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Course and Grade Level
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TopicStandardScale=3
Algebra I A/B
Algebra I
Geometry A/B
Geometry
Honors Geometry
Algebra II Part 1/Part 2
Algebra II Part 3/Part 4
Algebra II
Honors Algebra II
Precalculus
Honors Precalculus
AP Calculus
Statistics
AP Statistics
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Extend the properties of exponents to rational exponentsCCSS.MATH.CONTENT.HSN.RN.A.1 Explain how the definition of the meaning 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. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
The student can explain how the definition of the meaning 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. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.xxxx
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Extend the properties of exponents to rational exponentsCCSS.MATH.CONTENT.HSN.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.The student can rewrite expressions involving radicals and rational exponents using the properties of exponents.xxxxxx
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Use properties of rational and irrational numbersCCSS.MATH.CONTENT.HSN.RN.B.3 Explain why the sum or product of two 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.The student can explain why the sum or product of two 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.xx
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Reason quantitatively and use units to solve problemsCCSS.MATH.CONTENT.HSN.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units efficiently in formulas; choose and interpret the scale and the origin in graphs and data displays.The student can use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units efficiently in formulas; choose and interpret the scale and the origin in graphs and data displays.xx
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Reason quantitatively and use units to solve problemsCCSS.MATH.CONTENT.HSN.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling.The student can define appropriate quantities for the purpose of descriptive modeling.xxx
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Reason quantitatively and use units to solve problemsCCSS.MATH.CONTENT.HSN.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.The student can choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
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Perform arithmetic operations with complex numbersCCSS.MATH.CONTENT.HSN.CN.A.1 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.The student can 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.xxxxx
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Perform arithmetic operations with complex numbersCCSS.MATH.CONTENT.HSN.CN.A.2 Use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.The student can use the relation i2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.xxx
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Perform arithmetic operations with complex numbersCCSS.MATH.CONTENT.HSN.CN.A.3 (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.The student can (+) find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.xxx
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Represent complex numbers and their operations on the complex planeCCSS.MATH.CONTENT.HSN.CN.B.4 (+) 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.The student can (+) 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.
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Represent complex numbers and their operations on the complex planeCCSS.MATH.CONTENT.HSN.CN.B.5 (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3 i)3 = 8 because (-1 + √3 i) has modulus 2 and argument 120°.The student can (+) represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √3 i)3 = 8 because (-1 + √3 i) has modulus 2 and argument 120°.
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Represent complex numbers and their operations on the complex planeCCSS.MATH.CONTENT.HSN.CN.B.6 (+) 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.The student can (+) 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.
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Use complex numbers in polynomial identities and equationsCCSS.MATH.CONTENT.HSN.CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.The student can solve quadratic equations with real coefficients that have complex solutions.xxx
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Use complex numbers in polynomial identities and equationsCCSS.MATH.CONTENT.HSN.CN.C.8 (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x - 2i).The student can (+) extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x - 2i).
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Use complex numbers in polynomial identities and equationsCCSS.MATH.CONTENT.HSN.CN.C.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.The student can (+) know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.xxx
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Represent and model with vector quantitiesCCSS.MATH.CONTENT.HSN.VM.A.1 (+) 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).The student can (+) 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).x
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Represent and model with vector quantitiesCCSS.MATH.CONTENT.HSN.VM.A.2 (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.The student can (+) find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.x
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Represent and model with vector quantitiesCCSS.MATH.CONTENT.HSN.VM.A.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors.The student can (+) solve problems involving velocity and other quantities that can be represented by vectors.x
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Perform operations on vectorsCCSS.MATH.CONTENT.HSN.VM.B.4 (+) Add and subtract vectors.The student can (+) add and subtract vectors.x
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Perform operations on vectorsCCSS.MATH.CONTENT.HSN.VM.B.4.A 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.The student can 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.
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Perform operations on vectorsCCSS.MATH.CONTENT.HSN.VM.B.4.B Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.The student can, given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
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Perform operations on vectorsCCSS.MATH.CONTENT.HSN.VM.B.4.C Understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.The student can understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
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Perform operations on vectorsCCSS.MATH.CONTENT.HSN.VM.B.5 (+) Multiply a vector by a scalar.The student can (+) multiply a vector by a scalar.x
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Perform operations on vectorsCCSS.MATH.CONTENT.HSN.VM.B.5.A Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).The student can Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).
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Perform operations on vectorsCCSS.MATH.CONTENT.HSN.VM.B.5.B Compute the magnitude of a scalar multiple cv 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).The student can compute the magnitude of a scalar multiple cv 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).
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Perform operations on matrices and use matrices in applicationsCCSS.MATH.CONTENT.HSN.VM.C.6 (+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.The student can (+) use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.x
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Perform operations on matrices and use matrices in applicationsCCSS.MATH.CONTENT.HSN.VM.C.7 (+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.The student can (+) multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.x
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Perform operations on matrices and use matrices in applicationsCCSS.MATH.CONTENT.HSN.VM.C.8 (+) Add, subtract, and multiply matrices of appropriate dimensions.The student can (+) add, subtract, and multiply matrices of appropriate dimensions.x
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Perform operations on matrices and use matrices in applicationsCCSS.MATH.CONTENT.HSN.VM.C.9 (+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.The student can (+) understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.x
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Perform operations on matrices and use matrices in applicationsCCSS.MATH.CONTENT.HSN.VM.C.10 (+) 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.The student can(+) 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.xxx
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Perform operations on matrices and use matrices in applicationsCCSS.MATH.CONTENT.HSN.VM.C.11 (+) 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.The student can (+) 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.
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Perform operations on matrices and use matrices in applicationsCCSS.MATH.CONTENT.HSN.VM.C.12 (+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.The student can (+) work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.
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