Shelton School District Applied Algebra 2 Unit Name: Fundamentals of Algebra Instructional Days: 5 CCSS-M A-REI.A1 A-REI.D11 N-Q.A2 A-CED.A1 2014-2015 School Year Lesson & objective F-IF.C7 F-LE.A2 F-LE.B5 CCSS.Math.Content.HSN-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.A.2 Define appropriate quantities for the purpose of descriptive modeling. A-REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A-REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★ F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ F-LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a HC CORD 1.1, 1.2, 1.4, 1.5 *Solve equations *Know definitions of the number systems *Use reasoning to determine inclusion/exclusion of a given solution within number systems * Make connections between number systems *Find rate of change in linear equations *Graph linear equations and inequalities [September] Days 1-2 Formative Assessments (CORD Pg22) Mixed Review, #34-37 Assignments/Notes Allow 3 days for formative and summative assessments Complex Numbers will be addressed again in Exponents Unit Need supplemental materials that connect algebraic solutions and number systems 2 (CORD Pg22) Mixed Review, #38-41 Need supplemental materials that connect algebraic solutions and number systems 1 Shelton School District Applied Algebra 2 2014-2015 School Year relationship, or two input-output pairs (include reading these from a table). F-LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context. Standards for Mathematical Practice Addressed: CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them; CCSS.Math.Practice.MP4 Model with mathematics; CCSS.Math.Practice.MP5 Use appropriate tools strategically Assessment: (type) 2 Shelton School District Unit Name: Unit Name: Systems of Equations and Inequalities CCSS-M Applied Algebra 2 2014-2015 School Year [Instructional Days: 12] [September] Lesson & objective Days Formative Assessments/ Assignments CORD p100 Ch. Review, #1-8 HC CORD 2.1-2.2 Understand systems of equations 4-5 CCSS.Math.Content.HSN-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. HC CORD 2.3-2.4 Understand systems of inequalities 4-5 CORD p100 Ch. Review, #9-11 CCSS.Math.Content.HSA-REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. HC CORD 2.1-2.5 Determine the appropriate procedure for solving a given problem 2 (see above, and add #12-15) HC CORD 2.1,2.3 Solve systems of equations/ inequalities using graphs 4.2 HC CORD 2.2,2.3 Solve systems of equations/ inequalities using substitution 4.2 HC CORD 2.2,2.3 Solve systems of equations/ inequalities using elimination HC CORD 2.1-2.5 Analyze problem situations (see above) (see above) (see above) (see above) (see above) (see above) (see above) CORD p100 Ch. Review, #12-15 N-Q.A2 A-REI.C6,7 Alignment Notes Allow 3 days for formative and summative assessments *Include word problems CCSS.Math.Content.HSA-REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3. **Allow 4-5 days for assessments Standards for Mathematical Practice Addressed: CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them; CCSS.Math.Practice.MP4 Model with mathematics; CCSS.Math.Practice.MP5 Use appropriate tools strategically 3 Shelton School District Unit Name: Systems of 3 Equations CCSS-M Transition Applied Algebra 2 2014-2015 School Year [Instructional Days: 7] [] Lesson & objective HC CORD 2.5 Understand systems of three equations Days HC CORD 2.5 Solve systems of three equations using elimination (See Systems of Equations) (see above) HC CORD 2.5 Solve systems of three equations using substitution (see above) HC CORD 2.5 Solve systems of three equations using elimination (see above) HC CORD 2.5 Analyze problem situations (see above) HC CORD 3.1-3.5 Solve systems of three equations using matrices 7 Formative Assessments/ Assignments (See Systems of Equations) Alignment Notes Allow 3 days for formative and summative assessments CORD p148-149 Ch. Review, #1-11 Standards for Mathematical Practice Addressed: CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them; CCSS.Math.Practice.MP4 Model with mathematics; CCSS.Math.Practice.MP5 Use appropriate tools strategically Assessment: (type) 4 Shelton School District Applied Algebra 2 Unit Name: Functions 2014-2015 School Year Instructional Days: 12 CCSS-M Lesson & objective October Days Formative Assessments CORD p196-197 Ch. Review, #1-9 HC CORD 4.1, 4.2 Model problems using functions and equations 3 CCSS.Math.Content.HSF-BF.A.1b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. HC CORD 4.1, 4.2 Justify functions and equations that model problems (see (see above) above) CCSS.Math.Content.HSF-BF.B.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. 6.3,6.4 HC CORD 4.1, 4.2 Analyze problem situations (see (see above) above) CCSS.Math.Content.HSF-BF.B.4 Find inverse functions HC CORD 4.4 Solve problems involving special functions HC CORD 4.1, 4.2 Model problems using functions and equations 6.3,6.4 HC CORD 4.5 Make connections between changes in equations and changes in their graphs 6.3,6.4 HC CORD 4.5 Use identifiable terms within equations to predict 2 CORD p196-197 Ch. Review, #1012 2-3 CORD p196-197 Ch. Review, #14 F-BF.A1b F-BF.B3 F-BF.B4 N-Q.A2 F-IF.A3 F-IF.C7 F-IF.C9 FBF.B3,4a CSS.Math.Content.HSN-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. CCSS.Math.Content.HSF-IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. CCSS.Math.Content.HSF-IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. Assignments/ Notes Allow 3 days for formative and summative assessments (see (see above) above) 5 Shelton School District Applied Algebra 2 CCSS.Math.Content.HSF-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ CCSS.Math.Content.HSF-IF.C.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 quadratic function and an algebraic expression for another, say which has the larger maximum. changes in graphs 6.3,6.4 HC CORD 4.5 Perform translations, dilations and reflections on the coordinate plane HC CORD 4.2 Construct new functions by adding and subtracting functions 2014-2015 School Year (see (see above) above) (see (see above) above) Use CME p 501 #7; p518 #1; p181 #6 CCSS.Math.Content.HSF-BF.B.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. CCSS.Math.Content.HSF-BF.B.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 x3 or f(x) = (x+1)/(x–1) for x ≠ 1 Standards for Mathematical Practice Addressed: CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them; CCSS.Math.Practice.MP4 Model with mathematics; CCSS.Math.Practice.MP7 Look for and make use of structure. Assessment: (type) 6 Shelton School District Unit Name: Exponents and Complex Numbers Applied Algebra 2 Instructional Days: 12 CCSS-M Transition N-RN.A1 N-RN.A2 A-SSE.B3 A-REI.A2 N-Q.A2 2014-2015 School Year NCN.A1,2 N-RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5. Lesson & objective Days HC CORD 5.1,5.2 Understand and apply the laws of exponents 3-4 HC CORD 5.3 Make connections between rational exponents and radicals 2 HC CORD 5.1,5.2,5.3,5.4 Simplify exponential and radical expressions (8-9 total) HC CORD 5.1,5.2,5.3,5.4 Evaluate exponential and radical expressions HC CORD 5.1,5.2,5.3,5.4 Determine the appropriate rule(s) for simplifying a given expression HC CORD 5.5 Make connections between number systems HC CORD 5.5 Describe the number system(s) (see above) Formative Assessments Assignments/Notes Allow 3 days for formative and summative assessments CORD p238 Ch. Review, #1-8 (Complex numbers addressed previously) N-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ . N-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. SN-CN.A.1 Know there is a complex number i such that i2 = – 1, and every complex number has the form a + bi with a and b (see above) 2-3 (see CORD p238-239 above) Ch. Review, #107 Shelton School District real. Applied Algebra 2 appropriate to the solution of an algebraic equation 2014-2015 School Year 15 SN-CN.A.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers Standards for Mathematical Practice Addressed: CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them; CCSS.Math.Practice.MP4 Model with mathematics; CCSS.Math.Practice.MP7 Look for and make use of structure. Assessment: (type) 8 Shelton School District Applied Algebra 2 Unit Name: Quadratics CCSS-M Transition A-SSE.B3 N-Q.A2 A-CED.A1 A-REI.B4 F-IF.C8 N-CN.C7 A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ N-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.A.2 Define appropriate quantities for the purpose of descriptive modeling. A-REI.B.4 Solve quadratic equations in one variable. F-IF.C.9 Compare properties of two functions each represented in a 2014-2015 School Year Instructional Days: 28 Lesson & objective [MBA 1: Nov.18-22] Days HC CORD 6.1, 6.2, 6.3, 6.4 Make connections between and represent quadratic functions in standard, vertex and factored forms and in graphs; HC CORD 6.1, 6.2, 6.3, 6.4, 6.5, 6.6 Find the minimum, line of symmetry, and roots for quadratic equations in standard form HC CORD 6.1, 7.3 Find maxima/minima using quadratic functions in vertex form HC CORD 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 7.3 Use mathematical reasoning to analyze advantages of the forms of quadratic equations (15 total) HC CORD 6.5 Use the discriminant to (see above) Formative Assessments CORD p282 Ch. Review, #1-9 (see above) Assignments/Notes Allow 3 days for formative and summative assessments Supplement with Prentice-Hall Algebra 2 Ch. 5 (see above) (see above) different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. N-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions. CORD p267 Lesson 9 Shelton School District Applied Algebra 2 determine the number and nature of the roots of a quadratic equation HC CORD 6.6 Understand the connections between quadratic roots and complex numbers HC CORD 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 7.3 Understand and apply quadratic inequalities 2014-2015 School Year Assessment, #3-5 (see above) 3 Does not appear in materials Supplement with Prentice-Hall Algebra 2, Lesson 5-8 and Activity Lab p296; also PH Algebra 1 if needed Standards for Mathematical Practice Addressed: CCSS.Math.Practice.MP2 Reason abstractly and quantitatively; CCSS.Math.Practice.MP5 Use appropriate tools strategically; CCSS.Math.Practice.MP7 Look for and make use of structure; Assessment: (type) 10 Shelton School District Unit Name: Exponential and Logarithmic Functions Applied Algebra 2 Instructional Days: 13 CCSS-M Transition A-REI.D11 N-Q.A2 A-CED.A1 F-IF.C7 F-LE.B5 2014-2015 School Year F-IF.C8 F-IF.C9 F-LE.A2 F-LE.A4 Lesson & objective HC CORD 8.1,8.5,8.6 Understand exponential functions and equations [Start Benchmark 2—Nov. 25] Days 5 A-REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★ HC CORD 8.2,8.3,8.4 4 Understand logarithmic functions and equations N-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. HC CORD 8.1,8.2,8.3,8.4 Understand the inverse relationship of exponential and logarithmic functions (see above) HC CORD 8.1,8.2,8.3,8.4 Evaluate exponential and logarithmic expressions (see above) A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.A.2 Define appropriate quantities for the purpose of descriptive modeling. F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ F-IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the HC CORD Formative Assessments CORD p386-387 Ch. Review, #1-3, 12-15 Assignments/Notes Allow 3 days for formative and summative assessments CORD p386-387 Ch. Review, #4-11 (see above) 11 Shelton School District Applied Algebra 2 function. 8.1,8.2,8.3,8.4, 8.5 Understand exponential functions and equations F-IF.C.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 quadratic function and an algebraic expression for another, say which has the larger maximum. SF-LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). SF-LE.A.4 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. 2014-2015 School Year HC CORD 8.1,8.2,8.3,8.4, 8.5 Graph exponential and logarithmic expressions HC CORD 8.5 Understand exponential functions and equations; Understand logarithmic functions and equations HC CORD 8.5 Use the inverse relationship of exponential and logarithmic functions to solve equations (see above) (see above) (see above) CCSS.Math.Content.HSF-LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context. CCSS.Math.Content.HSF-LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context. Standards for Mathematical Practice Addressed: CCSS.Math.Practice.MP4 Model with mathematics; CCSS.Math.Practice.MP5 Use appropriate tools strategically; CCSS.Math.Practice.MP6 Attend to precision. Assessment: (type) 12 Shelton School District Unit Name: Polynomials Applied Algebra 2 Instructional Days: Day 20 CCSS-M Transition A-SSE.A2 A-SSE.B3 A-APR.B2 A-APR.B3 F-IF.B4 F-IF.B6 -- NEEDS SUPPLEMENTS N-Q.A2 AAPR.D6 F-IF.C7 F-IF.C9 A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★ Lesson & objective Days HC CORD 9.1-9.3 Operations with nth degree polynomials 6 2 2014-2015 School Year [MBA 2—Feb. 10-14] Formative Assessments CORD p426-7 Ch Review,, #1-9 CORD p426-7 Ch Review,, #10-12 Assignments/Notes Allow 3 days for formative and summative assessments Supplement with Prentice-Hall Algebra 2 Lesson 6.4 A-APR.B.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). A-APR.B.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. F-IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★ F-IF.B.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.★ A-APR.D.6 Rewrite simple rational expressions in different forms; write a(x)/ r(x)/ b(x) in the form q(x) + b(x), where a(x), b(x), q(x), and r(x) are 13 Shelton School District Applied Algebra 2 2014-2015 School Year polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. N-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ F-IF.C.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 quadratic function and an algebraic expression for another, say which has the larger maximum. Standards for Mathematical Practice Addressed: 2, 3, 7, 8CCSS.Math.Practice.MP2 Reason abstractly and quantitatively; CCSS.Math.Practice.MP7 Look for and make use of structure; CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning. 14 Shelton School District Applied Algebra 2 Unit Name: Rational Functions A-REI.D11 F-BF.A1b A-SSE.A2 N-Q.A2 CCSS-M A-APR.D6 A-CED.A1 F-IF.C7 F-IF.C9 CCSS.Math.Content.HSA-SSE.A.2 Use the structure of an expression to identify ways to rewrite it.For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). CCSS.Math.Content.HSN-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. CCSS.Math.Content.HSA-APR.D.6 Rewrite simple rational expressions in different forms; writea(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree ofr(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. CCSS.Math.Content.HSA-REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★ CCSS.Math.Content.HSF-BF.A.1b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Instructional Days: 19 2014-2015 School Year [February-March] 2.12,2.13,2.15 (see HC CORD above) 10.2,10.3,10.4 Understand factoring of rational and general algebraic expressions Simplify rational and general algebraic expressions; Multiply/divide rational and general algebraic expressions 2.15 (see HC CORD 10.3 above) Find common denominators of rational expressions; Add/subtract rational and general algebraic expressions 15 Shelton School District Applied Algebra 2 CCSS.Math.Content.HSA-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CCSS.Math.Content.HSF-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ CCSS.Math.Content.HSF-IF.C.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 quadratic function and an algebraic expression for another, say which has the larger maximum. HC CORD 10.6 Understand and apply inverse variations; Write inverse variation equations; Solve inverse variation equations for the missing value 6.2—(minimal treatment) HC CORD 10.1 Identify and describe graphs of rational functions 6.2—(minimal treatment) HC CORD 10.1 Identify asymptotes and points of discontinuity in graphs of rational functions 6.2—(minimal treatment) HC CORD 10.1 Sketch graphs of rational functions 2014-2015 School Year 1 HC CORD p471 Ch. Review, #13 2 (see above) (see above) Standards for Mathematical Practice Addressed: CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them; CCSS.Math.Practice.MP4 Model with mathematics; CCSS.Math.Practice.MP5 Use appropriate tools strategically. 16 Shelton School District Unit Name: Sequences and Series Applied Algebra 2 Instructional Days: 9 CCSS-M A-SSE.B4 F-BF.A1a F-BF.A2 N-Q.A2 F-IF.A3 F-LE.A2 CCSS.Math.Content.HSF-BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation from a context. CCSS.Math.Content.HSF-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.★ CCSS.Math.Content.HSA-SSE.B.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.★ CCSS.Math.Content.HSN-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. CCSS.Math.Content.HSF-IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. CCSS.Math.Content.HSF-LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Lesson & objective Days 7.10,7.11 HC CORD 11.1 Distinguish between explicit and recursive formulas; Express arithmetic and geometric sequences in both explicit and recursive forms 1 7.10,7.11 HC CORD 11.2, 11.3 Distinguish between an arithmetic and geometric series.; 5 7.10,7.11 HC CORD 11.2, 11.3 Find the terms and partial sums of an arithmetic or a geometric series. (see above) 7.12 HC CORD 11.4 Find the infinite sum of a geometric series 3 2014-2015 School Year [March-April] Formative Assessments HC CORD p514 Ch. Review, #1-3 Assignments/Notes Allow 3 days for formative and summative assessments HC CORD p514 Ch. Review, #4-9 HC CORD p515 Ch. Review, #1012 Standards for Mathematical Practice Addressed: CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them; CCSS.Math.Practice.MP7 Look for and make use of structure; CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning. 17 Shelton School District Unit Name: Sequences and Series Applied Algebra 2 Instructional Days: 9 CCSS-M A-SSE.B4 F-BF.A1a F-BF.A2 N-Q.A2 F-IF.A3 F-LE.A2 CCSS.Math.Content.HSF-BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation from a context. CCSS.Math.Content.HSF-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.★ CCSS.Math.Content.HSA-SSE.B.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.★ CCSS.Math.Content.HSN-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. CCSS.Math.Content.HSF-IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. CCSS.Math.Content.HSF-LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Lesson & objective Days 7.10,7.11 HC CORD 11.1 Distinguish between explicit and recursive formulas; Express arithmetic and geometric sequences in both explicit and recursive forms 1 7.10,7.11 HC CORD 11.2, 11.3 Distinguish between an arithmetic and geometric series.; 5 7.10,7.11 HC CORD 11.2, 11.3 Find the terms and partial sums of an arithmetic or a geometric series. (see above) 7.12 HC CORD 11.4 Find the infinite sum of a geometric series 3 2014-2015 School Year [March-April] Formative Assessments HC CORD p514 Ch. Review, #1-3 Assignments/Notes Allow 3 days for formative and summative assessments HC CORD p514 Ch. Review, #4-9 HC CORD p515 Ch. Review, #1012 Standards for Mathematical Practice Addressed: CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them; CCSS.Math.Practice.MP7 Look for and make use of structure; CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning. 18 Shelton School District Applied Algebra 2 2014-2015 School Year Instructional Days: Day 15 Unit Name: Statistics CCSS S-IC.B3,4,5,6 Lesson & objective [April-May] Days Formative Assessments/ Assignments Alignment Notes Create histograms of binomial distributions 1 Allow 3 days for formative and summative assessments Use Make connections between exponential functions and bivariate data 1 CORD Unit 19 w/ supplement from Integrated 3 text, Ch. 6 (6.2-6.3) and Prentice Hall Algebra 2 S-ID.B6 S-IC.A1 S-ID.A4 CCSS.Math.Content.HSS-IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. CCSS.Math.Content.HSS-IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. **Need supplemental materials—see Integrated 3 & Integrated 2 texts CCSS.Math.Content.HSS-IC.B.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. CCSS.Math.Content.HSS-IC.B.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. CCSS.Math.Content.HSS-IC.B.6 Evaluate reports based on data. CCSS.Math.Content.HSS-ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. CCSS.Math.Content.HSS-ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. Make connections between quadratic functions and bivariate data Use regression to find the equation of a function. 1 1 Supplement w/ Integrated Math 3, Ch. 6 Supplement w/ Integrated Math 3, Ch. 6 19 Shelton School District Applied Algebra 2 2014-2015 School Year Understand standard deviation and Know that range and standard deviation are measures of variability. Know the characteristics of a normal curve 3 CORD Unit 19 w/ supplement from Integrated 3 text, Ch. 6 (6.2-6.3) (see above) Calculate range and standard deviation for a given data set Compare and contrast data sets using normal distributions Make predictions using normal distributions (see above) Calculate margin of error Use margin of error to evaluate characteristics of the sample (see above) Supplement w/ Prentice-Hall Algebra 2 Lesson 12.4 & 12.7 Supplement w/ Integrated Math 3 Supplement w/ Integrated Math 3, Ch. 6 Supplement w/ Integrated Math 3, Ch. 6 Use Prentice-Hall Algebra 2 Lesson 12.5 (see above) (see above) Assessment: (type) Standards for Mathematical Practice Addressed: CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others; CCSS.Math.Practice.MP4 Model with mathematics. 20 Shelton School District Applied Algebra 2 2014-2015 School Year 21 Shelton School District Unit Name: Trigonometric Functions WA Standards CCSS-M Transition Applied Algebra 2 Instructional Days: Day 123 – 145 Lesson & objective Days 2014-2015 School Year [MBA #3—Apr. 28-May 02] Formative Assessments Assignments/Notes 22 Shelton School District Applied Algebra 2 2014-2015 School Year 23 Shelton School District Applied Algebra 2 2014-2015 School Year 24 Shelton School District Applied Algebra 2 2014-2015 School Year 25 Shelton School District Applied Algebra 2 2014-2015 School Year 26 Shelton School District Applied Algebra 2 2014-2015 School Year Process Standards Addressed: Assessment: (type) 27 Shelton School District Applied Algebra 2 2014-2015 School Year 28
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