Algebra 1 and Algebra 2 Petal Pacing Guide Lynchburg City Schools Curriculum Framework Algebra II

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1 Grading Period: 1 st Nine Weeks Days to Teach = 44 SOL & Enabling Objectives: Description Text Recommended Activities Time Frame Begin the school year with relationship building activities continue integrating relationship building throughout the school year Activity Ideas PRE-TEST (for Teacher Evaluation & School Improvement: Interactive Achievement) will be released by the division to be administered at a time TBA Begin teaching the 3 rd day of school. DO NOT FEEL BOUND TO THE TEXT BOOK! PLEASE USE ONLINE RESOURCES, APPLETS, & HANDS-ON ACTIVITIES **Review of Algebra 1 & arithmetic skills as evidenced by PRE-TEST 3 Algebraic Expressions A.1a Translate verbal quantitative situations into algebraic expressions and vice versa. 1-1, , 1-4, 1-5 ESS A.1ad Translate & Evaluate ESS A.1c Evaluating Simplifying Expressions ESS A3a Simplifying Square Roots unit = 4

2 A.1b Model real-world situations w/ algebraic expressions in a variety of representations (concrete, pictorial, symbolic, verbal). A.1c Evaluate algebraic expressions for a given replacement set to include rational numbers. A.3a Express square roots of a whole number in simplest form. A.3b Express the cube root of a whole number in simplest form. A.1d Evaluate expressions that contain absolute value, square roots, & cube roots. A.4b Simplify expressions using the field properties of the real numbers and properties of equality to justify simplification. 1-2, 1-4, 1-5, , 11-1 Not in text! Sq. Roots 11-4 No Cube, 1-4, 1-5, 1-6, 1-7 justify = 1-8 ESS A3.b Simplify Radical ESS A.1ad Translate & Evaluate ESS A4b A Mystery to Solve Solving Linear Equations A.4b Solve equations using the field properties of the real numbers & properties of equality to justify the solution. 2-1, 2-2 ESS A.4b a Mystery to Solve Model solving equations = p.127 ESS A.4e Algebra Tiles & Equation Solving for this unit = 5

3 A.4e Solve multi-step linear equations in one variable. A.4l Determine if a linear equation in one variable has one, an infinite number, or no solutions. 2-3, Model p.141 NLVM Algebra Balance Scales NLVM Algebra Balance Scales Negative A.4f Confirm algebraic solutions to linear equations using a graphing calculator. p. 102 ESS A.4f Solving Linear Equations A.4a Solve a literal equation (formula) for a specific variable. 2-6 Illuminations Lesson Geology Rocks Equations ESS A.4a solve for Unknown Solving Linear Inequalities A.5a Solve multi-step linear inequalities in one variable A.5b Justify steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers 3-1, 3-2, , 3-3 ESS A.5a Inequalities ESS A.5b Greetings Solve inequalities Virtual Lab for this unit = 2 A.5c Solve real-world problems involving inequalities. 3-1, 3-2, 3-3, 3-4 Relations for

4 A.7a Determine whether a relation, represented by a set of ordered pairs, a table, or a graph is a function. 5-2 ESS A.7d Square Patios this unit = 4 A.7d Represent relations & functions using All.7a concrete, verbal, numeric, graphic & algebraic forms. Given one representation, students will be able to represent the relation in another form. 5-2, 5-3, 5-4 ESS A.7b Functions 2 ESS A.7a Functions 1 A.7b Identify the domain, range, zeros & intercepts of a function presented algebraically or graphically Domain and Range Using Graphs NLVM Function Machine A.7c For each x in the domain of f, find f(x). 5-2 Illuminations Lesson Do You Notice Sum Thing? A.7e Detect patterns in data and represent arithmetic and geometric patterns algebraically. 5-4 Illuminations Lesson Rates & Taxes NLVM Function Grapher Graph, Domain and Range of Common Functions Slope for this unit

5 A.6f Recognize and describe a line with a slope that is positive, negative, zero, or undefined. A.6e Find the slope of a line, given the graph of a line Math Forum Activity Slope of a Line Interactive Activity Slop Slider ESS A 6d Submarine = 3 A.6c Find the slope of a line, given the equation of a linear function. A.6d Find the slope of a line, given the coordinates of two points on the line. 6-2, Illuminations Lesson Movement with f(x)s Illuminations Lesson Rise Run Triangles Graphing Linear Equations & Inequalities A.6a Graph linear equations in two variables, including those that arise from a variety of realworld problems. 6-2, 6-3, (inequalities) NLVM Line Plotter Line Grapher y=mx + b for this unit = 4 A.6b Use the parent function y = x and describe transformations defined by changes in the slope or y-intercept. p. 290 ESS A.6b Transformationally Speaking A.6h Write an equation of a line when given the graph of a line. 6-2 Interactive Activity Graphit A.6g Use transformational graphing to investigate Illuminations Lesson Trout Pond equation of line

6 effects of changes in equation parameters on the graph of the equations. A.6j Write an equation of a line given the slope and a point on the line whose coordinates are integers. A.6i Write an equation of a line when given two points on the line whose coordinates are integers. A.6k Write an equation of a vertical line as x = a p ESS A.6g Transformation Investigation Seeing math Activity Linear Transformer ESS A.6i Equations of Lines ESS A.6i Slippery Slope A.6l Write an equation of a horizontal line as y = c 6-3 ESS A.6k slope 2 slope Direct & Inverse Variation A.8a Given a situation, including a real-world situation, determine whether a direct variation exists. A.8c Write an equation for a direct variation, give a set of data ESS a.8a Direct Variation Illuminations Lesson Mow Whole Thing? Interactive Activity Graphit for this unit = 2 A.8e Graph an equation representing a direct variation, given a set of data. 5-5 ESS A.8b Inverse Variation

7 A.8b Given a situation, including a real-world situation, determine whether an inverse variation exists. A.8d Write an equation for an inverse variation, given a set of data Solving Systems of Linear Equations & Inequalities A.4h Given a system of two linear equations in two variables that has a unique solution, solve the system graphically by identifying the point of intersection. A.4g Given a system of two linear equations in two variables that has a unique solution, solve the system by substitution of elimination to find the ordered pair which satisfies both equations , 7-3 ESS A.4h Spring Fling Carnival ESS A4.g All.c How Much is that Tune Illuminations Lesson Supply & Demand A.4i Determine whether a system of two linear equations has one solutions, no solution, or infinite solutions. A.4j Write a system of two linear equations that models a real-world situation. 7-1, 7-2, , 7-2, 7-3, ESS A.4i Road Trip ESS A.4j2 Exercise Fields

8 A.4k Interpret and determine the reasonableness of the algebraic or graphical solution of a system of two linear equations that models a real-world situation , 7-2, 7-3, 7-4 ESS A.5d Graphing System Inequalities Interactive Activity Linear Inequalities A.5d Solve systems of linear inequalities algebraically and graphically. 7-6 Polynomials A.2a Simplify monomial expressions & ratios of monomial expressions in which the exponents are integers, using the laws of exponents. A.2b Model sum & difference of polynomials w/ concrete objects & their related pictorial representations. 8-1, 8-2, 8-3 Not in text! (For 8-1) ESS A2a Exponents (for 8-2) ESS A2 a Scientifically Speaking (sci. not.) Algebra Tiles (see A.2d, A.2e, A.2f) for this unit = 10 A.2c Relate concrete & pictorial manipulations that model polynomial operations to their corresponding symbolic representations. A.2d Find sums & differences of polynomials. Not in text! 9-1 Virtual Algebra Tiles ESS A2.d Add Subtract Polynomials Alg Tiles A.2b Model products of polynomials w/ concrete p.466 (Algebra Tiles (see A.2d, A.2e, A.2f)

9 objects & their related pictorial representations. A.2c Relate concrete & pictorial manipulations that model polynomial operations to their corresponding symbolic representations. A.2e Find the products of polynomials. The factors will have no more that five total terms. A.2b Model quotients of polynomials w/ concrete objects & related pictorial representations. A.2c Relate concrete & pictorial manipulations that model polynomial operations to their corresponding symbolic representations. A.2f Find the quotient of polynomials, using a monomial or binomial divisor, or a complete factored divisor. Not in text! 9-2, 9-3, 9-4 Not in text! Not in text! 9-2 (monomial) 12-5 (binomial) NLVM Algebra Tiles ESS A.2e Multiply Poly With Alg Tiles ESS A2.f Divide Poly with Alg. Tiles Flex /Remediation 2 Grading Period: 2 nd Nine Weeks Days to Teach = 45

10 SOL & Enabling Objective: Description Text Recommended Activities Time Frame Factoring Polynomials A.2g Factor completely first-and second-degree polynomials w/ integral coefficients 9-5, 9-6 ESS A.2g Factoring NLVM Algebra Tiles unit = 5 A.2h Identify prime polynomials Not in text! A.2i Use the x-intercepts from the graphical representation of the polynomial to determine & confirm its factors Not in text! Finding Roots of Expressions & Quadratic Equations A.3c Express the principal square root of a monomial algebraic expression in simplest form where variables are assumed to have positive values Cutting Corners solving quadratic equations lesson unit = 8 A.4c Solve quadratic equations. 10-4, 10-5 Solving quadratic equation practice A.4d Identify the roots or zeros of a quadratic function over the real number system as the solutions to the quadratic equation that is 10-4 ESS A4.d Factoring for Zeros

11 formed by setting the given quadratic expression equal to zero. Algebra 1 and Algebra 2 Petal Pacing Guide A.4f Confirm algebraic solutions to quadratic equations, using a graphing calculator. 10-1, 10-2 Statistics A.9a Analyze descriptive statistics to determine the implications for the real-world situations from which the data drive. Not in text! ESS A.9a Analyzing Interpreting Stats Interactive Activity Measures unit = 9 A.9b Given data, including data in a real-world context, calculate & interpret the mean absolute deviation of a data set. Not in text! Interactive Activity Normal Distribution ESS A9.b Exploring Stats A.9c Given data, including data in a real-world context, calculate variance & standard deviation of a data set & interpret the standard deviation. Not in text! ESS A.9c Calculating Measures Dispersion A.9d Given data, including data in a real-world context, calculate & interpret z-score for a data set. Not in text! ESS A9.d Z-scores A.9e Explain ways in which standard deviation Not in text!

12 addresses dispersion by examining the formula for standard deviation. ESS A10 Box-and Whisker Plots A.9f Compare & contrast mean absolute deviation & standard deviation in real-world context. A.10 Compare, contrast,& analyze data, including data from real-world situations displayed in box-and-whisker plots. Not in text! p. 740 Illuminations Activity Box Plotter Illuminations lesson plan_nba & box plots Properties of the Real Number System Akk3.b Determine which field properties apply to the complex number system. All3.f Place the following sets of numbers in a hierarchy of subsets: complex, pur imaginary, real, rational, irrational, integers, whole, & natural ESS All 3.a-h Complex Numbers Operations with Complex Numbers Ti-83 unit = 3 Solving Absolute Value Equations and Inequalities All.4a Solve absolute value equations & inequalities algebraically & graphically. 1-3, 1-4, 1-5 ESS All.4a Absolute Value Equations & Inequalities NLVM Solving equations with balance scales unit = 3 NLVM Graphing Function Transformations

13 Absolute Value Inequality Number Line Compound Inequality Game Absolute Value Functions All.6a Recognize graphs of parent functions. All.6b Given a transformation of a parent function, identify the graph of the transformed function ESS All.6a-f Transformational Graphing Transformation Activity Exponential & Absolute Value unit = 4 All.6c Given the equation & using a transformation approach, graph a function. All.6d Given the graph of a function, identify the parent function. NLVM Graphing Function Transformations All.6e Given the graph of a function, identify the transformations that map the pre-image to the image in order to determine the equation of the image. NLVM Function Grapher All.6f Using a transformational approach, write the equation of a function given its graph.

14 Flex & Remediation SOL Review & Testing Mid-term Exam day Grading Period: 3 rd Nine Weeks Days to Teach = 48 SOL & Enabling Objective: Description Text Recommended Activities Time Frame Linear and Quadratic Regressions All.9a Collect & analyze data 2-4 Illuminations Lesson Exploring Linear Data unit = 2 All.9b Investigate scaterplots to determine if patterns exist & then identify the patterns. 5-1 Illuminations Lesson How Tall? All.9c Find an equation for the curve of best fit for data, using a graphing calculator. Models will include polynomial, exponential, & logarithmic functions. NLVM Block Patterns curve of bets fit Illuminations Activity Line of Best Fit All.9d Make predictions, using data, scatterplots, or the equation of the curve of best fit. All.9e Given a set of data, determine the model that would best describe the data. Illuminations Lesson Barbie Bungee

15 Properties of Quadratics All.6a Recognize graphs of parent functions All.6b Given a transformation of a parent function, identify the graph of the transformed function NLVM Graphing Function Transformations unit = 4 All.6c Given the equation & using a transformation approach, graph a function. NLVM Function Grapher All.6d Given the graph of a function, identify the parent function. Matching garabola to equation All.6e Given the graph of a function, identify the transformations that map the pre-image to the image in order to determine the equation of the image. Illuminations Lesson Hanging Chains All.6f Using a transformational approach, write the equation of a function given its graph. Graph, Domain, and Range of Common Functions All.7a Identify the domain, range, zeros, & intercepts of a function presented algebraically & graphically. Factoring Polynomials

16 All.1h Factor polynomials by applying general patterns including difference of square, sum, & difference of cubes, & perfect square trinomials. All.1i Factor polynomials completely over the integers ESS All.1hi Factoring unit = 4 All.1j Verify polynomial identities including the difference of square, sum, & difference of cubes, & perfect square trinomials. Solving Quadratic Equations by Factoring All.7a Identify the domain, range, zeros, & intercepts of a function presented algebraically & graphically. All.8a Describe the relationship among solutions of an equation, zeros of a function, x-intercepts of a graph, & factors a polynomial expression. All.8b Define a polynomial function, given its zeros. All.8c Determine a factored form of a polynomial expression from the x-intercepts of the graph of its corresponding function. 5-5 ESS All.8abc Factors Zeros & Solutions Finding the Domain and Range of a Function from a graph NLVM Function Grapher unit = 4

17 All.8d For a function, identify zeros of multiplicity greater than 1 and describe the effect of those zeros on the graph of the function. Complex Numbers System All.1d Simplify radical expressions containing positive rational numbers & variables. p. 262 ESS All.3a-h Complex Numbers unit = 3 All.3a Recognize that the square root of -1 is represented as i. All.3b Determine which field properties apply to the complex number system. 5-6 Operations with Complex Numbers Ti-83 All.3c Simplify radical expressions containing negative rational numbers & express in a + bi form. Arithmetic Operations with complex numbers from vectors All.3d Simplify powers of i. All.3f Place the following sets of numbers in a hierarchy of subsets: complex, pure, imaginary, real, rational, irrational, integers, whole, & natural. All.3g Write a real number in a + bi form

18 All.3h Write a pure imaginary number in a + bi form Solving Quadratic Equations All.4b Solve a quadratic equation over the set of complex numbers using an appropriate strategy. All.4c Calculate the discriminant of a quadratic equation to determine the number of real & complex solutions. All.7a Identify the domain, range, zeros, & intercepts of a function presented algebraically & graphically. All.8a Describe the relationship among solutions of an equation, zeros of a function, x-intercepts of a graph, & factors of a polynomial expression Finding the Domain and Range of a Function from a graph NLVM Function Grapher Illuminations Activity Completing the Square Solve Quadratic Equations Graphically The Discriminant calculator The discriminant and roots of quadratic unit = 4 All.8e Given a polynomial equation, determine the number of real solutions & non-real solutions. All.4h Recognize that the quadratic formula can be derived by apply the completion of squares to a quadratic equation in standard form.

19 Solving Non-Linear Systems All.5a Predict the number of solutions to a nonlinear system of 2 equations. All.5b Solve linear-quadratic system of 2 equations algebraically & graphically. All.5c Solve a quadratic-quadratic system of 2 equations algebraically & graphically. p. 577 ESS All.5abc Nonlinear Systems of Equations Function Grapher Illuminations Pan Balance with expressions unit = 2 High Order Polynomials All.7e Describe the end behavior of a function. All.9e Given a set of data, determine the model that would best describe the data. All.9c Find an equation for the curve of best fit for data, using a graphing calculator. Models will include polynomial, exponential, & logarithmic functions. Simplifying Radicals p All.1d Simplifying radical expressions containing 7-1 Illuminations Lesson Shrinking Candles ESS All.7avce f(x)s: Domain Range End Behavior Activity: page 300 text NVLM Block Patterns curve of best fit unit = 2 unit = 5

20 positive rational numbers & variables All.1g x and radical expressions not requiring rationalizing the denominators All.1f + and radical expressions Radical Equations All.1e Convert from radical notation to exponential notation, & vice versa. 7-4 NLVM Function Grapher unit = 4 All.4e Solve an equation containing a radical expression algebraically & graphically. Radical Functions All.6a Recognize graphs of parent functions. All.6b Given a transformation of a parent function, identify the graph of transformed function. All.6c Given the equation & using a transformation approach, graph a function. All.6d Given the graph of a function, identify the parent function. All.6e Given the graph of a function, identify the NLVM Graphing Function Transformations NLVM Function Grapher Graph, Domain and Range of Common Functions unit = 4

21 transformations the map the pre-image to the image in order to determine the equation of image. Algebra 1 and Algebra 2 Petal Pacing Guide All.6f Using a transformational approach, write the equation of a function given its graph Direct, Inverse, and Joint Variation All.10a Translate y varies jointly as x and z as y = kxz All.10b Translate y is directly proportional to x as y = kx Variation activity with Ti-83 Illuminations Lesson Inverse Variation unit = 2 All.10c Translate y is inversely proportional to x as y = k/x All.10d Given a situation, determine the value of the content of proportionally. All.10e Set up & solve problems, including realworld problems, involving inverse variation, joint variation, & a combination of direct & inverse variations. Rational Functions All.7a Identify the domain, range, zeros, & 9-3 Finding the Domain and Range of a Function from unit = 4

22 intercepts of a functions presented algebraically & graphically. Algebra 1 and Algebra 2 Petal Pacing Guide a graph All.7b Describe restricted/discontinued domains & ranges. All.7c Given the graph of a function, identify intervals on which the function is increasing & decreasing. All.7d Find the equation of vertical & horizontal asymptotes of functions. All.7e Describe the end behavior of a function. Illuminations Lesson Domain Representations NLVM Function Grapher Rational Functions graphs, asymptotes, and holes Graph, domain and Range of Common Functions Illuminations lesson Whelk-Come Flex /Remediation 2 Grading Period: 4 th Nine Weeks Days to Teach = 43 SOL & Enabling Objective: Description Text Recommended Activities Time Frame Simplifying Rational Expressions All.1a +, -, x, rational algebraic expressions. 9-4 ESS All.1abc Rational Expressions unit = 5

23 All.1b Simplify a rational algebraic expression w/ common monomial or binomial factors. 9-5 All.1c Recognize a complex algebraic fraction, & simplify it as a quotient or product of simple algebraic fractions. Solving Rational Equations All.4d Solve equations containing rational algebraic expressions w/ monomial or binomial denominators algebraically & graphically. More Regression Equations All.9c Find an equation for the curve of best fit for data, using a graphing calculator. Models will include polynomial, exponential, & logarithmic functions ESS All.4df Rational Equations NLVM Function Grapher Illuminations Lesson Finding f(x)s with regression Illuminations Lesson Paying for Wheels unit = 4 unit = 5 All.9d Make predictions, using data, scatterplots, or the equation of the curve of best fit. All.9e Give a set of data, determine the model that would best describe the data. All.6a Recognize graphs of parent functions. NLVM Block patterns curve of best fit Graphing exponential functions with asymptote, domain, and range Transformation activity exponential & absolute value

24 All.6b Given a transformation of a parent function, identify the graph of the transformed function. All.6c Given the equation & using a transformation approach, graph a function. All.6d Given the graph of a function, identify the parent function. NLVM Graphing Function Transformations NLVM Function Grapher EggMath Embryo Exponential explanation Exponential penny growth word problems All.6e Give the graph of a function, identify the transformations that map the pre-image to the image in order to determine the equation of the image. All.6f Using a transformational approach, write the equation of a function given its graph. Functions and their Inverses All.7f Find the inverse of a function. All.7g Graph the inverse of a function as a reflection across the line y=x. 8-3 (8-4) Drawing an Inverse Illuminations Lesson Counting Trains unit = 5

25 All.7h Investigate exponential & logarithmic functions, using the graphing calculator. Solving Logarithmic Equations All.7 Convert between logarithmic & exponential forms of an equation w/ bases consisting of natural numbers. Sequences and Series All.2a Distinguish between a sequence & a series All.2b Generalize patterns in a sequence using explicit & recursive formulas. Graph Domain and Range of Common Functions EggMath Embryo exponential explanation 8-5 Frogger game with log expressions ESS All.2abcde Arith & Geo Sequence & Series NLVM Function Machine explicit & recursive definitions unit = 2 unit = 3 All.2c Use & interpret the notations All.2d Given the formula, find (the nth term) for an arithmetic or a geometric sequence. All.2e Given formulas, write the first n terms and find the sum, of the first n terms of of an arithmetic or a geometric sequence. All.2f Given the formulas, find the sum of a convergent infinite series Illuminations Activity Sums infinite series Geometric Series and sum calculations Visualizing an infinite series

26 Normal Curve All.11a Identify the properties of a normal probability distribution. All.11b Describe how the standard deviation & mean affect the graph of the normal distribution Illuminations activity data Grapher Illuminations activity sampling distribution Illuminations lesson do I have to mow whole thing? unit = 3 All.11c Compare 2 sets of normally distributed data using a standard normal distribution & z- scores Illuminations Activity Histograms Properties of the normal distribution curve All.11d Represent probability as area under the curve of a standard normal probability distribution. All.11e Use the graphing calculator or a standard normal probability table to determine probabilities or percentiles based on z- scores. Permutations & Combinations All.12a Compare & contrast permutations & 6-7 Permutation braid unit = 2

27 combinations. All.12b Calculate the number of permutations of n objects taken r at a time. All.12c Calculate the number of combinations of n objects taken r at a time. All.12d Use permutations & combinations as counting techniques to solve real-world problems. POST-TEST (for Teacher Evaluation & School Improvement use same test as PRE-TEST 1 day SOL Review & Testing: 11 Days Final Exam Review & Testing 2 RECOMMENDED WEBSITES for additional lesson plans, activities, virtual manipulatives, and applets: Illuminatinos_NCTM Henrico Algebra 1 Resources Algebra 1 resources Algebra Bits Project interactive Suffolk Algebra 1 Resources Texas Instruments Activities

28 National Library of Virtual Manipulatives NVLM Florida lesson plans Jefferson Lab Sol Review Henrico Algebra 2 Resources Suffolk Algebra 2 Resources Algebra 1: Math Cross Walk 2001 and 2009 SOLs Changes to the reporting categories for Algebra 1 sol test: Now there are 3 reporting categories instead of 4. Relations & functions and statistics have been combined into 1 strand. Also, the Algebra 1 Formula Sheet has been revised Reporting Category 2009 SOL # items % of test # of items % of test Expressions & A.1, A.2a-c, A % 12 24% Operations Equations & A.4a-f, A.5a-d, A6 a % 18 36% Inequalities b Functions & Statistics A.7a-f, A.8, A.9, A.10, A % 20 40%

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