Algebra I Big Ideas Math 2017-2018 SY · 2017-10-17 · 1 – Solving Linear Equations1 2 –...

THE SCHOOL DISTRICT OF PHILADELPHIA, OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT, CHRISTOPHER SHAFFER, DEPUTY, 2017-2018

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Algebra I Big Ideas Math 2017-2018 SY

Benchmark Cycle 1 Benchmark Cycle 2 Benchmark Cycle 3 Cycle 4

Dat

es

September 5 – October 31 BM Window Opens Nov 1 Term 1 ends Nov 13

November 1 – January 26 BM Window Opens Jan 29 Keystone Exam 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 Exam Window

Opens May 14 Cycle 4 ends Jun 12

Tota

l Sc

ho

ol

Day

s

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

Ch

apte

rs

1 – Solving Linear Equations1 2 – Graphing and Writing Linear

Equations2,1

3 – Solving Linear Inequalities1

4 – Solving Systems of Linear Equations1

5 –Linear Functions2 6 – Exponential Equations and

Functions1 7.1 – 7.3 – Polynomial

Equations and Factoring1

7.4 – 7.9 – Polynomial Equations and Factoring1

11.3 – 11.4 – Rational Equations and Functions1

12.1 – 12.8 – Data Analysis and Displays2

10.4 (Alg II) – Compound Events2

Keystone Exam Review Remediation and ExtensionBEC

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 Content from Module 1 of the Algebra I Keystone Exam.

2 Contains Eligible Content from Module 2 of the Algebra I Keystone Exam.

BEC Contains content that goes beyond the eligible content for the Algebra I Keystone Exam, i.e., material not included on the state assessment.


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Table of Contents

Block Schedule Options ...................................................................................................................................................................................................... 3

Benchmark Cycle 1 Standards ............................................................................................................................................................................................. 4

Benchmark Cycle 1 Scope and Sequence ........................................................................................................................................................................... 7

Benchmark Cycle 2 Standards ........................................................................................................................................................................................... 10

Benchmark Cycle 2 Scope and Sequence ......................................................................................................................................................................... 13

Benchmark Cycle 3 Standards ........................................................................................................................................................................................... 18

Benchmark Cycle 3 Scope and Sequence ......................................................................................................................................................................... 20

Cycle 4 Standards .............................................................................................................................................................................................................. 24

Cycle 4 Scope and Sequence ............................................................................................................................................................................................. 24

PA Core Standards by Cycle .............................................................................................................................................................................................. 29

Algebra Eligible Content Taught ....................................................................................................................................................................................... 31

Document Information Page ............................................................................................................................................................................................ 34


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Block Schedule Options

Note: With block schedules, generally follow the suggested sequence of lessons. Asterisked lessons are approximately 90-minutes in length. Non-asterisked lessons (approximately 45-minutes in length) may be combined, but consider combining them meaningfully, instead of simply teaching two-lessons back-to-back. 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

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Use the suggested pacing, but combine 45-minute (non-asterisked) lessons, in accordance with the general note above.

Full

Blo

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Fall

9/5– 9/29 Ch. 1 to Ch. 3

10/2 – 10/31 Ch. 4 to Ch. 6, Ch. 7.1 to 7.3

11/1 – 11/28 Ch. 7.4 to 7.9, Ch 11.3 to 11.4

11/29 – 1/5 Ch. 12.1 to 12.8, Ch 10.4 (Alg II) Keystone Exam Review

1/5 – 1/26 Remediation and Extension

Full

Blo

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Spri

ng

1/30– 2/28 Ch. 1 to Ch. 3

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 11.4

4/19 – 4/30 Ch. 12.1 to 12.8, Ch 10.4 (Alg II) Keystone Exam Review

5/1 – 5/11 Remediation and Extension

Benchmark Schedule

A /

B

Blo

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Follow Benchmark schedule indicated in the Scope and Sequence document that follows this page.

Full

Blo

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Fall

Benchmarks 1 and 2 (No need to complete

in one sitting)

None (Benchmark 3 not taken)

Full

Blo

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Spri

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Benchmarks 1 and 2

(No need to complete in one sitting)

None (Benchmark 3 not taken)


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Benchmark Cycle 1 Standards

PA Eligible Content PA Core Standards

A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values to solve problems. Note: Exponents should be integers from -10 to 10.

CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents. CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real-world or mathematical problems. CC.2.2.8.B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions.

A1.1.2.1.1 Write, solve, and/or apply a linear equation (including problem situations).

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.

A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation-solving process. Note: Linear equations only

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.

A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation. Note: Linear equations only.

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 multi-step problems.

A1.1.2.2.1 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.

CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC.2.2.8.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.

A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear equations.

A1.1.3.1.1 Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).

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.


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A1.1.3.1.2 Identify or graph the solution set to a linear inequality on a number line.

CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships.

A1.1.3.1.3 Interpret solutions to problems in the context of the problem situation. Note: Linear inequalities only.

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 multi-step problems.

A1.1.3.2.1 Write and/or solve a system of linear inequalities using graphing. Note: Limit systems to two linear inequalities.

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.

A1.1.3.2.2 Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear inequalities.

A1.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.

CC.2.2.8.C.1 Define, evaluate, and compare functions. CC.2.2.8.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 context. 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.

A1.2.1.2.1 Create, interpret, and/or use the equation, graph, or table of a linear function.

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 multi-step problems. CC.2.2.8.B.2 Understand the connections between proportional relationships, lines, and linear equations. CC.2.2.8.C.1 Define, evaluate, and compare functions. CC.2.2.8.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.

A1.2.1.2.2 Translate from one representation of a linear function to another (i.e., graph, table, and equation).


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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.

A1.2.2.1.1 Identify, describe, and/or use constant rates of change.

CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context. 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.

A1.2.2.1.2 Apply the concept of linear rate of change (slope) 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 context. 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.

A1.2.2.1.3 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.

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 exponential models to solve problems.

A1.2.2.1.4 Determine the slope and/or y-intercept represented by a linear equation or graph.

CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable.


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Benchmark Cycle 1 Scope and Sequence

Chapter 1: Solving Linear Equations

Suggested Dates

Chapter. Lesson

Lesson Title Lesson Topic(s) Eligible Content

9/5

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1/3

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1.1 Solving Simple Equationsa Use properties of equality to solve one-step equations.

A1.1.2.1.1, A1.1.2.1.2, A1.1.2.1.3

1.2 Solving Multi-Step Equations Solve multi-step equations by using inverse operations to isolate the variable.

1.3* Solving Equations with Variables on Both Sides

Solve equations with variables on both sides by using Properties of Equality and collecting variable terms on one side.

1.3 EXTb Extension: Solving Absolute Value Equations

Solve absolute value equations. A1.1.1.3.1

1.4 Rewriting Equations and Formulas

Use the techniques for solving equations to solve literal equations.

A1.1.2.1.1, A1.1.2.1.2, A1.1.2.1.3

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 explain their thinking.

* Lessons marked with an asterisk may require two 45-minute class periods, for which flex 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 Extension lessons sometimes contain content that is assessed on the Keystone Algebra I Exam. When Eligible Content is not included, these lessons are marked “Beyond Eligible Content.”

Review foundational knowledge and check for understanding, as needed, through “Do Nows” or “Bell Ringers,” homework, and teacher-created assessments. Review content from 8th Grade on integers and rational numbers, as you feel necessary. Be mindful of the suggested pacing with flex 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 Exam.

Rigor is elevated, when students have opportunities to make sense of and solve problems involving equality, using their own intuition and explaining 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 Extension in Cycle 4), algebra tiles (available, free and virtually at http://nlvm.usu.edu/), or SolveMe Puzzles (http://solveme.edc.org/). Also consider using flex days, on occasion, to work on the Big Ideas Projects (see Appendix A of the Teacher’s Edition).

http://solveme.edc.org/


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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 flex days may be used.

Chapter 2: Graphing and Writing Linear Equations

Suggested Dates

Chapter. Lesson

Lesson Title Lesson Topic Eligible Content

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6 2.1 Graphing Linear Equations Graph linear equations using a table of values.

A1.2.1.1.1, A1.2.2.1.1

2.2* Slope of a Line Find the slopes of lines in a variety of contexts.

A1.2.2.1.1, A1.2.2.1.2, A1.2.2.1.3, A1.2.2.1.4

2.2 EXT Extension: Slopes of Parallel and Perpendicular Lines

Use slope to determine if lines are parallel or perpendicular. A1.1.2.2.1, A1.1.2.2.2

2.3 Graphing Linear Equations in Slope-Intercept Form

Use slope-intercept form of a line to graph the line.

A1.2.2.1.1, A1.2.2.1.2, A1.2.2.1.3, A1.2.2.1.4

2.4* Graphing Linear Equations in Standard Form

Graph equations written in standard form.

2.5* Writing Equations in Slope-Intercept Form

Write an equation of a line given its slope and y-intercept.

2.6** Writing Equations in Point-Slope Form

Write the equation of a line given the slope and a point.

2.6 EXT Extension: Writing Equations of Parallel and Perpendicular Lines

Write the equation of a line that is either parallel or perpendicular to a given line.

A1.1.2.2.1, A1.1.2.2.2

2.7 Solving Real-Live Problems Solve real-life problems using equations, graphs, and intercepts.

A1.2.1.2.1, A1.2.1.2.2


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Chapter 3: Solving Linear Inequalities

Suggested Dates

Chapter. Lesson


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3.1* Writing and Graphing Inequalities

Translate inequalities from words to symbols and check to see if a value is a solution of the inequality.

A1.1.3.1.2, A1.1.3.1.3

3.2 Solving Inequalities Using Addition or Subtraction

Use the Addition and Subtraction Properties of Inequality to solve inequalities.

3.3 Solving Inequalities Using Multiplication or Division

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 Extension: Solving Compound Inequalities

Solve and graph compound inequalities. A1.1.3.1.1, A1.1.3.1.2, A1.1.3.1.3

3.5 Graphing Linear Inequalities in Two Variables

Graph linear inequalities in two variables. A1.1.3.2.1, A1.1.3.2.2

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 extends 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


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A1.1.1.1.1 Compare and/or order any real numbers. Note: Rational and irrational may be mixed.

CC.2.1.8.E.1 Distinguish between rational and irrational numbers using their properties. CC.2.1.8.E.4 Estimate irrational numbers by comparing them to rational numbers. CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents. CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real-world or mathematical problems.

A1.1.1.1.2 Simplify square roots (e.g., √24 =

2√6).

CC.2.1.6.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.

A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values to solve problems. Note: Exponents should be integers from -10 to 10.

CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents. CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real-world or mathematical problems. CC.2.2.8.B.1 Apply concepts of radicals and integer exponents to generate equivalent expressions.

A1.1.1.4.1 Use estimation to solve problems. CC.2.2.7.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.

A1.1.1.5.1 Add, subtract, and/or multiply polynomial expressions (express answers in simplest form). Note: Nothing larger than a binomial multiplied by a trinomial.

CC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of its context. CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems. CC.2.2.HS.D.3 Extend 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 Extend the knowledge of rational functions to rewrite in equivalent forms.


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A1.1.2.2.1 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.

CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC.2.2.8.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.

A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear equations.

A1.1.3.2.1 Write and/or solve a system of linear inequalities using graphing. Note: Limit systems to two linear inequalities.

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.

A1.1.3.2.2 Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear inequalities.

A1.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically.

CC.2.2.8.C.1 Define, evaluate, and compare functions. CC.2.2.8.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 context. 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.

A1.2.1.1.2 Determine whether a relation is a function, given a set of points or a graph.

A1.2.1.1.3 Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table).


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A1.2.1.2.1 Create, interpret, and/or use the equation, graph, or table of a linear function.

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 multi-step problems. CC.2.2.8.B.2 Understand the connections between proportional relationships, lines, and linear equations. CC.2.2.8.C.1 Define, evaluate, and compare functions. CC.2.2.8.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.

A1.2.1.2.2 Translate from one representation of a linear function to another (i.e., graph, table, and equation).


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Chapter 4: Solving Systems of Linear Equations

Suggested Dates

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4.1* Solving Systems of Linear Equations by Graphing

Solve a system of linear equations by graphing.

A1.1.2.2.1, A1.1.2.2.2

4.2 Solving Systems of Linear Equations by Substitution

Solve systems of linear equations by substitution.

4.3 Solving Systems of Linear Equations by Elimination

Solve systems of linear equations by elimination.

4.4* Solving Special Systems of Linear Equations

Solve special systems of linear equations, those that have one solution, no solutions, or infinitely many solutions.

4.4 EXT Extension: Solving Linear Equations by Graphing

Solve an equation with variables on both sides by graphing. Beyond Eligible

Content

4.5 Systems of Linear Inequalities Solve systems of linear inequalities by graphing. A1.1.3.2.1, A1.1.3.2.2

Note: In Chapter 4, students explore 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 Extension lesson is marked Beyond Eligible Content, 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.


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** Lesson 5.4 may require four 45-minute class periods, for which flex days may be used.

*** Pay close attention to the content in all sections of Chapter 5 marked with “Beyond Eligible Content.” Lessons 5-4 EXT and 5.5 may be taught after the Algebra I Keystone exam. But the bulk of Lessons 5.2 and 5.6 contain content that may be assessed on the Algebra I Keystone Exam.

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.

Chapter 5: Linear Functions

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5.1* Domain and Range of a Function Identify the domain and range of a function from a graph and table of values.

A1.2.1.1.3

5.1 EXT Extension: Relations and Functions

Determine whether a relation is a function using tables, maps, and the vertical line test.

A1.2.1.1.2

5.2 Discrete and Continuous Domains Graph functions and determine whether the domain is discrete or continuous.

A1.2.1.1.1, A1.2.1.1.3,

Beyond Eligible Content***

5.3* Linear Function Patterns Write linear functions by recognizing patterns in graphical and tabular information.

A1.2.1.1.1, A1.2.1.1.3,

5.4** Function Notation Use function notation to evaluate functions, graph functions, and vertically shift the graphs of functions.

A1.2.1.1.1, A1.2.1.2.1

5.4 EXT Extension: Special Linear Functions

Graph piecewise functions. Beyond Eligible

Content


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Focus: In Chapter 5, students investigate modeling and functions. Students develop an understanding of the relationship between function notation, graphs, tables, and verbal expressions. They address: How can you represent and describe functions? How do functions describe real-world-situations? Consider reviewing, as needed, two topics from Grade 8 before beginning this chapter: “define, evaluate, and compare functions” (CC.2.2.8.C.1); and “use concepts of functions to model relationships between quantities” (CC.2.2.8.C.2). Ideas underlying the essential questions, above, permeate algebra and higher mathematics.

Chapter 5: Linear Functions (cont.)

Suggested Dates

Chapter. Lesson


(see

pre

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5.5* Comparing Linear and Non-Linear Functions

Compare linear and non-linear functions. Beyond Eligible

Content

5.6 Arithmetic Sequences Describe and represent arithmetic sequences using an equation.

A1.2.1.1.1, A1.2.1.2.1, A1.2.1.2.2,

Beyond Eligible Content


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Chapter 6: Exponential Equations and Functions

Suggested Dates

Chapter. Lesson


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6.1** Properties of Square Roots

Use properties of square roots to simplify and evaluate expressions involving square roots.

A1.1.1.1.2, A1.1.1.4.1

6.1 EXT Real Number Operations Explore closure under addition, subtraction, multiplication, and division of rational and irrational numbers.

A1.1.1.1.1, A1.1.1.4.1,


6.2* Properties of Exponents Use properties of exponents to simplify expressions. A1.1.1.3.1, A1.1.1.4.1

6.3 Radicals and Rational Exponents

Evaluate expressions involving nth roots and rational exponents.

Note: Examples that do not include integer exponents / indices from -10 to 10 are Beyond Eligible Content.

A1.1.1.1.2, A1.1.1.3.1,


Note: In Chapter 6, students investigate these essential questions: How can you represent very large and very small numbers? How can you simplify expressions involving exponents? 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 problem-solving and reasoning abilities, including exploring 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 expressions to studying polynomials. Building on students understanding of exponents, students will compose and decompose linear expressions in performing operations with and factoring polynomial expressions. 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 Exam, and so these lessons have been moved until later in the year.

** Lesson 6.1 may require four 45-minute class periods, for which flex 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 examples include exponents 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 Exam.


17

Chapter 7: Polynomial Equations and Factoring

Suggested Dates

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7.1 Polynomials Classify polynomials.

A1.1.1.5.1 7.2* Adding and Subtracting Polynomials

Add and subtract polynomials.

7.3* Multiplying Polynomials Multiply polynomials.

Note: Nothing larger than a binomial multiplied by a trinomial.

Benchmark 2 Window: Jan 29 – Feb 13


18



A1.1.1.2.1 Write, solve, and/or apply a linear equation (including problem situations).

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 multi-step problems. CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC.2.2.8.B.3 Analyze and solve linear equations and pairs of simultaneous linear equations. CC.2.2.8.C.1 Define, evaluate, and compare functions. CC.2.2.8.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.

A1.1.1.5.1 Add, subtract, and/or multiply polynomial expressions (express answers in simplest form). Note: Nothing larger than a binomial multiplied by a trinomial.

CC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of its context. CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems. CC.2.2.HS.D.3 Extend 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 Extend the knowledge of rational functions to rewrite in equivalent forms.

A1.1.1.5.2 Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials are limited to the form ax2 + bx + c where a is equal to 1 after factoring out all monomial factors.

A1.1.1.5.3 Simplify/reduce a rational algebraic expression.

A1.2.3.1.1 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.


19


A1.2.3.2.1 Estimate or calculate to make predictions based on a circle, line, bar graph, measure of central tendency, or other representation.

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, experiments, and observational studies. A1.2.3.2.2 Analyze data, make predictions, and/or

answer questions based on displayed data (box-and-whisker plots, stem-and-leaf plots, scatter plots, measures of central tendency, or other representations).

A1.2.3.2.3 Make predictions using the equations or graphs of best-fit lines of scatter plots.

A1.2.3.3.1 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.

CC.2.4.7.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 experiments. CC.2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model.


20


Note: Chapter 7 addresses these essential questions: Can two algebraic expressions 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 exponents in Chapter 6. In this chapter, students combine linear expressions to make quadratic expressions, 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 expressions, 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 approximately three 45-minute class periods, for which flex days may be used.

Chapter 7: Polynomial Equations and Factoring

Suggested Dates

Chapter. Lesson


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-4/1

6

7.4* Special Products of Polynomials Use special product patterns to multiply binomials. A1.1.1.5.1

7.5 Solving Polynomial Equations in Factored Form

Solve polynomial equations using the Zero-Product Property. Beyond Eligible

Content

7.6 Factoring Polynomials Using the GCF

Factor polynomials using the greatest common factor. A1.1.1.2.1, A1.1.1.5.2

7.7 Factoring x2 + bx + c Factor trinomials of the form x2 + bx + c.

A1.1.1.5.2

7.8 Factoring ax2 + bx + c Factor trinomials of the form ax2 + bx + c, when a ≠ 1.

7.9** Factoring Special Products Factor perfect square trinomials, and factor the difference of two squares.

7.9 EXT Extension: Factoring Polynomials Completely

Factor higher-degree polynomials completely.


21

Chapter 11: Rational Equations and Functions

Suggested Dates

Chapter. Lesson


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11.3 Simplifying Rational Expressions Students will simplify rational expressions by factoring and dividing out common factors.

A1.1.1.5.3 11.4 Multiplying and Dividing Rational

Expressions Multiply and divide rational expressions.

Focus: Chapter 11 asks: How are rational expressions related? In Chapter 11, students continue studying polynomials, the thread that began in from Chapter 7 and that has roots extending 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 Exam, the remainder of Chapter 11 is covered later in the year.


22

Chapter 12: Data Analysis and Displays

Suggested Dates

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12.1 Measures of Central Tendency

Explore how an outlier affects the three measures of central tendency.

A1.2.3.2.1, A1.2.3.2.2

12.2 Measures of Dispersion

Find the range and standard deviation of a data set and compare two data sets.

Note: Standard deviation is Beyond Eligible Content, but finding the range supports making box-and-whisker plots.

A1.2.3.1.1, A1.2.3.2.1, A1.2.3.2.2,


12.3 Box-and-whisker plots Construct and analyze box-and-whisker plots. A1.2.3.1.1, A1.2.3.2.1, A1.2.3.2.2

12.4 Shapes and Distributions Students will describe the shape of a distribution and choose measures of central tendency and spread to describe the data.


12.5 Scatter Plots and Lines of Fit Students will construct scatter plots, draw the line of fit, and analyze the equation.

A1.2.2.2.1 A1.2.3.1.1, A1.2.3.2.2, A1.2.3.2.3


23

Chapter 12: Data Analysis and Displays

Suggested Dates

Chapter. Lesson

Lesson Title Lesson Topic Eligible Content (s

ee p

revi

ou

s)

12.6* Analyzing Lines of Fit Use residuals and find lines of best fit. A1.2.3.2.2, A1.2.3.2.3

12.7 Two-Way Tables Use two-way frequency tables to analyze data and to make predictions. A1.2.3.2.1,

A1.2.3.2.2 12.8 Choosing a Data Display

Students will choose and construct an appropriate data display.

Alg II: 10.4

Probability of Disjoint and Overlapping Events

Find probabilities of compound events A1.2.3.3.1

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 exists 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 Exam, 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 textbook, 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.


24

Cycle 4 Standards

No new Algebra I Keystone Eligible Content items.

Cycle 4 Scope and Sequence

Algebra I Keystone Exam 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 Content. Consider honing-in on essential content by reviewing the Performance Level Descriptors at http://static.pdesas.org/content/documents/Keystone_Algebra_I_PLD_021113.pdf. And consider using practice problems from http://www.pdesas.org/.

http://static.pdesas.org/content/documents/Keystone_Algebra_I_PLD_021113.pdf

http://www.pdesas.org/


25

Remediation and Extension 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 Appendix A are interdisciplinary projects that can support students’ problem-solving capacities and engagement with the Standards for Mathematical Practice.

Option 2: Cover Remaining

Content

Consider teaching the remaining content from the text, 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 exponents and exponential functions (Chapter 6), quadratic functions and equations (Chapters 8-9), radical expressions and equations (Chapter 10), and rational expressions and functions (Chapter 11).

Option 3: Mathematical Modeling in Three Acts

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: https://whenmathhappens.com/3-act-math/, https://gfletchy.com/3-act-lessons/, or within this Google Sheet.

Option 4: Miscellaneous

(Financial Literacy, Quantitative Reasoning,

Statistics, etc.)

The Federal Reserve Bank of Philadelphia has posted free lesson plans for high school teachers on financial literacy at: https://philadelphiafed.org/education/teachers/lesson-plans?tabNum=3. In addition, Census.gov has a number of data analysis activities, using real U.S. Census data, at: https://census.gov/schools/activities/math.html.html. Finally, consider other cross-curricular quantitative reasoning activities, such as those available at: https://ww2.kqed.org/education/.

https://whenmathhappens.com/3-act-math/

https://gfletchy.com/3-act-lessons/

https://docs.google.com/spreadsheets/d/1jXSt_CoDzyDFeJimZxnhgwOVsWkTQEsfqouLWNNC6Z4/edit#gid=0

https://philadelphiafed.org/education/teachers/lesson-plans?tabNum=3

https://census.gov/schools/activities/math.html.html

https://ww2.kqed.org/education/


26

Chapter 6: Exponential Equations and Functions

Suggested Dates

Chapter. Lesson


6.4 Exponential Functions Use the growth pattern of a set of data to determine whether the data represent a linear or an exponential function.


6.4 EXT Solving Exponential Equations Solve exponential equations of the form bx = by.

6.5 Exponential Growth Write and evaluate exponential growth functions.

6.6 Exponential Decay Write and evaluate exponential decay functions.

6.7 Geometric Sequences Extend and graph geometric sequences; write an equation for the nth term of a geometric sequence.

6.7 EXT Recursively Defined Sequences Students will write recursive rules for sequences.

Chapter 8: Graphing Quadratic Functions

Suggested Dates

Chapter. Lesson


8.1* Graphing y = ax2. Graph quadratic functions of the form y = ax2.


8.2 Focus of a Parabola Find and use the focus of a parabola.

8.3 Graphing y = ax2 + c Graph quadratic functions of the form y = ax2 + c.

8.4 Graphing y = ax2 + c Graph quadratic functions of the form y = ax2 + bx + c.

8.4 EXT Graphing y = a(x – h) 2 + k Graph quadratic functions of the form y = a(x – h) 2 + k.

8.5 Comparing Linear, Exponential, and Quadratic Functions

Identify, linear, exponential, and quadratic functions.

8.5 EXT Comparing Graphs of Functions Compare rates of change of linear, exponential, and quadratic functions.


27

Chapter 9: Solving Quadratic Equations

Suggested Dates

Chapter. Lesson


9.1 Solving Quadratic Equations by Graphing

Solve quadratic equations by graphing.


9.2 Solving Quadratic Equations Using Square Roots

Students will solve quadratic equations of the form ax2 + c = 0 using square roots.

9.3 Solving Quadratic Equations by Completing the Square

Solve quadratic equations by completing the square.

9.4 Solving Quadratic Equations Using the Quadratic Formula

Solve quadratic equations using the quadratic formula.

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.

Chapter 10: Square Root Functions and Geometry

Suggested Dates

Chapter. Lesson


10.1 Graphing Square Root Functions Graph square root functions.


10.1 EXT Extension: Rationalizing the Denominator

Simplify square root expressions by rationalizing the denominator.

10.2 Solving Square Root Equations Solve square root equations.

10.3 The Pythagorean Theorem Use the Pythagorean Theorem to find the missing lengths of a right triangle. M08.C-G.2.1.1,

M08.C-G.2.1.2 10.4 Using the Pythagorean Theorem

Use the converse of the Pythagorean Theorem and the distance formula.


28

Chapter 11: Rational Equations and Functions

Suggested Dates

Chapter. Lesson


11.1 Direct and Inverse Variation Write and graph direct and inverse variation equations.


11.2 Graphing Rational Functions Graph rational functions.

11.2 EXT Inverse of a Function Find inverses.

11.5 Dividing Polynomials Divide polynomials.

11.6 Adding and Subtracting Rational Expressions

Students will add and subtract rational expressions with like and unlike denominators.

11.7 Solving Rational Equations Solve rational equations.


29

PA Core Standards by Cycle

CYCLES

PA Core Standards

CC

.2.1

.6.E

.3

CC

.2.1

.8.E

.1

CC

.2.1

.8.E

.4

CC

.2.2

.7.B

.3

CC

.2.2

.8.B

.1

CC

.2.2

.8.B

.2

CC

.2.2

.8.B

.3

CC

.2.2

.8.C

.1

CC

.2.2

.8.C

.2

CC

.2.4

.7.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.1

0

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.7

1 2 3 4

Eligible Content ↓

MO

DU

LE 1

A1.1.1.1.1 x

A1.1.1.1.2 x

A1.1.1.2.1 x

A1.1.1.3.1 x x

A1.1.1.4.1 x

A1.1.1.5.1 x x

A1.1.1.5.2 x

A1.1.1.5.3 x

A1.1.2.1.1 x

A1.1.2.1.2 x

A1.1.2.1.3 x

A1.1.2.2.1 x x

A1.1.2.2.2 x x

A1.1.3.1.1 x

A1.1.3.1.2 x

A1.1.3.1.3 x

A1.1.3.2.1 x x

A1.1.3.2.2 x x


30

CYCLES

PA Core Standards

CC

.2.1

.6.E

.3

CC

.2.1

.8.E

.1

CC

.2.1

.8.E

.4

CC

.2.2

.7.B

.3

CC

.2.2

.8.B

.1

CC

.2.2

.8.B

.2

CC

.2.2

.8.B

.3

CC

.2.2

.8.C

.1

CC

.2.2

.8.C

.2

CC

.2.4

.7.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.1

0

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.7

1 2 3 4

Eligible Content ↓

MO

DU

LE 2

A1.2.1.1.1 x x

A1.2.1.1.2 x

A1.2.1.1.3 x

A1.2.1.2.1 x x

A1.2.1.2.2 x x

A1.2.2.1.1 x

A1.2.2.1.2 x

A1.2.2.1.3 x

A1.2.2.1.4 x

A1.2.2.2.1 ` x

A1.2.3.1.1 x

A1.2.3.2.1 x

A1.2.3.2.2 x

A1.2.3.2.3 x

A1.2.3.3.1 x


31

Algebra Eligible Content Taught

PA Eligible Content Cycle

1 Cycle

2 Cycle

3 Cycle

4

A1.1.1.1.1 Compare and/or order any real numbers. Note: Rational and irrational may be mixed. x

A1.1.1.1.2 Simplify square roots (e.g., √24 = 2√6). x

A1.1.1.2.1 Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials. x

A1.1.1.3.1 Simplify/evaluate expressions involving properties/laws of exponents, roots, and/or absolute values

to solve problems.Note: Exponents should be integers from –10 to 10. x x

A1.1.1.4.1 Use estimation to solve problems. x

A1.1.1.5.1 Add, subtract, and/or multiply polynomial expressions (express answers in simplest form). Note: Nothing larger than a binomial multiplied by a trinomial. x x

A1.1.1.5.2 Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials are

limited to the formax2+ bx + c where a is equal to 1 after factoring out all monomial factors. x

A1.1.1.5.3 Simplify/reduce a rational algebraic expression. x

A1.1.2.1.1 Write, solve, and/or apply a linear equation (including problem situations). x

A1.1.2.1.2 Use and/or identify an algebraic property to justify any step in an equation-solving process. Note: linear equations only. x

A1.1.2.1.3 Interpret solutions to problems in the context of the problem situation. Note: linear equations only. x

A1.1.2.2.1 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. x x

A1.1.2.2.2 Interpret solutions to problems in the context of the problem situation. Note: Limit systems to two linear equations. x x


32


1 Cycle

2 Cycle

3 Cycle

4

A1.1.3.1.1 Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities). x

A1.1.3.1.2 Identify or graph the solution set to a linear inequality on a number line. x

A1.1.3.1.3 Interpret solutions to problems in the context of the problem situation. Note: linear inequalities only. x

A1.1.3.2.1 Write and/or solve a system of linear inequalities using graphing. Note: limit systems to two linear inequalities. x x

A1.1.3.2.2 Interpret solutions to problems in the context of the problem situation. Note: limit systems to two linear inequalities. x x

A1.2.1.1.1 Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically. x x

A1.2.1.1.2 Determine whether a relation is a function, given a set of points or a graph. x

A1.2.1.1.3 Identify the domain or range of a relation (may be presented as ordered pairs, a graph, or a table). x

A1.2.1.2.1 Create, interpret, and/or use the equation, graph, or table of a linear function. x x

A1.2.1.2.2 Translate from one representation of a linear function to another (i.e., graph, table, and equation). x x

A1.2.2.1.1 Identify, describe, and/or use constant rates of change. x

A1.2.2.1.2 Apply the concept of linear rate of change (slope) to solve problems. x

A1.2.2.1.3 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. x

A1.2.2.1.4 Determine the slope and/or y-intercept represented by a linear equation or graph. x


33


1 Cycle

2 Cycle

3 Cycle

4

A1.2.2.2.1 Draw, identify, find, and/or write an equation for a line of best fit for a scatter plot. x

A1.2.3.1.1 Calculate and/or interpret the range, quartiles, and interquartile range of data. x

A1.2.3.2.1 Estimate or calculate to make predictions based on a circle, line, bar graph, measure of central tendency, or other representation. x

A1.2.3.2.2 Analyze data, make predictions, and/or answer questions based on displayed data (box-and- whisker plots, stem-and-leaf plots, scatter plots, measures of central tendency, or other representations). x

A1.2.3.2.3 Make predictions using the equations or graphs of best-fit lines of scatter plots. x

A1.2.3.3.1 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. x


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Document Information Page Overview of Contents of Document

The Cover Page lays out the Topics taught within each Cycle as well as the corresponding dates.

The Benchmark Cycle X Standards pages that precede each cycle outline all of the standards that are taught within that cycle. These are, therefore, all of the standards that may be on that Cycle’s Benchmark.

The Benchmark Cycle X Scope and Sequence pages provide suggested pacing that allows for 1 day per lesson plus some flex days. We recommend proactively using the flex days for: reviewing pre-requisite content, splitting lessons over multiple days, assessing, reteaching, and doing projects. Of course, some of these will also be taken by field trips and other school activities.

The PA Core Standards and Eligible Content by Cycle page lists all of the standards and indicates in which cycle(s) they are taught.

What is a Cycle?

We want to offer clarity on what appears on each benchmark. Additionally, there should be sufficient time to teach that content before it is tested. Because each school administers the benchmark on a different day, not necessarily corresponding with the last day of the Term, we have created Cycles. Each Cycle contains the content that is to be taught and tested on a given benchmark. Please refer to the dates on the Cover Page to ensure you are aware of the beginning and ending dates for each Cycle.

What If I Fall Behind?

We trust you to make decisions about what is best for your students. This pacing will prepare you for the Benchmarks and Algebra 1 Keystone Exam, but it is a suggested, not mandated, pacing. You may also wish to move at a faster pace. Do not feel you should slow down to match this guide.

If you are concerned about content that you may not reach before the Keystone Exam, consider implementing number talks and other short routines and games. For example, a lot of mathematics vocabulary and concepts could be taught through Which Once Doesn’t Belong. Rather than pushing to “cover” content, or using test prep resources, content can be infused through short but meaningful structures.


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The Standards for Mathematical Practice are:

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

You should try to infuse these Standards into your lessons regularly. Rather than thinking of them as a box to check, think about how you are providing students with opportunities to develop as mathematical thinkers and doers.

The Common Core has identified the following as the critical areas for Algebra I:

(1) Students analyze and explain the process of solving an equation, developing fluency in writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems;

(2) Students learn function notation and develop the concepts of domain and range; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations; they use this understanding to explore systems of linear equations and inequalities;

(3) Students use regression techniques to describe approximately linear relationships between quantities, and they use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models;

(4) They extended the laws of exponents to rational exponents; and (5) Students consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and exponential functions.

These do not necessarily reflect Keystone Exam content, but they are generally the essential content for preparing students for their studies of higher mathematics, including Geometry and Algebra II.

The School District of Philadelphia’s Vision for Mathematics Teaching and Learning:

All students think mathematically, and they will be empowered to own, share, and do mathematics.

Our Guiding Principles:

Equitable Discourse Rich + Meaningful Tasks Purpose-Driven Work

Questioning and Curiosity Valuing Diverse Thinking

If you have any questions or would like more information, please contact us at [email protected].

Algebra I Big Ideas Math 2017-2018 SY · 2017-10-17 · 1 – Solving Linear Equations1 2 –...

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Transcript of Algebra I Big Ideas Math 2017-2018 SY · 2017-10-17 · 1 – Solving Linear Equations1 2 –...