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NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE

SUBJECT: Math II TIMELINE: 4th 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: 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

SUBJECT: Math Algebra II TIMELINE: 4th 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. 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

SUBJECT: Math Algebra II TIMELINE: 4th 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 of , of real Core Textbook: Property for 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 matrices play a zero and identity matrices Core Textbook: role in matrix 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 of --Lesson 12-5 p. 801 of a is real numbers. M nonzero if and only if the matrix has a [Mathematical . Practices]:

[Assessment]:

Niobrara County School District #1, Fall 2012 Page 3 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE

SUBJECT: Math Algebra II TIMELINE: 4th 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 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

SUBJECT: Math Algebra II TIMELINE: 4th 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 and interpret the 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 , reflection, dilation, and 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

SUBJECT: Math Algebra II TIMELINE: 4th 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 i such that i2 = -1, is a 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

Niobrara County School District #1, Fall 2012 Page 6 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE

SUBJECT: Math Algebra II TIMELINE: 4th 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 .

Standards: N-CN.4. Represent I can represent [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

SUBJECT: Math Algebra II TIMELINE: 4th 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, , 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 the distance Synthesis [Mathematical Modulus distance between numbers in the between numbers in the Practices]: complex plane as the modulus of the complex plane as the MP-2, MP-7, MP-8 Midpoint difference, and then midpoint of a modulus of the difference. M segment as the average of the numbers at its endpoints. I can calculate the midpoint of a segment as the average [Assessment]: of the numbers at its endpoints. M

Domain:Use complex numbers in

Niobrara County School District #1, Fall 2012 Page 8 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE

SUBJECT: Math Algebra II TIMELINE: 4th quarter

Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices] identities and .

Standards: N-CN.7.Solve quadratic I can solve quadratic Application Pearson Alg. II Common Quadratic equations with real that equations with real Core: Equations have complex solutions. coefficients that have --Lesson 4-8 p.249 complex solutions. C --Lesson 5-5 p. 312 Coefficients [Assessment]: --Lesson 5-6 p. 319 Complex [Mathematical Solutions Practices]: MP-1, MP-7 Fundamental Theorem of Algebra

Domain:Use complex numbers in polynomial identities and equations.

Standards: N-CN.8. Extend I can apply the polynomial Synthesis Pearson Alg. II Common Polynomial polynomial identities to the complex identities to complex Core Textbook: Identities numbers. numbers. C --Lesson 4-8 p.248 --Lesson 5-5 p.312 [Assessment]: --Lesson 5-6 p.319

[Mathematical Practices]: MP-1, MP-7

Niobrara County School District #1, Fall 2012 Page 9 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE

SUBJECT: Math Algebra II TIMELINE: 4th quarter

Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices]

Domain:Use complex numbers in polynomial identities and equations.

Standards: N-CN.9. Know the I can state the Fundamental Analysis Pearson Alg. II Common Fundamental Fundamental Theorem of Algebra; Theorem of Algebra and Core Textbook: Theorem of show that it is true for quadratic prove that it is true for --Lesson 5-6 p. 319 Algebra . quadratic polynomials. M [Mathematical [Assessment]: Practices]: MP-1, MP-7 Domain: Solve equations and inequalities in one .

Standards: A-REI.4.Solve quadratic I can solve and transform Synthesis Supplement with Pearson Quadratic equations in one variable. quadratic equations in one Alg. I Common Core Equations variable by applying the Textbook: a) Use the method of completing the method completing the --Lesson 9-3 p.561 to transform any quadratic square into an of --Lesson 9--4 p.568 square. equation into an equation of the form the form (x – p)2 = q. M --Lesson 9-5 p.576 (x – p)2 = q that has the same --Lesson 9-6 p. 582 Quadratic solutions. Derive the I can derive the quadratic Formula from this form. formula from the above form. [Mathematical M Practices]: [Assessment]:

Complex Solutions

Niobrara County School District #1, Fall 2012 Page 10 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE

SUBJECT: Math Algebra II TIMELINE: 4th quarter

Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices]

Domain: Solve equations and inequalities in one variable.

Standards: A-REI.4.Solve the I can solve quadratic Evaluation Supplement with Pearson quadratic equations in one variable. equations through multiple Alg. I Common Core methods and differentiate Textbook: b) Solve quadratic equations by between methods and --Lesson 9-3 p.561 inspection (e.g., for x2 = 49) and taking determine which is --Lesson 9-4 p.568 square roots, completing the square, appropriate. M --Lesson 9-5 p.576 the quadratic formulat and factoring, --Lesson 9-6 p. 582 as appropriate to the initial form of the I can recognize when the equation. Recognize when the quadratic formula gives [Mathematical quadratic formula gives complex complex solutions. M Practices]: solutions and write them as a a +/- bi MP-2, MP-7, MP-8 for real numbers a and b.

[Assessment]:

Niobrara County School District #1, Fall 2012 Page 11 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE

SUBJECT: Math Algebra II TIMELINE: 4th quarter

Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices]

Domain: Calculate the expected values and use them to solve problems.

Standards: S-MD.1. Define a random I can define a random Analsis [Mathematical Random variable for a quantitiy of interest by variable for a quanity of Practices]: Variable assigning a numerical value to each interest by assigning event in a sample ; graph the numerical value to each Sample Space corresponding probability distribution event in the sample space. using the same graphical displays as M Probability for data distributions. Distribution [Assessment]: I can graph the corresponding probability Data distribution using the same Distribtution graphical displays as for data distributions. M Domain: Calculate expected values and use them to solve problems.

Standards: S-MD.2.Calculate the I can calculate the expected Comprehensive [Mathematical expected value of a random variable; value of a random variable Practices]: interpret it as the mean of the and interpret it as the mean probability distribution. of the probability [Assessment]: distribtution. M

Niobrara County School District #1, Fall 2012 Page 12 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE

SUBJECT: Math Algebra II TIMELINE: 4th quarter

Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices]

Domain: Calculate expected values and use them to solve problems.

Standards: S-MD.3.Develop a I will develop a probability Application [Mathematical Theoretical probability distribution for a random distribution for a random Practices]: Probabilities variable defined for a sample space in variable defined for a sample which theoretical probabilities can be space in which theoretical Expected calculated; find the expected value. probabilities can be Values calculated and then calculate [Assessment]: the expected value. M

Domain: Calculated expected values and use them solve problems.

Standards: S-MD.4.Develop a I will develop a probability Application [Mathematical Assigned probability distribution for a random distribution for a random Practices]: empirically variable defined for a sample space in variable defined for a sample which probabilities are assigned space in which probabilities empirically; find the expected value. are assigned empirically and

[Assessment]: then calculated the expected value. M

Niobrara County School District #1, Fall 2012 Page 13 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE

SUBJECT: Math Algebra II TIMELINE: 4th quarter

Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices]

Domain: Use probability to evaluate outcomes of decisions.

Standards:S-MD.5.Weigh the I can determine the possible Application [Mathematical Game of possible outcomes of a decision by outcomes of a decision by Practices]: chance assigning probabilities to payoff values assigning probabilities to and finding expected values. a)Find payoff values and expected Outcomes the expected payoff for a game of values, including the chance. expected payoff for a game of chance. M [Assessment]:

Domain: Use probability to evaluate outcomes of decisions.

Standards: S-MD.5.Weigh the I can evaluate and compare Evaluation [Mathematical possible outcomes of a decision by strategies on the of Practices]: assigning probabilities to payoff values expected values. M and finding expected values. b)Evaluate and compare strategies on the basis of expected values.

[Assessment]:

Niobrara County School District #1, Fall 2012 Page 14 NIOBRARA COUNTY SCHOOL DISTRICT #1 CURRICULUM GUIDE

SUBJECT: Math Algebra II TIMELINE: 4th quarter

Domain: Student Friendly Level of Resource Academic Standard: Learning Objective Thinking Correlation/Exemplar Vocabulary [Assessment] [Mathematical Practices]

Domain: Use probability to evaluate outcomes of decisions.

Standards: S-MD.6. Use probabilities I can use probabilities to Analysis Pearson Alg. II Common Fair decisions to make fair decisions (e.g., drawing make fair decisions. M Core Textbook: by lots, using a random number --Lesson 11-5 p.703 Random generator). Number [Mathematical Generator [Assessment]: Practices]:

Domain: Use probability to evaluate outcomes of decisions.

Standards: S-MD.7. Analyze I will analyze decisions and Analysis Pearson Alg. II Common Probability decisions and strategies using strategies using probability Core Textbook: Concepts probability concepts (e.g., concepts. --Lesson 11-5 p. 703 testing, medical testing, pulling a hockey goalie at the end of a game). [Mathematical Practices]: [Assessment]:

Niobrara County School District #1, Fall 2012 Page 15