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CCGPS Adv Alg Unit 1A: Polynomials Unit Essential Question: How do I analyze polynomial functions? Day Day 1 M – 8/4 Day 2 T- 8/5 Topic Classify by Terms & Degree, Add & Subtract Polynomials Multiplying Polynomials, Binomial Expansion Daily Essential Question How can we write a polynomial in standard form? How do I use various operations with Polynomials? How do I multiply polynomials? How can I use Binomial Expansion as another form of multiplying? Day 3 W – 8/6 All Operations, Function Notaion What is function notation? How can I use this notation with polynomial operations. Day 4 Th – 8/7 Dividing: Long and Synthetic How do I divide polynomial functions? QUIZ What have I learned about polynomial operations? Day 5 F – 8/8 Day 6 M – 8/11 Factoring: GCF, All Trinomials Day 7 T – 8/12 Factoring: DOTS, S&D of Cubes, Grouping Day 8 W – 8/13 All Factoring: Solve by Factoring How do I factor trinomials? What are the methods for factoring polynomials with 4 terms? What about sums & diffs of cubes? What are the methods for factoring polynomials? How does factoring help me solve for x? Standards MCC9‐12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients. MCC9‐12.A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. MCC9‐12.A.APR.5 (+) Know and apply that the Binomial Theorem gives the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle MCC9‐12.A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. MCC9‐12.F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Assignments HW: WS Polynomial Operations #1-14 HW: Multiplying and Binomial Expansion WS #1-8 DC: Classify, Add and Subtract Polynomials HW: WS Function Operations and Review DC: Binomial Expansion HW: Dividing and Quiz Review Catch up on any missed HW Days 1-4 MCC9‐12.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. MCC9‐12.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. MCC9‐12.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. HW: WS Factoring 1 HW: WS Factoring 2 DC: Factoring HW: WS Factoring 3 Day 9 Th – 8/14 Review Am I ready for the test? All Above HW: WS Review Test 1A Day 10 F – 8/15 Unit 1A Test: Polynomials What do I know about Polynomial Functions? All above none ESSENTIAL QUESTIONS • How can we write a polynomial in standard form? • How can we write a polynomial in factored form? • How do we add, subtract, multiply, and divide polynomials • In which operations does closure apply? • How can we apply Pascal’s Triangle to expand? • What is the Remainder Theorem and what does it tell us? • What is the Rational Root Theorem and what does it tell us? • What is the Fundamental Theorem Algebra and what does it tell us? • How can we solve polynomial equations? • Which sets of numbers can be solutions to polynomial equations? • What is the relationship between zeros and factors? • What characteristics of polynomial functions can be seen on their graphs? • How can we solve a system of a linear equation with a polynomial equation CONCEPTS/SKILLS TO MAINTAIN It is expected that students will have prior knowledge/experience related to the concepts and skills identified below. It may be necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these ideas. • Combining like terms and simplifying expressions • Long division • The distributive property • The zero property • Properties of exponents • Simplifying radicals with positive and negative radicands • Factoring quadratic expressions • Solving quadratic equations by factoring, taking square roots, using the quadratic formula and utilizing graphing calculator technology to finding zeros/ x-intercepts • Observing symmetry, end-behaviors, and turning points (relative maxima and relative minima) on graphs • Writing explicit and recursive formulas for geometric sequences Georgia Department of Education Common Core Georgia Performance Standards Framework Teacher Edition