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1 Algebra 2 Pacing Guide Teacher Name Period This Curriculum Guide is a suggestion for you to use as a guide. Each class should progress at its own pace. (written June 2015) Stards Benchmarks 1 st 9-weeks There are 41 teaching days. 8/17/15 10/15/15 Labor Day Holiday 9/7/15 Fall Holiday 9/23/15 First Week of School Activities NOTE TO TEACHERS: Remember that you will probably have a fire drill & assemblies in the first week of school. 1 The Baseline will be paper pencil, but the answer bubble sheets will be Baseline Progress scanned into Data Director for scoring. Monitoring Test 8/17-21/15 The Baseline should ONLY be 1 day. Stards Chapter 1 Expressions, Equations, Inequalities Benchmarks PERFORMANCE SCALES 4 Students will be able to do all things listed in #3, apply the concepts to real world situations, teach/explain to other students EQ How do variables help you model real-world situations? EQ - How can you use the properties of real numbers to simplify algebraic expressions? EQ - How do you solve an equation or inequality? 3 The students will be able to: Use variables to represent quantities in real world situations in patterns. Apply properties to real numbers variables. Use properties of numbers equality or inequality to solve an equation or inequality by finding increasingly simpler equations or inequalities which have the same solution as the original equation or inequality. 2 The students will be able to apply properties to real numbers only. 1 The students will be able to explain properties of real numbers. 1-4 Solving Equations EQ How can you use the properties of equality inverse operations to solve equations? A-CED.1.1 A-CED.1.4 MP 4, MP 6 (1) Solve equations Solve problems by writing equations CW - pg 30 #22,26,9,30,32 HW - pg 30 # 23,25,27,55,61 HW - pg 31 #56, 59, 54

2 1-5 Solving Inequalities EQ Just as you use properties of equality to solve equations, how can you use properties of inequality to solve inequalities? 1-6 Absolute Value Equations Inequalities EQ How can an absolute value equation have two solutions? Chapter 1 Review (including sections 1-3) A-CED.1.1, MP 7 A-SSE.1.1b A-CED.1.1 MP 1, MP 3 Chapter 1 Test (1) (2) Solve graph inequalities Write solve compound inequalities (2) Write solve equations inequalities involving absolute value pg 38 #15,21,25,39,41,51 CW - ph 46 # 11,16,18 HW - pg 46 #17,27,35 CW - pg 46 #73,69 (1) HW - pg 52 #18-34even, 35 Stards Chapter 2 Functions, Equations, Graphs EQ Does it matter which form of a linear equation you use? EQ How do you use transformations to help graph absolute value functions? EQ How can you model data with a linear function? Benchmarks PERFORMANCE SCALES 4 Students will be able to do all things listed in #3, apply the concepts to real world situations, teach/explain to other students 3 Students will be able to: Represent linear functions using slope intercept, point-slope, or stard form transform one version to another Use values of a, h, k to identify the transformations from a parent function Determine whether a relation is a function evaluate functions Graph piecewise functions 2 Students will be able to represent linear functions using slope intercept, point-slope, or stard form transform one form to another 1 Students will be able to identify the different forms of linear functions 2-1 Relations Functions F-IF.1.1 F-IF.1.2 (3) Graph relations Not in the EOC Item Specifications Not tested

3 EQ What is a relation how can you represent relations in 4 different ways? Identify functions Pg 65 #1-4all,10,11,14,15,17-23odd, Linear Functions Slope-Intercept Form EQ How do you find slope what is it on a nonvertical line? 2-4 More About Linear Equations EQ How do the slopes of two lines in the same plane show how the lines are related? Chapter 2 Mid-Chapter Quiz Concept Byte: Piecewise Functions EQ How can you graph, write, apply piecewise functions? 2-7 Absolute Value Functions Graphs F-IF.2.4 F-LE.2.5 F-IF.3.7 F-IF.3.9 F-LE.2.5 MP 1, MP 3, MP 7 F-IF.3.7b MP5 F-BF.2.3 F-IF.3.7b (1) Graph linear equations Write equations of lines Write an equation of a line given its slope a point on the line (2) Graph, write apply piecewise functions Pg 78 #11,17-35 odd Pg 87 #13-19 odd, all, 27,29, all, pg 91 go over. Do example 2 without calculator (2) Graph absolute value functions Pg 111 #9,11,21,23,27,29,30,31,35 EQ How do you explain the relationship of functions their absolute value? 2-6 Families of Functions EQ - How can you explain the relationships of a set of functions in creating families the parent? MP 1, MP 3, MP 5 F-IF.3.7 F-BF.2.3 MP 1, MP 3, MP 7 Chapter 2 Review (1) (1) Analyze transformations of functions Pg 104 #13,17-25 odd, 34,35

4 Chapter 2 Test (1) Stards Chapter 4 Quadratic Functions Equations EQ What are the advantages of a quadratic function in vertex form? In stard form? EQ How is any quadratic function related to the parent quadratic function y=x 2? EQ How are the real solutions of a quadratic equation related to the graph of the related quadratic function? 4-1 Quadratic Functions Transformations EQ How is the graph of any quadratic function a transformation of the graph of the parent function y=x 2? 4-2 Stard Form of a Quadratic Function EQ in the quadratic function f(x)= ax 2 + bx + c, what key information about Benchmarks PERFORMANCE SCALES 4 Students will be able to do all things listed in #3, apply the concepts to real world situations, teach/explain to other students 3 Students will be able to: Distinguish recognize advantages of the quadratic function in vertex stard forms. Be able to transform the parent function through reflections, translations, stretch compressions Show that the real solutions of the quadratic equation are the zeros of the related quadratic function the x-intercepts of its graph Underst that each point of a parabola is equidistant from a point called the focus a line called the directrix 2 Students will be able to show that the real solutions of the quadratic equation are the zeros of the related quadratic function the x-intercepts of its graph 1 Students will be able to recognize that a second degree function is a quadratic equation whose graph is a parabola F-BF.2.3 A-CED.1.1 F-IF.2.4 F-IF.2.6 MP 4, MP 7 F-IF.2.4 F-IF.2.6 F-IF.3.9 F-BF.1.1 (2) Identify graph quadratic functions (2) Graph quadratic functions written in stard form p # 7,9,15-16,18,23, 25 p # 27,31,35,37,39,43,45,49,51 p. 206 # 8-11,16-17,19,21 (change instructions for all problems to: graph each function, identify the vertex, axis of symmetry, y-intercept, direction of opening, min/max value, range) p. 206 # 26-27,30,32,33,35,38

5 the values of a, b, c, provide about the graph? 10-2 Parabolas (NOT including sideways) EQ What is a parabola? How is the focus directrix important to a parabola? G-GPE.1.2, MP 6 Quiz 4-1, 4-2, 10-2 (1) 4-4 Factoring Quadratic Expressions A-SSE.1.2 A-SSE.2.3 EQ How can you factor many quadratic trinomials (ax 2 + bx + c) into products of two binomials? 4-5 Quadratic Equations Concept Byte: Writing Equations from Roots EQ How can you find the zeros of a quadratic function y = ax 2 + bx + c? A-CED.1.1 A-APR.2.3 A-SSE.1.1a A-SSE.2.3a Quiz 4-4, 4-5 (1) 4-8 Complex Numbers A-CED.1.3 N-CN.1.1 Concept Byte: Quadratic N-CN.1.2 Inequalities N-CN.3.7 N-CN.3.8 EQ What are complex numbers? Why are they based on a number whose square if -1? 4-6 Completing the Square EQ How can you complete a perfect square trinomial MP 6 A-REI.2.4b A-SSE.2.3 (1) Write the equation of a parabola Graph parabolas (4) Find common binomial factors of quadratic expressions Factor special quadratic expressions (1) Solve quadratic equations by factoring Solve quadratic equations by graphing (2) Identify, graph, perform operations with complex numbers Find complex numbers solutions of quadratic equations (2) Solve equations by completing the square Pg 627 #8,9,13,14, factoring worksheets 1 through 4, see attached p. 229 # 9-17,43,44,47-50 p. 232 # 5-7 N-CN.3.8 not tested on EOC p. 253 # 9-25 odd,48-55 p. 253 # odd,45,47 p. 237 # 13-41odd (some fractions, some irrational) p. 237 # 43-45,46-51,63,65,67

6 into the square of a binomial? Rewrite functions by completing the square 4-7 The Quadratic Formula EQ How can you use different ways to solve a quadratic equation ax 2 + bx + c = 0, including a formula that gives values of x in terms of a, b, & c? A-REI.2.4b MP 4, MP 8 Chapter 4 Review (1) (2) Solve quadratic equations using the Quadratic Formula Determine the number of solutions by using the discriminant p. 245 # 11,14,17,20,23,25-27,37,58-60 p. 253 # 42,44 Chapter 4 Test (1) Teacher Planning Day 10/16/15 2 nd 9-weeks 10/19/15 There are 38 teaching days. 12/18/15 Veteran s Day Holiday 11/11/15 Thanksgiving Holiday 11/25/15 11/27/15 Semester Exams 12/16/15 Mid-Year Progress Monitoring Test 12/17/15 (Early Release Days) 12/18/15 Stards Chapter 3 Linear Systems Benchmarks PERFORMANCE SCALES 4 Students will be able to do all things listed in #3, apply the concepts to real world situations, teach/explain to other students 3 Students will be able to: Solve a system by graphing, substitution, elimination Determine the solution set of a system of linear inequalities using a graph Solve a system with three variables by substitution elimination

7 Solve quadratic systems by substitution, be able to graph 2 The students will be able to apply methods to solve two variable systems quadratic systems 1 The students will be able to apply methods to solve two variable systems 3-1 Solving Systems Using Tables Graphs EQ How do you use a set of values that replace the variables in the equations to solve a system of equations? 3-2 Solving Systems Algebraically EQ How can you use substitution to solve a system of equations? 2-8 Two-Variable Inequalities A-REI.3.6 A-REI.4.11 A-CED.1.3 MP 4, MP 5 A-CED.1.3 A-REI.3.5 A-REI.3.6 MP 1, MP 2, MP 3 F-IF.3.7b (1) Solve a linear system using a graph or a table Pg odd odd (2) Solve linear systems algebraically A-REI.3.5 not tested on EOC Pg 146 #11,13,19,23,25,31-37 odd (1) Graph two-variable inequalities 118 #13-21 odd, 39-44all EQ How is graphing a line graphing an inequality similar different? 3-3 Systems of Inequalities EQ How do you solve a system of inequalities by graphing? Chapter 3 Mid-Chapter Quiz 3-5 Systems with Three Variables EQ How can you use the algebraic methods needed to solve a system of two, MP 5, MP 7 A-REI.4.12 A-REI.3.6 A-CED.1.3 MP 4, MP 7 A-REI.3.6 MP 1, MP 3 (1) Solve systems of linear inequalities (1) (1) Solve systems in three variables using elimination Solve systems in three variables using substitution A-REI.4.12 not tested on EOC Pg 153 #17-31 odd Pg 171 #9,15,39

8 equations to solve a system of three equations. 4-3 Modeling With Quadratic Functions Concept Byte: Identifying Quadratic Data EQ Explain how three noncollinear points, where no two of which are in line vertically, are on the graph of exactly one quadratic function? 4-9 Quadratic Systems Concept Byte: Powers of Complex Numbers EQ How are the methods similar in solving quadratic equations to the ones used to solve system of linear equations? 3-4 Linear Programming Concept Byte: Graphs in Three Dimensions F-IF.2.4 F-IF.2.5 F-IF.2.6 F-IF.3.7 A-CED.1.3 A-REI.3.7 A-REI.4.11 MP 4 A-CED.1.3 F-LE.2.5 (2) Model data with quadratic functions (2) Solve graph systems of linear quadratic equations Solve graph systems of quadratic inequalities (2) Solve problems using linear programming Pg. 212 #7,9,13,16,17,23 Pg. 262 #11-23 odd, 47 Pg 160 #11,12,22 EQ How can we use linear programming to solve realworld situations? Chapter 3 Review (1) Chapter 3 Test (1) Stards Benchmarks

9 Chapter 5 Polynomials Polynomial Functions PERFORMANCE SCALES 4 Students will be able to do all things listed in #3, apply the concepts to real world situations, teach/explain to other students 3 Students will be able to: State the degree of a polynomial Describe end behavior of a polynomial function Find zeros, x-intercepts, factors Determine if the function is even or odd Sketch the graph using end behavior zeros Divide polynomials using synthetic long division Determine the remainder using the Remainder Theorem 2 Students will be able to state the degree end behavior find zeros by factoring 1 Students will be able to state the degree whether the function is even or odd 5-9 Transforming Polynomial Functions EQ What does each variable represent tell you about the graph of the equation y = af (x h) + k? 5-1 Polynomial Functions EQ How can you explain the distinguishing behaviors in looking at the algebraic form its graph what it tells you about the polynomial function? 5-2 Polynomials, Linear Factors Zeros EQ Explain how finding the zeros of a polynomial function will help you factor the polynomial, graph the F-BF.2.3 F-IF.3.7c F-IF.3.9 MP 4, MP 7 F-IF.3.7 A-SSE.1.1a MP 5 F-BF.1.1 F-IF.3.7c A-APR.2.3 A-SSE.1.1 MP 4, MP 5 (2) Apply transformations to graphs of polynomials (2) Classify polynomials Graph polynomial functions describe end behavior (2) Analyze the factored form of a polynomial Write a polynomial function from its zeros PG 343 #7-12, 28-29, 32-37, 45 Day 1 pg 285 #8-30 even, even Day 2 pg 285 #5-7 all, 32, 34-40all, all Day 1 pg 293 #8-26 even, 45,51 Day 2 pg 293 #27-34,40,43,50,52-54

10 function, solve the related polynomial equation? 5-3 Solving Polynomial Equations EQ Explain how when you solve a polynomial equation that has a factor of (x a), that the polynomial has value 0 when x = a? Also, explain that if a is a real number, then the graph of the polynomial has (a, 0) is an x-intercept? 5-4 Dividing Polynomials EQ How the steps in solving a long division problem similar to the steps needed to divide polynomials? Chapter 5 Mid-Chapter Quiz 5-5 Theorems About Roots of Polynomial Equations Concept Byte: Using Polynomial Identities EQ How can you use the factors of the numbers a n a 0 to help you factor P(x) solve the equation P(x) = 0? 5-6 The Fundamental Theorem of Algebra Concept Byte: Graphing Polynomials Using Zeros A-REI.4.11 A-SSE.1.2 MP 5, MP 6 A-APR.2.2 A-APR.1.1 A-APR.4.6 MP 6, MP 7 N-CN.3.7 N-CN.3.8 A-APR.3.4 MP 4, MP 8 N-CN.3.7 N-CN.3.8 N-CN.3.9 A-APR.2.3 (1) Solve polynomial equations by factoring Solve polynomial equations by graphing (2) Divide polynomials using long division Divide polynomial using synthetic division (1) (2) Solve equations using the Rational Root Theorem Use the Conjugate Root Theorem (2) Use the Fundamental Theorem of Algebra to solve polynomial equations with complex solutions Day 1 p. 300 #1-7, 10-24even, 39-41,52 Day 2 Practice Workbook p (5-3) #1-16,25-32 Day 1 p. 308 #6, 9-19odd, 16 Day 2 p. 308 #1-5, 21-29odd, 32-36,49-61odd, 67,68 N-CN.3.8 not tested on EOC Day 1 Workbook (5-5) p #1-6, Day 2 Workbook (5-5) p. 133 #1-3; p. 135 #7-12, N-CN.3.8 N-CN.3.9 not tested on EOC Day 1 p. 322 #15-21odd, 25, Day 2 p. 325 #1-6; p. 348 #5-9odd, 13-19odd

11 EQ How does the degree of a polynomial equation tell you how many roots the equation has? 5-8 Polynomial Models in the Real World EQ How can you use polynomial functions to model many real-world situations? MP 4 F-IF.2.5 F-IF.2.4 F-IF.2.6 F-IF.3.7, MP 5 Chapter 5 Review (1) (1) Fit data to linear, quadratic, cubic, or quartic models Pg 335 #9,11 Chapter 5 Test (1) Semester Exams Mid-Year Progress Monitoring Test (Early Release Days) 12/16/15 12/17/15 12/18/15 Winter Holidays 12/21/15 1/3/16

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