Algebra I Big Ideas Math SY

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1 Algebra I Big Ideas Math SY Benchmark Cycle 1 Benchmark Cycle 2 Benchmark Cycle 3 Cycle 4 September 5 October 31 BM Window Opens Nov 1 Term 1 ends Nov 13 November 1 January 26 BM Window Opens Jan 29 Keystone Eam Window Opens Jan 8 Term 2 ends Jan 29 January 29 April 6 BM Window Opens April 9 Term 3 ends Apr 9 April 9 June 12 Keystone Eam Window Opens May 14 Cycle 4 ends Jun 12 Total School Days 39 Total Days Including 1 Half Day 51 Total Days Including 4 Half Days 46 Total Days Including 3 Half Days 46 Total Days Including 13 Half Day Chapters 1 Solving Linear Equations 1 2 Graphing and Writing Linear Equations 2,1 3 Solving Linear Inequalities 1 4 Solving Systems of Linear Equations 1 5 Linear Functions 2 6 Eponential Equations and Functions Polynomial Equations and Factoring Polynomial Equations and Factoring Rational Equations and Functions Data Analysis and Displays (Alg II) Compound Events 2 Keystone Eam Review Remediation and Etension BEC Notes A Benchmark Cycle is defined as the time allotted to teach the content on each benchmark, assuming the benchmark is taken on the first day of the window. This means that, even though you may give the benchmark later in the window, you should move into new content as of the first date in the BM Window or you will fall behind the suggested pacing. 1 Contains Eligible from Module 1 of the Algebra I Keystone Eam. 2 Contains Eligible from Module 2 of the Algebra I Keystone Eam. BEC Contains content that goes beyond the eligible content for the Algebra I Keystone Eam, i.e., material not included on the state assessment. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

2 Table of s Block Schedule Options... 3 Benchmark Cycle 1 Standards... 4 Benchmark Cycle 1 Scope and Sequence... 7 Benchmark Cycle 2 Standards Benchmark Cycle 2 Scope and Sequence Benchmark Cycle 3 Standards Benchmark Cycle 3 Scope and Sequence Cycle 4 Standards Cycle 4 Scope and Sequence PA Core Standards by Cycle Algebra Eligible Taught Document Information Page THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

3 Block Schedule Options Note: With block schedules, generally follow the suggested sequence of lessons. Asterisked lessons are approimately 90-minutes in length. Non-asterisked lessons (approimately 45-minutes in length) may be combined, but consider combining them meaningfully, instead of simply teaching two-lessons back-toback. When single non-asterisked lessons precede or follow an asterisked one, consider using Concept Bytes, Mathematical Modeling, or Common Core Performance Tasks to start or complete the lesson (using 45 available minutes to construct a full 90-minute lesson). Benchmark Cycle 1 Benchmark Cycle 2 Benchmark Cycle 3 Cycle 4 Suggested Pacing A / B Block Use the suggested pacing, but combine 45-minute (non-asterisked) lessons, in accordance with the general note above. Full Block Fall Full Block Spring 9/5 9/29 Ch. 1 to Ch. 3 10/2 10/31 Ch. 4 to Ch. 6, Ch. 7.1 to /1 11/28 Ch. 7.4 to 7.9, Ch 11.3 to /29 1/5 Ch to 12.8, Ch 10.4 (Alg II) Keystone Eam Review 1/5 1/26 Remediation and Etension 1/30 2/28 Ch. 1 to Ch. 3 Benchmark Schedule 3/1 4/6 Ch. 4 to Ch. 6, Ch. 7.1 to 7.3 4/9 4/18 Ch. 7.4 to 7.9, Ch 11.3 to /19 4/30 Ch to 12.8, Ch 10.4 (Alg II) Keystone Eam Review 5/1 5/11 Remediation and Etension A / B Block Follow Benchmark schedule indicated in the Scope and Sequence document that follows this page. Full Block Fall Full Block Spring Benchmarks 1 and 2 (No need to complete in one sitting) None (Benchmark 3 not taken) Benchmarks 1 and 2 (No need to complete in one sitting) None (Benchmark 3 not taken) THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

4 Benchmark Cycle 1 Standards PA Eligible A Simplify/evaluate epressions involving properties/laws of eponents, roots, and/or absolute values to solve problems. Note: Eponents should be integers from -10 to 10. A Write, solve, and/or apply a linear equation (including problem situations). A Use and/or identify an algebraic property to justify any step in an equation-solving process. Note: Linear equations only A Interpret solutions to problems in the contet of the problem situation. Note: Linear equations only. A Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination. Note: Limit systems to two linear equations. A Interpret solutions to problems in the contet of the problem situation. Note: Limit systems to two linear equations. A Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities). PA Core Standards CC.2.1.HS.F.1 Apply and etend the properties of eponents to solve problems with rational eponents. CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real-world or mathematical problems. CC B.1 Apply concepts of radicals and integer eponents to generate equivalent epressions. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable. CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable. CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.1.HS.F.4 Use units as a way to understand problems and to guide the solution of multistep problems. CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC B.3 Analyze and solve linear equations and pairs of simultaneous linear equations. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

5 PA Eligible A Identify or graph the solution set to a linear inequality on a number line. A Interpret solutions to problems in the contet of the problem situation. Note: Linear inequalities only. A Write and/or solve a system of linear inequalities using graphing. Note: Limit systems to two linear inequalities. A Interpret solutions to problems in the contet of the problem situation. Note: Limit systems to two linear inequalities. A Analyze a set of data for the eistence of a pattern and represent the pattern algebraically and/or graphically. A Create, interpret, and/or use the equation, graph, or table of a linear function. A Translate from one representation of a linear function to another (i.e., graph, table, and equation). PA Core Standards CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.1.HS.F.4 Use units as a way to understand problems and to guide the solution of multistep problems. CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. CC C.1 Define, evaluate, and compare functions. CC C.2 Use concepts of functions to model relationships between quantities. CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their contet. CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables. CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.1.HS.F.4 Use units as a way to understand problems and to guide the solution of multistep problems. CC B.2 Understand the connections between proportional relationships, lines, and linear equations. CC C.1 Define, evaluate, and compare functions. CC C.2 Use concepts of functions to model relationships between quantities. CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

6 PA Eligible A Identify, describe, and/or use constant rates of change. A Apply the concept of linear rate of change (slope) to solve problems. A Write or identify a linear equation when given the graph of the line, two points on the line, or the slope and a point on the line. Note: Linear equation may be in point-slope, standard, and/or slope-intercept form. A Determine the slope and/or y-intercept represented by a linear equation or graph. PA Core Standards CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. CC.2.2.HS.C.4 Interpret the effects transformations have on functions and find the inverses of functions. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables. CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their contet. CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable. CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their contet. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable. CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. CC.2.2.HS.C.5 Construct and compare linear, quadratic, and eponential models to solve problems. CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their contet. CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

7 Benchmark Cycle 1 Scope and Sequence 9/5-9/20: 1 Day Per Lesson + 8 Days Suggested 9/5-9/11 1/30-2/6 Chapter. Lesson Chapter 1: Solving Linear Equations Lesson Title Lesson Topic(s) Eligible 1.1 Solving Simple Equations a Use properties of equality to solve one-step equations. 1.2 Solving Multi-Step Equations 1.3* 1.3 EXT b 1.4 Solving Equations with Variables on Both Sides Etension: Solving Absolute Value Equations Rewriting Equations and Formulas Solve multi-step equations by using inverse operations to isolate the variable. Solve equations with variables on both sides by using Properties of Equality and collecting variable terms on one side. Solve absolute value equations. Use the techniques for solving equations to solve literal equations. A , A , A A A , A , A Note: Chapter 1 concentrates on two essential questions: Can equations that appear different be equivalent? How can you solve equations and make sense of their solutions? Be certain to maintain rigor during this chapter and beyond by asking students to eplain their thinking. * Lessons marked with an asterisk may require two 45-minute class periods, for which fle days may be used. a Each lesson is preceded by an Activity, intended to support students in problem-solving and the PA Core Standards for Mathematical Practice. b Note also that Etension lessons sometimes contain content that is assessed on the Keystone Algebra I Eam. When Eligible is not included, these lessons are marked Beyond Eligible. Review foundational knowledge and check for understanding, as needed, through Do Nows or Bell Ringers, homework, and teacher-created assessments. Review content from 8 th Grade on integers and rational numbers, as you feel necessary. Be mindful of the suggested pacing with fle days for this sort of review, but note that much of the content related to these topics is not directly assessed on the Algebra I Keystone Eam. Rigor is elevated, when students have opportunities to make sense of and solve problems involving equality, using their own intuition and eplaining their ideas. Concentrate on encouraging students to use models to represent their thinking throughout this chapter and beyond. Consider using Which One Doesn t Belong (wodb.ca), Estimation180.com, Three-Act Math modeling activities (see Remediation and Etension in Cycle 4), algebra tiles (available, free and virtually at or SolveMe Puzzles ( Also consider using fle days, on occasion, to work on the Big Ideas Projects (see Appendi A of the Teacher s Edition). THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

8 9/25-10/17: 1 Day Per Lesson + 10 Days Suggested 9/12-9/20 2/7-2/16 Chapter. Lesson Lesson Title Chapter 2: Graphing and Writing Linear Equations Lesson Topic 2.1 Graphing Linear Equations Graph linear equations using a table of values. 2.2* Slope of a Line Find the slopes of lines in a variety of contets. 2.2 EXT * 2.5* 2.6** 2.6 EXT Etension: Slopes of Parallel and Perpendicular Lines Graphing Linear Equations in Slope-Intercept Form Graphing Linear Equations in Standard Form Writing Equations in Slope- Intercept Form Writing Equations in Point-Slope Form Etension: Writing Equations of Parallel and Perpendicular Lines 2.7 Solving Real-Live Problems Use slope to determine if lines are parallel or perpendicular. Use slope-intercept form of a line to graph the line. Graph equations written in standard form. Write an equation of a line given its slope and y-intercept. Write the equation of a line given the slope and a point. Write the equation of a line that is either parallel or perpendicular to a given line. Solve real-life problems using equations, graphs, and intercepts. Eligible A , A A , A , A , A A , A A , A , A , A A , A A , A Note: Students looking at one family of related functions: linear functions. They investigate these questions: What information does the equation of a line give you? What does the slope of a line indicate about the line? Note that this chapter largely covers Module 2 content. Efforts have been made to keep Module 1 content together and Module 2 content together, as long as the progression of ideas is not significantly interrupted. This material should be considered more than techniques to master and instead part of a broader theme making sense of phenomena that grow or diminish at constant rates. How do we know whether temperatures are changing, wealth is becoming concentrated, or even whether trains will arrive on time? Problem-solving and the tools of algebra, analyzing linearity, help us defend our thinking. ** Lesson 2.6 may require three 45-minute class periods, for which fle days may be used. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

9 10/18-10/31: 1 Day Per Lesson Days Suggested 9/25-9/29 2/20-2/28 Chapter. Lesson Lesson Title 3.1* Writing and Graphing Inequalities Solving Inequalities Using Addition or Subtraction Solving Inequalities Using Multiplication or Division Chapter 3: Solving Linear Inequalities Lesson Topic Translate inequalities from words to symbols and check to see if a value is a solution of the inequality. Use the Addition and Subtraction Properties of Inequality to solve inequalities. Use the Multiplication and Division Properties of Inequality to solve inequalities. 3.4** Solving Multi-step Inequalities Solve and graph multi-step inequalities. 3.4 EXT 3.5 Etension: Solving Compound Inequalities Graphing Linear Inequalities in Two Variables Solve and graph compound inequalities. Graph linear inequalities in two variables. Eligible A , A A , A , A A , A Focus: In Chapter 3, students address these questions: How do you represent relationships between quantities that are not equal? Can inequalities that appear different be equivalent? How can you solve inequalities and make sense of their solutions? Chapter 3 etends ideas from Chapter 2, investigating inequality. Students will draw on their previous understanding of inequality, as they learned about making comparisons and representing inequalities with symbols throughout elementary and middle school. Throughout this Chapter, students should be encouraged to make sense of algebraic inequalities by substituting the variable with specific values and determining whether the result is true or false. Students can also model their thinking, as with equations. Benchmark 1 Window: Nov 1 Nov 17 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

10 Benchmark Cycle 2 Standards PA Eligible A Compare and/or order any real numbers. Note: Rational and irrational may be mied. A Simplify square roots (e.g., 24 = 2 6). A Simplify/evaluate epressions involving properties/laws of eponents, roots, and/or absolute values to solve problems. Note: Eponents should be integers from -10 to 10. A Use estimation to solve problems. A Add, subtract, and/or multiply polynomial epressions (epress answers in simplest form). Note: Nothing larger than a binomial multiplied by a trinomial. PA Core Standards CC E.1 Distinguish between rational and irrational numbers using their properties. CC E.4 Estimate irrational numbers by comparing them to rational numbers. CC.2.1.HS.F.1 Apply and etend the properties of eponents to solve problems with rational eponents. CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real-world or mathematical problems. CC E.3 Develop and/or apply number theory concepts to find common factors and multiples. CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real-world or mathematical problems. CC.2.1.HS.F.1 Apply and etend the properties of eponents to solve problems with rational eponents. CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real-world or mathematical problems. CC B.1 Apply concepts of radicals and integer eponents to generate equivalent epressions. CC B.3 Model and solve real-world and mathematical problems by using and connecting numerical, algebraic, and/or graphical representations. CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.1 Interpret the structure of epressions to represent a quantity in terms of its contet. CC.2.2.HS.D.2 Write epressions in equivalent forms to solve problems. CC.2.2.HS.D.3 Etend the knowledge of arithmetic operations and apply to polynomials. CC.2.2.HS.D.5 Use polynomial identities to solve problems. CC.2.2.HS.D.6 Etend the knowledge of rational functions to rewrite in equivalent forms. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

11 PA Eligible A Write and/or solve a system of linear equations (including problem situations) using graphing, substitution, and/or elimination. Note: Limit systems to two linear equations. A Interpret solutions to problems in the contet of the problem situation. Note: Limit systems to two linear equations. A Write and/or solve a system of linear inequalities using graphing. Note: Limit systems to two linear inequalities. A Interpret solutions to problems in the contet of the problem situation. Note: Limit systems to two linear inequalities. A Analyze a set of data for the eistence of a pattern and represent the pattern algebraically and/or graphically. A Determine whether a relation is a function, given a set of points or a graph. A Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table). PA Core Standards CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC B.3 Analyze and solve linear equations and pairs of simultaneous linear equations. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. CC C.1 Define, evaluate, and compare functions. CC C.2 Use concepts of functions to model relationships between quantities. CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their contet. CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

12 PA Eligible A Create, interpret, and/or use the equation, graph, or table of a linear function. A Translate from one representation of a linear function to another (i.e., graph, table, and equation). PA Core Standards CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.1.HS.F.4 Use units as a way to understand problems and to guide the solution of multistep problems. CC B.2 Understand the connections between proportional relationships, lines, and linear equations. CC C.1 Define, evaluate, and compare functions. CC C.2 Use concepts of functions to model relationships between quantities. CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. CC.2.2.HS.C.4 Interpret the effects transformations have on functions and find the inverses of functions. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

13 Benchmark Cycle 2 Scope and Sequence Suggested Chapter. Lesson Chapter 4: Solving Systems of Linear Equations Lesson Title Lesson Topic Eligible 11/1-11/30: 1 Day Per Lesson + 11 Days + 2 Half Days 10/2-10/6 3/1-3/7 4.1* * 4.4 EXT Solving Systems of Linear Equations by Graphing Solving Systems of Linear Equations by Substitution Solving Systems of Linear Equations by Elimination Solving Special Systems of Linear Equations Etension: Solving Linear Equations by Graphing Solve a system of linear equations by graphing. Solve systems of linear equations by substitution. Solve systems of linear equations by elimination. Solve special systems of linear equations, those that have one solution, no solutions, or infinitely many solutions. Solve an equation with variables on both sides by graphing. 4.5 Systems of Linear Inequalities Solve systems of linear inequalities by graphing. A , A Beyond Eligible A , A Note: In Chapter 4, students eplore systems of linear equations and inequalities, raising such questions as: How can you solve a system of equations or inequalities and make sense of their solutions? How do systems of equations and inequalities model real-world situations? Note that while the 4.4 Etension lesson is marked Beyond Eligible, it contains useful material on solving equations applicable to graphing calculators and other technology tools (e.g., Desmos). Also note that the core ideas of Chapter 2 (containing Module 2 content) establish a foundation for Chapter 4 (linear systems), which contains Module 1 content. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

14 Suggested Chapter. Lesson Lesson Title 5.1* Domain and Range of a Function Chapter 5: Linear Functions Lesson Topic Identify the domain and range of a function from a graph and table of values. Eligible A /1-12/22: 1 Lesson Per Day Days 10/9-10/16 3/8-3/ EXT Etension: Relations and Functions 5.2 Discrete and Continuous Domains 5.3* Linear Function Patterns 5.4** Function Notation Determine whether a relation is a function using tables, maps, and the vertical line test. Graph functions and determine whether the domain is discrete or continuous. Write linear functions by recognizing patterns in graphical and tabular information. Use function notation to evaluate functions, graph functions, and vertically shift the graphs of functions. A A , A , Beyond Eligible *** A , A , A , A EXT Etension: Special Linear Functions Graph piecewise functions. Beyond Eligible ** Lesson 5.4 may require four 45-minute class periods, for which fle days may be used. *** Pay close attention to the content in all sections of Chapter 5 marked with Beyond Eligible. Lessons 5-4 EXT and 5.5 may be taught after the Algebra I Keystone eam. But the bulk of Lessons 5.2 and 5.6 contain content that may be assessed on the Algebra I Keystone Eam. In Lesson 5.2, support students in deepening their understanding of functions and analyzing data. But do not emphasize discrete domains (nor the vocabulary of discrete and continuous domains). In Lesson 5.6, below, support students in creating and using linear functions and analyzing linear data, but do not emphasize the term arithmetic sequence and you may find using function notation a more helpful representation. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

15 Suggested (see previous) Chapter. Lesson 5.5* Lesson Title Comparing Linear and Non-Linear Functions 5.6 Arithmetic Sequences Chapter 5: Linear Functions (cont.) Lesson Topic Compare linear and non-linear functions. Describe and represent arithmetic sequences using an equation. Eligible Beyond Eligible A , A , A , Beyond Eligible Focus: In Chapter 5, students investigate modeling and functions. Students develop an understanding of the relationship between function notation, graphs, tables, and verbal epressions. They address: How can you represent and describe functions? How do functions describe realworld-situations? Consider reviewing, as needed, two topics from Grade 8 before beginning this chapter: define, evaluate, and compare functions (CC C.1); and use concepts of functions to model relationships between quantities (CC C.2). Ideas underlying the essential questions, above, permeate algebra and higher mathematics. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

16 Suggested Chapter. Lesson Lesson Title Chapter 6: Eponential Equations and Functions Lesson Topic Eligible 1/3-1/17: 1 Day Per Lesson + 7 Days 10/17-10/23 3/20-3/28 6.1** Properties of Square Roots 6.1 EXT Real Number Operations Use properties of square roots to simplify and evaluate epressions involving square roots. Eplore closure under addition, subtraction, multiplication, and division of rational and irrational numbers. 6.2* Properties of Eponents Use properties of eponents to simplify epressions. 6.3 Radicals and Rational Eponents Evaluate epressions involving n th roots and rational eponents. Note: Eamples that do not include integer eponents / indices from -10 to 10 are Beyond Eligible. A , A A , A , Beyond Eligible *** A , A A , A , Beyond Eligible Note: In Chapter 6, students investigate these essential questions: How can you represent very large and very small numbers? How can you simplify epressions involving eponents? In Lesson 6.3, focus on square roots and perfect cube roots to address the Assessment Anchors. This topic is traditionally presented as a set of rules to memorize. To foster deeper understanding, instead, students should draw on their problemsolving and reasoning abilities, including eploring with calculators and whole numbers, to conjecture and justify these rules themselves. Note that Chapter 6 plays a crucial role in transitioning from studying linear functions and epressions to studying polynomials. Building on students understanding of eponents, students will compose and decompose linear epressions in performing operations with and factoring polynomial epressions. Also note that the remaining lessons in this chapter (Lessons 6.4 to 6.7) go beyond the eligible content for the Algebra I Keystone Eam, and so these lessons have been moved until later in the year. ** Lesson 6.1 may require four 45-minute class periods, for which fle days may be used. *** Note, as with Chapter 5, some lessons go beyond the eligible content. Use Lesson 6.1 as an opportunity to support students with comparing, ordering, and estimating rational and irrational numbers by asking targeted questions during discussions. Do not emphasize the terminology closed. In Lesson 6.3, some eamples include eponents that are not integers from -10 to 10, but only non-integer square roots and perfect cube roots represent content that is eligible to be assessed on the Algebra I Keystone Eam. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

17 Suggested Chapter. Lesson Lesson Title Chapter 7: Polynomial Equations and Factoring Lesson Topic Eligible 1/18-1/26: 1 Day Per Lesson + 4 Days 10/23-10/31 4/3-4/6 7.1 Polynomials Classify polynomials. 7.2* Adding and Subtracting Polynomials 7.3* Multiplying Polynomials Add and subtract polynomials. Multiply polynomials. Note: Nothing larger than a binomial multiplied by a trinomial. A Benchmark 2 Window: Jan 29 Feb 13 THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

18 Benchmark Cycle 3 Standards PA Eligible A Write, solve, and/or apply a linear equation (including problem situations). A Add, subtract, and/or multiply polynomial epressions (epress answers in simplest form). Note: Nothing larger than a binomial multiplied by a trinomial. A Factor algebraic epressions, including difference of squares and trinomials. Note: Trinomials are limited to the form a 2 + b + c where a is equal to 1 after factoring out all monomial factors. A Simplify/reduce a rational algebraic epression. PA Core Standards CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.1.HS.F.4 Use units as a way to understand problems and to guide the solution of multistep problems. CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC B.3 Analyze and solve linear equations and pairs of simultaneous linear equations. CC C.1 Define, evaluate, and compare functions. CC C.2 Use concepts of functions to model relationships between quantities. CC.2.2.HS.C.3 Write functions or sequences that model relationships between two quantities. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.8 Apply inverse operations to solve equations or formulas for a given variable. CC.2.2.HS.D.9 Use reasoning to solve equations and justify the solution method. CC.2.2.HS.D.10 Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. CC.2.2.HS.D.1 Interpret the structure of epressions to represent a quantity in terms of its contet. CC.2.2.HS.D.2 Write epressions in equivalent forms to solve problems. CC.2.2.HS.D.3 Etend the knowledge of arithmetic operations and apply to polynomials. CC.2.2.HS.D.5 Use polynomial identities to solve problems. CC.2.2.HS.D.6 Etend the knowledge of rational functions to rewrite in equivalent forms. A Calculate and/or interpret the range, quartiles, and interquartile range of data. CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable. CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

19 PA Eligible A Estimate or calculate to make predictions based on a circle, line, bar graph, measure of central tendency, or other representation. A Analyze data, make predictions, and/or answer questions based on displayed data (boand-whisker plots, stem-and-leaf plots, scatter plots, measures of central tendency, or other representations). A Make predictions using the equations or graphs of best-fit lines of scatter plots. A Find probabilities for compound events (e.g., find probability of red and blue, find probability of red or blue) and represent as a fraction, decimal, or percent. PA Core Standards CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable. CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data. CC.2.4.HS.B.5 Make inferences and justify conclusions based on sample surveys, eperiments, and observational studies. CC B.3 Investigate chance processes and develop, use, and evaluate probability models. CC.2.4.HS.B.4 Recognize and evaluate random processes underlying statistical eperiments. CC.2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

20 Benchmark Cycle 3 Scope and Sequence Suggested Chapter. Lesson Chapter 7: Polynomial Equations and Factoring Lesson Title Lesson Topic Eligible 1/29-2/16: 1 Day Per Lesson + 6 Days + 2 Half Days 11/1-11/22 4/9-4/16 7.4* Special Products of Polynomials Use special product patterns to multiply binomials. A Solving Polynomial Equations in Factored Form Factoring Polynomials Using the GCF Solve polynomial equations using the Zero-Product Property. Factor polynomials using the greatest common factor. 7.7 Factoring 2 + b + c Factor trinomials of the form 2 + b + c. 7.8 Factoring a 2 + b + c Factor trinomials of the form a 2 + b + c, when a ** Factoring Special Products 7.9 EXT Etension: Factoring Polynomials Completely Factor perfect square trinomials, and factor the difference of two squares. Factor higher-degree polynomials completely. Beyond Eligible A , A A Note: Chapter 7 addresses these essential questions: Can two algebraic epressions that appear different be equivalent? How are the properties of real numbers related to polynomials? In Lesson 7.9 and 7.9 EXT, concentrate on factoring trinomials where a = 1 after factoring out all monomials. Chapter 7 ties together storylines from three previous chapters: linear functions in Chapters 2 and 5, and eponents in Chapter 6. In this chapter, students combine linear epressions to make quadratic epressions, just as they combined prime numbers to make composite numbers in elementary school. Likewise, students connect their understanding of factoring whole numbers with factoring quadratics. Students may reason incorrectly about algebraic epressions, relying on their understanding of numbers. To promote depth of understanding, ask students to investigate their conjectures about polynomials by substituting a value for the variable and seeing whether their approach yields a true or false result. ** Lesson 7.9 may take approimately three 45-minute class periods, for which fle days may be used. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

21 Suggested Chapter 11: Rational Equations and Functions Chapter. Lesson Lesson Title Lesson Topic Eligible 11.3 Simplifying Rational Epressions Students will simplify rational epressions by factoring and dividing out common factors. 2/20-2/27: 1 Day Per Lesson + 5 Days 11/27-11/28 4/14-4/ Multiplying and Dividing Rational Epressions Multiply and divide rational epressions. A Focus: Chapter 11 asks: How are rational epressions related? In Chapter 11, students continue studying polynomials, the thread that began in from Chapter 7 and that has roots etending back into linear equations in Chapter 2. Since much of Chapter 11 contains material that goes beyond the eligible content for the Algebra I Keystone Eam, the remainder of Chapter 11 is covered later in the year. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

22 Suggested Chapter. Lesson Chapter 12: Data Analysis and Displays Lesson Title Lesson Topic Eligible 12.1 Measures of Central Tendency Eplore how an outlier affects the three measures of central tendency. A , A /28-3/28: 1 Day Per Lesson Days 11/29-12/15 4/19-4/ Measures of Dispersion Find the range and standard deviation of a data set and compare two data sets. Note: Standard deviation is Beyond Eligible, but finding the range supports making bo-and-whisker plots Bo-and-whisker plots Construct and analyze bo-and-whisker plots Shapes and Distributions 12.5 Scatter Plots and Lines of Fit Students will describe the shape of a distribution and choose measures of central tendency and spread to describe the data. Students will construct scatter plots, draw the line of fit, and analyze the equation. A , A , A , Beyond Eligible *** A , A , A Beyond Eligible A A , A , A THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

23 Suggested (see previous) Chapter. Lesson Chapter 12: Data Analysis and Displays Lesson Title Lesson Topic Eligible 12.6* Analyzing Lines of Fit Use residuals and find lines of best fit Two-Way Tables 12.8 Choosing a Data Display Alg II: 10.4 Probability of Disjoint and Overlapping Events Use two-way frequency tables to analyze data and to make predictions. Students will choose and construct an appropriate data display. Find probabilities of compound events A , A A , A A Focus: In Chapter 12, students investigate these questions: How can collecting and analyzing data help you make decisions or predictions? How can you make and interpret different representations of data? How is probability related to real-world events? Students should be familiar with many of the ideas underlying this chapter, because data analysis and probability are important threads throughout K-12 mathematics. Chapter 12 deepens students understanding by formalizing statistical approaches and counting methods. Chapter 12 also builds on concepts developed throughout the year, involving bivariate relationships. In some sense, many of the previous chapters deal with ideal data that eists only in a perfect world, and Chapter 12 offers tools for handling messy, real-world data. Benchmark 3 Window: Apr 9 Apr 25 *** As in previous chapters, note that several sections of this chapter go beyond the eligible content on the Algebra I Keystone Eam, but that some of this material may be motivating to students and may help tie the chapter together. Consider including this material, as time permits. Note that you will may use the online edition of the Big Ideas Math Algebra II tetbook, to teach Lesson 10.4 on compound probabilities. You may need to supplement Lesson 10.4 with material from earlier in Chapter 10 of Algebra II. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

24 Cycle 4 Standards No new Algebra I Keystone Eligible items. Cycle 4 Scope and Sequence Algebra I Keystone Eam Preparation 4/30-5/11 10 Days Use data to determine which topics/skills to revisit. Consider observation data, formative assessments, other teacher-created assessment data, and benchmark assessment data to refresh students knowledge of Eligible. Consider honing-in on essential content by reviewing the Performance Level Descriptors at And consider using practice problems from THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

25 Remediation and Etension Options Option 1: Revisit Activities or Big Ideas Math Projects Each chapter contains an opening Activity, intended to deepen students understanding of the content, as they proceed through the lessons. As students develop and strengthen tools for solving the Activity, they can return to them and approach them in a different light. Activities could be used to summarize and wrap-up the school year. In addition, the Big Ideas Math Projects in Appendi A are interdisciplinary projects that can support students problem-solving capacities and engagement with the Standards for Mathematical Practice. Option 2: Cover Remaining Consider teaching the remaining content from the tet, which can be a springboard for work in subsequent years. You may also want to check with your colleagues about what content you could pre-teach or what content they would like you to revisit. On the following pages, you will see several possibilities, related to eponents and eponential functions (Chapter 6), quadratic functions and equations (Chapters 8-9), radical epressions and equations (Chapter 10), and rational epressions and functions (Chapter 11). Option 3: Mathematical Modeling in Three Acts Option 4: Miscellaneous (Financial Literacy, Quantitative Reasoning, Statistics, etc.) Students may remember Three-Act mathematical modeling activities from Grades 6-8. During the remainder of the year, consider offering students opportunities to engage authentically in the Standards for Mathematical Practice through the Three-Act Math activities. You can find Three-Act modeling activities at: or within this Google Sheet. The Federal Reserve Bank of Philadelphia has posted free lesson plans for high school teachers on financial literacy at: In addition, Census.gov has a number of data analysis activities, using real U.S. Census data, at: Finally, consider other cross-curricular quantitative reasoning activities, such as those available at: THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

26 Suggested Chapter. Lesson Lesson Title 6.4 Eponential Functions Chapter 6: Eponential Equations and Functions Lesson Topic Use the growth pattern of a set of data to determine whether the data represent a linear or an eponential function. 6.4 EXT Solving Eponential Equations Solve eponential equations of the form b = b y. 6.5 Eponential Growth Write and evaluate eponential growth functions. 6.6 Eponential Decay Write and evaluate eponential decay functions. 6.7 Geometric Sequences Etend and graph geometric sequences; write an equation for the n th term of a geometric sequence. 6.7 EXT Recursively Defined Sequences Students will write recursive rules for sequences. Eligible Beyond Eligible Suggested Chapter. Lesson Lesson Title Chapter 8: Graphing Quadratic Functions Lesson Topic 8.1* Graphing y = a 2. Graph quadratic functions of the form y = a Focus of a Parabola Find and use the focus of a parabola. Eligible 8.3 Graphing y = a 2 + c Graph quadratic functions of the form y = a 2 + c. 8.4 Graphing y = a 2 + c Graph quadratic functions of the form y = a 2 + b + c. 8.4 EXT Graphing y = a( h) 2 + k Graph quadratic functions of the form y = a( h) 2 + k. 8.5 Comparing Linear, Eponential, and Quadratic Functions 8.5 EXT Comparing Graphs of Functions Identify, linear, eponential, and quadratic functions. Compare rates of change of linear, eponential, and quadratic functions. Beyond Eligible THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

27 Suggested Chapter. Lesson 9.1 Lesson Title Solving Quadratic Equations by Graphing Chapter 9: Solving Quadratic Equations Lesson Topic Solve quadratic equations by graphing. Eligible 9.2 Solving Quadratic Equations Using Square Roots Students will solve quadratic equations of the form a 2 + c = 0 using square roots Solving Quadratic Equations by Completing the Square Solving Quadratic Equations Using the Quadratic Formula Solve quadratic equations by completing the square. Solve quadratic equations using the quadratic formula. Beyond Eligible 9.4 EXT Choosing a Solution Method Choose methods to solve quadratic equations. 9.5 Solving Systems of Linear and Quadratic Equations Students will solve systems of equations consisting of one linear equation and one quadratic equation. Suggested Chapter. Lesson Lesson Title Chapter 10: Square Root Functions and Geometry 10.1 Graphing Square Root Functions Graph square root functions EXT Etension: Rationalizing the Denominator Lesson Topic Simplify square root epressions by rationalizing the denominator Solving Square Root Equations Solve square root equations The Pythagorean Theorem 10.4 Using the Pythagorean Theorem Use the Pythagorean Theorem to find the missing lengths of a right triangle. Use the converse of the Pythagorean Theorem and the distance formula. Eligible Beyond Eligible M08.C-G.2.1.1, M08.C-G THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

28 Suggested Chapter. Lesson Chapter 11: Rational Equations and Functions Lesson Title Lesson Topic Eligible 11.1 Direct and Inverse Variation Write and graph direct and inverse variation equations Graphing Rational Functions Graph rational functions EXT Inverse of a Function Find inverses Dividing Polynomials Divide polynomials. Beyond Eligible 11.6 Adding and Subtracting Rational Epressions Students will add and subtract rational epressions with like and unlike denominators Solving Rational Equations Solve rational equations. THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,

29 PA Core Standards by Cycle CYCLES PA Core Standards Eligible CC E.3 CC E.1 CC E.4 CC B.3 CC B.1 CC B.2 CC B.3 CC C.1 CC C.2 CC B.3 CC.2.1.HS.F.1 CC.2.1.HS.F.2 CC.2.1.HS.F.3 CC.2.1.HS.F.4 CC.2.1.HS.F.5 CC.2.2.HS.D.1 CC.2.2.HS.D.2 CC.2.2.HS.D.3 CC.2.2.HS.D.5 CC.2.2.HS.D.6 CC.2.2.HS.D.7 CC.2.2.HS.D.8 CC.2.2.HS.D.9 CC.2.2.HS.D.10 CC.2.2.HS.C.1 CC.2.2.HS.C.2 CC.2.2.HS.C.3 CC.2.2.HS.C.4 CC.2.2.HS.C.5 CC.2.2.HS.C.6 CC.2.4.HS.B.1 CC.2.4.HS.B.2 CC.2.4.HS.B.3 CC.2.4.HS.B.4 CC.2.4.HS.B.5 CC.2.4.HS.B A A A A A A A MODULE 1 A A A A A A A A A A A THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY,