Algebra 2 Pearson High School 2017-2018 SY10 – Quadratic Relations and ... 13 – Periodic Functions and Trigonometry BEC 14 – Trigonometric Identities and Equations BEC Notes

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

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Algebra 2 Pearson High School 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

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ho

ol

Day

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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 – Expressions, Equations, and Inequalities1

2 – Functions, Equations, and Graphs1, 2

3 – Linear Systems1, BEC

4 – Quadratic Functions and Equations1 (4-1 to 4-3)

4 – Quadratic Functions and Equations1 (4-4 to 4-9)

5 – Polynomials and Polynomial Functions 2

6 – Radical Functions and Rational Exponents 1

7 – Exponential and Logarithmic Functions 1, 2

8 – Rational Function1

9 – Sequences and Series 2

11 – Probability and Statistics 2, BEC

10 – Quadratic Relations and Conic Sections BEC

12 – Matrices BEC

13 – Periodic Functions and Trigonometry BEC

14 – Trigonometric Identities and Equations BEC

Notes

A Benchmark (BM) 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 blueprint.


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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 ........................................................................................................................................................................................... 12

Benchmark Cycle 2 Scope and Sequence ......................................................................................................................................................................... 15

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

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

Cycle 4 Standards .............................................................................................................................................................................................................. 33

Cycle 4 Scope and Sequence ............................................................................................................................................................................................. 34

PA Core Standards by Cycle .............................................................................................................................................................................................. 39

Algebra Eligible Content Taught ....................................................................................................................................................................................... 41

Document Information Page ............................................................................................................................................................................................ 43


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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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Fal

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9/5 – 10/2 Ch. 1 to Ch. 4-3

10/3 – 10/31 Ch. 4-4 to Ch. 6

11/1 – 11/9 Ch. 7

11/13 – 12/8 Ch. 8 to Ch. 9, Ch. 11

12/11 – 1/29 Ch. 10, Ch. 12 to Ch. 14 Remediation and Extension

Full

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Spri

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1/30 – 2/27 Ch. 1 to Ch. 4-3

2/28 – 3/28 Ch. 4-4 to Ch. 6

4/3 – 4/10 Ch. 7

4/11 – 5/4 Ch. 8 to Ch. 9, Ch. 11

5/7 – 6/12 Ch. 10, Ch. 12 to Ch. 14 Remediation and Extension

Benchmark Schedule

A /

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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

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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

A2.1.2.1.1 Use exponential expressions to represent rational numbers.

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. A2.1.2.1.2 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).

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.

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.

A2.1.2.2.2 Simplify rational algebraic expressions.

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.

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.

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).


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


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).

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.

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.

A2.2.1.1.2 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).


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

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.2.3.HS.A.10 Translate between the geometric description and the equation for a conic section.

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.)

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).




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.


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.

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

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


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Benchmark Cycle 1 Scope and Sequence

Chapter 1: Expressions, Equations, and Inequalities

Suggested Dates

Chapter- Lesson

Lesson Title Lesson Topic(s) Eligible Content

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1-1 Patterns and Expressions Reviewsa

Identify and describe patterns. A2.1.2.2.1 A2.1.2.2.2

1-2 Properties of Real Numbers Reviews

Graph and order real numbers. Identify properties of real numbers.

A1.1.1.1.1 A1.1.1.1.2 A1.1.1.2.1 A1.1.1.3.1

1-3 Algebraic Expressions Evaluate algebraic expressions. Simplify algebraic expressions.

A2.1.2.2.1 A2.1.2.2.2

1-4 Solving Equations Solve equations. Solve problems by writing 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

1-5* Solving Inequalities Solve and graph inequalities. Write and solve compound inequalities.

a A Solve It! begins every lesson, providing students opportunities to strengthen their problem-solving skills. Students draw on prior knowledge and connect with key concepts from the lesson before refining solution methods. The Solve It! is an essential component of the program.

* Lessons marked with an asterisk may require two45-minute class periods, for which flex days may be used. Note: Consider beginning the year by laying foundations for problem-solving via: WODB.ca, Estimation180.com, SolveMe. Also consider using flex days, on occasion, to complete or present the Common Core Performance Tasks and Mathematical Modeling in Three Acts (on Pearson Realize), 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 1: Expressions, Equations, and Inequalities (cont.)

Suggested Dates

Chapter- Lesson

Lesson Title Lesson Topic(s) Eligible Content

(See

pre

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1-6* Absolute Value Equations and

Inequalities

Write and solve equations and inequalities involving absolute value.

A2.1.2.2.1 A2.1.2.2.2


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Chapter 2: Functions, Equations, and Graphs

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Chapter- Lesson

Lesson Title Lesson Topic Eligible Content

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2-1* Relations and Functions Reviews

Graph relations. Identify 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

2-2 Direct Variation Write and interpret direct 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 A2.2.1.1.1 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 A2.2.3.1.1 A2.2.3.1.2

2-3 Linear Functions and Slope-Intercept Form

Graph linear equations. Write equations of lines.

2-4* More About Linear Equations Write an equation of a line given tits slope and point on the line.

2-5 Using Linear Models Write linear equations that model real-world data Make predictions from linear models

2-6* Families of Functions Analyze transformations 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

2-7* Absolute Value Functions and Graphs

Graph absolute value functions.

2-8* Two-Variable Inequalities Graph two-variable inequalities


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Chapter 3:Linear Systems

Suggested Dates

Chapter- Lesson


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3-1* Solving Systems Using Tables

and Graphs Solve linear systems using a graph or a table.

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

3-2* Solving Systems Algebraically Solve linear systems algebraically.

3-3 Systems of Inequalities Solve systems of linear inequalities.

3-4 Linear Programming Solve problems using linear programming.

3-5BEC Systems with Three Variables Solve systems in three variables using elimination. To solve systems in three variables using substitution.

3-6BEC Solving Systems Using Matrices

CC Performance Task: Planning a Triathlon

Represent a system of linear equations with a matrix. Solve a system of linear equations using matrices.


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Chapter 4: Quadratic Functions and Equations

Suggested Dates

Chapter- Lesson


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4-1* Quadratic Functions and

Transformations Identify and graph 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 A2.2.1.1.1 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

4-2* Standard Form of a Quadratic Function

Graph quadratic functions written in standard form.

4-3* Modeling With Quadratic Functions

Model data with quadratic functions. A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.2.3.1.1 A2.2.3.1.2

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).

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

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).
















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(e.g., 10/(x + 3) + 12/(x – 2) = 1 or 14212 xx .


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











CC.2.1.HS.F.7 Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems.


14



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.
















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Benchmark Cycle 2 Scope and Sequence 1

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Mathematical Modelingc

Piles of Tiles Estimate area.

A2.1.2.2.1 A2.1.2.2.2

Concept Byted

Identifying Quadratic Data Model data with quadratic functions.

4-4* Factoring Quadratic Expressions Find common and binomial factors of quadratic expressions. Factor special quadratic expressions.

4-5* Algebra Review: Square Roots and Radicals Reviews

Quadratic Equations

Solve quadratic equations by factoring Solve quadratic equations by graphing

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 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

c Mathematical Modeling in Three Acts are activities that offer students rich opportunities to engage with the PA Core Standards for Mathematical Practice (SMPs). The focus of these activities is on the process of problem-solving and reasoning.

d Concept Bytes are to be used either before or after lessons (as indicated) to build conceptual understanding, support development of problem-solving skills, to engage with the PA Core Standards for Mathematical Practice, and to integrate learning with technology (consider either TI calculators or Desmos for these).

Chapter 4: Quadratic Functions and Equations (cont.)

Suggested Dates

Chapter- Lesson



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Chapter 4: Quadratic Functions and Equations (cont.)

Suggested Dates

Chapter- Lesson


(see

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4-6* Completing the Square Solve equations by completing the square Rewrite functions by completing the square A2.1.3.1.1

A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4

4-7* The Quadratic Formula Solve quadratic equations using the Quadratic Formula Determine the number of solutions by using the discriminant

4-8* Complex Numbers Identify, graph, and perform operations with complex numbers Find complex number solutions of quadratic equations

A2.1.1.1.1 A2.1.1.1.2 A2.1.1.1.3 A2.1.1.1.4 A2.1.1.2.1 A2.1.1.2.2 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

4-9* Quadratic Systems Solve and graph systems of linear and quadratic equations Solve and graph systems of quadratic inequalities

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


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Chapter 5: Polynomials and Polynomial Functions

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5-1* Polynomial Functions Classify polynomials. Graph polynomial functions and describe end behavior.

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

5-2* Polynomials, Linear Factors, and Zeros

Analyze the factored form of a polynomial. Write a polynomial function from its zeros.

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

5-3* Solving Polynomial Equations Solve polynomial equations by factoring. Solve polynomial equations by graphing.

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

5-4* Dividing Polynomials Divide polynomials using long division. Divide polynomials using synthetic division.


18

Chapter 5: Polynomials and Polynomial Functions (cont.)

Suggested Dates

Chapter- Lesson


(see

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5-5* Theorems About Roots of Polynomial Equations

Solve equations using Rational Root Theorem. Use the Conjugate Root Theorem.

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

5-6* The Fundamental Theorem of Algebra

Use the Fundamental Theorem to solve polynomial equations with complex solutions.

5-7 The Binomial Theorem Expand a binomial using Pascal’s Triangle. Use the Binomial Theorem.

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


19

Chapter 5: Polynomials and Polynomial Functions (cont.)

Suggested Dates

Chapter- Lesson


(see

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5-8 Polynomial Models in the Real World

Fit data to linear, quadratic, cubic, or quartic models. A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4 A2.2.3.1.1 A2.2.3.1.2

5-9* Transforming Polynomial Functions

CC Performance Task: Determining the Dimensions of a Diorama

Apply transformations to graphs of polynomials. 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


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Chapter 6: Radical Functions and Rational Exponents

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6-1 Roots and Radical Expressions Find the nth root.

A2.1.2.2.1 A2.1.2.2.2

6-2* Multiplying and Dividing Radical Expressions

Multiply and divide radical expressions.

6-3* Binomial Radical Expressions Add and subtract radical expressions.

6-4* Rational Exponents Simplify expressions with rational exponents. A2.1.2.1.1 A2.1.2.1.2 A2.1.2.1.3 A2.1.2.1.4

6-5* Solving Square Root and Other Radical Equations

Solve square root and other radical 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 A2.2.1.1.1 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: Radical Functions and Rational Exponents (cont.)

Suggested Dates

Chapter- Lesson


(see

ab

ove

) 6-6* Function Operations Add, subtract, multiply, and divide functions.

Find the composite of two 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

6-7* Inverse Relations and Functions Find the inverse of a relation or function.

6-8* Graphing Radical Functions Graph square root and other radical functions. A2.1.3.1.1 A2.1.3.1.2 A2.1.3.1.3 A2.1.3.1.4

Benchmark 2 Window: Jan 29 – Feb 13


22
























(e.g., 10/(x + 3) + 12/(x – 2) = 1 or 14212 xx .



23


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

















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.





24















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






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.

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.

CC.2.4.HS.B.4 Recognize and evaluate random processes underlying statistical experiments. CC.2.4.HS.B.5


25


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

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.

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


26

Benchmark Cycle 3 Scope and Sequence

Chapter 7: Exponential and Logarithmic Functions

Suggested Dates

Chapter- Lesson


1/2

9-2

/9: 1

Day

Per

Les

son

+ 4

Day

s

11

/1-1

1/9

4/3

-4/1

0

7-1 Exploring Exponential Models Model exponential growth and decay. 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

7-2 Properties of Exponential Functions

Explore the property of functions in the form y = abx. Graph exponential functions that have base e.

A2.2.1.1.1 A2.2.1.1.2 A2.2.1.1.3 A2.2.1.1.4 A2.2.3.1.1 A2.2.3.1.2


27

Chapter 7: Exponential and Logarithmic Functions (cont.)

Suggested Dates

Chapter- Lesson


(see

ab

ove

) 7-3* Logarithmic Functions as

Inverses Write and evaluate logarithmic expressions. Graph logarithmic 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 A2.2.2.1.1 A2.2.2.1.2 A2.2.2.1.3 A2.2.2.1.4

7-4* Properties of Logarithms Use the properties of logarithms. 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

7-5* Exponential and Logarithmic Equations

Solve exponential and logarithmic equations.

7-6* Natural Logarithms Evaluate and simplify natural logarithmic expressions. Solve equations using natural logarithms.


28

Chapter 8: Rational Functions

Suggested Dates

Chapter- Lesson


2/1

2-2

/28

: 1 D

ay P

er L

esso

n +

6 D

ays

11

/13

-11

/17

4/1

1-4

/17

8-1 Inverse Variation Recognize and use inverse variations.

Use joint and other variations. 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

8-2 The Reciprocal Function Family Graph reciprocal functions. Graph translations of reciprocal 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 A2.2.1.13 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

8-3* Rational Functions and Their Graphs

Identify properties of rational functions. Graph rational functions.

8-4* Rational Expressions Simplify rational expressions. Multiply and divide rational expressions. A2.1.2.2.1

A2.1.2.2.2


29

Chapter 8: Rational Functions (cont.)

Suggested Dates

Chapter- Lesson


(see

ab

ove

) 8-5* Adding and Subtracting Rational

Expressions Add and subtract rational expressions. 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

8-6* Solving Rational Equations Solve rational equations. Use rational equations to solve problems.

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


30

Chapter 9: Sequences and Series

Suggested Dates

Chapter- Lesson


3/1

-3/1

2: 1

Day

Per

Les

son

+3

Day

s

11

/20

-11

/29

4/1

8-4

/25

9-1 Mathematical Patterns Identify mathematical patterns found in a sequence.

Use a formula to find the nth term of a sequence. A2.1.2.1.1 A2.1.2.1.2 A2.1.2.1.3 A2.1.2.1.4

9-2 Arithmetic Sequences To define, identify, and apply arithmetic sequences. 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

9-3* Geometric Sequences Define, identify and apply geometric sequences.

9-4* Arithmetic Series Extends Define arithmetic series and find their sums.

9-5* Geometric Series Define geometric series and find their sums.


31

Chapter 11: Probability and Statistics

Suggested Dates

Chapter- Lesson


3/1

3-4

/6: 1

Day

Per

Les

son

+ 6

Day

s

11

/30

-12

/8

4/2

6-5

/4

11-1* Permutations and Combinations Count permutations. Count combinations.

A2.2.3.2.1 A2.2.3.2.2 A2.2.3.2.3

11-2* Probability Find the probability of an event using theoretical, experimental, and simulation methods.

11-3* Probability Multiple Events Find the probability of the event A and B. Find the probability of the event A or B.

11-4 Conditional Probability Find conditional probabilities. Use tables and tree diagrams to determine conditional probabilities.

11-5 Probability Models Use probabilities to make fair decisions and analyze decisions.

11-6 Analyzing Data Calculate measures of central tendency. Draw and interpret box-and-whisker plots.

11-7 Standard Deviation Find the standard deviation and variance of a set of values. Apply standard deviation and variance.

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


32

Chapter 11: Probability and Statistics (cont.)

Suggested Dates

Chapter- Lesson


(see

ab

ove

) 11-8 Samples and Surveys Identify sampling methods.

Recognize bias in samples and surveys. A2.2.3.2.1 A2.2.3.2.2 A2.2.3.2.3

11-9* Binomial Distributions Find binomial probabilities and us binomial distribution. Beyond Eligible

Content 11-10* Normal Distributions Use a normal distribution.

Benchmark 3 Window: Apr 9 – Apr 25


33

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.10 Translate between the geometric description and the equation for a conic

section.

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

No Algebra 2 Eligible Content Alignment CC.2.4.HS.B.1 Summarize, represent, and interpret data on a single count or measurement variable.


34

Cycle 4 Scope and Sequence

Chapter 10: Quadratic Relations and Conic Sections

Suggested Dates

Chapter- Lesson


4/9

-4/2

0: 1

Day

Per

Les

son

+ 4

Day

s

12

/11

-12

/15

5/7

-5/1

1

10-1* Exploring Conic Sections Graph and identify conic sections.

Beyond Eligible Content

10-2 Parabolas Write the equations of a parabola and graph parabolas.

10-3 Circles Write and graph the equation of a circle. Find the center and radius of a circle and use them to graph the circle.

10-4* Ellipses Write the equation of an ellipse. Find the foci of an ellipse. Graph an ellipse.

10-5* Hyperbolas Graph hyperbolas. Find and use the foci of a hyperbola.

10-6* Translating Conic Sections Write the equation of a translated conic section. Identify a translated conic section from an equation.


35

Chapter 12: Matrices

Suggested Dates

Chapter- Lesson


4/2

3-5

/8: 1

Day

Per

Les

son

+ 6

Day

s

12

/18

-1/3

5/1

4-5

/22

12-1* Adding and Subtracting

Matrices Add and subtract matrices and solve matrix equations.


12-2* Matrix Multiplication Multiply matrices using scalar and matrix multiplication.

12-3* Determinants and Inverses Find the inverse of a matrix.

12-4* Inverse Matrices and Systems Solve systems of equations using matrix inverses and multiplication.

12-5* Geometric Transformations Transform geometric figures using matrix operations.

12-6* Vectors

CC Performance Task: Animal Care

Use basic vector operations and the dot product.


36

Chapter 13: Periodic Functions and Trigonometry

Suggested Dates

Chapter- Lesson


5/9

-5/2

9: 1

Day

Per

Les

son

+ 4

Day

s

1/4

-1/1

6

5/2

3-6

/4

13-1* Exploring Periodic Data Identify cycles and periods of periodic functions. Find the amplitude of periodic functions.


13-2* Angles and the Unit Circle Work with angles in standard position. Find coordinates of prints on the unit circle.

13-3* Radian Measure Use radian measure for angles. Find the length of an arc of a circle.

13-4* The Sine Function Identify properties of the sine function. Graph sine curves.

13-5* The Cosine Function Graph and write cosine functions. Solve trigonometric equations.

13-6 The Tangent Function Graph the tangent function.

13-7* Translating Sine and Cosine Functions

Graph translations of trigonometric functions Write equations of translations.

13-8* Reciprocal Trigonometric Functions

CC Performance Task: Animating a Game

Evaluate reciprocal trigonometric functions. Graph reciprocal trigonometric functions.


37

Chapter 14: Trigonometric Identities and Equations

Suggested Dates

Chapter- Lesson


5/3

0-6

/12

: 1 D

ay P

er L

esso

n +

3 D

ay

1/1

7-1

/26

6/5

-6/1

2

14-1* Trigonometric Identities Verify trigonometric identities.


14-2* Solving Trigonometric Equations Using Inverses

Evaluate inverse trigonometric functions. Solve trigonometric equations.

14-3* Right Triangles and Trigonometric Ratios

Find lengths of siders in a right triangle. Find measures of angels in a right triangle.

14-4 Area and the Law of Sines Find the area of any triangle. Use the Law of Sines.

14-5 The Law of Cosines Use the Law of Cosines in finding the measures of sides of angles of a triangle.

14-6* Angle Identities Extends Verify and use angle identities. Verify and use sum and difference identities.

14-7* Double-Angle and Half-Angle Identities

Verify and use double-angle identities. Verify and use half-angle identities.


38

Remediation and Extension Options

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: 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 Mathematical Modeling activities available on Pearson Realize. You can find additional three-act modeling activities at: https://whenmathhappens.com/3-act-math/, https://gfletchy.com/3-act-lessons/, or within 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/


39

PA Core Standards by Cycle

CYCLES

PA Core Standards

Eligible

Content ↓ CC

.2.1

.HS.

F.1

CC

.2.1

.HS.

F.3

CC

.2.1

.HS.

F.4

CC

.2.1

.HS.

F.5

CC

.2.1

.HS.

F.6

CC

.2.1

.HS.

F.7

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

.2.2

.HS.

D.1

CC

.2.2

.HS.

D.2

CC

.2.2

.HS.

D.3

CC

.2.2

.HS.

D.4

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

.2.3

.HS.

A.1

0

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.6

CC

.2.4

.HS.

B.7

1 2 3 4

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 X

A2.1.2.1.2

X X X

A2. 1.2.1.3

X X X

A2. 1.2.1.4

X X X

A2. 1.2.2.1

X X X

A2.1.2.2.2

X 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


40

CYCLES

PA Core Standards

Eligible

Content ↓ CC

.2.1

.HS.

F.1

CC

.2.1

.HS.

F.3

CC

.2.1

.HS.

F.4

CC

.2.1

.HS.

F.5

CC

.2.1

.HS.

F.6

CC

.2.1

.HS.

F.7

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

.2.2

.HS.

D.1

CC

.2.2

.HS.

D.2

CC

.2.2

.HS.

D.3

CC

.2.2

.HS.

D.4

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

.2.3

.HS.

A.1

0

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.6

CC

.2.4

.HS.

B.7

1 2 3 4

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

A2.2.3.1.1

X X

A2.2.3.1.2

X X

A2.2.3.2.1

X

A2.2.3.2.2

X

A2.2.3.2.3

X


41

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 ex X X X

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).

X X X

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.

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 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 X

A2.1.2.2.2 Simplify rational algebraic expressions. X 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

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?).

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


X X X


X X X


42

PA Eligible Content Cycle

1 Cycle

2 Cycle

3 Cycle

4

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


X X X

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


X 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


43

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.


44

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].

Documents

Algebra 2 Pearson High School 2017-2018 SY10 – Quadratic Relations and ... 13 – Periodic Functions and Trigonometry BEC 14 – Trigonometric Identities and Equations BEC Notes