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Algebra II Calendar 2013-2014 August Monday Tuesday Wednesday Thursday Friday 1 2 5 6 7 8 9 12 13 14 15 16 In-Service Day In-Service Day In-Service Day 1st Day Procedures F.BF.2 (See 8/19) F.LE.2 (See 8/20) Analyze Arithmetic Sequences pg 802-809 Sec 12.2 1 day 19 20 21 22 23 F.LE.2 (See 8/20) F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Graph Arith Sequence pg 802-809 Sec 12.2 1 day F.BF.2 (See 8/19) A.SSE.4 (See 8/21) F.LE.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). Analyze Geometric Sequence pg 810-819 Sec 12.3 1 day F.BF.2 (See 8/19) F.LE.2 (See 8/20) A.SSE.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. Geometric Sequences (Graphing) pg 810-819 Sec 12.3 1 day F.BF.2 (See 8/19) F.LE.2 (See 8/20) A.SSE.4 (See 8/21) Geometric Series pg 810-819 Sec 12.3 LTF: TAPP, p. 20 1 day F.LE.2 (See 8/20) Find Sums of Infinite Geometric Series pg 820-826 Sec 12.4 1 day 29 30 26 27 F.BF.1 (See 8/27) F.IF.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. F.IF.3 (See 8/26) F.BF.1 Write a function that describes a relationship between two quantities. Use Recursive Rules w/ Seq & Functions pg 827-833 Sec 12.5 Day 2 28 Review Test Labor Day Use Recursive Rules w/ Seq & Functions pg 827-833 Sec 12.5 2 days AI: Alien Invasion ASTG: And So They Grow AWLF: Another Way to Look at Factoring AWQF: Accumulation with Quadratic Function CTS: Completing the Square EFE: Exponential Functions Exploration ENLF: Exponential & Natural Logarithmic Functions GT: Graphical Transformation IAUC: Investigating Area Under a Curve IIN: Introducing Interval Notation PFC: Parent Function Charades QO: Quadratic Optimization RFOP: A Rational Function Optimization Problem RQ: Random Quadratics SPG: A Study of Population Growth SSLE: Solve Systems of Linear Equations TAPP: The Amusement Park Problem TPF: Transformations of Piecewise Functions WTL: Walk the Line Algebra II Calendar 2013-2014 September Monday Tuesday 2 Wednesday 3 Thursday 4 A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Solve Linear Systems by Graphing pg 153-158 Sec 3.1 LTF Mod 2: SSLE, p. 16 Supplemental Material s Needed 1 day In-Service Day Labor Day 9 10 11 A.REI.6 (See 9/4) Linear Applications pg 160-167 Sec 3.1 & 3.2 Additional Resources Needed Day 3 A.REI.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. Graph Systems of Linear Inequalities pg 168-177 Sec 3.3 1 day A.REI.11 (See 9/10) Solve Systems of Linear Equations in 3 Variables pg 178-185 Sec 3.4 2 days 16 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. Graph Quadratic Functions in Standard Form pg 236-243 Sec 4.1 1 day 17 F.BF.3 (See 9/16) Graph Quadratic Functions in Vertex or Intercept Form pg 245-251 Sec 4.2 3 days 18 F.BF.3 (See 9/16) Graph Quadratic Functions in Vertex or Intercept Form pg 245-251 Sec 4.2 Day 2 Friday 5 A.REI.6 (See 9/4) Solve Linear Systems Algebraically pg 160-167 Sec 3.2 3 days 6 A.REI.6 (See 9/4) Solve Linear Systems Algebraically pg 160-167 Sec 3.2 Day 2 12 A.REI.11 (See 9/10) Solve Systems of Linear Equations in 3 Variables pg 178-185 Sec 3.4 Day 2 19 F.BF.3 (See 9/16) Graph Quadratic Functions in Vertex or Intercept Form pg 245-251 Sec 4.2 McDougal On-line Supplemental Lesson: Theoretical & Reasonable Domain & Range LTF: AWQF, p. 33-34 QO Mod 9, p. 32 Day 3 23 24 25 26 G.GPE.2 Derive the equation of a parabola given a focus and directrix. Graph & Write Quadratic Functions in Vertex or Intercept Form pg 620-625 Sec 9.2 Translate & Classify Conics pg 650-657 Sec 9.6 1 day A.REI.4b Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. Solve x2+bx+c=0 By Factoring; Factor & Solve Polynomial Equations pg 252-258 Sec 4.3 1 day A.REI.4b (See 9/24) A.APR.4 (See 9/26) A.SSE.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). Solve ax2+bx+c=0 By Factoring; Factor & Solve Polynomial Equations pg 259-265 Sec 4.4/5.4 LTF: AWLF, p. 16 2 days A.REI.4b (See 9/24) A.SSE.2 (See 9/25) A.APR.4 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples. Solve ax2+bx+c=0 By Factoring; Factor & Solve Polynomial Equations pg 259-265 Sec 4.4/5.4 LTF: RQ, p. 44-45 Day 2 13 Quiz/Test 20 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 x3 for x > 0 or f(x) = (x+1)/(x–1) for x ≠ 1. Use Inverse Functions (Parabolas) pg 438-445 Sec 6.4 1 day 27 A.REI.4b (See 9/24) Solve Quadratic Equations By Finding Square Roots pg 266-271 Sec 4.5 1 day 30 Curriculum Adjustment AI: Alien Invasion ASTG: And So They Grow AWLF: Another Way to Look at Factoring AWQF: Accumulation with Quadratic Function CTS: Completing the Square EFE: Exponential Functions Exploration ENLF: Exponential & Natural Logarithmic Functions GT: Graphical Transformation IAUC: Investigating Area Under a Curve IIN: Introducing Interval Notation PFC: Parent Function Charades QO: Quadratic Optimization RFOP: A Rational Function Optimization Problem RQ: Random Quadratics SPG: A Study of Population Growth SSLE: Solve Systems of Linear Equations TAPP: The Amusement Park Problem TPF: Transformations of Piecewise Functions WTL: Walk the Line Algebra II Calendar 2013-2014 October Monday Tuesday Wednesday 1 7 Sec 4.7 8 G.GPE.2 Derive the equation of a parabola given a focus and directrix. Translate & Classify Conic Sections (Parabolas Only) pg 650-657 Sec 9.6 Additional Resources Needed 1 day 14 9 Weeks Test 21 AI: Alien Invasion ASTG: And So They Grow AWLF: Another Way to Look at Factoring AWQF: Accumulation with Quadratic Function CTS: Completing the Square 10 17 23 24 A.APR.3 (See 10/31) F.IF.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. Analyze Graphs of Polynomial Functions pg 387-392 Sec 5.8 LTF QO 1 day 30 31 A.APR.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). Apply the Remainder and Factor Theorems (Synthetic Only) pg 362-368 Sec 5.5 1 day A.APR.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. N.CN.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Find Rational Zeros; Apply Fundamental Theorem Algebra pg 370-386 Sec 5.6/5.7 3 days EFE: Exponential Functions Exploration ENLF: Exponential & Natural Logarithmic Functions GT: Graphical Transformation IAUC: Investigating Area Under a Curve IIN: Introducing Interval Notation 11 Review 18 Fall Break F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. Evaluate & Graph Polynomial Functions pg 337-344 Sec 5.2 1 day 29 Curriculum Adjustment 4 N.CN.7 (See 10/3) A.REI.4b Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. Complete the Square pg 284-291 Sec 4.7 LTF: CTS 2 days Review 16 22 28 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. 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 quadratic function and an algebraic expression for another, say which has the larger maximum. Describe and Compare Function Characteristics (Average Rate of Change: Even and Odd) CC9-CC16 Sec 8.6A LTF: IIN GT Mod 11, p.76-81 1 day 3 9 Weeks Test A.REI.4b (See 10/4) Graph & Solve Quadratic Inequalites pg 300-307 Sec 4.9 1 day Friday A.REI.4b (See 10/4) N.CN.7 Solve quadratic equations with real coefficients that have complex solutions. Use the Quadratic Formula and the Discriminant pg 292-299 Sec 4.8 LTF Mod 10: QO, p. 32 1 day 9 Curriculum Adjustment 15 Review A.REI.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. Solve Quadratic Systems pg 658-664 Sec 9.7 1 day 2 A.REI.4b (See 10/4) N.CN.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 real. N.CN.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Perform Operations with Complex Numbers pg 275-282 Sec 4.6 1 day Quiz/ MidChapter Test N.CN.7 (See 10/3) A.REI.4b (See 10/4) Complete the Square pg 284-291 Day 2 Thursday PFC: Parent Function Charades QO: Quadratic Optimization RFOP: A Rational Function Optimization Problem RQ: Random Quadratics SPG: A Study of Population Growth 25 Parent/Teacher Conference SSLE: Solve Systems of Linear Equations TAPP: The Amusement Park Problem TPF: Transformations of Piecewise Functions WTL: Walk the Line Algebra II Calendar 2013-2014 November Monday Tuesday Wednesday Thursday Friday 1 A.APR.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. N.CN.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Find Rational Zeros Apply Fundamental Theorem Algebra pg 370-386 Sec 5.6/5.7 Day 2 4 5 A.APR.3 & N.CN.9 (See 11/1) Find Rational Zeros Apply Fundamental Theorem Algebra (Parabolas Only) pg 370-386 Sec 5.6/5.7 Day 3 6 Review 7 F.BF.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. Perform Function Operations and Composition pg 428-434 Sec 6.3 2 days Quiz Test 8 F.BF.1b (See 11/7) Perform Function Operations and Composition pg 428-434 Sec 6.3 Day 2 11 12 13 14 15 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 x3 for x > 0 or f(x) = (x+1)/(x– 1) for x ≠ 1. Use Inverse Functions (Inverse of Rationals) pg 438-446 Sec 6.4 Additional Resources Needed 2 days F.BF.4a (See 11/11) Use Inverse Functions (Inverse of Rationals) pg 438-446 Sec 6.4 Additional Resources Needed Day 2 A.APR.6 Rewrite simple rational expressions in different forms; write a(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 of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. Apply the Remainder and Factor Theorems (Long Division) pg 362-368 Sec 5.5 1 day F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph Simple Rational Functions pg 558-563 Sec 8.2 LTF Mod 8: EFE 1 day A.APR.6 (See 11/13) Rewrite Rational Expressions CC5-CC6 Sec 8.2A 1 day 19 20 18 F.IF.7d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Graph General Rational Functions (Includes Slant Asymptote) pg 565-571 Sec 8.3 2 days F.IF.7d (See 11/18) Graph General Rational Functions (Includes Slant Asymptote) pg 565-571 Sec 8.3 LTF Mod 8: EFE Day 2 25 A.APR.6 (See 11/13) Add and Subtract Rational Expressions pg 582-588 Sec 8.5 Day 2 Curriculum Adjustment 26 A.APR.6 (See 11/13) Add and Subtract Rational Expressions pg 582-588 Sec 8.5 Day 3 AI: Alien Invasion ASTG: And So They Grow AWLF: Another Way to Look at Factoring AWQF: Accumulation with Quadratic Function CTS: Completing the Square EFE: Exponential Functions Exploration ENLF: Exponential & Natural Logarithmic Functions GT: Graphical Transformation IAUC: Investigating Area Under a Curve IIN: Introducing Interval Notation 21 A.APR.6 (See 11/13) Multiply and Divide Rational Expressions pg 573-580 Sec 8.4 1 day 27 22 A.APR.6 (See 11/13) Add and Subtract Rational Expressions pg 582-588 Sec 8.5 3 days 28 Thanksgiving PFC: Parent Function Charades QO: Quadratic Optimization RFOP: A Rational Function Optimization Problem RQ: Random Quadratics SPG: A Study of Population Growth SSLE: Solve Systems of Linear Equations TAPP: The Amusement Park Problem TPF: Transformations of Piecewise Functions WTL: Walk the Line 29 Algebra II Calendar 2013-2014 December Monday Tuesday Wednesday Thursday 2 3 4 A.REI.2 (See 12/3) A.REI.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. Solve Rational Functions pg 589 Sec 8.6 2 days A.REI.1 (See 12/2) A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Solve Rational Functions pg 589 Sec 8.6 LTF Mod 9 RFOP, p. 59-64 Day 2 A.REI.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. Solve Rational Inequalities pg 598 Sec 8.6 Extension 1 day 9 N.RN.1 (See 12/10) N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Evaluate Nth Roots and Use Rational Exponents pg 414 Sec 6.1 1 day Friday 5 Review 10 11 12 N.RN.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. Use and Apply Properties of Exponents pg 330/ pg 420 Sec 5.1/ 6.2 2 days N.RN.1 (See 12/10) Use and Apply Properties of Exponents pg 330/ pg 420 Sec 5.1/ 6.2 Day 2 N.RN.1 (See 12/10) Binomials Continuing Radicals Additional Resources Needed pg 420-427 Sec 6.2 McDougal On-line Supplemental Lessons: Binomials Containing Radicals Sum of Radicals Using Radicals 1 day 17 18 19 16 Review Review 23 Semester Test 24 6 Test Semester Test 25 13 Review 20 Semester Test 26 Winter Break, Dec. 23 - Jan. 7 30 31 Winter Break AI: Alien Invasion ASTG: And So They Grow AWLF: Another Way to Look at Factoring AWQF: Accumulation with Quadratic Function CTS: Completing the Square EFE: Exponential Functions Exploration ENLF: Exponential & Natural Logarithmic Functions GT: Graphical Transformation IAUC: Investigating Area Under a Curve IIN: Introducing Interval Notation PFC: Parent Function Charades QO: Quadratic Optimization RFOP: A Rational Function Optimization Problem RQ: Random Quadratics SPG: A Study of Population Growth SSLE: Solve Systems of Linear Equations TAPP: The Amusement Park Problem TPF: Transformations of Piecewise Functions WTL: Walk the Line 27 Algebra II Calendar 2013-2014 January Monday Tuesday Wednesday Thursday Friday 1 2 3 Winter Break 6 Record Day 7 8 9 10 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 x3 for x > 0 or f(x) = (x+1)/(x– 1) for x ≠ 1. Use Inverse Functions (radicals) pg 438-445 Sec 6.4 1 day F.IF.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. Graph Square & Cube Root Functions pg 446-451 Sec 6.5 1 day A.REI.2 (See 1/10) A.REI.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. Solve Radical Equations pg 452-459 Sec 6.6 2 days A.REI.1 (See 1/9) A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Solve Radical Equations pg 452-459 Sec 6.6 Day 2 14 15 16 13 A.REI.1 (See 1/9) A.REI.2 (See 1/10) Solve Radical Inequalities pg 462 Sec 6.6 Extension 1 day Curriculum Adjustment 20 MLK Jr Day Test 21 22 23 24 F.BF.3 (See 1/22) F.BF.1 (See 1/22) F.IF.7e (See 1/23) F.IF.4 (See 1/8) A.SSE.3c Use the properties of exponents to transform expressions for exponential functions. For example the 12t expression 1.15t can be rewritten as (1.151/12)12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. F.IF.8b Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay. F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context. Include Compound Interest; Graph Exponential Growth/ Decay Functions pg 478-491 CC2 Sec 7.1/ 7.2/ 7.2A LTF Mod 8: SPG, p. 27-32 Day 2 A.SSE.3c (See 1/21) F.IF.8b (See 1/21) F.LE.8.5(See 1/21) F.IF.7e (See 1/23) F.IF.4 (See 1/8) F.BF.1 Write a function that describes a relationship between two quantities. 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. Include Compound Interest; Graph Exponential Growth/ Decay Functions pg 478-491, CC2 Sec 7.1/ 7.2/ 7.2A LTF: SPG Mod 10, 27-32 Day 3 F.IF.4 (See 1/8) F.BF.5 (See 1/24) F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Use Functions Involving ‘e’ Interest Compounded Continuously (include graphing) pg 492-498 Sec 7.3 1 day F.BF.5 (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. Evaluate & Graph Log Functions pg 499-506 Sec 7.4 1 day 27 F.BF.5 (See 1/24) Evaluate & Graph Log Functions pg 499-506 Sec 7.4 LTF: ENLF Day 2 Review 17 A.SSE.3c (See 1/21) F.IF.8b (See 1/21) F.LE.5(See 1/21) F.BF.3 (See 1/22) F.BF.1 (See 1/22) F.IF.7e (See 1/23) F.IF.4 (See 1/8) Include Compound Interest; Graph Exponential Growth/ Decay Functions pg 478-491, CC2 Sec 7.1/ 7.2/ 7.2A LTF Mod 8: AI, p. 8-10 3 days 28 F.BF.5 (See 1/24) Supporting Other Objectives Apply Properties of Logs pg 507-514 Sec 7.5 1 day AI: Alien Invasion ASTG: And So They Grow AWLF: Another Way to Look at Factoring AWQF: Accumulation with Quadratic Function CTS: Completing the Square 29 30 31 A.CED.1 (See 1/30) A.REI.11 (See 1/31) F.LE.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. Solve Exponential & Logarithmic Equations pg 515-525 Sec 7.6 2 days F.LE.4 (See 1/29) A.REI.11 (See 1/31) A.CED.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. Solve Exponential & Logarithmic Equations pg 515-525 Sec 7.6 Day 2 A.REI.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. Inequalities pg 526-527 Sec 7.6 Extension 1 day EFE: Exponential Functions Exploration ENLF: Exponential & Natural Logarithmic Functions GT: Graphical Transformation IAUC: Investigating Area Under a Curve IIN: Introducing Interval Notation PFC: Parent Function Charades QO: Quadratic Optimization RFOP: A Rational Function Optimization Problem RQ: Random Quadratics SPG: A Study of Population Growth SSLE: Solve Systems of Linear Equations TAPP: The Amusement Park Problem TPF: Transformations of Piecewise Functions WTL: Walk the Line Algebra II Calendar 2013-2014 February Tuesday Wednesday Monday 3 4 F.IF.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. A.CED.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. S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models. Write & Apply Exponential and Power Functions pg 529-536 Sec 7.7 LTF: ASTG 1 day 5 Curriculum Adjustment 10 11 S.MD.5.b Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident. Define and Use Probability pg 698-704 Sec 10.3 1 day 17 18 S.CP.5 (See 2/18) S.CP.6 (See 2/18) S.CP.8 (See 2/18) S.CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. S.CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. Find Probabilities of Independent and Dependent Events pg 717-723 Sec 10.5 2 days S.CP.2 (See 2/17) S.CP.3 (See 2/17) S.CP.4 (See 2/17) S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. S.CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model. S.CP.8 (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. Find Probabilities of Independent and Dependent Events pg 717-723 Sec 10.5 Day 2 24 25 AI: Alien Invasion ASTG: And So They Grow AWLF: Another Way to Look at Factoring AWQF: Accumulation with Quadratic Function CTS: Completing the Square Test Friday 6 Review S.CP.9 (See 2/7) Use Combinations and the Binomial Theorem pg 690-697 Sec 10.2 1 day Review Thursday 12 Curriculum Adjustment 19 Curriculum Adjustment 7 S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems. Apply the Counting Principle & Permutations pg 682-689 Sec 10.1 1 day Test 13 14 S.CP.7 (See 2/14) S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). Find Probabilities of Disjoint and Overlapping Events pg 707-713 Sec 10.4 2 days S.CP.1 (See 2/13) S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. Find Probabilities of Disjoint and Overlapping Events pg 707-713 Sec 10.4 Day 2 20 21 Curriculum Adjustment Zone Day 26 27 28 SIC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? Use Simulation to Test an Assumption (Include Computer Spreadsheet Practice) CC17-CC24 Sec 10.6A 2 days S.IC.2 (See 2/26) Use Simulation to Test an Assumption (Include Computer Spreadsheet Practice) CC17-CC24 Sec 10.6A Day 2 S.ID.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. Find Measures of Central Tendency and Dispersion pg 744-749 Sec 11.1 McDougal Online Supplemental Lesson: Weighted Averages & Expected Values 1 day EFE: Exponential Functions Exploration ENLF: Exponential & Natural Logarithmic Functions GT: Graphical Transformation IAUC: Investigating Area Under a Curve IIN: Introducing Interval Notation PFC: Parent Function Charades QO: Quadratic Optimization RFOP: A Rational Function Optimization Problem RQ: Random Quadratics SPG: A Study of Population Growth SSLE: Solve Systems of Linear Equations TAPP: The Amusement Park Problem TPF: Transformations of Piecewise Functions WTL: Walk the Line Algebra II Calendar 2013-2014 March Monday Tuesday Wednesday 3 S.ID.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. Use Normal Distributions pg 757-762 Sec 11.3 1 day 4 S.ID.4 (See 3/3) Investigate the Shapes of Data Distributions CC31-CC32 Sec 11.3A 1 day 10 5 Review 17 Curriculum Adjustment 12 7 Curriculum Adjustment 13 9 Weeks Test 18 Friday 6 S.ID.4 (See 3/3) Find the Area Under a Normal Curve CC33 Sec 11.3B 1 day 11 Review Thursday 9 Weeks Test 19 14 Parent/Teacher Conference 20 21 Spring Break 24 25 26 27 28 S.IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. Select and Draw Conclusions from Samples pg 766-771 Sec 11.4 1 day S.ID.1 (See 3/24) S.IC.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. Estimate a Population Proportion CC34-CC35 Sec 11.4A 1 day S.IC.6 Evaluate reports based on data. S.IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. Compare Surveys, Experiments and Observational Studies CC36-CC41 Sec 11.5A 1 day S.IC.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. Simulate an Experimental Difference CC42-CC43 Sec 11.5B 1 day S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models. Choose the Best Model for TwoVariable Data pg 775-780 Sec 11.5 2 days 31 S.ID.6a (See 3/28) Choose the Best Model for Two-Variable Data pg 775-780 Sec 11.5 Activity (p. 774) Day 2 AI: Alien Invasion ASTG: And So They Grow AWLF: Another Way to Look at Factoring AWQF: Accumulation with Quadratic Function CTS: Completing the Square EFE: Exponential Functions Exploration ENLF: Exponential & Natural Logarithmic Functions GT: Graphical Transformation IAUC: Investigating Area Under a Curve IIN: Introducing Interval Notation PFC: Parent Function Charades QO: Quadratic Optimization RFOP: A Rational Function Optimization Problem RQ: Random Quadratics SPG: A Study of Population Growth SSLE: Solve Systems of Linear Equations TAPP: The Amusement Park Problem TPF: Transformations of Piecewise Functions WTL: Walk the Line Algebra II Calendar 2013-2014 April Monday Tuesday Wednesday 1 Quiz 7 FIF.7b (See 4/2) Piecewise Functions Additional Resources Needed pg 130 Sec 2.7 Extension WTL, p. 1-5 Day 4 14 EOI Review & Prep 4 F.IF.7b (See 4/2) Piecewise Functions Additional Resources Needed pg 130 Sec 2.7 Extension LTF: IAUC, p. 13-15 Day 3 9 10 EOI Review & Prep 16 EOI Review & Prep 11 EOI Review & Prep 17 EOI Review & Prep 18 EOI Review & Prep 22 23 24 25 F.TF.1 (See 4/21) Define General Angles & Use Radian Measures pg 859 Sec 13.2 2 days F.TF.1 (See 4/21) Define General Angles & Use Radian Measures pg 859 Sec 13.2 Day 2 F.TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Evaluate Trig Functions pg 866 Sec 13.3 3 days F.TF.2 (See 4/24) Evaluate Trig Functions pg 866 Sec 13.3 Day 2 28 F.TF.2 (See 4/24) Evaluate Trig Functions pg 866 Sec 13.3 Day 3 3 F.IF.7b (See 4/2) Piecewise Functions Additional Resources Needed pg 130 Sec 2.7 Extension LTF Mod 11: PFC, p. 54-67 LTF Mod 11: TPF, p. 68-75 Day 2 15 21 F.TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Use Trig with Right Triangles pg 852 Sec 13.1 1 day 2 EOI Review & Prep EOI Review & Prep Friday F.IF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Piecewise Functions pg 130 Sec 2.7 Extension 4 days 8 EOI Review & Prep Thursday 29 30 F.TF.5 (See 4/30) F.IF.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.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph Sine, Cosine & Tangent Functions pg 908 Sec 14.1 3 days F.IF.4 & F.IF.7 (See 4/29) F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. Graph Sine, Cosine & Tangent Functions pg 908 Sec 14.1 Day 2 AI: Alien Invasion ASTG: And So They Grow AWLF: Another Way to Look at Factoring AWQF: Accumulation with Quadratic Function CTS: Completing the Square EFE: Exponential Functions Exploration ENLF: Exponential & Natural Logarithmic Functions GT: Graphical Transformation IAUC: Investigating Area Under a Curve IIN: Introducing Interval Notation PFC: Parent Function Charades QO: Quadratic Optimization RFOP: A Rational Function Optimization Problem RQ: Random Quadratics SPG: A Study of Population Growth SSLE: Solve Systems of Linear Equations TAPP: The Amusement Park Problem TPF: Transformations of Piecewise Functions WTL: Walk the Line Algebra II Calendar 2013-2014 May Monday Tuesday Wednesday Thursday Friday 1 F.TF.5 (See 5/2) F.IF.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.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph Sine, Cosine & Tangent Functions pg 908 Sec 14.1 Day 3 5 F.TF.5 & F.IF.7e (See 5/1) 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. Translate & Reflect Trig Graphs pg 915 Sec 14.2 Day 2 6 12 7 F.TF.8 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. Verify Trig Identities pg 924 Sec 14.3 3 days Curriculum Adjustment 13 S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models. Write Trig Functions & Models pg 941 Sec 14.5 1 day Review 19 20 Review Review 8 F.TF.8 (See 5/7) Verify Trig Identities pg 924 Sec 14.3 Day 2 14 Test 9 F.TF.8 (See 5/7) Verify Trig Identities pg 924 Sec 14.3 Day 3 15 Curriculum Adjustment 21 Review 2 F.BF.3 (See 5/5) F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Translate & Reflect Trig Graphs pg 915 Sec 14.2 2 days 16 Curriculum Adjustment 22 Semester Test 23 Semester Test Last Day of School 26 Memorial Day 27 28 29 Record Day OR Last Day of School if Snow Day Needed AI: Alien Invasion ASTG: And So They Grow AWLF: Another Way to Look at Factoring AWQF: Accumulation with Quadratic Function CTS: Completing the Square EFE: Exponential Functions Exploration ENLF: Exponential & Natural Logarithmic Functions GT: Graphical Transformation IAUC: Investigating Area Under a Curve IIN: Introducing Interval Notation PFC: Parent Function Charades QO: Quadratic Optimization RFOP: A Rational Function Optimization Problem RQ: Random Quadratics SPG: A Study of Population Growth SSLE: Solve Systems of Linear Equations TAPP: The Amusement Park Problem TPF: Transformations of Piecewise Functions WTL: Walk the Line 30