TN STATE STANDARDS CONTENT RESOURCES & CONNECTIONS Polynomials and Polynomial Functions (Allow approximately 4 weeks for instruction, review, and assessment) Domain: Arithmetic with Polynomials and Rational Expressions Cluster: Understand the relationship between zeros and factors of Polynomials 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. Domain: Quantities Cluster: Reason quantitatively and use units to solve problems. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Enduring Understanding(s): The algebraic form of a polynomial function gives information about its graph. Its graph gives information about its algebraic form. Knowing the zeros of a polynomial function gives information about its graph. A polynomial of degree n has n linear factors. The graph of the related function crosses the x-axis an even or odd number of times depending if n is even or odd. Essential Question(s): How can algebra describe the relationship between a function and its graph? Objective(s): Students will classify polynomials. Students will polynomials and describe end behavior. Use the following Lesson(s) to introduce concepts/build conceptual understanding. Use the textbook resources to address procedural skill and fluency. Pearson 5-1 Polynomial Functions Glencoe 6.1 Operations with Polynomials Lesson Videos Vocabulary Monomial, degree of a monomial, polynomial, degree of a polynomial, polynomial function, standard form of a polynomial function, turning point, end behavior Writing in Math Why does the end behavior depend on the leading term? Have students to write a sentence(s) and create at least two examples about their thinking. Graphic Organizer
Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met. Tasks: Domain: Linear, Quadratic, and Exponential Models Cluster: Interpret functions that arise in applications in terms of the context. Calculate and interpret the average rate of change of a function (presented symbolically or as a over a specified interval. Estimate the rate of change from a graph. Domain: Interpreting Functions Cluster: Analyze functions using different representations. F-IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Essential Question(s): How are the linear factors of a polynomial related to the zeros of the polynomial? Objective(s): Students will analyze the factored form of a polynomial. Students will write a polynomial function given its zeros and use the zeros to construct a rough graph of the function defined by the polynomial. Use the following Lesson(s) to introduce concepts/build conceptual understanding. Use the textbook resources to address procedural skill and fluency. Pearson 5-2 Polynomials, Linear Factors, and Zeros Glencoe 6.3 Polynomials Functions Lesson Videos Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met. Vocabulary Factor theorem, multiple zero, multiplicity, relative maximum, relative minimum Writing in Math Can zero be a solution of a polynomial function? Have students to write a sentence(s) and create and solve an example about their thinking. Graphic Organizer
hand in simple cases and using technology for more complicated cases e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. There is no additional scope or clarification information for this standard. 8. Write a function defined by an expression in different but equivalent Domain: Seeing Structure in Expressions Cluster: Interpret the structure of expressions. Use the structure of an expression to identify ways to rewrite it. Domain: Seeing Structure in Expressions Cluster: Interpret the structure of expressions. . 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. Domain: Interpreting Functions Cluster: Analyze functions using different representations. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the Enduring Understanding(s): The factor a in y=abx can stretch, compress, and possibly reflect the of the parent function y=bx. The function y=abx, a>0, b>01, models exponential growth. y=abx models exponential decay if 0<b<1. Essential Question(s): Why is y=aex considered to be an exponential function? Objective(s): Students will explore the properties of functions of the form y=abx. Students will graph exponential functions that have base e. Students will determine the growth or decay factor of an exponential function or situation. Students will write an exponential function Use the following Lesson(s) to introduce concepts/build conceptual understanding. Use the textbook resources to address procedural skill and fluency. Pearson 7.2 Properties of Exponential Functions Lesson Videos Vocabulary Natural base exponential function, continuously compounded interest Writing in Math Write three different examples of exponential functions that stretch, compress, and reflect. Explain why each function moves the way that it does. Have students to write a sentence(s) and create examples about their thinking.
function. b. 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. Domain: Building Functions Cluster: Build a function that models a relationship between two quantities ★ Write a function that describes a relationship between two quantities. b. 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. given a growth or decay situation using y=a(1+r)t. Students will write an exponential function for continuously compounded interest using y-aert. Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met. Tasks: TN Task Arc – Natural Order of Things Domain: Linear, Quadratic, and Exponential Models Cluster: Construct and compare linear, quadratic, and exponential models and solve problems. Use the structure of an expression to identify ways to rewrite it. Essential Question(s): The exponential function y=bx is so its inverse x=by is a function. To express y as a function of x for the inverse, write y=logbx. Logarithms are exponents. In fact, logba =c if and only if bc=a. Objective(s): Students will write and evaluate logarithmic expressions. Students will graph logarithmic functions. Students will y=logbx as the parent Use the following Lesson(s) to introduce concepts/build conceptual understanding. Vocabulary Logarithm, logarithmic function, common logarithm, logarithmic scale Writing in Math How are the domain and range related from the exponential function to the logarithmic function? Have students to write a sentence(s), create examples, and graph about their thinking.
logarithmic expressions Students will solve equations using natural logarithms. the intended outcome and of rigor (mainly conceptual understanding and application) of the standards are met. Tasks: RESOURCE TOOLBOX Textbook Resources Pearson Tools: ( ELL, Enrichment, Re-teaching, Quizzes/Tests, Think About a Plan, Test Prep, Extra Practice, Find the Errors, Activities/Games/Puzzles, Video Tutor, Chapter Project, Performance Task, and Student Companion) Glencoe Tools: Standards Edutoolbox (formerly TNCore) Tennessee Blueprints PARCC Blueprints and Test Specifications FAQ Algebra 2 TN State Standards Videos Literacy: (Math, p. 22) Calculator Others: Interactive Manipulatives Additional Sites NWEA MAP Resources: - Sign in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum)