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Course Title: Algebra 2B Highly Qualified Teacher: Matt Goebel, Chris McCallum Advisor: Chris Burke, Matt Goebel, Josh Hansen, Molly Johnson, Karen MacDonald, Eric Magi, Chris McCallum, Amanda St. Pierre, Nathan Ziegler Dates of Class: 8/31/2015 – 6/15/2016 Credits: 0.50 Certificated Contact Method: In-person instructional contact Class Description: Building on their work with linear, quadratic, and exponential functions, students extend their repertoire of functions to include polynomial, rational, and trigonometric functions. Students work closely with the expressions that define the functions, and continue to expand and home their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using logarithms. Learning Materials: Aleks, Khan, Math XL Algebra 2. Holt McDougal. 2011 Computer & Internet Learning Goals: Numbers, Expressions, and Operations: A2.2.A explains how whole, integer, rational, real and complex numbers are related, and identifies the number systems within which a given algebraic equation can be solved A2.2.B uses the laws of exponents to simplify and evaluate numeric and algebraic expressions that contain rational exponents A2.2.C Adds, subtracts, multiplies, divides and simplifies rational and more general algebraic expressions Quadratic Functions and Equations: A2.3.A Translates between the standard form of a quadratic function, the vertex form, and the factored form; graphs and interprets the meaning of each form A2.3.B determines the number and nature of the roots of a quadratic function A2.3.C solves quadratic equations and inequalities, including equations with complex roots Exponential and Logarithmic Functions and Equations: A2.4.C solves exponential and logarithmic equations A2.4.A Knows and uses basic properties of exponential and logarithmic functions and the inverse relationship between them A2.4.B Graphs and exponential function of the form f(x) = abx and its inverse logarithmic Function. Additional Functions and Equations: A2.5.A Constructs new functions using the transformations f(x-h), f(x) + K, c (f(x)), and by adding and subtracting functions and describes the effect on the original graph(s) A2.5.B Plots points, sketches, and describes the graphs of square root functions and solves related equations A2.5.C Plots points, sketches, and describes the graphs of inverse variation functions and solves related equations A2.5.D Plots points, sketches, and describes the graphs and cubic functions and solves related Equations Probability, Data, and Distributions: A2.6.A applies the fundamental counting principle and the ideas of order and replacement to calculate probabilities in situations arising from two-stage experiments (compound events) A2.6.B given a finite sample space consisting of equally-likely outcomes and containing events A + B, determines whether A and B are independent, and finds the conditional probability of A given B A2.6.F Calculates and interprets measures of variability and standard deviation and uses these measures and the characteristics of the normal distribution to describe and compare data sets A2.6.C Computes permutations and combinations and uses the results to calculate probabilities Additional Key Content A2.7.A Solves systems of three equations with three variables College Readiness Standard 7.2 7.2.a Find the sum, difference, or product of two polynomials, then simplify the result. 7.2.b Factor out the greatest common factor from polynomials of any degree. 7.2.c Factor quadratic polynomials with integer coefficients into a product of linear terms. 7.2.d Simplify quotients of polynomials given in factored form, or in a form which can be factored. 7.2.e Add, subtract, multiply, and divide two rational expressions of the form, a/bx+ c, where a, b, and c are real numbers and B is non-zero and of the form p(x)/q(x ), where p(x) and q(x) are polynomials. College Readiness Standard 7.3 7.3.f Use a variety of strategies to solve quadratic equations including those with irrational solutions and recognize when solutions are non-real. Simplify complex solutions and check algebraically. Solve quadratic equations by completing the square and by taking roots. College Readiness Standard 8.2 8.2.b Describe relationship between the algebraic features of a function and the features of its graph and/or its tabular representation. 8.2.g Sketch the graph of a polynomial given the degree, zeros, max/min values, and /or initial conditions. College Readiness Standard 8.3 8.3.d Recognize and sketch, without the use of technology, the graphs of the following families of functions: linear, quadratic, cubic quartic, exponential, logarithmic, square root, cube root, absolute value, &rational functions of the type f(x)=1/(x-a). 8.3.e Understand the relationship between the degree of a polynomial and the number of roots; interpret the multiplicity of roots graphically. College Readiness Standard 8.4 8.4 Model situations and relationships using a variety of basic functions (linear, quadratic, logarithmic, exponential, and reciprocal) and piecewise-defined functions. Performance Objectives: Student will: Extend their understanding of number systems and solutions to equations to include the entire complex number system. Understand non-real roots to quadratic equations. Make use of the vertex form of quadratic equations. Understand inverse functions through the application of logarithms. Use these functions to algebraically and graphically model and solve practical problems. Use transformations to construct and graph new functions. Apply counting principles to calculate probabilities. Calculate and interpret measures of variability among data sets. Learning Activities: Unit 3: Exponents & Polynomial Expressions, Quadratic & Polynomial Functions 9 Weeks Complete 25% of all topics Complete ALL Unit 1 Worksheets Complete ALL Unit 1 Assessments Complete Unit 1 Notebook Review Unit 4: Radicals and Advanced Functions, Exponential and Logarithmic Functions, Rational Expressions, Conic Sections, Sequences of Probability 9 Weeks Complete 25% of all topics Complete ALL Unit 1 Worksheets Complete ALL Unit 1 Assessments Complete Unit 1 Notebook Review Progress Criteria/Methods of Evaluation: Units are arranged so that students work through the math program to master the ‘I can’ statements for each target. Once they have gained the skill they will then complete activities for each target that requires them to apply their skills to real – world problems. The unit is then completed with an assessment of both skills and application problems. • Work in ALEKS/Khan/Math XL/Holt • Quizzes through ALEKS/Khan/Math XL/Holt • Activity completion • Unit Assessment By completing Progress assessments and summative assessments, students will show evidence of understanding of the learning goals. CEDARS Codes: 02056 Algebra II 02056 (9-12) District Code: 3353A