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SB_Precalculus-to-Common-Core

VIEWS: 19 PAGES: 7

									                                                                                                                                    SpringBoard Precalculus to
                                                                                                                         Common Core Common Core State Standards Initiative


Grade(s)      CCS         CCS Standard          CCS Standard                                             CCS Standard Level 4                                                 CCS Standard Level 5   Standard           SpringBoard Activity
            Standard        Level 2               Level 3                                                                                                                                               ID
             Level 1

Grades 9-12 Number and   The Complex Number Perform arithmetic          3. Find the conjugate of a complex number; use conjugates to find moduli and quotients of                                    N-CN.3     Precalculus, Unit 2, Activity 2-3: Complex
            Quantity     System N -CN       operations with complex     complex numbers.                                                                                                                        Polynomial Roots and Inequalities
                                            numbers.
Grades 9-12 Number and   The Complex Number Represent complex           4. Represent complex numbers on the complex plane in rectangular and polar form (including                                   N-CN.4     Precalculus, Unit 5, Activity 5-6: DeMoivre’s
            Quantity     System N -CN       numbers and their           real and imaginary numbers), and explain why the rectangular and polar forms of a given                                                 Theorem
                                            operations on the           complex number represent the same number.
                                            complex plane.
Grades 9-12 Number and   The Complex Number Represent complex           5. Represent addition, subtraction, multiplication, and conjugation of complex numbers                                       N-CN.5     Precalculus, Unit 2, Getting Ready
            Quantity     System N -CN       numbers and their           geometrically on the complex plane; use properties of this representation for computation. For
                                            operations on the           example, (–1 + √3 i)³ = 8 because (–1 + √3 i) has modulus 2 and argument 120°.
                                            complex plane.
Grades 9-12 Number and   The Complex Number Represent complex           5. Represent addition, subtraction, multiplication, and conjugation of complex numbers                                       N-CN.5     Precalculus, Unit 2, Activity 2-3: Complex
            Quantity     System N -CN       numbers and their           geometrically on the complex plane; use properties of this representation for computation. For                                          Polynomial Roots and Inequalities
                                            operations on the           example, (–1 + √3 i)³ = 8 because (–1 + √3 i) has modulus 2 and argument 120°.
                                            complex plane.
Grades 9-12 Number and   The Complex Number Represent complex           5. Represent addition, subtraction, multiplication, and conjugation of complex numbers                                       N-CN.5     Precalculus, Unit 2, Unit Practice
            Quantity     System N -CN       numbers and their           geometrically on the complex plane; use properties of this representation for computation. For
                                            operations on the           example, (–1 + √3 i)³ = 8 because (–1 + √3 i) has modulus 2 and argument 120°.
                                            complex plane.
Grades 9-12 Number and   The Complex Number Represent complex           5. Represent addition, subtraction, multiplication, and conjugation of complex numbers                                       N-CN.5     Precalculus, Unit 5, Getting Ready
            Quantity     System N -CN       numbers and their           geometrically on the complex plane; use properties of this representation for computation. For
                                            operations on the           example, (–1 + √3 i)³ = 8 because (–1 + √3 i) has modulus 2 and argument 120°.
                                            complex plane.
Grades 9-12 Number and   The Complex Number Represent complex           5. Represent addition, subtraction, multiplication, and conjugation of complex numbers                                       N-CN.5     Precalculus, Unit 5, Activity 5-6: DeMoivre’s
            Quantity     System N -CN       numbers and their           geometrically on the complex plane; use properties of this representation for computation. For                                          Theorem
                                            operations on the           example, (–1 + √3 i)³ = 8 because (–1 + √3 i) has modulus 2 and argument 120°.
                                            complex plane.
Grades 9-12 Number and   The Complex Number Represent complex           6. Calculate the distance between numbers in the complex plane as the modulus of the                                         N-CN.6     Precalculus, Unit 5, Activity 5-6: DeMoivre’s
            Quantity     System N -CN       numbers and their           difference, and the midpoint of a segment as the average of the numbers at its endpoints.                                               Theorem
                                            operations on the
                                            complex plane.
Grades 9-12 Number and   Vector and Matrix   Represent and model with 1. Recognize vector quantities as having both magnitude and direction. Represent vector                                        N-VM.1     Precalculus, Unit 6, Activity 6-2: Introduction
            Quantity     Quantities N -VM    vector quantities.       quantities by directed line segments, and use appropriate symbols for vectors and their                                                   to Vectors
                                                                      magnitudes (e.g., v , |v |, ||v ||, v ).
Grades 9-12 Number and   Vector and Matrix   Represent and model with 1. Recognize vector quantities as having both magnitude and direction. Represent vector                                        N-VM.1     Precalculus, Unit 6, Activity 6-3: Vectors in
            Quantity     Quantities N -VM    vector quantities.       quantities by directed line segments, and use appropriate symbols for vectors and their                                                   Two and Three Dimensions
                                                                      magnitudes (e.g., v , |v |, ||v ||, v ).
Grades 9-12 Number and   Vector and Matrix   Represent and model with 1. Recognize vector quantities as having both magnitude and direction. Represent vector                                        N-VM.1     Precalculus, Unit 6, Activity 6-4: Parametric
            Quantity     Quantities N -VM    vector quantities.       quantities by directed line segments, and use appropriate symbols for vectors and their                                                   Equations Revisited
                                                                      magnitudes (e.g., v , |v |, ||v ||, v ).
Grades 9-12 Number and   Vector and Matrix   Represent and model with 1. Recognize vector quantities as having both magnitude and direction. Represent vector                                        N-VM.1     Precalculus, Unit 6, EA 6-1: Parametric
            Quantity     Quantities N -VM    vector quantities.       quantities by directed line segments, and use appropriate symbols for vectors and their                                                   Equations and Vectors
                                                                      magnitudes (e.g., v , |v |, ||v ||, v ).
Grades 9-12 Number and   Vector and Matrix   Represent and model with 1. Recognize vector quantities as having both magnitude and direction. Represent vector                                        N-VM.1     Precalculus, Unit 6, Unit Practice
            Quantity     Quantities N -VM    vector quantities.       quantities by directed line segments, and use appropriate symbols for vectors and their
                                                                      magnitudes (e.g., v , |v |, ||v ||, v ).
Grades 9-12 Number and   Vector and Matrix   Represent and model with 1. Recognize vector quantities as having both magnitude and direction. Represent vector                                        N-VM.1     Precalculus, Unit 6, Unit Reflection
            Quantity     Quantities N -VM    vector quantities.       quantities by directed line segments, and use appropriate symbols for vectors and their
                                                                      magnitudes (e.g., v , |v |, ||v ||, v ).
Grades 9-12 Number and   Vector and Matrix   Represent and model with 1. Recognize vector quantities as having both magnitude and direction. Represent vector                                        N-VM.1     Precalculus, Unit 6, Math Standards Review
            Quantity     Quantities N -VM    vector quantities.       quantities by directed line segments, and use appropriate symbols for vectors and their
                                                                      magnitudes (e.g., v , |v |, ||v ||, v ).
Grades 9-12 Number and   Vector and Matrix   Represent and model with 2. Find the components of a vector by subtracting the coordinates of an initial point from the                                 N-VM.2     Precalculus, Unit 6, Activity 6-2: Introduction
            Quantity     Quantities N -VM    vector quantities.       coordinates of a terminal point.                                                                                                          to Vectors

Grades 9-12 Number and   Vector and Matrix   Represent and model with 2. Find the components of a vector by subtracting the coordinates of an initial point from the                                 N-VM.2     Precalculus, Unit 6, Activity 6-3: Vectors in
            Quantity     Quantities N -VM    vector quantities.       coordinates of a terminal point.                                                                                                          Two and Three Dimensions

Grades 9-12 Number and   Vector and Matrix   Represent and model with 2. Find the components of a vector by subtracting the coordinates of an initial point from the                                 N-VM.2     Precalculus, Unit 6, Activity 6-4: Parametric
            Quantity     Quantities N -VM    vector quantities.       coordinates of a terminal point.                                                                                                          Equations Revisited

Grades 9-12 Number and   Vector and Matrix   Represent and model with 2. Find the components of a vector by subtracting the coordinates of an initial point from the                                 N-VM.2     Precalculus, Unit 6, EA 6-1: Parametric
            Quantity     Quantities N -VM    vector quantities.       coordinates of a terminal point.                                                                                                          Equations and Vectors

Grades 9-12 Number and   Vector and Matrix   Represent and model with 2. Find the components of a vector by subtracting the coordinates of an initial point from the                                 N-VM.2     Precalculus, Unit 6, Unit Practice
            Quantity     Quantities N -VM    vector quantities.       coordinates of a terminal point.

Grades 9-12 Number and   Vector and Matrix   Represent and model with 3. Solve problems involving velocity and other quantities that can be represented by vectors.                                  N-VM.3     Precalculus, Unit 4, Activity 4-5: Law of
            Quantity     Quantities N -VM    vector quantities.                                                                                                                                                 Cosines




                                                                                                                                                      Page 1 of 7
                                                                                                                                    SpringBoard Precalculus to
                                                                                                                         Common Core Common Core State Standards Initiative


Grade(s)      CCS         CCS Standard          CCS Standard                                             CCS Standard Level 4                                                               CCS Standard Level 5                                  Standard            SpringBoard Activity
            Standard        Level 2               Level 3                                                                                                                                                                                            ID
             Level 1

Grades 9-12 Number and   Vector and Matrix   Represent and model with 3. Solve problems involving velocity and other quantities that can be represented by vectors.                                                                              N-VM.3       Precalculus, Unit 4, Activity 4-6: Law of
            Quantity     Quantities N -VM    vector quantities.                                                                                                                                                                                               Sines

Grades 9-12 Number and   Vector and Matrix   Represent and model with 3. Solve problems involving velocity and other quantities that can be represented by vectors.                                                                              N-VM.3       Precalculus, Unit 4, Unit Practice
            Quantity     Quantities N -VM    vector quantities.

Grades 9-12 Number and   Vector and Matrix   Represent and model with 3. Solve problems involving velocity and other quantities that can be represented by vectors.                                                                              N-VM.3       Precalculus, Unit 6, Activity 6-2: Introduction
            Quantity     Quantities N -VM    vector quantities.                                                                                                                                                                                               to Vectors

Grades 9-12 Number and   Vector and Matrix   Represent and model with 3. Solve problems involving velocity and other quantities that can be represented by vectors.                                                                              N-VM.3       Precalculus, Unit 6, Activity 6-3: Vectors in
            Quantity     Quantities N -VM    vector quantities.                                                                                                                                                                                               Two and Three Dimensions

Grades 9-12 Number and   Vector and Matrix   Represent and model with 3. Solve problems involving velocity and other quantities that can be represented by vectors.                                                                              N-VM.3       Precalculus, Unit 6, Activity 6-4: Parametric
            Quantity     Quantities N -VM    vector quantities.                                                                                                                                                                                               Equations Revisited

Grades 9-12 Number and   Vector and Matrix   Represent and model with 3. Solve problems involving velocity and other quantities that can be represented by vectors.                                                                              N-VM.3       Precalculus, Unit 6, EA 6-1: Parametric
            Quantity     Quantities N -VM    vector quantities.                                                                                                                                                                                               Equations and Vectors

Grades 9-12 Number and   Vector and Matrix   Represent and model with 3. Solve problems involving velocity and other quantities that can be represented by vectors.                                                                              N-VM.3       Precalculus, Unit 6, Unit Practice
            Quantity     Quantities N -VM    vector quantities.

Grades 9-12 Number and   Vector and Matrix   Perform operations on      4. Add and subtract vectors.                                                                  a. Add vectors end-to-end, component-wise, and by the parallelogram rule. N-VM.4.a      Precalculus, Unit 6, Activity 6-2: Introduction
            Quantity     Quantities N -VM    vectors.                                                                                                                 Understand that the magnitude of a sum of two vectors is typically not the              to Vectors
                                                                                                                                                                      sum of the magnitudes.
Grades 9-12 Number and   Vector and Matrix   Perform operations on      4. Add and subtract vectors.                                                                  a. Add vectors end-to-end, component-wise, and by the parallelogram rule. N-VM.4.a      Precalculus, Unit 6, Activity 6-3: Vectors in
            Quantity     Quantities N -VM    vectors.                                                                                                                 Understand that the magnitude of a sum of two vectors is typically not the              Two and Three Dimensions
                                                                                                                                                                      sum of the magnitudes.
Grades 9-12 Number and   Vector and Matrix   Perform operations on      4. Add and subtract vectors.                                                                  a. Add vectors end-to-end, component-wise, and by the parallelogram rule. N-VM.4.a      Precalculus, Unit 6, Activity 6-4: Parametric
            Quantity     Quantities N -VM    vectors.                                                                                                                 Understand that the magnitude of a sum of two vectors is typically not the              Equations Revisited
                                                                                                                                                                      sum of the magnitudes.
Grades 9-12 Number and   Vector and Matrix   Perform operations on      4. Add and subtract vectors.                                                                  a. Add vectors end-to-end, component-wise, and by the parallelogram rule. N-VM.4.a      Precalculus, Unit 6, EA 6-1: Parametric
            Quantity     Quantities N -VM    vectors.                                                                                                                 Understand that the magnitude of a sum of two vectors is typically not the              Equations and Vectors
                                                                                                                                                                      sum of the magnitudes.
Grades 9-12 Number and   Vector and Matrix   Perform operations on      4. Add and subtract vectors.                                                                  a. Add vectors end-to-end, component-wise, and by the parallelogram rule. N-VM.4.a      Precalculus, Unit 6, Unit Practice
            Quantity     Quantities N -VM    vectors.                                                                                                                 Understand that the magnitude of a sum of two vectors is typically not the
                                                                                                                                                                      sum of the magnitudes.
Grades 9-12 Number and   Vector and Matrix   Perform operations on      4. Add and subtract vectors.                                                                  b. Given two vectors in magnitude and direction form, determine the        N-VM.4.b     Precalculus, Unit 6, Activity 6-2: Introduction
            Quantity     Quantities N -VM    vectors.                                                                                                                 magnitude and direction of their sum.                                                   to Vectors

Grades 9-12 Number and   Vector and Matrix   Perform operations on      4. Add and subtract vectors.                                                                  b. Given two vectors in magnitude and direction form, determine the        N-VM.4.b     Precalculus, Unit 6, Activity 6-3: Vectors in
            Quantity     Quantities N -VM    vectors.                                                                                                                 magnitude and direction of their sum.                                                   Two and Three Dimensions

Grades 9-12 Number and   Vector and Matrix   Perform operations on      4. Add and subtract vectors.                                                                  b. Given two vectors in magnitude and direction form, determine the        N-VM.4.b     Precalculus, Unit 6, Activity 6-4: Parametric
            Quantity     Quantities N -VM    vectors.                                                                                                                 magnitude and direction of their sum.                                                   Equations Revisited

Grades 9-12 Number and   Vector and Matrix   Perform operations on      4. Add and subtract vectors.                                                                  b. Given two vectors in magnitude and direction form, determine the        N-VM.4.b     Precalculus, Unit 6, EA 6-1: Parametric
            Quantity     Quantities N -VM    vectors.                                                                                                                 magnitude and direction of their sum.                                                   Equations and Vectors

Grades 9-12 Number and   Vector and Matrix   Perform operations on      4. Add and subtract vectors.                                                                  b. Given two vectors in magnitude and direction form, determine the        N-VM.4.b     Precalculus, Unit 6, Unit Practice
            Quantity     Quantities N -VM    vectors.                                                                                                                 magnitude and direction of their sum.

Grades 9-12 Number and   Vector and Matrix   Perform operations on      4. Add and subtract vectors.                                                                  c. Understand vector subtraction v – w as v + (–w ), where –w is the         N-VM.4.c   Precalculus, Unit 6, Activity 6-2: Introduction
            Quantity     Quantities N -VM    vectors.                                                                                                                 additive inverse of w , with the same magnitude as w and pointing in the                to Vectors
                                                                                                                                                                      opposite direction. Represent vector subtraction graphically by connecting
                                                                                                                                                                      the tips in the appropriate order, and perform vector subtraction component-
                                                                                                                                                                      wise.
Grades 9-12 Number and   Vector and Matrix   Perform operations on      4. Add and subtract vectors.                                                                  c. Understand vector subtraction v – w as v + (–w ), where –w is the         N-VM.4.c   Precalculus, Unit 6, Activity 6-3: Vectors in
            Quantity     Quantities N -VM    vectors.                                                                                                                 additive inverse of w , with the same magnitude as w and pointing in the                Two and Three Dimensions
                                                                                                                                                                      opposite direction. Represent vector subtraction graphically by connecting
                                                                                                                                                                      the tips in the appropriate order, and perform vector subtraction component-
                                                                                                                                                                      wise.
Grades 9-12 Number and   Vector and Matrix   Perform operations on      4. Add and subtract vectors.                                                                  c. Understand vector subtraction v – w as v + (–w ), where –w is the         N-VM.4.c   Precalculus, Unit 6, Activity 6-4: Parametric
            Quantity     Quantities N -VM    vectors.                                                                                                                 additive inverse of w , with the same magnitude as w and pointing in the                Equations Revisited
                                                                                                                                                                      opposite direction. Represent vector subtraction graphically by connecting
                                                                                                                                                                      the tips in the appropriate order, and perform vector subtraction component-
                                                                                                                                                                      wise.
Grades 9-12 Number and   Vector and Matrix   Perform operations on      4. Add and subtract vectors.                                                                  c. Understand vector subtraction v – w as v + (–w ), where –w is the         N-VM.4.c   Precalculus, Unit 6, EA 6-1: Parametric
            Quantity     Quantities N -VM    vectors.                                                                                                                 additive inverse of w , with the same magnitude as w and pointing in the                Equations and Vectors
                                                                                                                                                                      opposite direction. Represent vector subtraction graphically by connecting
                                                                                                                                                                      the tips in the appropriate order, and perform vector subtraction component-
                                                                                                                                                                      wise.




                                                                                                                                                    Page 2 of 7
                                                                                                                                       SpringBoard Precalculus to
                                                                                                                            Common Core Common Core State Standards Initiative


Grade(s)      CCS         CCS Standard          CCS Standard                                                 CCS Standard Level 4                                                                      CCS Standard Level 5                                      Standard           SpringBoard Activity
            Standard        Level 2               Level 3                                                                                                                                                                                                           ID
             Level 1

Grades 9-12 Number and   Vector and Matrix   Perform operations on       4. Add and subtract vectors.                                                                           c. Understand vector subtraction v – w as v + (–w ), where –w is the         N-VM.4.c       Precalculus, Unit 6, Unit Practice
            Quantity     Quantities N -VM    vectors.                                                                                                                           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.
Grades 9-12 Number and   Vector and Matrix   Perform operations on       5. Multiply a vector by a scalar.                                                                      a. Represent scalar multiplication graphically by scaling vectors and possibly   N-VM.5.a   Precalculus, Unit 6, Activity 6-3: Vectors in
            Quantity     Quantities N -VM    vectors.                                                                                                                           reversing their direction; perform scalar multiplication component-wise, e.g.,              Two and Three Dimensions
                                                                                                                                                                                as c (v x, v y) = (cv x, cv y).
Grades 9-12 Number and   Vector and Matrix   Perform operations on       5. Multiply a vector by a scalar.                                                                      a. Represent scalar multiplication graphically by scaling vectors and possibly   N-VM.5.a   Precalculus, Unit 6, Activity 6-4: Parametric
            Quantity     Quantities N -VM    vectors.                                                                                                                           reversing their direction; perform scalar multiplication component-wise, e.g.,              Equations Revisited
                                                                                                                                                                                as c (v x, v y) = (cv x, cv y).
Grades 9-12 Number and   Vector and Matrix   Perform operations on       5. Multiply a vector by a scalar.                                                                      a. Represent scalar multiplication graphically by scaling vectors and possibly   N-VM.5.a   Precalculus, Unit 6, EA 6-1: Parametric
            Quantity     Quantities N -VM    vectors.                                                                                                                           reversing their direction; perform scalar multiplication component-wise, e.g.,              Equations and Vectors
                                                                                                                                                                                as c (v x, v y) = (cv x, cv y).
Grades 9-12 Number and   Vector and Matrix   Perform operations on       5. Multiply a vector by a scalar.                                                                      a. Represent scalar multiplication graphically by scaling vectors and possibly   N-VM.5.a   Precalculus, Unit 6, Unit Practice
            Quantity     Quantities N -VM    vectors.                                                                                                                           reversing their direction; perform scalar multiplication component-wise, e.g.,
                                                                                                                                                                                as c (v x, v y) = (cv x, cv y).
Grades 9-12 Number and   Vector and Matrix   Perform operations on       5. Multiply a vector by a scalar.                                                                      b. Compute the magnitude of a scalar multiple c v using ||c v || = |c |v .       N-VM.5.b   Precalculus, Unit 6, Activity 6-3: Vectors in
            Quantity     Quantities N -VM    vectors.                                                                                                                           Compute the direction of c v knowing that when |c |v ≠ 0, the direction of                  Two and Three Dimensions
                                                                                                                                                                                c v is either along v (for c > 0) or against v (for c < 0).

Grades 9-12 Number and   Vector and Matrix   Perform operations on       5. Multiply a vector by a scalar.                                                                      b. Compute the magnitude of a scalar multiple c v using ||c v || = |c |v .       N-VM.5.b   Precalculus, Unit 6, Activity 6-4: Parametric
            Quantity     Quantities N -VM    vectors.                                                                                                                           Compute the direction of c v knowing that when |c |v ≠ 0, the direction of                  Equations Revisited
                                                                                                                                                                                c v is either along v (for c > 0) or against v (for c < 0).

Grades 9-12 Number and   Vector and Matrix   Perform operations on       5. Multiply a vector by a scalar.                                                                      b. Compute the magnitude of a scalar multiple c v using ||c v || = |c |v .       N-VM.5.b   Precalculus, Unit 6, EA 6-1: Parametric
            Quantity     Quantities N -VM    vectors.                                                                                                                           Compute the direction of c v knowing that when |c |v ≠ 0, the direction of                  Equations and Vectors
                                                                                                                                                                                c v is either along v (for c > 0) or against v (for c < 0).

Grades 9-12 Number and   Vector and Matrix   Perform operations on       5. Multiply a vector by a scalar.                                                                      b. Compute the magnitude of a scalar multiple c v using ||c v || = |c |v .       N-VM.5.b   Precalculus, Unit 6, Unit Practice
            Quantity     Quantities N -VM    vectors.                                                                                                                           Compute the direction of c v knowing that when |c |v ≠ 0, the direction of
                                                                                                                                                                                c v is either along v (for c > 0) or against v (for c < 0).

Grades 9-12 Number and   Vector and Matrix   Perform operations on       6. Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence                                                                                               N-VM.6     Precalculus, Unit 6, Activity 6-3: Vectors in
            Quantity     Quantities N -VM    matrices and use            relationships in a network.                                                                                                                                                                        Two and Three Dimensions
                                             matrices in applications.

Grades 9-12 Number and   Vector and Matrix   Perform operations on       7. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a                                                                                          N-VM.7     Precalculus, Unit 6, Activity 6-3: Vectors in
            Quantity     Quantities N -VM    matrices and use            game are doubled.                                                                                                                                                                                  Two and Three Dimensions
                                             matrices in applications.

Grades 9-12 Number and   Vector and Matrix   Perform operations on       8. Add, subtract, and multiply matrices of appropriate dimensions.                                                                                                                      N-VM.8     Precalculus, Unit 6, Activity 6-3: Vectors in
            Quantity     Quantities N -VM    matrices and use                                                                                                                                                                                                               Two and Three Dimensions
                                             matrices in applications.

Grades 9-12 Number and   Vector and Matrix   Perform operations on       9. Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is                                                                                      N-VM.9     Algebra 2, Unit 1, Activity 1-6: Matrix
            Quantity     Quantities N -VM    matrices and use            not a commutative operation, but still satisfies the associative and distributive properties.                                                                                                      Operations
                                             matrices in applications.

Grades 9-12 Number and   Vector and Matrix   Perform operations on       9. Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is                                                                                      N-VM.9     Algebra 2, Unit 1, Activity 1-7: Matrix
            Quantity     Quantities N -VM    matrices and use            not a commutative operation, but still satisfies the associative and distributive properties.                                                                                                      Properties and Equations
                                             matrices in applications.

Grades 9-12 Number and   Vector and Matrix   Perform operations on       10. Understand that the zero and identity matrices play a role in matrix addition and multiplication                                                                                    N-VM.10    Algebra 2, Unit 1, Activity 1-6: Matrix
            Quantity     Quantities N -VM    matrices and use            similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero                                                                                                  Operations
                                             matrices in applications.   if and only if the matrix has a multiplicative inverse.

Grades 9-12 Number and   Vector and Matrix   Perform operations on       10. Understand that the zero and identity matrices play a role in matrix addition and multiplication                                                                                    N-VM.10    Algebra 2, Unit 1, Activity 1-7: Matrix
            Quantity     Quantities N -VM    matrices and use            similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero                                                                                                  Properties and Equations
                                             matrices in applications.   if and only if the matrix has a multiplicative inverse.

Grades 9-12 Number and   Vector and Matrix   Perform operations on       11. Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions                                                                                         N-VM.11    Geometry, Unit 5, EA 5-3: Matrices,
            Quantity     Quantities N -VM    matrices and use            to produce another vector. Work with matrices as transformations of vectors.                                                                                                                       Transformations, and Vectors
                                             matrices in applications.

Grades 9-12 Number and   Vector and Matrix   Perform operations on       11. Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions                                                                                         N-VM.11    Geometry, Unit 5, Activity 5-7:
            Quantity     Quantities N -VM    matrices and use            to produce another vector. Work with matrices as transformations of vectors.                                                                                                                       Transformations with Matrices
                                             matrices in applications.




                                                                                                                                                         Page 3 of 7
                                                                                                                                            SpringBoard Precalculus to
                                                                                                                                 Common Core Common Core State Standards Initiative


Grade(s)       CCS        CCS Standard              CCS Standard                                                CCS Standard Level 4                                                                      CCS Standard Level 5                                   Standard            SpringBoard Activity
             Standard       Level 2                   Level 3                                                                                                                                                                                                       ID
              Level 1

Grades 9-12 Number and   Vector and Matrix       Perform operations on       12. Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of                                                                                   N-VM.12     Geometry, Unit 5, EA 5-3: Matrices,
            Quantity     Quantities N -VM        matrices and use            the determinant in terms of area.                                                                                                                                                               Transformations, and Vectors
                                                 matrices in applications.

Grades 9-12 Number and   Vector and Matrix       Perform operations on       12. Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of                                                                                   N-VM.12     Geometry, Unit 5, Activity 5-7:
            Quantity     Quantities N -VM        matrices and use            the determinant in terms of area.                                                                                                                                                               Transformations with Matrices
                                                 matrices in applications.

Grades 9-12 Algebra      Reasoning with          Solve systems of            8. Represent a system of linear equations as a single matrix equation in a vector variable.                                                                                         A-REI.8     Algebra 2, Unit 1, Activity 1-6: Matrix
                         Equations and           equations                                                                                                                                                                                                                   Operations
                         Inequalities A -REI
Grades 9-12 Algebra      Reasoning with          Solve systems of            8. Represent a system of linear equations as a single matrix equation in a vector variable.                                                                                         A-REI.8     Algebra 2, Unit 1, Activity 1-7: Matrix
                         Equations and           equations                                                                                                                                                                                                                   Properties and Equations
                         Inequalities A -REI
Grades 9-12 Algebra      Reasoning with          Solve systems of            9. Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using                                                                                 A-REI.9     Algebra 2, Unit 1, Activity 1-6: Matrix
                         Equations and           equations                   technology for matrices of dimension 3 × 3 or greater).                                                                                                                                         Operations
                         Inequalities A -REI
Grades 9-12 Algebra      Reasoning with          Solve systems of            9. Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using                                                                                 A-REI.9     Algebra 2, Unit 1, Activity 1-7: Matrix
                         Equations and           equations                   technology for matrices of dimension 3 × 3 or greater).                                                                                                                                         Properties and Equations
                         Inequalities A -REI
Grades 9-12 Functions    Interpreting Functions Analyze functions using      7. Graph functions expressed symbolically and show key features of the graph, by hand in simple d. Graph rational functions, identifying zeros and asymptotes when suitable         F-IF.7.d    Precalculus, Unit 2, Unit Overview
                         F-IF                   different representations    cases and using technology for more complicated cases.                                          factorizations are available, and showing end behavior.

Grades 9-12 Functions    Interpreting Functions Analyze functions using      7. Graph functions expressed symbolically and show key features of the graph, by hand in simple d. Graph rational functions, identifying zeros and asymptotes when suitable         F-IF.7.d    Precalculus, Unit 2, Activity 2-3: Complex
                         F-IF                   different representations    cases and using technology for more complicated cases.                                          factorizations are available, and showing end behavior.                                         Polynomial Roots and Inequalities

Grades 9-12 Functions    Interpreting Functions Analyze functions using      7. Graph functions expressed symbolically and show key features of the graph, by hand in simple d. Graph rational functions, identifying zeros and asymptotes when suitable         F-IF.7.d    Precalculus, Unit 2, Activity 2-4: Rational
                         F-IF                   different representations    cases and using technology for more complicated cases.                                          factorizations are available, and showing end behavior.                                         Functions

Grades 9-12 Functions    Interpreting Functions Analyze functions using      7. Graph functions expressed symbolically and show key features of the graph, by hand in simple d. Graph rational functions, identifying zeros and asymptotes when suitable         F-IF.7.d    Precalculus, Unit 2, Activity 2-5: Rational
                         F-IF                   different representations    cases and using technology for more complicated cases.                                          factorizations are available, and showing end behavior.                                         Functions

Grades 9-12 Functions    Interpreting Functions Analyze functions using      7. Graph functions expressed symbolically and show key features of the graph, by hand in simple d. Graph rational functions, identifying zeros and asymptotes when suitable         F-IF.7.d    Precalculus, Unit 2, EA 2-2: Rational
                         F-IF                   different representations    cases and using technology for more complicated cases.                                          factorizations are available, and showing end behavior.                                         Functions

Grades 9-12 Functions    Interpreting Functions Analyze functions using      7. Graph functions expressed symbolically and show key features of the graph, by hand in simple d. Graph rational functions, identifying zeros and asymptotes when suitable         F-IF.7.d    Precalculus, Unit 2, Activity 2-8:
                         F-IF                   different representations    cases and using technology for more complicated cases.                                          factorizations are available, and showing end behavior.                                         Transformations of Functions

Grades 9-12 Functions    Interpreting Functions Analyze functions using      7. Graph functions expressed symbolically and show key features of the graph, by hand in simple d. Graph rational functions, identifying zeros and asymptotes when suitable         F-IF.7.d    Precalculus, Unit 2, Activity 2-9: Effects of
                         F-IF                   different representations    cases and using technology for more complicated cases.                                          factorizations are available, and showing end behavior.                                         Transformations

Grades 9-12 Functions    Interpreting Functions Analyze functions using      7. Graph functions expressed symbolically and show key features of the graph, by hand in simple d. Graph rational functions, identifying zeros and asymptotes when suitable         F-IF.7.d    Precalculus, Unit 2, EA 2-3: Transformed
                         F-IF                   different representations    cases and using technology for more complicated cases.                                          factorizations are available, and showing end behavior.                                         Functions

Grades 9-12 Functions    Interpreting Functions Analyze functions using      7. Graph functions expressed symbolically and show key features of the graph, by hand in simple d. Graph rational functions, identifying zeros and asymptotes when suitable         F-IF.7.d    Precalculus, Unit 2, Unit Practice
                         F-IF                   different representations    cases and using technology for more complicated cases.                                          factorizations are available, and showing end behavior.

Grades 9-12 Functions    Interpreting Functions Analyze functions using      7. Graph functions expressed symbolically and show key features of the graph, by hand in simple d. Graph rational functions, identifying zeros and asymptotes when suitable         F-IF.7.d    Precalculus, Unit 2, Math Standards Review
                         F-IF                   different representations    cases and using technology for more complicated cases.                                          factorizations are available, and showing end behavior.

Grades 9-12 Functions    Building Functions F-   Build a function that       1. Write a function that describes a relationship between two quantities.                             c. Compose functions. For example, if T(y) is the temperature in the           F-BF.1.c   Precalculus, Unit 2, Activity 2-7: Logarithms
                         BF                      models a relationship                                                                                                             atmosphere as a function of height, and h(t) is the height of a weather
                                                 between two quantities                                                                                                            balloon as a function of time, then T(h(t)) is the temperature at the location
                                                                                                                                                                                   of the weather balloon as a function of time.

Grades 9-12 Functions    Building Functions F-   Build a function that       1. Write a function that describes a relationship between two quantities.                             c. Compose functions. For example, if T(y) is the temperature in the           F-BF.1.c   Precalculus, Unit 2, Activity 2-8:
                         BF                      models a relationship                                                                                                             atmosphere as a function of height, and h(t) is the height of a weather                   Transformations of Functions
                                                 between two quantities                                                                                                            balloon as a function of time, then T(h(t)) is the temperature at the location
                                                                                                                                                                                   of the weather balloon as a function of time.

Grades 9-12 Functions    Building Functions F-   Build a function that       1. Write a function that describes a relationship between two quantities.                             c. Compose functions. For example, if T(y) is the temperature in the           F-BF.1.c   Precalculus, Unit 2, Activity 2-9: Effects of
                         BF                      models a relationship                                                                                                             atmosphere as a function of height, and h(t) is the height of a weather                   Transformations
                                                 between two quantities                                                                                                            balloon as a function of time, then T(h(t)) is the temperature at the location
                                                                                                                                                                                   of the weather balloon as a function of time.

Grades 9-12 Functions    Building Functions F-   Build a function that       1. Write a function that describes a relationship between two quantities.                             c. Compose functions. For example, if T(y) is the temperature in the           F-BF.1.c   Precalculus, Unit 2, EA 2-3: Transformed
                         BF                      models a relationship                                                                                                             atmosphere as a function of height, and h(t) is the height of a weather                   Functions
                                                 between two quantities                                                                                                            balloon as a function of time, then T(h(t)) is the temperature at the location
                                                                                                                                                                                   of the weather balloon as a function of time.




                                                                                                                                                               Page 4 of 7
                                                                                                                                         SpringBoard Precalculus to
                                                                                                                              Common Core Common Core State Standards Initiative


Grade(s)       CCS       CCS Standard              CCS Standard                                              CCS Standard Level 4                                                                      CCS Standard Level 5                                      Standard           SpringBoard Activity
             Standard      Level 2                   Level 3                                                                                                                                                                                                        ID
              Level 1

Grades 9-12 Functions   Building Functions F-   Build a function that      1. Write a function that describes a relationship between two quantities.                           c. Compose functions. For example, if T(y) is the temperature in the           F-BF.1.c      Precalculus, Unit 7, Activity 7-1: Modeling
                        BF                      models a relationship                                                                                                          atmosphere as a function of height, and h(t) is the height of a weather                      Functions
                                                between two quantities                                                                                                         balloon as a function of time, then T(h(t)) is the temperature at the location
                                                                                                                                                                               of the weather balloon as a function of time.

Grades 9-12 Functions   Building Functions F-   Build new functions from   4. Find inverse functions.                                                                          b. Verify by composition that one function is the inverse of another.             F-BF.4.b   Precalculus, Unit 2, Activity 2-7: Logarithms
                        BF                      existing functions
Grades 9-12 Functions   Building Functions F-   Build new functions from   4. Find inverse functions.                                                                          b. Verify by composition that one function is the inverse of another.             F-BF.4.b   Precalculus, Unit 2, Activity 2-8:
                        BF                      existing functions                                                                                                                                                                                                          Transformations of Functions
Grades 9-12 Functions   Building Functions F-   Build new functions from   4. Find inverse functions.                                                                          b. Verify by composition that one function is the inverse of another.             F-BF.4.b   Precalculus, Unit 2, Activity 2-9: Effects of
                        BF                      existing functions                                                                                                                                                                                                          Transformations
Grades 9-12 Functions   Building Functions F-   Build new functions from   4. Find inverse functions.                                                                          b. Verify by composition that one function is the inverse of another.             F-BF.4.b   Precalculus, Unit 2, EA 2-3: Transformed
                        BF                      existing functions                                                                                                                                                                                                          Functions
Grades 9-12 Functions   Building Functions F-   Build new functions from   4. Find inverse functions.                                                                          c. Read values of an inverse function from a graph or a table, given that the     F-BF.4.c   Precalculus, Unit 3, Getting Ready
                        BF                      existing functions                                                                                                             function has an inverse.
Grades 9-12 Functions   Building Functions F-   Build new functions from   4. Find inverse functions.                                                                          c. Read values of an inverse function from a graph or a table, given that the     F-BF.4.c   Precalculus, Unit 3, Activity 3-6 Inverse
                        BF                      existing functions                                                                                                             function has an inverse.                                                                     Trigonometric Functions
Grades 9-12 Functions   Building Functions F-   Build new functions from   4. Find inverse functions.                                                                          d. Produce an invertible function from a non-invertible function by restricting   F-BF.4.d   Precalculus, Unit 3, Getting Ready
                        BF                      existing functions                                                                                                             the domain.
Grades 9-12 Functions   Building Functions F-   Build new functions from   4. Find inverse functions.                                                                          d. Produce an invertible function from a non-invertible function by restricting   F-BF.4.d   Precalculus, Unit 3, Activity 3-6 Inverse
                        BF                      existing functions                                                                                                             the domain.                                                                                  Trigonometric Functions
Grades 9-12 Functions   Building Functions F-   Build new functions from   5. Understand the inverse relationship between exponents and logarithms and use this                                                                                                  F-BR.5     Precalculus, Unit 2, Activity 2-6: Exponential
                        BF                      existing functions         relationship to solve problems involving logarithms and exponents.                                                                                                                               Functions
Grades 9-12 Functions   Building Functions F-   Build new functions from   5. Understand the inverse relationship between exponents and logarithms and use this                                                                                                  F-BR.5     Precalculus, Unit 2, Activity 2-7: Logarithms
                        BF                      existing functions         relationship to solve problems involving logarithms and exponents.
Grades 9-12 Functions   Building Functions F-   Build new functions from   5. Understand the inverse relationship between exponents and logarithms and use this                                                                                                  F-BR.5     Precalculus, Unit 2, Activity 2-8:
                        BF                      existing functions         relationship to solve problems involving logarithms and exponents.                                                                                                                               Transformations of Functions
Grades 9-12 Functions   Building Functions F-   Build new functions from   5. Understand the inverse relationship between exponents and logarithms and use this                                                                                                  F-BR.5     Precalculus, Unit 2, Activity 2-9: Effects of
                        BF                      existing functions         relationship to solve problems involving logarithms and exponents.                                                                                                                               Transformations
Grades 9-12 Functions   Building Functions F-   Build new functions from   5. Understand the inverse relationship between exponents and logarithms and use this                                                                                                  F-BR.5     Precalculus, Unit 2, EA 2-3: Transformed
                        BF                      existing functions         relationship to solve problems involving logarithms and exponents.                                                                                                                               Functions
Grades 9-12 Functions   Building Functions F-   Build new functions from   5. Understand the inverse relationship between exponents and logarithms and use this                                                                                                  F-BR.5     Precalculus, Unit 2, Unit Practice
                        BF                      existing functions         relationship to solve problems involving logarithms and exponents.
Grades 9-12 Functions   Building Functions F-   Build new functions from   5. Understand the inverse relationship between exponents and logarithms and use this                                                                                                  F-BR.5     Precalculus, Unit 2, Unit Reflection
                        BF                      existing functions         relationship to solve problems involving logarithms and exponents.
Grades 9-12 Functions   Trigonometric           Extend the domain of       3. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3,                                                                                      F-TF.3     Precalculus, Unit 3, Activity 3-3:
                        Functions F-TF          trigonometric functions    π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x ,                                                                                                Trigonometric Functions and the Unit Circle
                                                using the unit circle      π+x , and 2π–x in terms of their values for x , where x is any real number.

Grades 9-12 Functions   Trigonometric           Extend the domain of       3. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3,                                                                                      F-TF.3     Precalculus, Unit 3, Activity 3-4: Graphs of
                        Functions F-TF          trigonometric functions    π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x ,                                                                                                the form y = A sin[B(x – C)] + D
                                                using the unit circle      π+x , and 2π–x in terms of their values for x , where x is any real number.

Grades 9-12 Functions   Trigonometric           Extend the domain of       3. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3,                                                                                      F-TF.3     Precalculus, Unit 3, Activity 3-5: Graphs of
                        Functions F-TF          trigonometric functions    π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x ,                                                                                                Other Trigonometric Functions
                                                using the unit circle      π+x , and 2π–x in terms of their values for x , where x is any real number.

Grades 9-12 Functions   Trigonometric           Extend the domain of       3. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3,                                                                                      F-TF.3     Precalculus, Unit 3, EA 3-1: Angles, Unit
                        Functions F-TF          trigonometric functions    π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x ,                                                                                                Circle, Trigonometric Graphs
                                                using the unit circle      π+x , and 2π–x in terms of their values for x , where x is any real number.

Grades 9-12 Functions   Trigonometric           Extend the domain of       3. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3,                                                                                      F-TF.3     Precalculus, Unit 3, Activity 3-6 Inverse
                        Functions F-TF          trigonometric functions    π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x ,                                                                                                Trigonometric Functions
                                                using the unit circle      π+x , and 2π–x in terms of their values for x , where x is any real number.

Grades 9-12 Functions   Trigonometric           Extend the domain of       3. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3,                                                                                      F-TF.3     Precalculus, Unit 3, Activity 3-7: Solving
                        Functions F-TF          trigonometric functions    π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x ,                                                                                                Simple Trigonometric Equations
                                                using the unit circle      π+x , and 2π–x in terms of their values for x , where x is any real number.

Grades 9-12 Functions   Trigonometric           Extend the domain of       3. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3,                                                                                      F-TF.3     Precalculus, Unit 3, EA 3-2: Inverse Trig
                        Functions F-TF          trigonometric functions    π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x ,                                                                                                Functions and Equations
                                                using the unit circle      π+x , and 2π–x in terms of their values for x , where x is any real number.

Grades 9-12 Functions   Trigonometric           Extend the domain of       3. Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3,                                                                                      F-TF.3     Precalculus, Unit 3, Unit Practice
                        Functions F-TF          trigonometric functions    π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x ,
                                                using the unit circle      π+x , and 2π–x in terms of their values for x , where x is any real number.

Grades 9-12 Functions   Trigonometric           Extend the domain of       4. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric                                                                                            F-TF.4     Precalculus, Unit 3, Activity 3-4: Graphs of
                        Functions F-TF          trigonometric functions    functions.                                                                                                                                                                                       the form y = A sin[B(x – C)] + D
                                                using the unit circle




                                                                                                                                                          Page 5 of 7
                                                                                                                                              SpringBoard Precalculus to
                                                                                                                                   Common Core Common Core State Standards Initiative


Grade(s)         CCS          CCS Standard             CCS Standard                                               CCS Standard Level 4                                                  CCS Standard Level 5   Standard           SpringBoard Activity
               Standard         Level 2                  Level 3                                                                                                                                                  ID
                Level 1

Grades 9-12 Functions        Trigonometric          Extend the domain of        4. Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric                                     F-TF.4     Precalculus, Unit 3, Activity 3-5: Graphs of
                             Functions F-TF         trigonometric functions     functions.                                                                                                                                Other Trigonometric Functions
                                                    using the unit circle
Grades 9-12 Functions        Trigonometric          Model periodic              6. Understand that restricting a trigonometric function to a domain on which it is always                                      F-TF.6     Precalculus, Unit 3, Activity 3-6 Inverse
                             Functions F-TF         phenomena with              increasing or always decreasing allows its inverse to be constructed.                                                                     Trigonometric Functions
                                                    trigonometric functions
Grades 9-12 Functions        Trigonometric          Model periodic              6. Understand that restricting a trigonometric function to a domain on which it is always                                      F-TF.6     Precalculus, Unit 3, Activity 3-7: Solving
                             Functions F-TF         phenomena with              increasing or always decreasing allows its inverse to be constructed.                                                                     Simple Trigonometric Equations
                                                    trigonometric functions
Grades 9-12 Functions        Trigonometric          Model periodic              6. Understand that restricting a trigonometric function to a domain on which it is always                                      F-TF.6     Precalculus, Unit 3, EA 3-2: Inverse Trig
                             Functions F-TF         phenomena with              increasing or always decreasing allows its inverse to be constructed.                                                                     Functions and Equations
                                                    trigonometric functions
Grades 9-12 Functions        Trigonometric          Model periodic              6. Understand that restricting a trigonometric function to a domain on which it is always                                      F-TF.6     Precalculus, Unit 3, Unit Practice
                             Functions F-TF         phenomena with              increasing or always decreasing allows its inverse to be constructed.
                                                    trigonometric functions
Grades 9-12 Functions        Trigonometric          Model periodic              7. Use inverse functions to solve trigonometric equations that arise in modeling contexts;                                     F-TF.7     Precalculus, Unit 3, Activity 3-7: Solving
                             Functions F-TF         phenomena with              evaluate the solutions using technology, and interpret them in terms of the context.                                                      Simple Trigonometric Equations
                                                    trigonometric functions
Grades 9-12 Functions        Trigonometric          Model periodic              7. Use inverse functions to solve trigonometric equations that arise in modeling contexts;                                     F-TF.7     Precalculus, Unit 3, EA 3-2: Inverse Trig
                             Functions F-TF         phenomena with              evaluate the solutions using technology, and interpret them in terms of the context.                                                      Functions and Equations
                                                    trigonometric functions
Grades 9-12 Functions        Trigonometric          Model periodic              7. Use inverse functions to solve trigonometric equations that arise in modeling contexts;                                     F-TF.7     Precalculus, Unit 3, Unit Practice
                             Functions F-TF         phenomena with              evaluate the solutions using technology, and interpret them in terms of the context.
                                                    trigonometric functions
Grades 9-12 Functions        Trigonometric          Prove and apply             9. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to                                   F-TF.9     Precalculus, Unit 4, Activity 4-3: Multiple
                             Functions F-TF         trigonometric identities    solve problems.                                                                                                                           Angle Identities
Grades 9-12 Functions        Trigonometric          Prove and apply             9. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to                                   F-TF.9     Precalculus, Unit 4, EA 4-1: Trigonometric
                             Functions F-TF         trigonometric identities    solve problems.                                                                                                                           Equations and Identities
Grades 9-12 Functions        Trigonometric          Prove and apply             9. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to                                   F-TF.9     Precalculus, Unit 4, Unit Practice
                             Functions F-TF         trigonometric identities    solve problems.
Grades 9-12 Functions        Trigonometric          Prove and apply             9. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to                                   F-TF.9     Precalculus, Unit 4, Math Standards Review
                             Functions F-TF         trigonometric identities    solve problems.
Grades 9-12 Geometry         Expressing Geometric   Translate between the       3. Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or                              G-GPE.3    Precalculus, Unit 5, Activity 5-2: Ellipses and
                             Properties with        geometric description and   difference of distances from the foci is constant.                                                                                        Hyperbolas
                             Equations G-GPE        the equation for a conic
                                                    section
Grades 9-12 Geometry         Expressing Geometric Translate between the     3. Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or                                  G-GPE.3    Precalculus, Unit 5, Unit Practice
                             Properties with      geometric description and difference of distances from the foci is constant.
                             Equations G-GPE      the equation for a conic
                                                  section
Grades 9-12 Geometry         Geometric              Explain volume formulas     2. Give an informal argument using Cavalieri’s principle for the formulas for the volume of a                                  G-GMD.2    Geometry, Unit 6, Activity 6-3: Volume
                             Measurement and        and use them to solve       sphere and other solid figures.
                             Dimension G-GMD        problems
Grades 9-12 Statistics and Using Probability to Calculate expected values 1. Define a random variable for a quantity of interest by assigning a numerical value to each                                        S-MD.1     Algebra 2, Unit 6, Activity 6-3: Normal
            Probability    Make Decisions S-MD and use them to solve      event in a sample space; graph the corresponding probability distribution using the same                                                        Distribution
                                                problems                  graphical displays as for data distributions.
Grades 9-12 Statistics and Using Probability to Calculate expected values 2. Calculate the expected value of a random variable; interpret it as the mean of the probability                                    S-MD.2     Algebra 2, Unit 6, Activity 6-3: Normal
            Probability    Make Decisions S-MD and use them to solve      distribution.                                                                                                                                   Distribution
                                                problems
Grades 9-12 Statistics and Using Probability to Calculate expected values 3. Develop a probability distribution for a random variable defined for a sample space in which                                      S-MD.3     Algebra 2, Unit 6, Activity 6-3: Normal
            Probability    Make Decisions S-MD and use them to solve      theoretical probabilities can be calculated; find the expected value. For example, find the                                                     Distribution
                                                problems                  theoretical probability distribution for the number of correct answers obtained by guessing on
                                                                          all five questions of a multiple-choice test where each question has four choices, and find the
                                                                          expected grade under various grading schemes.

Grades 9-12 Statistics and Using Probability to Calculate expected values 4. Develop a probability distribution for a random variable defined for a sample space in which                                      S-MD.4     Geometry, Unit 7, Activity 7-1: Probability
            Probability    Make Decisions S-MD and use them to solve      probabilities are assigned empirically; find the expected value. For example, find a current data                                               Experiments
                                                problems                  distribution on the number of TV sets per household in the United States, and calculate the
                                                                          expected number of sets per household. How many TV sets would you expect to find in 100
                                                                          randomly selected households?

Grades 9-12 Statistics and Using Probability to Calculate expected values 4. Develop a probability distribution for a random variable defined for a sample space in which                                      S-MD.4     Geometry, Unit 7, EA 7-1: Counting and
            Probability    Make Decisions S-MD and use them to solve      probabilities are assigned empirically; find the expected value. For example, find a current data                                               Probability
                                                problems                  distribution on the number of TV sets per household in the United States, and calculate the
                                                                          expected number of sets per household. How many TV sets would you expect to find in 100
                                                                          randomly selected households?




                                                                                                                                                               Page 6 of 7
                                                                                                                                          SpringBoard Precalculus to
                                                                                                                               Common Core Common Core State Standards Initiative


Grade(s)         CCS          CCS Standard             CCS Standard                                            CCS Standard Level 4                                                                CCS Standard Level 5                                Standard            SpringBoard Activity
               Standard         Level 2                  Level 3                                                                                                                                                                                          ID
                Level 1

Grades 9-12 Statistics and Using Probability to Calculate expected values 4. Develop a probability distribution for a random variable defined for a sample space in which                                                                             S-MD.4       Geometry, Unit 7, Activity 7-2: Dependent
            Probability    Make Decisions S-MD and use them to solve      probabilities are assigned empirically; find the expected value. For example, find a current data                                                                                        and Independent Events
                                                problems                  distribution on the number of TV sets per household in the United States, and calculate the
                                                                          expected number of sets per household. How many TV sets would you expect to find in 100
                                                                          randomly selected households?

Grades 9-12 Statistics and Using Probability to Calculate expected values 4. Develop a probability distribution for a random variable defined for a sample space in which                                                                             S-MD.4       Geometry, Unit 7, EA 7-2: Compound
            Probability    Make Decisions S-MD and use them to solve      probabilities are assigned empirically; find the expected value. For example, find a current data                                                                                        Events, Probability,
                                                problems                  distribution on the number of TV sets per household in the United States, and calculate the                                                                                              Simulation
                                                                          expected number of sets per household. How many TV sets would you expect to find in 100
                                                                          randomly selected households?

Grades 9-12 Statistics and Using Probability to Calculate expected values 4. Develop a probability distribution for a random variable defined for a sample space in which                                                                             S-MD.4       Geometry, Unit 7, Activity 7-3: Dependent
            Probability    Make Decisions S-MD and use them to solve      probabilities are assigned empirically; find the expected value. For example, find a current data                                                                                        Compound Events
                                                problems                  distribution on the number of TV sets per household in the United States, and calculate the
                                                                          expected number of sets per household. How many TV sets would you expect to find in 100
                                                                          randomly selected households?

Grades 9-12 Statistics and Using Probability to Calculate expected values 4. Develop a probability distribution for a random variable defined for a sample space in which                                                                             S-MD.4       Geometry, Unit 7, Activity 7-4: Geometric
            Probability    Make Decisions S-MD and use them to solve      probabilities are assigned empirically; find the expected value. For example, find a current data                                                                                        Probability
                                                problems                  distribution on the number of TV sets per household in the United States, and calculate the
                                                                          expected number of sets per household. How many TV sets would you expect to find in 100
                                                                          randomly selected households?

Grades 9-12 Statistics and Using Probability to Calculate expected values 4. Develop a probability distribution for a random variable defined for a sample space in which                                                                             S-MD.4       Algebra 2, Unit 4, Activity 4-7: Binomial
            Probability    Make Decisions S-MD and use them to solve      probabilities are assigned empirically; find the expected value. For example, find a current data                                                                                        Probability
                                                problems                  distribution on the number of TV sets per household in the United States, and calculate the
                                                                          expected number of sets per household. How many TV sets would you expect to find in 100
                                                                          randomly selected households?

Grades 9-12 Statistics and Using Probability to Use probability to            5. Weigh the possible outcomes of a decision by assigning probabilities to payoff values and    a. Find the expected payoff for a game of chance. For example, find the   S-MD.5.a   MSM3, Unit 5, Activity 5-1: Probability
            Probability    Make Decisions S-MD evaluate outcomes of           finding expected values.                                                                        expected winnings from a state lottery ticket or a game at a fast-food
                                                decisions                                                                                                                     restaurant.
Grades 9-12 Statistics and Using Probability to Use probability to            5. Weigh the possible outcomes of a decision by assigning probabilities to payoff values and    b. Evaluate and compare strategies on the basis of expected values. For   S-MD.5.b   MSM3, Unit 5, Activity 5-1: Probability
            Probability    Make Decisions S-MD evaluate outcomes of           finding expected values.                                                                        example, compare a high-deductible versus a low-deductible automobile
                                                decisions                                                                                                                     insurance policy using various, but reasonable, chances of having a minor
                                                                                                                                                                              or a major accident.




                                                                                                                                                           Page 7 of 7

								
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