graph showing intercepts, maxima, and minima, and end behavior.F.IF.C.7.P

Identify appropriate key features of linear, quadratic, and exponential functions from a graph showing intercepts (linear, quadratic, and exponential), maximum or minimum (quadratic), and end behavior (linear, quadratic, and end behavior).F.IF.C.7.Ba

Match descriptions of key features of linear, quadratic, and exponential functions to the appropriate parts of the graph including intercepts (linear, quadratic, and exponential), maximum or minimum (quadratic), and end behavior (linear, quadratic, and end behavior).F.IF.C.7.BeB

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.F.IF.C.8

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.F.IF.C.8.Ad

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.F.IF.C.8.P

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.F.IF.C.8.Ba

May be able to write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.F.IF.C.8.BeB

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).F.IF.C.9

Create different representations of two functions (algebraically, graphically, numerically in tables, or by verbal description) from a given representation. Compare and contrast properties of those functions, specifically highlighting what each representation reveals.F.IF.C.9.Ad

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).F.IF.C.9.P

Compare properties of two functions when given only two different representations at a time (algebraically, graphically, numerically in tables, or by verbal descriptions).F.IF.C.9.Ba

May be able to match properties of two functions when given only two different representations at a time (algebraically, graphically, numerically in tables, or by verbal descriptions).F.IF.C.9.BeB

Write a function that describes a relationship between two quantities.F.BF.D.1

Write a function that describes a relationship between two quantities.F.BF.D.1.Ad

Write a function that describes a relationship between two quantities.F.BF.D.1.P

Write a function that describes a relationship between two quantities.F.BF.D.1.Ba

May be able to write a function that describes a relationship between two quantities.F.BF.D.1.BeB

(+) Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.F.BF.D.2

(+) The Advanced student is able to:<ul><li>Compare the graphical representation, tabular representation, explicit and recursive formulas, and contextual representation for arithmetic and geometric sequences. Draw parallels to linear and exponential functions, respectively. AND/OR</li><li>Describe a real-world situation that can be modeled linearly or exponentially and develop the explicit or recursive formulas to model the situation.</li></ul>F.BF.D.2.Ad

(+) Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.F.BF.D.2.P

(+) Write arithmetic and geometric sequences both recursively and with an explicit formula given a modeling situation.F.BF.D.2.Ba

(+) May be able to write an explicit or recursive formula for the model of an arithmetic and geometric sequence given the other formula.F.BF.D.2.BeB

Identify the effect on the graph of replacing f(x) by f(x) + k, kf(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 with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.F.BF.E.3

The Advanced student is able to:<ul><li>Write the equation for a transformed parent function given the graph or verbal description of the transformations. OR</li><li>Write a description of the transformations using function notation given a verbal description of the transformations of f(x) or the original f(x) graph and its transformed graph. OR</li><li>Generalize effects of a transformation on domains and ranges, including effects on ordered pairs, when exploring all of the different types of transformations in multiple representations of f(x).</li></ul>F.BF.E.3.Ad

Identify the effect on the graph of replacing f(x) by f(x) + k, kf(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 with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.F.BF.E.3.P

Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.F.BF.E.3.Ba

May be able to match the equation to the graph showing the effect on the graph of replacing f(x) by f(x) + k, kf(x), and f(x + k) for specific values of k (both positive and negative); write a description of the transformation. Experiment with cases and illustrate an explanation of the effects on the graph using technology.F.BF.E.3.BeB

Find inverse functions.F.BF.E.4

Find inverse functions.F.BF.E.4.Ad

Find inverse functions.F.BF.E.4.P

Understand inverse functions.F.BF.E.4.Ba

May be able to understand inverse functions.F.BF.E.4.BeB

(+) Build new functions from existing functions. Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.F.BF.E.5

(+) Solve real-world problems involving logarithms and exponents.F.BF.E.5.Ad

(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.F.BF.E.5.P

(+) The Basic student is able to:<ul><li>Given an expression written in logarithmic form, write the equivalent expression in exponential form. AND</li><li>Given an expression in exponential form, write the equivalent expression in logarithmic form.</li></ul>F.BF.E.5.Ba

(+) Does not meet the basic performance level.F.BF.E.5.BeB

Distinguish between situations that can be modeled with linear functions and with exponential functions.F.LE.F.1

In addition to Proficient, the Advanced student is able to distinguish between situations that can be modeled with linear functions and with exponential functions.F.LE.F.1.Ad

Distinguish between situations that can be modeled with linear functions and with exponential functions.F.LE.F.1.P

Distinguish between situations that can be modeled with linear functions and with exponential functions.F.LE.F.1.Ba

May be able to distinguish between situations that can be modeled with linear functions and with exponential functions.F.LE.F.1.BeB

Construct linear and exponential functions using a graph, a description of a relationship, or two input-output pairs (include reading these from a table).F.LE.F.2

The Advanced student is able to:<ul><li>Explain how exponential and linear function values differ as x approaches positive or negative infinity. AND</li><li>Relate algebraic representations of linear and exponential functions to the explicit and recursive forms of arithmetic and geometric sequences, respectively. AND/OR</li><li>Create a real-world scenario and develop linear or exponential tables or graphs representing the scenario.</li></ul>F.LE.F.2.Ad

Construct linear and exponential functions using a graph, a description of a relationship, or two input-output pairs (include reading these from a table).F.LE.F.2.P

Construct linear and exponential functions using two of the following representations: a graph, a description of a relationship, or two input-output pairs (include reading these from a table).F.LE.F.2.Ba

May be able to match linear and exponential functions to their graph, description of a relationship, and two input-output pairs (include reading these from a table).F.LE.F.2.BeB

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.F.LE.F.3

Use an algebraic argument or informal proof to show that an increasing exponential function eventually exceeds an increasing linear function.F.LE.F.3.Ad

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.F.LE.F.3.P

Identify which function eventually exceeds the others when given the graphs and tables of increasing linear, quadratic, and exponential functions.F.LE.F.3.Ba

Compare the output values for increasing x -values of increasing linear, quadratic, and exponential functions to determine which function has the greatest output value.F.LE.F.3.BeB

For exponential models, express as a logarithm the solution to ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.F.LE.F.4

Construct an exponential model using given contextual data. Predict the input from a graph or table then use logarithms to find the exact solution of an independent value from the context, given a dependent value. Compare and discuss the exact solution to a graphical or tabular solution.F.LE.F.4.Ad

For exponential models, express as a logarithm the solution to ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.F.LE.F.4.P

For exponential models, express as a logarithm the solution to ab ^t = d where a and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.F.LE.F.4.Ba

For exponential models, express as a logarithm the solution to b^twhere d is a real number and the base b is 2, 10, or e; evaluate the logarithm using technology.F.LE.F.4.BeB

Interpret the parameters in a linear or exponential function in terms of a context.F.LE.G.5

Model real-world scenarios with linear and exponential functions with appropriate parameters.F.LE.G.5.Ad

Interpret the parameters in a linear or exponential function in terms of a context.F.LE.G.5.P

Identify appropriate parameters for linear or exponential functions in terms of a context.F.LE.G.5.Ba

May be able to match parameters for linear or exponential functions to the appropriate parts of the graph.F.LE.G.5.BeB

(+) Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.F.TF.H.1

(+) Solve problems using radian measure.F.TF.H.1.Ad

(+) Demonstrate that radian measure of an angle is the length of the arc on the unit circle subtended by the angle.F.TF.H.1.P

(+) Convert between degree and radian measures.F.TF.H.1.Ba

(+) Does not meet the basic performance level.F.TF.H.1.BeB

(+) Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.F.TF.H.2

(+) Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed clockwise and counterclockwise around the unit circle.F.TF.H.2.Ad

(+) Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.F.TF.H.2.P

(+) Explain how the unit circle in the coordinate plane enables the extension of the sine and cosine functions to the special angles (e.g., π/6, π/4, π/3, π/2), interpreted as radian measures of angles traversed counterclockwise once around the unit circle.F.TF.H.2.Ba

(+) Does not meet the basic performance level.F.TF.H.2.BeB

(+) Use special triangles to determine geometrically the values of sine, cosine, and 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 for x, where x is any real number.F.TF.H.3

(+) Use special triangles to determine geometrically the values of the six trigonometric functions for π/3, π/4, and π/6, and use the unit circle to express the values of the six trigonometric functions for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number.F.TF.H.3.Ad

(+) Use special triangles to determine geometrically the values of sine, cosine, and 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 for x, where x is any real number.F.TF.H.3.P

(+) Use special triangles to determine geometrically the values of sine and cosine for π/3, π/4, and π/6, and use the unit circle to express the values of sine and cosine for the reference angles of π/3, π/4, and π/6.F.TF.H.3.Ba

(+) Does not meet the basic performance level.F.TF.H.3.BeB

(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.F.TF.H.4

(+) Verify the relationships for symmetry (odd and even) of trigonometric functions holds for values of theta outside of the first quadrant of the unit circle.F.TF.H.4.Ad

(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.F.TF.H.4.P

(+) Use the unit circle to explain periodicity of trigonometric functions.F.TF.H.4.Ba

(+) Does not meet the basic performance level.F.TF.H.4.BeB

(+) Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.F.TF.I.5

(+) Model trigonometric functions of periodic phenomena by identifying amplitude, frequency, and midline, and writing the equation when given a data set.F.TF.I.5.Ad

(+) Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.F.TF.I.5.P

(+) Choose trigonometric functions to model periodic phenomena with specified amplitude and midline.F.TF.I.5.Ba

(+) Does not meet the basic performance level.F.TF.I.5.BeB

(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.F.TF.I.6

(+) Identify key features of an inverse trigonometric function when given a trigonometric function whose domain is always increasing or always decreasing.F.TF.I.6.Ad

(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.F.TF.I.6.P

(+) Understand that restricting the sine and cosine functions to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.F.TF.I.6.Ba

(+) Does not meet the basic performance level.F.TF.I.6.BeB

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.F.TF.I.7

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; extrapolate solutions to the model based on periodicity, and interpret them in terms of the context.F.TF.I.7.Ad

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.F.TF.I.7.P

(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology.F.TF.I.7.Ba

(+) Does not meet the basic performance level.F.TF.I.7.BeB

(+) Prove the Pythagorean identity sin² A + cos² A = 1 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle.F.TF.J.8

(+) Prove the other two Pythagorean identities using sin² A + cos² A = 1.F.TF.J.8.Ad

(+) Prove the Pythagorean identity sin² A + cos² A = 1 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A and the quadrant of the angle.F.TF.J.8.P

(+) Use the Pythagorean identity sin² A + cos² A = 1 to find sin A or cos A given sin A or cos A and the quadrant of the angle.F.TF.J.8.Ba

(+) Does not meet the basic performance level.F.TF.J.8.BeB

(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.F.TF.J.9

(+) Use the addition formula to prove multiple-angle identities and use them to solve problems.F.TF.J.9.Ad