GATEWAY REGIONAL HIGH SCHOOL

PACING GUIDE

# PURPOSE STATEMENT/PHILOSOPHY

The Algebra II curriculum is comprised of the following major concepts or ‘Big Ideas’:  (1) expressions, equations, and inequalities; (2) polynomial functions and graphs; (3) rational, irrational, and complex numbers; (4) quadratic equations and inequalities; (5) rational functions and graphs; (6) exponential and logarithmic functions; (7) sequences and series; (8) statistics and probability; and (9) matrices.  While knowledge of content is being developed, students are engaged in hands-on and cooperative activities that encourage mathematical reasoning, problem solving, communicating, and making connections.  Through these activities students utilize technology such as graphing calculators, computers, and calculator-based lab equipment.  In addition, they are encouraged to think more critically through activities that will involve investigations, explorations, and discovery.  Finally, evaluations appear in several formats:  pencil and paper tests, performance tasks, and long- and short-term projects.

PACING GUIDE

 CPI# Cumulative Progress Indicator (CPI) A.REI.4b Solve quadratic equations in one variable. b. 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. 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). F.IF.7c Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. ★          c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior

 GATEWAY GROUP CURRICULUM UNIT PLAN Content Area: Algebra II Unit Title: Expressions and Equations Timeframe:  6 weeks/MP I Lesson Components UNIT SUMMARY In this unit, Students will be able to…  Extend the properties of exponents to rational exponents.Understand solving equations as a process of reasoning and explain the reasoning.Write expressions in equivalent forms to solve problems.Interpret functions that arise in applications in terms of the content. LEARNING TARGETS ESSENTIAL QUESTIONS ENDURING UNDERSTANDINGS What are the properties of exponents?How can you solve equations?How do interpret functions? Identify the properties of exponentsSolve equations.Interpret functions. Global Awareness:  Understanding how Exponents are communicated in other cultures.Financial, Economic, Business, and Entrepreneurial Literacy: Examining how functions are used in the workplace to make businesses more profitable. Creativity and Innovation: Working in collaborative teams to express original methods for solving real-world problems.Critical Thinking and Problem Solving:  Learning the components of logical arguments and applying this skill to functions.Communication and Collaboration:  Using cooperative teams to develop notes and problem solving strategies.Information Literacy: Maintaining complete and accurate notes of terms and formulas in Algebra II. Media Literacy:  Using graphs to examine the veracity of advertisements.ICT Literacy-Information, Communications and Technology: Accessing necessary information to solve problems using Chrome Books and Smart Phones and demonstrating that information on presentation technology.Life and Career Skills: Completing self-evaluations throughout the year to gage individual progress. EVIDENCE OF LEARNING AssessmentExtend the properties of exponents to rational exponents.Understand solving equations as a process of reasoning and explain the reasoning.Write expressions in equivalent forms to solve problems.Interpret functions that arise in applications in terms of the content.. Integration of Technology: Use of SmartNotebookUse of Mobile LabsUse of InternetUse of SmartBoard/ProjectorUse of Chromebooks/Smart Phones Materials/Equipment:Screens/LCD ProjectorTransparencies/markersChromebooksSmartboard, Handouts, texts, articles

 Goals/ObjectivesStudents will: CPI# Learning Activities/Instructional Strategies(Interdisciplinary Connections; Technology; Integration of 21st Century Skills) Assessment Tasks(More on the summative side) Use properties of integer exponents to explain and convert between expressions involving radicals and rational exponents, using correct notation. N.RN.1 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. Traditional AssessmentConvert between expressions involving radicals and rational exponents Alternative AssessmentApply the properties of integers Solve simple rational and radical equations in one variable and use them to solve problems. A.REI.1 Justify each step in the process and the solution and in the case of rational and radical equations show how extraneous solutions may arise. Traditional AssessmentSimple Rational and Radical EquationsAlternative AssessmentApply the properties of rational and radical. Choose and produce equivalent expressions for exponential functions using the properties of exponents. Produce equivalent expressions for exponential functions using the properties of exponents. Produce equivalent expressions for exponential functions using the properties of exponents. 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. ★ Using Desmos, create graphs and tables to give a visual example of behaviors. Differentiation/Adaptations/Modifications:Study GuidesIndividual instructionUse of review guides

 CPI# Cumulative Progress Indicator (CPI) A.REI.2 Expressions and EquationsExplain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents tothose 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. ASSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. 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.