The following Practice Standards and Literacy Skills will be used throughout the course: Standards for Mathematical Practice Literacy Skills for Mathematical Proficiency 1. Make sense of problems and persevere in solving them. 1. Use multiple reading strategies. 2. Reason abstractly and quantitatively. 2. Understand and use correct mathematical vocabulary. 3. Construct viable arguments and critique the reasoning of others. 3. Discuss and articulate mathematical ideas. 4. Model with mathematics. 4. Write mathematical arguments. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Ongoing Standards Note to Teachers: The following ongoing standards will be practiced all year long and embedded into your instruction instead of being taught in isolation. A2.N.Q.A.1 Identify, interpret, and justify appropriate quantities for the purpose of descriptive modeling. A2.A.REI.A.1 Explain each step in solving an 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. A2.F.BF.A.1 Write a function that describes a relationship between two quantities. *Resources are from <Insert Name of Textbook>.
Unit 1 12 Days Algebra 2 TN Ready Performance Standards by Unit Algebra 2 Curriculum Overview by Standard Number Quarter 1 Quarter 2 Quarter 3 Quarter 4 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 28 Days 25 Days 15 Days 13 Days 25 Days 10 Days Unit 8 10 Days Introduction to Functions A2.A.CED.A.1 A2.A.REI.C.4 A2.A.REI.D.6 A2.F.IF.A.1 A2.F.IF.A.2 A2.F.IF.B.3a A2.F.BF.B.3 A2.F.BF.B.4a Quadratics Polynomials Rationals Radicals Exponential & Logarithms Standards (By number) A2.N.CN.A.1 A2.A.SSE.A.1 A2.A.SSE.A.1 A2.N.RN.A.1 A2.A.SSE.A.1 A2.N.CN.A.2 A2.A.APR.A.1 A2.A.APR.A.2 A2.N.RN.A.2 A2.A.SSE.B.2a A2.N.CN.B.3 A2.A.APR.A.2 A2.A.APR.C.4 A2.A.CED.A.2 A2.A.SSE.B.3 A2.A.APR.A.2 A2.A.APR.B.3 A2.A.CED.A.1 A2.A.REI.A.1 A2.A.CED.A.1 A2.A.CED.A.1 A2.A.APR.C.4 A2.A.CED.A.2 A2.A.REI.A.2 A2.A.CED.A.2 A2.A.CED.A.2 A2.A.CED.A.2 A2.A.REI.A.1 A2.F.IF.A.1 A2.A.REI.A.1 A2.A.REI.A.1 A2.A.REI.A.1 A2.A.REI.A.2 A2.F.IF.B.3a A2.A.REI.D.6 A2.A.REI.B.3a A2.A.REI.D.6 A2.A.REI.D.6 A2.F.BF.B.4a A2.F.IF.A.1 A2.A.REI.C.5 A2.F.IF.A.1 A2.F.IF.A.2 A2.A.REI.D.6 A2.F.IF.A.2 A2.F.IF.B.3c A2.F.IF.A.1 A2.F.IF.B.3a A2.F.IF.B.4a A2.F.IF.A.2 A2.F.IF.B.3b A2.F.IF.B.5 A2.F.IF.B.3a A2.F.IF.B.5 A2.F.BF.A.1a A2.F.IF.B.3b A2.F.BF.A.1a A2.F.BF.A.1b A2.F.IF.B.5 A2.F.BF.B.3 A2.F.BF.A.2 A2.F.BF.A.1a A2.S.ID.B.2a A2.F.BF.B.3 A2.F.BF.B.3 A2.F.BF.B.4a A2.S.ID.B.2a A2.F.LE.A.1 A2.F.LE.A.2 A2.F.LE.B.3 A2.S.ID.B.2a Trigonometry A2.F.TF.A.1a A2.F.TF.A.1b A2.F.TF.A.2 A2.F.TF.B.3a A2.F.TF.B.3b Probability & Statistics A2.S.ID.A.1 A2.S.IC.A.1 A2.S.IC.A.2 A2.S.CP.A.1 A2.S.CP.A.2 A2.S.CP.A.3 A2.S.CP.A.4 A2.S.CP.B.5 A2.S.CP.B.6 Green=Major Content
Unit 1 INTRODUCTION TO FUNCTIONS 12 Days Standards I Can Statements Number and Quantity Algebra A2.A.CED.A.1 Create equations and inequalities in one variable and I can solve absolute value equations and inequalities. use them to solve problems A2.A.REI.C.4 Write and solve a system of linear equations in context. I can solve 3x3 systems of equations algebraically and using A2.A.REI.D.6 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 approximate solutions using Functions A2.F.IF.A.1 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. A2.F.IF.A.2 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. A2.F.IF.B.3 Graph functions expressed symbolically and show key features of the graph, by hand and using a. Graph square root, cube root, and piecewise defined functions, I can solve 2x2 systems graphically. I understand that the intersection of two equations is the solution to the system of equations. Include cases where the functions are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. I can find the intersection of any two functions using graphing I can view graphs and/or tables as relationships between quantities and identify the following when given graphs and/or tables of absolute value functions: o Vertex o Symmetries o Domain and range o Intercepts o Increasing and decreasing intervals o Positive and negative intervals o Relative maximums and minimums o End behavior I can calculate and estimate the rate of change from a graph. I can graph piecewise and step functions. I can name the vertex, max or min, and the x and y intercepts of an absolute value function.
including step functions and absolute value functions. I can graph an absolute value function by hand and using A2.F.BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + I can identify the effect on a graph from a constant k. (i.e. f(x) + k, k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and f(kx), k f(x), and f(x + k)) whether k is positive or negative. negative); find the value of k given the graphs. Experiment with cases I can identify and explain the difference between an even and odd and illustrate an explanation of the effects on the graph using function. A2.F.BF.B.4 Find inverse functions. I can write the inverse of a function by solving f(x) = c for x. a. Find the inverse of a function when the given function is one-to- I can write the inverse of a function by interchanging the values of the one. x and y values and solving for y. Statistics and Probability Sections/Topics Added Resources TenMarks Edgenuity Shell Center Short Cycle Tasks www.map.mathshell.org Vocabulary Equation Inequality Linear Absolute Value Piecewise Step Function Parent Function System of Linear Equations Inverses Intersection Extraneous Solutions Rate of Change Vertex Domain & Range Intercepts Increasing & Decreasing Intervals Positive & Negative Intervals Relative Maximum & Minimum Transformation Translation Reflection Symmetries
Standards Number and Quantity A2.N.CN.A.1 Know there is a complex number i such that i 2 = 1, and every complex number has the form a + bi with a and b real. Algebra 2 TN Ready Performance Standards by Unit A2.N.CN.A.2 Know and use the relation i 2 = 1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. A2.N.CN.B.3 Solve quadratic equations with real coefficients that have complex solutions. Algebra A2.A.APR.A.2 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. A2.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. A2.A.CED.A.2 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations A2.A.REI.A.1 Explain each step in solving an 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. A2.A.REI.B.3 Solve quadratic equations and inequalities in one variable. a. Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of Unit 2 QUADRATICS 28 Days I Can Statements I can identify that i is a complex number where i 2 = 1 and i = 1. I can identify that a complex number is written in the form a + bi where a and b are real numbers. I can simplify the square root of a negative number. I can add, subtract, and multiply complex numbers. Given a complex number, I can find its conjugate and use it to find quotients of complex numbers. I can solve real-world quadratic problems and identify which answer(s) are appropriate. I can solve quadratic equations with real coefficients. I can determine when a quadratic equation in standard form, ax 2 +bx = c has complex roots by looking at a graph or by inspecting the discriminant. I can factor a quadratic. I can identify the zeros of a quadratic equation and use them to construct a graph. I can create quadratic equations and inequalities and use them to solve problems. I can rearrange a quadratic equation into standard form, vertex form or factored form. I can justify steps to solve a quadratic equation. I can determine the order of the steps to solve a quadratic equation. I can solve quadratic equations using a variety of methods. I can solve quadratic inequalities.
the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. A2.A.REI.C.5 Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Algebra 2 TN Ready Performance Standards by Unit A2.A.REI.D.6 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 approximate solutions using Functions A2.F.IF.A.1 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. I can solve a system containing a linear equation and a quadratic equation graphically and algebraically. I can graph a system containing a linear inequality and a quadratic inequality. I understand that the intersection of two equations is the solution to the system of equations. Include cases where the functions are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. I can find the intersection of any two functions using graphing I can view graphs and/or tables as relationships between quantities and identify the following when given graphs and/or tables of quadratic functions: o Vertex o Symmetries o Domain and range o Intercepts/Zeros/Solutions/Roots o Increasing and decreasing intervals o Positive and negative intervals o Relative maximums and minimums o End behavior A2.F.IF.A.2 Calculate and interpret the average rate of change of a I can calculate the rate of change from one point another on a function (presented symbolically or as a table) over a specified quadratic function. interval. Estimate rate of change from a curve on a graph. A2.F.IF.B.3 Graph functions expressed symbolically and show key I can graph quadratic functions by hand and using features of the graph, by hand and using Identifying: a. Graph square root, cube root, and piecewise defined functions, o Vertex including step functions and absolute value functions. o Symmetries b. Graph polynomial functions, identifying zeros when suitable o Domain and range factorizations are available and showing end behavior o Intercepts/Zeros/Solutions/Roots o Increasing and decreasing intervals o Positive and negative intervals o Relative maximums and minimums
A2.F.IF.B.5 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). A2.F.BF.A.1 Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. A2.F.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 Statistics and Probability A2.S.ID.B.2 Represent data on two quantitative variables on a scatter plot and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. o End behavior I can compare information given by multiple functions and in multiple and/or different ways (algebraically, graphically, numerically in tables, or by verbal descriptions) and determine which function meets a set parameter. I can create a polynomial regression function given a real-world x and y value. I can make predictions using the polynomial regression function from a real-world x and y value. I can identify the effect on a graph from a constant k. (i.e. f(x) + k, f(kx), k f(x), and f(x + k)) whether k is positive or negative. I can identify and explain the difference between an even and odd function. I can determine if a set of data best fits a quadratic model. I can write a quadratic regression equation from a set of data. I can use a quadratic regression equation to make predictions. Sections/Topics Added Resources TenMarks Edgenuity Shell Center Short Cycle Tasks www.map.mathshell.org Vocabulary Linear Quadratic Polynomial Standard Form Vertex Form Complex Number i Imaginary Number i Square Root Roots Rational Roots Irrational Roots Intersection Vertex Domain & Range Intercepts Increasing & Decreasing Intervals Positive & Negative Intervals Relative Maximum & Minimum Transformation Translation
Imaginary Roots Solutions Zeros Complex Roots Conjugate Completing the Square Quadratic Formula Discriminant Factoring Reflection Symmetries Rate of Change End Behavior System of Equations Quadratic Regression Regression Equation Curve of Best Fit Correlation Coefficient
Unit 3 POLYNOMIALS 25 Days Standards Number and Quantity Algebra A2.A.SSE.A.1 Use the structure of an expression to identify ways to rewrite it. A2.A.APR.A.1 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). A2.A.APR.A.2 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. A2.A.APR.B.3 Know and use polynomial identities to describe numerical relationships. For example, compare (31)(29)=(30+1)(30-1)=302-12with (x+y)(x-y)=x2-y2 A2.A.APR.C.4 Rewrite rational expressions in different forms. A2.A.CED.A.2 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations A2.A.REI.A.1 Explain each step in solving an 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. A2.A.REI.D.6 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 approximate solutions using Functions A2.F.IF.A.1 For a function that models a relationship between two I Can Statements I can recognize the patterns in the sum and differences of cubes. I can factor sum and difference of cubic expressions. I can explain and apply the Remainder Theorem to check answers when dividing polynomials. I understand that a is a root of a polynomial function if and only if x-a is a factor of the function. I can find the zeros of a polynomial when the polynomial is factored. I can multiply polynomials and use the patterns observed in identities such as the difference of squares to multiply polynomials. I can divide polynomials using long division and synthetic division. I can rearrange a polynomial equation into standard form or factored form. I can justify steps to solve a polynomial equation. I can determine the order of the steps to solve a polynomial equation. I understand that the intersection of two equations is the solution to the system of equations. Include cases where the functions are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. I can find the intersection of any two functions using graphing I can view graphs and/or tables as relationships between quantities and
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. A2.F.IF.A.2 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate rate of change from a curve on a graph. A2.F.IF.B.3 Graph functions expressed symbolically and show key features of the graph, by hand and using a. Graph square root, cube root, and piecewise defined functions, including step functions and absolute value functions. b. Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior Algebra 2 TN Ready Performance Standards by Unit A2.F.IF.B.5 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). A2.F.BF.A.1 Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. A2.F.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 Statistics and Probability A2.S.ID.B.2 Represent data on two quantitative variables on a scatter plot and describe how the variables are related. identify the following when given graphs and/or tables of polynomial functions: o Domain and range o Intercepts/Zeros/Solutions/Roots o Increasing and decreasing intervals o Positive and negative intervals o Relative maximums and minimums o End behavior I can calculate the rate of change from one point another on a quadratic function. I can graph polynomials functions by hand and using Identifying: o Vertex o Domain and range o Intercepts/Zeros/Solutions/Roots o Increasing and decreasing intervals o Positive and negative intervals o Relative maximums and minimums o End behavior I can compare information given by multiple functions and in multiple and/or different ways (algebraically, graphically, numerically in tables, or by verbal descriptions) and determine which function meets a set parameter. I can create a quadratic regression function given a real-world x and y value. I can make predictions using the quadratic regression function from a real-world x and y value. I can identify the effect on a graph from a constant k. (i.e. f(x) + k, f(kx), k f(x), and f(x + k)) whether k is positive or negative. I can identify and explain the difference between an even and odd function. I can graph a polynomial function. I can determine if a set of data best fits a polynomial model. I can write a polynomial regression equation from a set of data.
a. Fit a function to the data; use functions fitted to data to solve I can use a polynomial regression equation to make predictions. problems in the context of the data. Sections/Topics Added Resources TenMarks Edgenuity Shell Center Short Cycle Tasks www.map.mathshell.org Vocabulary Linear Remainder Theorem Quadratic Long Division Polynomial Synthetic Division Degree Vertex Leading Coefficient Domain & Range Standard Form Intercepts Complex Number i Increasing & Decreasing Imaginary Number i Intervals Multiplicity Positive & Negative Intervals Roots Relative Maximum & Rational Roots Minimum Irrational Roots Turning Point Imaginary Roots Transformation Solutions Translation Zeros Reflection Complex Roots Rate of Change Conjugate End Behavior Quadratic Formula System of Equations Discriminant Polynomial Regression Factoring Regression Equation Sum & Difference of Cubes Curve of Best Fit Difference of Squares Correlation Coefficient Intersections
Unit 4 Rationals 15 Days Standards Number and Quantity Algebra A2.A.SSE.A.1 Use the structure of an expression to identify ways to rewrite it. A2.A.APR.A.2 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. A2.A.APR.C.4 Rewrite rational expressions in different forms. A2.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. A2.A.CED.A.2 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations A2.A.REI.A.1 Explain each step in solving an 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. A2.A.REI.A.2 Solve rational and radical equations in one variable, and identify extraneous solutions when they exist. A2.A.REI.D.6 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 approximate solutions using A2.A.REI.D.6 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 approximate solutions using I Can Statements I can rewrite a rational equation using factors and common denominators. I can factor the numerator and denominator of a rational equation and use the zeros and undefined to construct a rough graph. I can add, subtract, multiply, divide and simplify rational expressions to rewrite the rational expression. I can create rational equations and inequalities and use them to solve problems. I can rearrange a rational equation to solve real-world problems. I can justify steps to solve a rational equation. I can determine the order of the steps to solve a rational equation. I can simplify rational expressions by adding, subtracting, multiplying or dividing. I can identify and define extraneous solution. I can solve a rational equation in one variable. I understand that the intersection of two equations is the solution to the system of equations. Include cases where the functions are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. I can find the intersection of any two functions using graphing I understand that the intersection of two equations is the solution to the system of equations. Include cases where the functions are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
I can find the intersection of any two functions using graphing Functions Statistics and Probability Sections/Topics Added Resources TenMarks Edgenuity Shell Center Short Cycle Tasks www.map.mathshell.org Rational Expression Rational Inequality Rational Function Numerator Denominator Least Common Multiple Common Denominator Extraneous Solutions Domain & Range End Behavior Vocabulary Complex Fraction Continuous & Discontinuous Function Hyperbola Vertical & Horizontal Asymptote Transformations Translation Reflection Intersection
Unit 5 Radicals 13 Days Standards I Can Statements Number and Quantity A2.N.RN.A.1 Explain how the definition of the meaning of rational I can evaluate and simplify an expression with a rational exponent. exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. A2.N.RN.A.2 Rewrite expressions involving radicals and rational I can move flexibly between radical notation and rational exponents. exponents using the properties of exponents. Algebra A2.A.CED.A.2 Rearrange formulas to highlight a quantity of interest, I can rearrange the formula for a square root or cubed root function in using the same reasoning as in solving equations. order to highlight a quantity in context. A2.A.REI.A.1 Explain each step in solving an 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. A2.A.REI.A.2 Solve rational and radical equations in one variable, and identify extraneous solutions when they exist. Functions A2.F.IF.A.1 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. A2.F.IF.B.3 Graph functions expressed symbolically and show key features of the graph, by hand and using a. Graph square root, cube root, and piecewise defined functions, including step functions and absolute value functions. A2.F.BF.B.4 Find inverse functions. a. Find the inverse of a function when the given function is one-toone. Statistics and Probability I can explain each step in solving a square root or cube root equation and construct a viable argument to justify the solution method. I can solve an equation containing radicals or rational exponents. I can identify an extraneous solution and explain why the solution is extraneous. I can interpret key features of square root and cube root functions when given a graph or table. Key features include, intercepts, intervals where the function is increasing/decreasing, and end behavior. I can sketch the graphs of square root and cube root functions, showing key features, when given a verbal description of the relationship. I can graph a square root and cube root function by hand and using I can find the inverses of simple quadratic and cubic functions.
Sections/Topics Added Resources TenMarks Edgenuity Shell Center Short Cycle Tasks www.map.mathshell.org Vocabulary Radical Function Vertex Radical Inequality Domain & Range Radicand Increasing & Decreasing Index Intervals Radical Symbol Positive & Negative Intervals Rationalize the Denominator Transformation Rational Exponent Translation Numerator Reflection Denominator Rate of Change Square Root End Behavior Cube Root System of Equations Inverses Intersection Extraneous Solution
Unit 6 Exponential and Logarithms 25 Days Standards Number and Quantity Algebra A2.A.SSE.A.1 Use the structure of an expression to identify ways to rewrite it. rewrite it. A2.A.SSE.B.2 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Use the properties of exponents to rewrite expressions for exponential functions. A2.A.SSE.B.3 Recognize a finite geometric series (when the common ratio is not 1), and know and use the sum formula to solve problems in context. A2.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. A2.A.CED.A.2 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. A2.A.REI.A.1 Explain each step in solving an 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. A2.A.REI.D.6 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 approximate solutions using Functions A2.F.IF.A.1 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. I Can Statements I can use the structure of an exponential expression to identify ways to I can rewrite exponential functions using the properties of exponents, including revealing an approximate equivalent monthly interest rate given the annual rate. I know and can use the formula for the sum of a finite geometric series to solve problems in context. I can create exponential equations and inequalities in one variable and use them to solve problems in context. I can rearrange logarithmic formulas in order to solve for a specified variable in the context of the problem. I can construct a convincing argument to justify each step in the solution process of a logarithmic equation, assuming the equation has a solution. I can explain why the intersection of y=f(x) and y=g(x) is the solution of f(x) = g(x) when exponential and logarithmic functions are involved. I can use technology to graph systems involving exponential and logarithmic functions and use the graph to find the points of intersection. I can interpret key features of an exponential or logarithmic graph and table in context. Key features include x-and y- intercepts, intervals where the function is increasing, decreasing, positive, or negative, and end behavior. I can sketch the graph of an exponential or logarithmic function and
A2.F.IF.A.2 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. A2.F.IF.B.3 Graph functions expressed symbolically and show key features of the graph, by hand and using c. Graph exponential and logarithmic functions, showing intercepts and end behavior. A2.F.IF.B.4 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Know and use the properties of exponents to interpret expressions for exponential functions. Algebra 2 TN Ready Performance Standards by Unit A2.F.IF.B.5 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). A2.F.BF.A.1 Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. A2.F.BF.A.1 Write a function that describes a relationship between two quantities. b. Combine standard function types using arithmetic operations. A2.F.BF.A.2 Know and write arithmetic and geometric sequences with an explicit formula and use them to model situations. show key features of the function given a verbal description of the situation. I can calculate and interpret the average rate of change of an exponential or logarithmic function (presented symbolically or as a table) over a specified interval in context. I can estimate the rate of change from a graph for an exponential or logarithmic function. I can graph an exponential or logarithmic function, expressed as an equation, both by hand and using technology to show intercepts and end behavior. I can use the properties of logarithms to condense and expand expressions. I can solve exponential and logarithmic equations. I can use properties of exponents to rewrite an exponential function to emphasize one of its properties. I can explain the meaning of each variable in a real-world exponential function in standard form. I can compare the properties of two exponential or logarithmic functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal description). I can write an exponential function that describes a relationship between two quantities in context. I can combine standard function types, including an exponential function, using arithmetic operations. I can write a formula for an arithmetic or geometric sequence. I can differentiate between arithmetic and geometric sequences. I can decide when a real-world problem models an arithmetic or geometric sequence and write an equation to model the situation. I can find the common difference or common ratio between two terms in an arithmetic or geometric sequence. I can experiment to identify, using technology, the transformational A2.F.BF.B.3 Identify the effect on the graph of replacing f(x) by effects on the graph of an exponential or logarithmic function f(x)
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 A2.F.BF.B.4 Find inverse functions. a. Find the inverse of a function when the given function is oneto-one. A2.F.LE.A.1 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or input-output pairs. Algebra 2 TN Ready Performance Standards by Unit A2.F.LE.A.2 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 A2.F.LE.B.3 Interpret the parameters in a linear or exponential function in terms of a context. Statistics and Probability A2.S.ID.B.2 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. when f(x) is replaced by f(x)+k, k f(x), f(kx), and f(x+k) for specific values of k, both positive and negative. I can find the value of k given the graph of a transformed exponential or logarithmic function. I can recognize even and odd functions from their graphs and equations. I can find the inverse of exponential and logarithmic functions. I can create an exponential function, including geometric sequences, given a graph, a table, a description of a relationship, or input-output pairs. I can create a function for arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or input-output pairs. I can translate between exponential and logarithmic forms. I can evaluate logarithms when the base b is 2, 10, or e using I can explain the meaning (using appropriate units) of the constants a, b, c, and the y-intercept in the exponential function, f(x) = a b x + c. I can represent exponential data on two quantitative variables on a scatter plot, and describe the relationship. I can use technology to find an exponential function to fit a data set and use the function to make predictions in the context of the problem. Sections/Topics Added Resources TenMarks Edgenuity Shell Center Short Cycle Tasks www.map.mathshell.org Vocabulary Exponential Function Logarithmic Function Natural Logarithm Common Logarithm Exponential Growth & Decay Growth & Decay Rate Transformations Translation Reflection Intersection Rate of Change Curve of Best Fit
Logarithm Compound Interest Compounded Continuously Domain & Range Increasing & Decreasing Intervals Positive & Negative Intervals End Behavior Inverses Continuous & Discontinuous Function Vertical & Horizontal Asymptote Exponential Regression Logarithmic Regression Summation Infinite & Finite Sequence Recursive Formula Explicit Formula Arithmetic Sequence & Series Terms of a Sequence Common Difference Geometric Sequence & Series Common Ratio Converge & Diverge
Standards Number and Quantities Algebra Functions A2.F.TF.A.1 Understand and use radian measure of an angle. a. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. A2.F.TF.A.1 Understand and use radian measure of an angle. b. Use the unit circle to find sin θ, cos θ, and tan θ when θ is a commonly recognized angle between 0 and 2π. A2.F.TF.A.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. Algebra 2 TN Ready Performance Standards by Unit A2.F.TF.B.3 Know and use trigonometric identities to to find values of trig functions. a. Given a point on a circle centered at the origin, recognize and use the right triangle ratio definitions of sin θ, cos θ, and tan θ to evaluate the trigonometric functions. A2.F.TF.B.3 Know and use trigonometric identities to to find values of trig functions. Unit 7 Trigonometry 10 Days I Can Statements I can define a unit circle, central angle and an intercepted arc. I can define the radian measure of an angle. I can find the values of sin θ, cos θ, and tan θ when θ is a commonly recognized angle between 0 and 2π on the unit circle. I can define coterminal angles. I can use reference angles to evaluate trigonometric ratios. I can draw positive or negative angles in standard position using radians or degrees. I can recognize and use the right triangle definitions of sin θ, cos θ, and tan θ, when given a point on a circle centered at the origin, to evaluate the trigonometric functions. I can use the identity sin 2 θ + cos 2 θ = 1 to find sin θ given cos θ, or vice versa when given the quadrant of the angle. b. Given the quadrant of the angle, use the identity sin 2 θ + cos 2 θ = 1 to find sin θ given cos θ, or vice versa. Statistics and Probability Sections/Topics Added Resources TenMarks Edgenuity Shell Center Short Cycle Tasks www.map.mathshell.org Vocabulary Sine Unit Circle
Cosine Tangent Cotangent Secant Cosecant Standard Position Initial Side Terminal Side Positive & Negative Angles Angles of Rotation Conterminal Angle Reference Angle Pythagorean Theorem Reciprocal Identities Pythagorean Identities Quotient Identities Trigonometric Function Inverse Trigonometric Functions Periodic Function Amplitude Cycle Period Frequency Phase Shift Radian Special Right Triangles Central Angle Intercepted Arc
Standards Number and Quantity Algebra Functions Statistics and Probability A2.S.ID.A.1 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using the Empirical Rule. A2.S.IC.A.1 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each A2.S.IC.A.2 Use data from a sample survey to estimate a population mean or proportion; use a given margin of error to solve a problem in context. A2.S.CP.A.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 ). A2.S.CP.A.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. A2.S.CP.A.3 Know and 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. Unit 8 Probability and Statistics 10 Days I Can Statements I can calculate the mean and standard deviation for a set of data. I can apply the 68-95-99.7 rule for the normal distribution to estimate population percentages. I can identify situations as sample surveys, experiments, or observational studies and can discuss the importance of randomization in these processes. I can explain why randomization is used to draw a sample that represents a population well I can estimate the total population values including the margin of error using sample means. I can define a sample space and events within the sample space. I can identify subsets within a sample space. I can give examples of unions, intersections and complements of sets and events. I can identify if two events are independent, explain my reasoning, and verify my statement by calculating probabilities. I can calculate the probability of independent events. I can calculate conditional probability and interpret independence of two events.
A2.S.CP.A.4 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. A2.S.CP.B.5 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. A2.S.CP.B.6 Know and 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. Algebra 2 TN Ready Performance Standards by Unit I can recognize the concept of conditional probability and independence and explain the concept with everyday language and in everyday situations. I can find and interpret the conditional probability based on the context of the given problem. I can choose a probability model for a problem situation. I can apply the addition rule to two events and interpret the results in terms of the context. Sections/Topics Added Resources TenMarks Edgenuity Shell Center Short Cycle Tasks www.map.mathshell.org Vocabulary Mean Standard Deviation Normal Distribution Variance Outlier Population Sample Space Survey Experiments Observational Study Dependent & Independent Events Randomization Margin of Error Events Subsets Union Outcome Intersection Complements Conditional Probability Theoretical Probability Experimental Probability Combination & Permutations