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Niobrara County School District #1 Curriculum Guide NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE th SUBJECT: Math Algebra II TIMELINE: 4 quarter Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices] Domain: Perform operations on matrices and use matrices in applications. Standards: N-VM.6.Use matrices to I can represent and Application Pearson Alg. II Textbook: Matrix represent and manipulated data, e.g., manipulate data to represent --Lesson 12-2 p. 772 (Matrices) to represent payoffs or incidence data. M --Concept Byte 12-2 p. relationships in a network. 780 Data --Lesson 12-5 p. 801 [Assessment]: --Concept Byte 12-2 p. 780 [Mathematical Practices]: Niobrara County School District #1, Fall 2012 Page 1 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE th SUBJECT: Math Algebra II TIMELINE: 4 quarter Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices] Domain: Perform operations on matrices and use matrices in applications. Standards: N-VM.7. Multiply matrices I can multiply matrices by Application Pearson Alg. II Textbook: Scalars by scalars to produce new matrices, scalars to produce new --Lesson 12-2 p. 772 e.g., as when all of the payoffs in a matrices. M --Lesson 12-5 p. 801 game are doubled. [Assessment]: [Mathematical Practices]: Domain: Perform operations on matrices and use matrices in applications. Standards:N-VM.8.Add, subtract and I can perform operations on Knowledge Pearson Alg. II Common Matrix multiply matrices of appropriate matrices and reiterate the Core Textbook: Dimensions dimensions. limitations on matrix --Lesson 12-1p. 764 [Assessment]: dimensions. M --Concept Byte 12-1 p. --Concept Byte 12-1 p. 771 771 --Lesson 12-2 p. 772 --Lesson 12-4 p. 792 [Mathematical Practices]: Niobrara County School District #1, Fall 2012 Page 2 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE th SUBJECT: Math Algebra II TIMELINE: 4 quarter Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices] Domain: Perform operations on matrices and use matrices in applications. Standards: N-VM.9.Understand that , I can demonstrate that the Knowledge Pearson Alg. II Common Commutative unlike multiplication of numbers, commutative property of real Core Textbook: Property matrix multiplication for square numbers does not apply to --Lesson 12-2 p. 772 matrices is not a commutative matrix multiplication, but that Associative operaton, but still statisfies the the associative and [Mathematical Property associative and distributive properties. distributive properties do. M Practices]: Distributive [Assessment]: Property Domain: Perform operations on matrices and use matrices in applications. Standards: N-VM.10. Understand that I can demonstrate that the Knowledge Pearson Alg. II Common the zero and identity matrices play a zero and identity matrices Core Textbook: role in matrix addition and have a similar effect in matrix --Lesson 12-1 p. 764 multiplication similar to the role of 0 addition and multiplication --Lesson 12-3 p. 782 and 1 in the real numbers. The that 0 and 1 do in the set of --Lesson 12-5 p. 801 determinant of a square matrix is real numbers. M nonzero if and only if the matrix has a [Mathematical multiplicative inverse. Practices]: [Assessment]: Niobrara County School District #1, Fall 2012 Page 3 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE th SUBJECT: Math Algebra II TIMELINE: 4 quarter Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices] Domain: Perform operations on matrices and use matrices in applications. Standards: N-VM.11.Multiply a vector I can represent a vector with Synthesis Pearson Alg. II Common Vector (regarded as a matrix with one a single column matrix and Core Textbook: column) by a matrix of suitable then multiply that matrix by --Lesson 12-6 p.809 Transfor m dimenstions to produce another another matrix, of vector. Work with matrices as appropriate dimensions, to NCTM Illuminations Magnitude transformations of vectors. produce another vector or “Vector Investigation”-- transform a vector. C Move the boat around the [Assessment]: water by changing the magnitude and direction of the boat's speed (blue vector) or the magnitude and direction of the water current (red vector). Try to land the boat on the island — but be careful not to hit the walls! http://illuminations.nctm.or g/ActivityDetail.aspx?ID=4 2 [Mathematical Practices]: Niobrara County School District #1, Fall 2012 Page 4 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE th SUBJECT: Math Algebra II TIMELINE: 4 quarter Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices] Domain: Perform operations on matrices and use matrices in applications. Standards: N-VM.12.Work with 2 x 2 I can manipulate 2 x 2 Synthesis Pearson Alg. II Common 2 x 2 matrix matrices as transformations of the matrices to represent Core Textbook: Transformations plane and interpret the absolute value transformations of the --Lesson 12-3 p.12-3 of the determininant in terms of area. plane.M Plane NCTM Illuminations [Assessment]: I can interpret the absolute “Computer Animation” Absolute Value value of the determinatnt in Lesson-- terms of area. M In this lesson, students Determinant transform images through rotation, reflection, dilation, and translation using matrix multiplication. After digitizing images by representing the images as matrices, they multiply image matrices by various transformation matrices, producing transformed images. http://illuminations.nctm.or g/LessonDetail.aspx?id=L 841 [Mathematical Practices]: Niobrara County School District #1, Fall 2012 Page 5 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE th SUBJECT: Math Algebra II TIMELINE: 4 quarter Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices] Domain: Perform arithmetic operations with complex numbers. Standards: N-CN.1.Know there is a I can demonstrate that there Knowledge Pearson Alg. II Common Complex complex number i such that i2 = -1, is a complex number i and Core Textbook: number, i and every complex number has the the included properties.M --Lesson 4-8 p. 248 form a + bi with a and b real. [Mathematical [Assessment]: Practices]: MP-2, MP-6 Domain: Perform arithmetic operations with complex numbers. Standards: N-CN.2.Use the relation i2 I can apply the relation i2 = - Application Pearson Alg. II Common Commutative = -1 and the commutative, 1, the commutative, Core Textbook: Property assoiciative, and distributive associative and distributive --Lesson 4-8 p. 248 properties to add, subtract, and properties to add, subtract Associative multiply complex numbers. and multiply complex [Mathematical Property numbers.M Practices]: [Assessment]: MP-2, MP-7, MP-8 Distributive Property Niobrara County School District #1, Fall 2012 Page 6 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE th SUBJECT: Math Algebra II TIMELINE: 4 quarter Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices] Domain: Perform arithmetic operations with complex numbers. Standards: N-CN.3.Find the I can derive the conjugate of Synthesis Pearson Alg. II Common Conjugate conjugate of a complex number; use a complex number and use Core Textbook: conjugates to find moduli and the conjugate to determine --Lesson 4-8 p. 248 Moduli quotients of complex numbers. moduli and quotients of complete numbers. M [Mathematical Quotient [Assessment]: Practices]: MP-2, MP-7, MP-8 Domain: Represent complex numbers and their operations on the complex plane. Standards: N-CN.4. Represent I can represent complex Analysis [Mathematical Rectangular complex numbers on the complex numbers on the complex Practices]: Form plane in rectangular and polar form plane in both rectangular and MP-2, MP-7, MP-8 (including real and imaginary polar form and explain why Polar Form numbers), and explain why the the rectangular and polar rectangular and polar forms of a given forms of a given complex Complex Plane complex number represent the same number represent the same number. number. M [Assessment]: Niobrara County School District #1, Fall 2012 Page 7 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE th SUBJECT: Math Algebra II TIMELINE: 4 quarter Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices] Domain: Represent complex numbers and their operations on the complex plane. Standards: N-CN.5. Represent I can represent addition, Analysis [Mathematical Geometric addition, subtraction, multiplication subtraction, multiplication Practices]: Representation and conjugation of complex numbers and conjugation of complex MP-2, MP-7, MP-8 geometrically on the complex plane; numbers geometrically on use properties of this representation the complex plane and apply for computation. properties of this representation for [Assessment]: computation. M Domain: Represent complex numbers and their operations on the complex plane. Standards: N-CN.6. Calculate the I can calculate
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