# Georgia Standards of Excellence Curriculum Map. Mathematics. Accelerated GSE Geometry B / Algebra II

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1 Georgia Standards of Excellence Curriculum Map Mathematics Accelerated GSE Geometry B / Algebra II These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

2 Georgia Department of Education Accelerated GSE Geometry B/Algebra II Curriculum Map 1 st Semester 2 nd Semester Unit 1 (5 6 weeks) Circles and Volume MGSE9-12.G.C.1 MGSE9-12.G.C.2 MGSE9-12.G.C.3 MGSE9-12.G.C.4 MGSE9-12.G.C.5 MGSE9-12.G.GMD.1 MGSE9-12.G.GMD.2 MGSE9-12.G.GMD.3 MGSE9-12.G.GMD.4 Unit 2 Geometric and Algebraic Connections MGSE9-12.G.GPE.1 MGSE9-12.G.GPE.4 MGSE9-12.G.GPE.5 MGSE9-12.G.GPE.6 MGSE9-12.G.GPE.7 MGSE9-12.G.MG.1 MGSE9-12.G.MG.2 MGSE9-12.G.MG.3 Unit 3 Applications of Probability MGSE9-12.S.CP.1 MGSE9-12.S.CP.2 MGSE9-12.S.CP.3 MGSE9-12.S.CP.4 MGSE9-12.S.CP.5 MGSE9-12.S.CP.6 MGSE9-12.S.CP.7 Unit 4 (2 3 weeks) Quadratics Revisited MGSE9-12.N.CN.1 MGSE9-12.N.CN.2 MGSE9-12.N.CN.3 MGSE9-12.N.CN.7 MGSE9-12.N.CN.8 MGSE9-12.A.REI.4 MGSE9-12.A.REI.4b MGSE9-12.N.RN.1 MGSE9-12.N.RN.2 Unit 5 (2 3 weeks) Operations With Polynomials MGSE9-12.A.APR.1 MGSE9-12.A.APR.5 MGSE9-12.A.APR.6 MGSE9-12.F.BF.1 MGSE9-12.F.BF.1b MGSE9-12.F.BF.1c MGSE9-12.F.BF.4 MGSE9-12.F.BF.4a MGSE9-12.F.BF.4b MGSE9-12.F.BF.4c Unit 6 Polynomial Functions MGSE9-12.N.CN.9 MGSE9-12.A.SSE.1 MGSE9-12.A.SSE.1a MGSE9-12.A.SSE.1b MGSE9-12.A.SSE.2 MGSE9-12.A.APR.2 MGSE9-12.A.APR.3 MGSE9-12.A.APR.4 MGSE9-12.F.IF.4 MGSE9-12.F.IF.7 MGSE9-12.F.IF.7c Unit 7 (4 5 weeks) Rational & Radical Relationships MGSE9-12.A.APR.7 MGSE9-12.A.CED.1 MGSE9-12.A.CED.2 MGSE9-12.A.REI.2 MGSE9-12.F.IF.4 MGSE9-12.F.IF.5 MGSE9-12.F.IF.7 MGSE9-12.F.IF.7b MGSE9-12.F.IF.7d Unit 8 Exponential & Logarithms MGSE9-12.A.SSE.3 MGSE9-12.A.SSE.3c MGSE9-12.F.IF.7 MGSE9-12.F.IF.7e MGSE9-12.F.IF.8 MGSE9-12.F.IF.8b MGSE9-12.F.BF.5 MGSE9-12.F.LE.4 Unit 9 Mathematical Modeling MGSE9-12.A.SSE.4 MGSE9-12.A.CED.1 MGSE9-12.A.CED.2 MGSE9-12.A.CED.3 MGSE9-12.A.CED.4 MGSE9-12.A.REI.11 MGSE9-12.F.IF.6 MGSE9-12.F.IF.9 MGSE9-12.F.BF.3 These units were written to build upon concepts from prior units, so later units contain tasks that depend upon the concepts addressed in earlier units. All units will include the Mathematical Practices and indicate skills to maintain. NOTE: Mathematical standards are interwoven and should be addressed throughout the year in as many different units and tasks as possible in order to stress the natural connections that exist among mathematical topics. Grade 9-12 Key: Number and Quantity Strand: RN = The Real Number System, Q = Quantities, CN = Complex Number System, VM = Vector and Matrix Quantities Algebra Strand: SSE = Seeing Structure in Expressions, APR = Arithmetic with Polynomial and Rational Expressions, CED = Creating Equations, REI = Reasoning with Equations and Inequalities Functions Strand: IF = Interpreting Functions, LE = Linear and Exponential Models, BF = Building Functions, TF = Trigonometric Functions Geometry Strand: CO = Congruence, SRT = Similarity, Right Triangles, and Trigonometry, C = Circles, GPE = Expressing Geometric Properties with Equations, GMD = Geometric Measurement and Dimension, MG = Modeling with Geometry Statistics and Probability Strand: ID = Interpreting Categorical and Quantitative Data, IC = Making Inferences and Justifying Conclusions, CP = Conditional Probability and the Rules of Probability, MD = Using Probability to Make Decisions July 2016 Page 1 of 5

4 MGSE9-12.G.GMD.4 Identify the shapes of twodimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. Georgia Department of Education also belong to A, and interpret the answer in context. MGSE9-12.S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) P(A and B), and interpret the answers in context. July 2016 Page 3 of 5

6 functions MGSE9-12.F.BF.4 Find inverse functions. MGSE9-12.F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2(x 3 ) or f(x) = (x+1)/(x-1) for x 1. MGSE9-12.F.BF.4b Verify by composition that one function is the inverse of another. MGSE9-12.F.BF.4c Read values of an inverse function from a graph or a table, given that the function has an inverse. identity (x 2 + y 2 ) 2 = (x 2 y 2 ) 2 + (2xy) 2 can be used to generate Pythagorean triples. Interpret functions that arise in applications in terms of the context MGSE9-12.F.IF.4 Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Analyze functions using different representations MGSE9-12.F.IF.7 Graph functions expressed algebraically and show key features of the graph both by hand and by using technology. MGSE9-12.F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Georgia Department of Education maximums and minimums; symmetries; end behavior; and periodicity. Interpret functions that arise in applications in terms of the context MGSE9-12.F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. Analyze functions using different representations MGSE9-12.F.IF.7 Graph functions expressed algebraically and show key features of the graph both by hand and by using technology. MGSE9-12.F.IF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. MGSE9-12.F.IF.7d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. Construct and compare linear, quadratic, and exponential models and solve problems MGSE9-12.F.LE.4 For exponential models, express as a logarithm the solution to ab (ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. f(x) = g(x) is the x-value where the y- values of f(x) and g(x) are the same. Interpret functions that arise in applications in terms of the context MGSE9-12.F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. MGSE9-12.F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one function and an algebraic expression for another, say which has the larger maximum. Build new functions from existing functions MGSE9-12.F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. July 2016 Page 5 of 5

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