Algebra 2 Big Ideas Math 2017-2018 SY · 1 Algebra 2 Big Ideas Math 2017-2018 SY Benchmark Cycle1...

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

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Algebra 2 Big Ideas Math 2017-2018 SY

Benchmark Cycle1 Benchmark Cycle2 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 - Linear Functions1, 2 2 - Quadratic Functions1 3 - Quadratic Equations and

Complex Numbers1 (Lesson 3-1)

3 - Quadratic Equations and Complex Numbers1 (Lessons 3-2 to 3-6)

4 - Polynomial Functions1 5 - Rational Exponents and

Radical Functions1 6 - Exponential and Logarithmic

Functions1, 2

7 - Rational Functions1 8 - Sequences and Series2 10 – Probability 2, BEC 11 - Data Analysis and

Statistics2, BEC

9 - Trigonometric Ratios and Functions BEC

Remediate and Enrich

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 II Keystone Exam.

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

BEC Contains content that goes beyond the eligible content for the Algebra II 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 ........................................................................................................................................................................... 8

Benchmark Cycle 2 Standards ........................................................................................................................................................................................... 12

Benchmark Cycle 2 Scope and Sequence ......................................................................................................................................................................... 17

Benchmark Cycle 3 Standards ........................................................................................................................................................................................... 22

Benchmark Cycle 3 Scope and Sequence ......................................................................................................................................................................... 26

Cycle 4 Standards .............................................................................................................................................................................................................. 31

Cycle 4 Scope and Sequence ............................................................................................................................................................................................. 32

PA Core Standards by Cycle .............................................................................................................................................................................................. 34

Algebra Eligible Content Taught ....................................................................................................................................................................................... 36

Document Information Page ............................................................................................................................................................................................ 38


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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 – 10/4 Ch. 1 to Ch. 3

10/5 – 10/31 Ch. 4 to Ch. 6

11/1 – 12/14 Ch. 7 to Ch. 8 Ch. 10 to Ch. 11

12/15 – 1/26 Ch. 9 Remediate and Enrich

Full

Blo

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pri

ng 1/29 – 3/1

Ch. 1 to Ch. 3

3/2 – 4/6 Ch. 3 to Ch. 6

4/9 – 5/11 Ch. 7 to Ch. 8 Ch. 10 to Ch. 11

5/14 – 6/12 Ch. 9 Remediate and Enrich

Benchmark Schedule

A /

B

Blo

ck

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

ck

Spri

ng

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

A2.1.2.1.1 Use exponential expressions to represent rational numbers.

A2.1.2.1.2 Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers—exponents should not exceed power of 10).

A2.1.2.1.3 Simplify/evaluate expressions involving multiplying with exponents (e.g., x6 • x7 = x13), powers of powers (e.g., (x6)7 = x42), and powers of products (e.g., (2x2)3 = 8x6). Note: Limit to rational exponents.

A2.1.2.1.4 Simplify or evaluate expressions involving logarithms and exponents (e.g., log28 = 3 or log42 = ½).

CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents. CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems.

A2.1.2.2.1 Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials limited to the form ax2+bx+c where a is not equal to 0.

A2.1.2.2.2 Simplify rational algebraic expressions.

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.4 Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs. CC.2.2.HS.D.5 Use polynomial identities to solve problems.

A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).

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.


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A2.1.3.1.2 Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x – 2) = 1 or 14212 xx .

A2.1.3.1.3Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).

A2.1.3.1.4Write, solve, and/or apply linear or exponential growth or decay (including problem situations).

CC.2.2.HS.C.4 Interpret the effects transformations have on functions, and find the inverses of functions. CC.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. 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. 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.

A2.1.3.2.1 Determine how a change in one variable relates to a change in a second variable

(e.g., y = 4/x; if x doubles, what happens to y?).

A2.1.3.2.2 Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r).

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.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.


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A2.2.1.1.1 Analyze a set of data for the existence of a pattern, and represent the pattern with a rule algebraically and/or graphically.

A2.2.1.1.2 Identify and/or extend a pattern as either an arithmetic or geometric sequence (e.g., given a geometric sequence, find the 20th term).

A2.2.1.1.3 Determine the domain, range, or inverse of a relation.

A2.2.1.1.4 Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function (e.g., intervals of increase/decrease, intercepts, zeros, and asymptotes).

CC.2.1.HS.F.7 Apply concepts of complex numbers in polynomial identities and quadratic equations 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.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. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. CC.2.3.HS.A.10 Translate between the geometric description and the equation for a conic section. CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables.

A2.2.2.1.1 Create, interpret, and/or use the equation, graph, or table of a polynomial function (including quadratics).

A2.2.2.1.2 Create, interpret, and/or use the equation, graph, or table of an exponential or logarithmic function (including common and natural logarithms).

A2.2.2.1.3 Determine, use, and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial, exponential, or logarithmic function.

A2.2.2.1.4 Translate a polynomial, exponential, or logarithmic function from one representation of a function to another (graph, table, and equation.)

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.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.5 Construct and compare linear, quadratic, and exponential models to solve problems. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model.


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CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.3.HS.A.10 Translate between the geometric description and the equation for a conic section.

A2.2.2.2.1 Identify or describe the effect of changing parameters within a family of functions

(e.g., y = x2 and y = x2 + 3, or y = x2 and y = 3x2).

CC.2.2.HS.C.4 Interpret the effects transformations have on functions, and find the inverses of functions. CC.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model.


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Benchmark Cycle 1 Scope and Sequence

Chapter 1: Linear Functions

Suggested Dates

Chapter- Lesson

Lesson Title Lesson Topic(s) Eligible Content

9/5

-9/2

9: 8

Inst

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1.1* Parent Functions and Transformations

Identify families of functions. Describe transformations of parent functions. Describe combinations for transformations.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.1.3.2.1 A2.1.3.2.2 A2.2.1.1.1 A2.2.1.1.2 A2.2.1.1.3 A2.2.1.1.4 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4

1.2* Transformations of Linear and Absolute Value Functions

Write functions representing translations and reflections. Write functions representing stretches and shrinks. Write functions representing combinations of transformations.

1.3 Modeling with Linear Functions

Write equations of linear functions using points and slopes. Find lines of fit and lines of best fit.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.1.3.2.1 A2.1.3.2.2 A2.2.1.1.1 A2.2.1.1.2 A2.2.1.1.3 A2.2.1.1.4 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4


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Chapter 1: Linear Functions

Suggested Dates

Chapter- Lesson

Lesson Title Lesson Topic(s) Eligible Content (s

ee a

bo

ve)

1.4* Solving Linear Systems Visualize solutions of systems of linear equations in three variables. Solve systems of linear equations in three variables algebraically. Solve real-life problems.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.1.3.2.1 A2.1.3.2.2 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4

* Lessons marked with an asterisk may require two 45-minute class periods, for which flex days may be used.


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Chapter 2: Quadratic Functions

Suggested Dates

Chapter- Lesson

Lesson Title Lesson Topic Eligible Content

10

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4: 8

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6 2.1 Transformations of Quadratic

Functions Describe transformations of quadratic functions. Write transformations of quadratic functions.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.1.3.2.1 A2.1.3.2.2 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4

2.2* Characteristics of Quadratic Functions

Explore properties of parabolas. Find maximum and minimum values of quadratic functions. Graph quadratic functions using x-intercepts. Solve real-like problems.

A2.1.2.1.1 A2.1.2.1.2 A2.1.2.1.3 A2.1.2.1.4 A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.1.3.2.1 A2.1.3.2.2 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4

2.3* Focus of a Parabola Explore the focus and the directrix of a parabola. Write equations of parabolas. Solve real-life problems.

2.4* Modeling with Quadratic Functions

Write equations of quadratic functions using vertices, points, and x-intercepts. Write quadratic equations to model date sets.

Consider beginning the year by laying foundations for problem-solving via: WODB.ca and Estimation180.com. Also consider using flex days, on occasion, to complete or present the Common Core Performance Tasks, which support increased rigor. Review foundational knowledge and check for understanding, as needed, through “Do Nows” or “Bell Ringers,” homework, and teacher-created assessments.


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Chapter 3: Quadratic Equations and Complex Numbers

Suggested Dates

Chapter- Lesson


10

/25

-10

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: 4.5

Day

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9/2

5-9

/26

2/2

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3.1* Solving Quadratic Equations Solve quadratic equations by graphing.

Solve quadratic equations algebraically. Solve real-life problems. A2.1.2.1.1

A2.1.2.1.2 A2.1.2.1.3 A2.1.2.1.4 A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4

Benchmark 1 Window: Nov 1 – Nov 17


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A2.1.1.1.1 Simplify/write square roots in terms of i (e.g., √-24 = 2i√6).

A2.1.1.1.2 Simplify/evaluate expressions involving powers of i (e.g., i6 + i3 = –1 – i).

A2.1.1.2.1 Add and subtract complex numbers (e.g., (7 – 3i) – (2 + i) = 5 – 4i).

A2.1.1.2.2 Multiply and divide complex numbers (e.g., (7 – 3i)(2 + i) = 17 + i).

CC.2.1.HS.F.6 Extend the knowledge of arithmetic operations and apply to complex numbers.

A2.1.2.1.1 Use exponential expressions to represent rational numbers.



A2.1.2.1.4 Simplify or evaluate expressions involving logarithms and exponents (e.g., log28 = 3 or log42 = ½).

CC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents. CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems.


A2.1.3.1.2 Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x – 2) = 1 or 14212 xx .

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.


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CC.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. 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. 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.2.1.HS.F.7 Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems. CC.2.2.HS.C.1


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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.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. CC.2.3.HS.A.10 Translate between the geometric description and the equation for a conic section. 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 multi-step problems. 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.5 Construct and compare linear, quadratic, and exponential models to solve problems. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.3.HS.A.10 Translate between the geometric description and the equation for a conic section.


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Chapter 3: Quadratic Equations and Complex Numbers

Suggested Dates

Chapter- Lesson


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3.2* Complex Numbers Define and use the imaginary unit i. Add, subtract, and multiply complex numbers. Find complex solutions and zeros.

A2.1.1.1.1 A2.1.1.1.2 A2.1.1.2.1 A2.1.1.2.2 A2.1.2.2.1 A2.1.2.2.2 A2.2.1.1.1 A2.2.1.1.2 A2.2.1.1.3 A2.2.1.1.4

3.3 Completing the Square Solve quadratic equations using square roots. Solve quadratic equations by completing the square. Write quadratic functions in vertex form.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.2.1.1.1 A2.2.1.1.2 A2.2.1.1.3 A2.2.1.1.4

3.4* Using the Quadratic Formula Solve quadratic equations using the Quadratic Formula. Analyze the discriminant to determine the number and type of solutions. Solve real-life problems.

3.5* Solving Nonlinear Systems Solve systems of nonlinear equations. Solve quadratic equations by graphing.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.1.3.2.1 A2.1.3.2.2 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4

3.6* Quadratic Inequalities Graph quadratic inequalities in two variables. Solve quadratic inequalities in on variable.


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Chapter 4. Polynomial Functions

Suggested Dates

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4.1* Graphing Polynomial Functions Identify polynomial functions. Graph polynomial functions using tables and end behavior.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4

4.2 Adding, Subtracting, and Multiplying Polynomials

Add and subtract polynomials. Multiply polynomials. Use the Factor Theorem. Use Pascal’s Triangle to expand binomials.

A2.1.2.1.1 A2.1.2.1.2 A2.1.2.1.3 A2.1.2.1.4 A2.1.2.2.1 A2.1.2.2.2 A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4

4.3* Dividing Polynomials Use long division to divide polynomials by other polynomials. Use synthetic division to divide polynomials by binomials of the form x – k.

A2.1.2.2.1 A2.1.2.2.2 A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4

4.4 Factoring Polynomials Factor polynomials. Use the Remainder Theorem.

A2.1.2.2.1 A2.1.2.2.2

4.5* Solving Polynomial Equations Find solutions of polynomial equations and zeros of polynomial functions. Use the Rational Root Theorem. Use the Irrational Root Theorem.


18

Chapter 4. Polynomial Functions

Suggested Dates

Chapter- Lesson


(see

ab

ove

) 4.6* The Fundamental Theorem of

Algebra Use the Fundamental Theorem of Algebra. Find conjugate pairs of complex zeros of polynomial functions. Use Descartes’s Rule of Signs.

A2.1.2.2.1 A2.1.2.2.2 A2.2.1.1.1 A2.2.1.1.2 A2.2.1.1.3 A2.2.1.1.4

4.7* Transformations of Polynomial Functions

Describe transformations of polynomial functions. Write transformations of polynomial functions.

A2.1.2.2.1 A2.1.2.2.2 A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.1.3.2.1 A2.1.3.2.2 A2.2.1.1.1 A2.2.1.1.2 A2.2.1.1.3 A2.2.1.1.4 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4

4.8* Analyzing Graphs of Polynomial Functions

Use x-intercepts to graph polynomial functions. Use the Location Principle to identify zeros of polynomial functions. Find turning points and identify local maximums and local minimums of graphs of polynomial functions. Identify even and odd functions.

4.9* Modeling with Polynomial Functions

Write polynomial functions for sets of points. Writ polynomial functions using finite differences. Use technology to find models for date sets.


19

Chapter5. Rational Exponents and Radical Functions

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Chapter- Lesson


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5.1 nth Roots and Rational Exponents

Find the nth roots of numbers. Evaluate expressions with rational exponents. Solve equations using nth roots.

A2.1.2.1.1 A2.1.2.1.2 A2.1.2.1.3 A2.1.2.1.4

5.2 Properties of Rational Exponents and Radicals

Use properties of rational exponents to simplify expressions with rational exponents. Use properties of radicals to simplify and write radical expressions in simplest form.

5.3* Graphing Radical Functions Graph radical functions. Write transformations of radical functions. Graph parabolas and circles.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.1.3.2.1 A2.1.3.2.2 A2.2.1.1.1 A2.2.1.1.2 A2.2.1.1.3 A2.2.1.1.4 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4

5.4* Solving Radical Equations and Inequalities

Solve equations containing radicals and rational exponents. Solve radical inequalities.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.1.3.2.1 A2.1.3.2.2

5.5 Performing Function Operations Add, subtract, multiply, and divide functions. A2.1.3.2.1 A2.1.3.2.2 A2.2.1.1.1 A2.2.1.1.2 A2.2.1.1.3 A2.2.1.1.4


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Chapter5. Rational Exponents and Radical Functions

Suggested Dates

Chapter- Lesson


(see

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) 5.6* Inverse of a Function Explore inverses of functions.

Find the verify inverses of nonlinear functions. Solve real-life problems using inverse functions.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.1.3.2.1 A2.1.3.2.2 A2.2.1.1.1 A2.2.1.1.2 A2.2.1.1.3 A2.2.1.1.4 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4


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Chapter 6: Exponential and Logarithmic Functions

Suggested Dates

Chapter- Lesson


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6.1* Exponential Growth and Decay Functions

Graph exponential growth and decay functions. Use exponential models to solve real-life problems.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.2.1.1.1 A2.2.1.1.2 A2.2.1.1.3 A2.2.1.1.4 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4 A2.2.2.2.1

6.2 The Natural Base e Define and use the natural base e. Graph natural base functions. Solve real-life problems.

6.3* Logarithms and Logarithmic Functions

Define and evaluate logarithms. Use inverse properties of logarithms and exponential functions. Graph logarithmic functions.

6.4* Transformations of Exponential and Logarithmic Functions

Transform graphs of exponential functions. Transform graphs of logarithmic functions. Write transformations of graphs of exponential and logarithmic functions.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.1.3.2.1 A2.1.3.2.2 A2.2.1.1.1 A2.2.1.1.2 A2.2.1.1.3 A2.2.1.1.4 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4 A2.2.2.2.1

6.5* Properties of Logarithms Use the properties of logarithms to evaluate logarithms. Use the properties of logarithms to expand or condense logarithmic expressions. Use the change-of-base formula to evaluate logarithms.

6.6* Solving Exponential and Logarithmic Equations

Solve exponential equations. Solve logarithmic equations. Solve exponential and logarithmic inequalities.

6.7* Modeling with Exponential and Logarithmic Functions

Classify data sets. Write exponential functions. Use technology to find exponential and logarithmic models.

Benchmark 2 Window: Jan 29 – Feb 13


22



A2.1.2.2.1 Factor algebraic expressions, including difference of squares and trinomials. Note: Trinomials limited to the form ax2+bx+c where a is not equal to 0.

A2.1.2.2.2 Simplify rational algebraic expressions.

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.4 Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs. CC.2.2.HS.D.5 Use polynomial identities to solve problems.


A2.1.3.1.2 Solve equations involving rational and/or radical expressions (e.g., 10/(x + 3) + 12/(x

– 2) = 1 or 14212 xx .



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.5 Construct and compare linear, quadratic, and exponential models to solve problems. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. 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. 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.


23


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.7 Apply concepts of complex numbers in polynomial identities and quadratic equations 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.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. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. CC.2.3.HS.A.10 Translate between the geometric description and the equation for a conic section.


24


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 multi-step problems. 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.5 Construct and compare linear, quadratic, and exponential models to solve problems. CC.2.2.HS.C.6 Interpret functions in terms of the situations they model. CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.3.HS.A.10 Translate between the geometric description and the equation for a conic section.




A2.2.3.1.1 Draw, identify, find, interpret, and/or write an equation for a regression model (lines and curves of best fit) for a scatter plot. A2.2.3.1.2 Make predictions using the equations or graphs of regression models (lines and curves of best fit) of scatter plots.

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.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables.


25


CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data.

A2.2.3.2.1 Use combinations, permutations, and the fundamental counting principle to solve problems involving probability. A2.2.3.2.2 Use odds to find probability and/or use probability to find odds. A2.2.3.2.3 Use probability for independent, dependent, or compound events to predict outcomes.

CC.2.4.HS.B.4 Recognize and evaluate random processes underlying statistical experiments. CC.2.4.HS.B.5 Make inferences and justify conclusions based on sample surveys, experiments, and observational studies. CC.2.4.HS.B.6 Use the concepts of independence and conditional probability to interpret data. CC.2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model.


26


Chapter 7. Rational Functions

Suggested Dates

Chapter- Lesson


1/2

9-2

/12

: 1 D

ay P

er L

esso

n +

5 D

ays

11

/1-1

1/1

3

4/9

-4/1

7

7.1 Inverse Variation Classify direct and inverse variations. Write inverse variation equations.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.1.3.2.1 A2.1.3.2.2 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4

7.2* Graphing Rational Functions Graph simple rational functions. Translate simple rational functions. Graph other rational functions.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.1.3.2.1 A2.1.3.2.2 A2.2.1.1.1 A2.2.1.1.2 A2.2.1.1.3 A2.2.1.1.4 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4

7.3 Multiplying and Dividing Rational Expressions

Simplify rational expressions. Multiply rational expressions. Divide rational expressions.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4

7.4* Adding and Subtracting Rational Expressions

Add or subtract rational expressions. Rewrite rational expressions and graph the related function. Simplify complex fractions.


27

Chapter 7. Rational Functions

Suggested Dates

Chapter- Lesson


(see

ab

ove

) 7.5* Solving Rational Equations Solve rational equations by cross multiplying.

Solve rational equations by using the least common denominator. Use inverses of functions.

A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.1.3.2.1 A2.1.3.2.2 A2.2.1.1.1 A2.2.1.1.2 A2.2.1.1.3 A2.2.1.1.4 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4


28

Chapter 8: Sequences and Series

Suggested Dates

Chapter- Lesson


2/1

3-2

/28

: 1 D

ay P

er L

esso

n +

5 D

ays

11

/14

-11

/22

4/1

8-4

/24

8.1* Defining and Using Sequences and Series

Use sequence notation to write terms of sequences. Write a rule for the nth term of a sequence. Sum the terms of a sequence to obtain a series and use summation notation.

A2.2.1.1.1 A2.2.1.1.2

8.2* Analyzing Arithmetic Sequences and Series

Identify arithmetic sequences. Write rules for arithmetic sequences. Find sums of finite arithmetic series.

8.3 Analyzing Geometric Sequences and Series

Identify geometric sequences. Write rules for geometric sequences. Find sums of finite geometric series.

8.4 Finding Sums of Infinite Geometric Series

Find partial sums of infinite geometric series. Find sums of infinite geometric series.

8.5* Using Recursive Rules with Sequences

Evaluate recursive rules for sequences. Write recursive rules for sequences. Translate between recursive and explicit rules for sequence. Use recursive rules to solve real-life problems.


29

Chapter 10: Probability

Suggested Dates

Chapter- Lesson


3/1

-3/1

6: 1

Day

Per

Les

son

+ 5

Day

s

11

/27

-12

/5

4/2

5-5

/2

10.1* Sample Spaces and Probability Find sample space. Find theoretical probabilities. Find experimental probabilities.

A2.2.3.2.1 A2.2.3.2.2 A2.2.3.2.3

10.2* Independent and Dependent Events

Determine whether events are independent events. Find probabilities of independent and dependent events. Find conditional probability.

10.3* Two-Way Tables and Probability Make two-way tables. Find relative and condition conditional relative frequencies. Use conditional relative frequencies to find conditional probabilities.

10.4* Probability of Disjoint and Overlapping Events

Find probabilities of compound events. Use more than one probability rule to solve real-life problems.

10.5* Permutations and Combinations Use the formula for the number of permutations. Use the formula for the number of combinations. Use combinations and the Binomial Theorem to expand binomials.

A2.1.2.2.1 A2.1.2.2.2 A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.2.3.2.1 A2.2.3.2.2 A2.2.3.2.3

10.6* Binomial Distributions Construct and interpret probability distributions. Construct and interpret binomial distributions.

A2.2.3.2.1 A2.2.3.2.2 A2.2.3.2.3


30

Chapter 11: Data Analysis and Statistics

Suggested Dates

Chapter- Lesson


3/1

9-4

/6: 1

Day

Per

Les

son

+ 5

Day

s

12

/6-1

2/1

4

5/3

-5/1

1

11.1* Using Normal Distributions Calculate probabilities using normal distributions. Use z-scores and the standard normal table to find probabilities. Recognize data sets that are normal.

A2.2.3.2.1 A2.2.3.2.2 A2.2.3.2.3

11.2* Populations, Samples, and Hypotheses

Distinguish between populations and samples. Analyze hypotheses.

11.3* Collecting Data Identify types of sampling methods in statistical studies. Recognize bias in sampling. Analyze methods of collection data. Recognize bias in survey questions.

11.4* Experimental Design Describe experiments. Recognize how randomization applies to experiments and observational studies. Analyze experimental designs.

11.5* Making Inferences from Sample Surveys

Estimate population parameters. Analyze estimated population parameters. Find margins of error for surveys.

11.6* Making Inferences from Experiments

Organize data from an experiment with two samples. Resample data using a simulation to analyze a hypothesis. Make inferences about a treatment.

Benchmark 3 Window: Apr 9 – Apr 25


31

Cycle 4 Standards


No Algebra 2 Eligible Content Alignment CC.2.2.HS.C.7 Apply radian measure of an angle and the unit circle to analyze the trigonometric functions.

No Algebra 2 Eligible Content Alignment CC.2.2.HS.C.8 Choose trigonometric functions to model periodic phenomena and describe the properties of the graphs

No Algebra 2 Eligible Content Alignment CC.2.3.HS.A.7 Apply trigonometric ratios to solve problems involving right triangles.


32

Cycle 4 Scope and Sequence

Chapter 9: Trigonometric Ratios and Functions

Suggested Dates

Chapter- Lesson


4/9

-5/7

: 2 D

ays

Pe

r Le

sso

n +

5 D

ays

12

/15

-1/2

2

5/1

4-5

/31

9.1* Right Triangle Trigonometry Evaluate trigonometric functional of acute angles.

Find unknown side lengths and angle measure of right triangles. Use trigonometric functions to solve real-life problems.

Beyond Eligible Content

9.2 Angles and Radian Measure Draw angles in standard position. Find coterminal angles. Use radian measure.

9.3* Trigonometric Functions of Any Angle

Evaluate trigonometric functions of any angle. Find and use reference angles to evaluate trigonometric functions.

9.4* Graphing Sine and Cosine Functions

Explore characteristics of sine and cosine functions. Stretch and shrink graphs of sine and cosine functions. Translate graphs of sine and cosine functions. Reflect graphs of sine and cosine functions.

9.5* Graphing Other Trigonometric Functions

Explore characteristics of tangent and cotangent functions. Graph tangent and cotangent functions. Graph secant and cosecant functions.

9.6* Modeling with Trigonometric Functions

Interpret and use frequency. Write trigonometric functions. Use technology to find trigonometric models.

9.7* Using Trigonometric Identities Use trigonometric identities to evaluate trigonometric functions and simplify trigonometric expressions. Verify trigonometric identities.

9.8* Using Sum and Difference Formulas

Use sum and difference formulas to evaluate and simplify trigonometric expressions. Use sum and difference formulas to solve trigonometric equations and rewrite real-life formulas.


33

Remediation and Extension Options 5/8-6/12 24 Days

Option 1: Revisit Common Core

Performance Tasks

Each chapter contains a Common Core Performance Task (CCPT), intended to deepen students’ understanding of the content, as they proceed through the lessons. The CCPT may be previewed before beginning a chapter, and students can share their early ideas on how to approach it. Later, as they develop and strengthen tools for solving the CCPT, they can return to it and approach it in a different light. CCPTs can be used as summative assessments for individual chapter or you can return to them to wrap-up the school year.

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.

Option 3: 3-Act Math

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 a series of Three-Act modeling activities. You can find some at: https://whenmathhappens.com/3-act-math/, https://gfletchy.com/3-act-lessons/, or this Google Sheet.

Option 4: Mathematics

Assessment Project

Classroom Challenges are lessons that support teachers in formative assessment. There are 100 lessons in total, 20 at each grade from 6 to 8 and 40 for ‘Career and College Readiness’ at High School Grades 9 and above. Some lessons are focused on developing math concepts, others on solving non-routine problems. http://map.mathshell.org/lessons.php

The Brief Guide for teachers and administrators (PDF) is recommended reading before using these lessons for the first time. Each lesson is downloadable as an all-in-one PDF to print out, and a supporting PowerPoint presentation.

Option 5: 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

http://map.mathshell.org/lessons.php

http://map.mathshell.org/guides/map_cc_teacher_guide.pdf

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

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

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


34

PA Core Standards by Cycle

Cycle

PA Core Standards

CC

.2.1

.HS.

F.1

C

C.2

.1.H

S.F.

3

C

C.2

.1.H

S.F.

4

C

C.2

.1.H

S.F.

5

C

C.2

.1.H

S.F.

6

C

C.2

.1.H

S.F.

7

C

C.2

.2.H

S.D

.1

C

C.2

.2.H

S.D

.2

C

C.2

.2.H

S.D

.3

C

C.2

.2.H

S.D

.4

C

C.2

.2.H

S.D

.5

C

C.2

.2.H

S.D

.6

C

C.2

.2.H

S.D

.7

C

C.2

.2.H

S.D

.8

C

C.2

.2.H

S.D

.9

C

C.2

.2.H

S.D

.10

C

C.2

.2.H

S.C

.1

C

C.2

.2.H

S.C

.2

C

C.2

.2.H

S.C

.3

C

C.2

.2.H

S.C

.4

C

C.2

.2.H

S.C

.5

C

C.2

.2.H

S.C

.6

C

C.2

.4.H

S.B

.2

C

C.2

.4.H

S.B

.3

C

C.2

.4.H

S.B

.4

C

C.2

.4.H

S.B

.5

C

C.2

.4.H

S.B

.6

C

C.2

.4.H

S.B

.7

1 2 3 4

Eligible Content ↓

MO

DU

LE 1

A2.1.1.1.1 X

A2.1.1.1.2 X

A2.1.1.2.1 X

A2.1.1.2.2 X

A2.1.2.1.1 X X

A2.1.2.1.2 X X

A2.1.2.1.3 X X

A2.1.2.1.4 X X

A2.1.2.2.1 X X

A2.1.2.2.2 X X

A2.1.3.1.1 X X X

A2.1.3.1.2 X X X

A2.1.3.1.3 X X X

A2.1.3.1.4 X X X

A2.1.3.2.1 X X X

A2.1.3.2.2 X X X


35

Cycle

PA Core Standards

CC

.2.1

.HS.

F.1

C

C.2

.1.H

S.F.

3

C

C.2

.1.H

S.F.

4

C

C.2

.1.H

S.F.

5

C

C.2

.1.H

S.F.

6

C

C.2

.1.H

S.F.

7

C

C.2

.2.H

S.D

.1

C

C.2

.2.H

S.D

.2

C

C.2

.2.H

S.D

.3

C

C.2

.2.H

S.D

.4

C

C.2

.2.H

S.D

.5

C

C.2

.2.H

S.D

.6

C

C.2

.2.H

S.D

.7

C

C.2

.2.H

S.D

.8

C

C.2

.2.H

S.D

.9

C

C.2

.2.H

S.D

.10

C

C.2

.2.H

S.C

.1

C

C.2

.2.H

S.C

.2

C

C.2

.2.H

S.C

.3

C

C.2

.2.H

S.C

.4

C

C.2

.2.H

S.C

.5

C

C.2

.2.H

S.C

.6

C

C.2

.4.H

S.B

.2

C

C.2

.4.H

S.B

.3

C

C.2

.4.H

S.B

.4

C

C.2

.4.H

S.B

.5

C

C.2

.4.H

S.B

.6

C

C.2

.4.H

S.B

.7

1 2 3 4

Eligible Content ↓

MO

DU

LE 2

A2.2.1.1.1 X X X

A2.2.1.1.2 X X X

A2.2.1.1.3 X X X

A2.2.1.1.4 X X X

A2.2.2.1.1 X X X

A2.2.2.1.2 X X X

A2.2.2.1.3 X X X

A2.2.2.1.4 X X X

A2.2.2.2.1 X X X

A2.2.3.1.1 X

A2.2.3.1.2 X

A2.2.3.2.1 X

A2.2.3.2.2 X

A2.2.3.2.3 X


36

Algebra Eligible Content Taught

PA Eligible Content Cycle

1 Cycle

2 Cycle

3 Cycle

4

A2.1.1.1.1 Simplify/write square roots in terms of i (e.g., √-24 = 2i√6). X

A2.1.1.1.2 Simplify/evaluate expressions involving powers of i (e.g., i6 + i3 = –1 – i). X

A2.1.1.2.1 Add and subtract complex numbers (e.g., (7 – 3i) – (2 + i) = 5 – 4i). X

A2.1.1.2.2 Multiply and divide complex numbers (e.g., (7 – 3i)(2 + i) = 17 + i). X

A2.1.2.1.1 Use exponential expressions to represent rational numbers. X X


X X


X X

A2.1.2.1.4 Simplify or evaluate expressions involving logarithms and exponents (e.g., log28 = 3

or log42 = ½). X X

A2.1.2.2.1 Factor algebraic expressions, including difference of squares and trinomials.

Note: Trinomials limited to the form ax2+bx+c where a is not equal to 0. X X

A2.1.2.2.2 Simplify rational algebraic expressions. X X

A2.1.3.1.1 Write and/or solve quadratic equations (including factoring and using the Quadratic Formula). X X X

A2.1.3.1.2 Solve equations involving rational and/or radical expressions

(e.g., 10/(x + 3) + 12/(x – 2) = 1 or √x2 + 21x = 14). X X X

A2.1.3.1.3 Write and/or solve a simple exponential or logarithmic equation (including common and natural logarithms).

X X X

A2.1.3.1.4 Write, solve, and/or apply linear or exponential growth or decay (including problem situations). X X X


(e.g., y = 4/x; if x doubles, what happens to y?). X X X

A2.1.3.2.2 Use algebraic processes to solve a formula for a given variable (e.g., solve d = rt for r). X X X


37

PA Eligible Content Cycle

1 Cycle

2 Cycle

3 Cycle

4


X X X


X X X

A2.2.1.1.3 Determine the domain, range, or inverse of a relation. X X X


X X X


X X X


X X X


X X X

A2.2.2.1.4 Translate a polynomial, exponential, or logarithmic function from one representation of a function to another (graph, table, and equation).

X X X


(e.g., y = x2 and y = x2 + 3, or y = x2 and y = 3x2). X X X

A2.2.3.1.1 Draw, identify, find, interpret, and/or write an equation for a regression model (lines and curves of best fit) for a scatter plot.

X

A2.2.3.1.2 Make predictions using the equations or graphs of regression models (lines and curves of best fit) of scatter plots.

X

A2.2.3.2.1 Use combinations, permutations, and the fundamental counting principle to solve problems involving probability.

X

A2.2.3.2.2 Use odds to find probability and/or use probability to find odds. X

A2.2.3.2.3 Use probability for independent, dependent, or compound events to predict outcomes. X


38

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.


39

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 II:

(1) Students draw on analogies between polynomial arithmetic and base-ten computation, focusing on properties of operations, particularly the distributive property; they identify zeros of polynomials, including complex zeros of quadratic polynomials, and make connections between zeros of polynomials and solutions of polynomial equations;

(2) Students now use the coordinate plane to extend trigonometry to model periodic phenomena; (3) They explore the effects of transformations on graphs of diverse functions, including functions arising in an application, in order to abstract

the general principle that transformations on a graph always have the same effect regardless of the type of the underlying function; and (4) Students identify different ways of collecting data—including sample surveys, experiments, and simulations—and the role that randomness

and careful design play in the conclusions that can be drawn.

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

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 2 Big Ideas Math 2017-2018 SY · 1 Algebra 2 Big Ideas Math 2017-2018 SY Benchmark Cycle1...

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