MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

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1 Topic IV: Polynomial Functions, Expressions, and Equations Pacing Date(s) Traditional 18 10/29/18 11/28/18 Block 9 10/29/18 11/28/18 Topic IV Assessment Window 11/16/18 11/28/18 MATHEMATICS FLORIDA STATE STANDARDS (MAFS) & MATHEMATICAL PRACTICES (MP) ESSENTIAL CONTENT OBJECTIVES MAFS.912.A-APR.1.1: 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. (MP.2, MP.7) MAFS.912.A-APR.2.3: 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. (MP.1, MP.2, MP.4, MP.5, MP.8) MAFS.912.A-APR.3.4: Prove polynomial identities and use them to describe numerical relationships. (MP.7, MP.8) MAFS.912.A-APR.3.5: Know and apply the Binomial Theorem for 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.(+) MAFS.912.A-APR.2.2: 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). (MP.2, MP.3, MP.8) MAFS.912.A-SSE.1.1: Interpret expressions that represent a quantity in terms of its context. (MP.1, MP.2, MP.4, MP.7) MAFS.912.A-SSE.1.2: Use the structure of an expression to identify ways to rewrite it. For example, see x 4 - y 4 as (x²)² (y²)², thus recognizing it as a difference of squares that can be factored as (x² y²)(x² + y²). (MP.2, MP.7) MAFS.912.A-APR.4.6 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. (MP.2, MP.4, MP.5, MP.6, MP.7, MP.8) MAFS.912.N-CN.3.8: Extend polynomial identities to the complex numbers. For example, rewrite x² + 4 as (x + 2i)(x 2i). (+) MAFS.912.N-CN.3.9: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. (+) A. Polynomials 1. Adding and Subtracting Polynomials. 2. Multiplying Polynomials 3. The Binomial Theorem 4. Factoring Polynomials 5. Dividing Polynomials B. Polynomial Equations 1. Finding Rational Solutions of Polynomial Equations 2. Finding Complex Solutions of Polynomials Equations. I can: apply their understanding of closure to adding, subtracting, and multiplying polynomials. add, subtract, and multiply polynomials with rational coefficients. use polynomial identities to describe numerical relationships. use the structure of algebra to complete an algebraic proof of a polynomial identity. find the zeros of a polynomial function when the polynomial is in factored form. identify a rough graph of a polynomial function in factored form by examining the zeros of the function. use the x-intercepts of a polynomial function and end behavior to graph the function. graph a polynomial function using key features. use polynomial long division to divide a polynomial by a polynomial. use the Remainder Theorem to determine if (x a) is a factor of a polynomial. use the Remainder Theorem to determine the remainder of p(x)/(x a). rewrite algebraic expressions in different equivalent forms using factoring techniques (e.g., common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor completely) or simplifying expressions (i.e., combining like terms, using the distributive property, and using other operations with polynomials). Division of Academics - Department of Mathematics Page 1 of 6

2 INSTRUCTIONAL TOOLS Core Text Book: Houghton Mifflin Harcourt Algebra 2 Algebra 2 Honors Course Description - CPALMS Pacing Date(s) Traditional 18 10/29/18 11/28/18 Block 9 10/29/18 11/28/18 Topic IV Assessment Window 11/16/18 11/28/18 RECOMMENDED INSTRUCTIONAL DESIGN AND PLANNING CONTINUUM Before During After During the lesson: Activate (or supply) prior knowledge and/or spiral back o Warm ups, Bell Ringers, Openers, etc. Tailor lesson experiences to the different needs and ability of the learners. Clarify vocabulary and mathematical notation. Incorporate a variety of higher order questions to encourage and increase critical thinking skills. Continuously check for student understanding and provide feedback. Provide opportunities for students to develop selfassessment and to reflect about their understanding and work. Bring closure to the lesson so that the students can articulate what they have learned. Prior to the lesson: Outline content standard(s). Determine learning targets. Anticipate student understanding and misconceptions. Determine prerequisite skills. Plan for learning experiences that target Rigor o Conceptual Understanding o Procedural Fluency o Application Determine the task students will demonstrate to reach the desired learning targets. Plan instructional delivery methods that will maximize initial engagement and sustain it throughout the lesson. Decide how students will reflect upon, self-assess, and set goals for their future learning. After the lesson: Analyze evidence of student learning to develop intervention, enrichment, and future instruction. Discuss results of assessments with students. Engage students in reflective processes and goal setting. Engage in self-reflection to adapt/modify teaching strategies to improve instruction. Unit Resources Unit Tests A, B, and C Performance Assessment Module Resources Module Test B Common Core Assessment Readiness Advanced Learners Challenge Worksheets Algebra 2 Honors H.M.H. Resources Unit Resources Math in Careers Video Assessment Readiness (Mixed Review) Lesson Resources Lessons Work text/interactive Student Edition Practice and Problem Solving: A/B Advanced Learners - Practice and Problem Solving: C PMT Preferences: Auto-assign for intervention and enrichment: NO Auto-assign Test and Quizzes for intervention and enrichment: NO Homework PMT Preferences: Auto-assign for intervention and enrichment: YES Auto-assign Standard-Based for intervention Intervention and enrichment: NO Course Intervention Daily Intervention Division of Academics - Department of Mathematics Page 2 of 6

3 INSTRUCTIONAL TOOLS STANDARDS MODULES TEACHER NOTES MAFS.912.A-APR.1.1 MAFS.912.A-APR.2.2 MAFS.912.A-APR.2.3 MAFS.912.A-APR.3.4 MAFS.912.A-APR.3.5 (+) MAFS.912.A-APR.4.6 MAFS.912.A-SSE.1.1a MAFS.912.A-SSE.1.2 MAFS.912.N-CN.3.8 (+) MAFS.912.N-CN.3.9 (+) Module 6 Module 7 Algebra 2 Honors Block Schedule Suggested Pace Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day Topic Test Topic IV Assessment: Polynomial Functions, Expressions, and Equations (Also assesses Topic III) (+) Additional mathematics that students should learn in fourth credit courses or advanced courses such as calculus, advanced statistics, or discrete mathematics MODULE LESSON STANDARDS 6.1 MAFS.912.A-APR.1.1 SUGGESTED PROBLEMS BY TEACHERS FOR TEACHERS* 2, 3, 8, 9, 14, 22, 24 NOTES / RESOURCES 6.2 MAFS.912.A-APR.1.1 MAFS.912.A-APR.3.4 2, 4, 6, 12, 13, 14 Illustrative Mathematics Task(s): Non-Negative Polynomials, Trina s Triangle Module MAFS.912.A-APR , 15 17, 19, MAFS.912.A-SSE.1.1a MAFS.912.A-SSE.1.2 MAFS.912.A-APR.2.3 MAFS.912.A-APR.2.2 MAFS.912.A-APR.4.6 1, 2, 3, 5, 8, 10, 15, 16, 19, 21, 26 1, 3, 5, 7, 9, 11 13, 16, 21, 23 GeoGebra: Factors and Zeros Illustrative Mathematics Task(s): Zeroes and factorization of a general polynomial, Zeroes and factorization of a quadratic polynomial I, The Missing Coefficient, Graphing from Factors III Module MAFS.912.A-APR.2.2 MAFS.912.A-APR MAFS.912.N-CN.3.9 (+) 1, 2, 6, 7, 14, 16, 18, 19 1, 2, 5, 6, 12 *Problems were suggested by M-DCPS teachers during May Algebra 2 PD. Division of Academics - Department of Mathematics Page 3 of 6

4 INSTRUCTIONAL TOOLS Vocabulary: Binomial, monomial, polynomial, synthetic division, trinomial, cubic function, polynomial function, root, multiplicity. STEM/STEAM Corner Science Connection: Chemistry Honors Year-At-A-Glance N/A STEM Lessons - Model Eliciting Activity STEM Lessons CPALMS Perspectives Videos Professional/Enthusiasts Base 16 Notation in Computing Expert Jumping Robots and Quadratics Engineering Design Process The engineering design process is a series of steps that guides engineering teams as we solve problems. The design process is iterative, meaning that we repeat the steps as many times as needed, making improvements along the way as we learn from failure and uncover new design possibilities to arrive at great solutions. Ask: Identify the Need & Constraints Research the Problem Imagine: Develop Possible Solutions Plan: Select a Promising Solution Create: Build a Prototype Test and Evaluate Prototype Improve: Redesign as Needed Division of Academics - Department of Mathematics Page 4 of 6

5 TECHNOLOGY TOOLS CPALM RESOURCES LESSON PLANS Wonka's Golden Ticket! (Polynomial Operations) Building Connections Sorting Equations and Identities Manipulating Polynomials Using algebra tiles and tables to factor trinomials (less guess and check!) Hip to be (completing the) Square VIRTUAL MANIPULATIVE Curve Fitting Number Cruncher Data Flyer Function Flyer PROBLEM-SOLVING TASK Zeroes and factorization of a non-polynomial function The Physics Professor Equivalent Expressions TUTORIAL Addition and Subtraction of Polynomials Multiplying and Dividing Monomials Division of Polynomials GRAPHING CALCULATOR CORRELATION TEXAS INSTRUMENT MATH ACTIVITY TITLE McLaurin Polynomials Application of Polynomials Zeros of Polynomials Multiplying Polynomials Exploring Polynomials: Factors, Roots, and Zeros Division of Academics - Department of Mathematics Page 5 of 6

6 GIZMOS CORRELATION GIZMO TITLE Addition of Polynomials Polynomials and Linear Factors Dividing Polynomials Using Synthetic Division Modeling the Factorization of ax 2 +bx+c Distance-Time and Velocity-Time Graphs Quadratics in Polynomial Form TOPIC IV DISCOVERY EDUCATION CORRELATION VIDEO TITLE Math Factor: Factoring and Graphing Polynomial Functions Functions, Domain, and Range -- Burning Calories MATH EXPLANATION TITLE Algebra II: Division of Polynomials Example 2: Independent and Dependent Variables--Swimming MATH OVERVIEW Solving Polynomial Equations Algebra II: Graphing Square and Cube Root Functions Division of Academics - Department of Mathematics Page 6 of 6