Pentucket Regional High School

Teacher  Allyson Bird   Subject  Algebra II

Time Frame	Content/Concepts	Skills/Thinking Processes	Assessment	Essential Questions
September	1. Linear regression 2. Relations and functions 3. Working with functions 4. Vertical and horizontal translations 5. Permutations 6. Linear equations and slope 7. Direct variation	1. Calculate line of best fit w/ TI-83;represent data graphically 2. Defining relations and functions; deciding whether a relation is a function 3. Evaluating single and composite functions; performing operations with functions 4. Identifying and analyzing vertical and horizontal translations 5. Finding permutations 6. Defining and interpreting slope; using slope-intercept, point-slope and standard form to write linear equations 7. Writing and interpreting direct variation equations	Quizzes/Tests:  open response, problems	What is linear regression, and how can it be used to make predictions about data? What is the difference between a relation and a function? How can we use translations to help us graph functions? What are the properties of lines?
October	1. One-variable and two-variable equations and inequalities 2. Absolute value equations and inequalities 3. Experimental and theoretical probability 4. Operations with matrices 5. Matrix equations 6. Identity and inverse matrices 7. Two-variable linear systems	1. and 2.  Solving one- and two-variable equations and inequalities with and without absolute value 3. Calculating and comparing experimental and theoretical probability 4. Evaluating equal matrices; performing operations with matrices 5. Solving matrix equations 6. Finding and using identity and inverse matrices 7. Solving two-variable linear systems by graphing, substitution and elimination	Quizzes/Tests:  open response, problems Writing assignment: Methods of solving systems of linear equations Project:  Theoretical vs. experimental probability	What are the steps to solving equations and inequalities? What are the steps to solving equations and inequalities with absolute value? What is a matrix? How can matrices be used to solve equations?
November	1. Linear programming 2. Three-variable linear systems 3. Quadratic regression 4. Properties and forms of parabolas 5. Max/min problems	1. Identifying the objective function and constraints; solving linear programming problems 2. Solving three-variable linear systems using substitution, elimination and inverse matrices 3. Deciding when to use quadratic as opposed to linear regression; using the TI-83 to calculate the quadratic regression model 4. Finding the maximum or minimum value of a parabola algebraically and using the calculator	Quizzes/Tests:  open response, problems Writing assignment:  Choosing a regression model	What are the parts of a linear programming problem? How do you determine which regression model best fits a set of data? What are the properties of parabolas? How do find the maximum or minimum of a parabola?
December	1. Factoring 2. Quadratic equations 3. The discriminant 4. Imaginary numbers 5. Inverse and square root functions 6. Properties of exponents 7. Power functions and their inverses	1. Factoring quadratic expressions 2. Solving quadratic equations by factoring, square roots, completing the square, and the quadratic formula 3. Using the discriminant to determine the number and type of solutions to a quadratic equation 4. Defining imaginary numbers; finding imaginary solutions to quadratic equations 5. Understanding the relationship between a function and its inverse; finding the inverse of a quadratic function 6. Using the properties of exponents to simplify algebraic expressions 7. Finding the inverse of a power function; determining if a power function is even or odd; using inverse functions to solve power functions; recognizing extraneous solutions	Quizzes/Tests:  open response, problems	What are the steps to factoring trinomials? What are the methods that can be used to solve quadratic equations, and when should each be used? What is an imaginary number? What are the properties of exponents? What are the steps to solving equations with exponents and roots?
January	1. Polynomial equations 2. Linear factors of polynomials 3. Polynomial division 4. Combinations 5. Pascal’s Triangle and the binomial theorem 6. Probability of combinations	1. Classifying polynomial functions; identifying end behavior; modeling data with cubic and quartic regression 2. Expressing a polynomial in factored form; finding the relative minimum and maximum of a polynomial function; the factor theorem; volume word problems 3. Dividing polynomials using long division and synthetic division 4. Deciding to use permutations or combinations; finding combinations 5. Using Pascal’s Triangle or the binomial theorem to expand polynomials to the n^th degree 6. Using the binomial theorem to calculate probability	Quizzes/Tests:  open response, problems	What are the steps for dividing polynomials using either long division or synthetic division? What is the difference between a combination and a permutation? How can Pascal’s Triangle or the Binomial Theorem be used to expand binomials? How can the Binomial Theorem be applied to solving probability problems?
February	1. Exponential modeling 2. Logarithmic functions as  inverses 3. Properties of logarithms 4. Exponential and logarithmic equations 5. Natural logarithms	1. Using algebraic equations and the TI-83 to model exponential situations such as population growth or decline, compound interest, continuously compounded interest, and half-life 2. Using logarithmic notation; evaluating log expressions; graphing log functions 3. Simplifying and expanding log expressions; applying the properties of logs to solve equations 4. Solving exponential and logarithmic equations 5. Using natural logs to solve equations	Quizzes/Tests:  open response, problems	What are some applications of exponential equations? What is a logarithm? What are the properties of logarithms? What are the steps to solving exponential equations? What are the steps to solving logarithmic equations?
March	1. Inverse variation 2. Rational functions and their graphs 3. Operations with rational expressions 4. Rational equations	1. Identifying and solving inverse variation problems 2. Identifying vertical and horizontal asymptotes and holes; graphing inverse variations and rational functions 3. Multiplying, dividing, adding and subtracting rational expressions; finding the LCD 4. Solving rational equations	Quizzes/Tests:  open response, problems Project:  Comparing and contrasting direct, inverse and joint variation	What is the difference between direct and inverse variation? What are the steps for graphing rational functions? How do you find the LCM of polynomials? What are the steps for performing the four basic operations with rational expressions? What re the steps for solving rational equations?
April	1. Probability of multiple events 2. Periodic functions 3. The unit circle 4. Radian measure 5. Trigonometric functions 6. Right triangle trig 7. Law of Sines and Law of Cosines	1. Identifying independent and mutually exclusive events; finding the probability of multiple events 2. Recognizing periodic functions; parts of a periodic function 3. Drawing angles in standard position; reference angles; finding exact coordinates of points on the unit circle 4. Comparing degree and radian measure; converting between degree and radian measure; exact radian measure of common angles 5. Learning the properties of sine, cosine and tangent functions; graphing sine, cosine and tangent functions 6. Using sine, cosine and tangent ratios to solve right triangles and angle of elevation/depression problems 7. Using the Law of Sines and Law of Cosines to find missing triangle side and angle measures	Quizzes/Tests:  open response, problems Oral contest:  Unit circle facts Project:  Writing periodic functions to explain common natural phenomena such as tides	How do calculate and & or probability? What are the characteristics of periodic functions? What is the unit circle? How can reference angles and the unit circle be used to find the exact coordinates of points on the unit circle quickly? What are the properties of sine, cosine and tangent graphs?
May	1. Mathematical patterns 2. Arithmetic and geometric sequences 3. Arithmetic and geometric series 4. Conic sections 5. Parabolas	1. Writing the rule for a recursive sequence of numbers; finding the n^th term of a sequence based on the rule 2. Identifying and generating each type of sequence; finding the n^th or any term in each type of sequence; finding arithmetic and geometric means 3. Writing a series from a sequence; finding the sum of a series 4. Identifying conic sections: parabolas, circles, ellipses, hyperbolas 5. Finding the focus and directrix; graphing parabolas	Quizzes/Tests:  open response, problems	What is a recursive sequence? What is the difference between and arithmetic and geometric series? What is a conic section? What are the properties of parabolas as conic sections?
June	1. Circles 2. Ellipses 3. Hyperbolas 4. Translations of conic sections	1. Finding the center and radius of a circle; graphing a circle 2. Identifying the major and minor axis, the vertices and co-vertices, and the foci of an ellipse; graphing an ellipse with the center at the origin 3. Identifying the transverse axis, vertices and foci of a hyperbola; graphing a hyperbola with the center at the origin 4. Graphing conic sections with centers not at the origin	Quizzes/Tests:  open response, problems	What are the properties of circles? What are the properties of ellipses? What are the properties of hyperbolas? How do you graph a conic section whose center is not at the origin?