Columbus City Schools High School CCSS Mathematics III - High School PARRC Model Content Frameworks Mathematics - Core Standards And Math Practices

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1 A Correlation of III Common Core To the CCSS III - - Core Standards And s

2 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s Introduction This document demonstrates how - III Common Core meets the standards of the CCSS III - and the within the Core Math III. Correlation references are to the pages of the Student and Teacher s Editions., fully aligned to the, offers a hybrid instructional model that consists of digital delivery of content during instructional time, supplemented by a Write-In Student Edition in which students record their understandings of the concepts presented as they work through the problems. The in-class instruction can be further enhanced with the robust math tools and dynamic activities that are part of the digital courseware. The in-class learning is supported out of the classroom with both digital and print resources. Students have full access to the animated content presented in class. They also can easily access math tutor videos. In the Write-In Student Edition, students will find instructional summaries of key concepts in each lesson. The Teacher s Guide is a comprehensive tool that teachers can use as they plan for and teach every phase of the 5- part lesson of the program. At the chapter level, teachers will find math background, tips for error prevention, and assignment guides to help them in planning. At the lesson level, teachers will find resources for instruction, practice, assessment, and remediation. To help with planning, there are teaching notes and probing questions to the left of images of each Solve It! and problem that teachers will be presenting from the digital courseware. This document demonstrates the high degree of success students will achieve by using Pearson Integrated High School, III Common Core. Copyright 2015 Pearson Education, Inc. or its affiliate(s). All rights reserved

3 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s Table of Contents Topic 1 Statistics... 1 Topic 2 A Variety of Functions... 5 Topic 3 Polynomial Functions Topic 4 Rational Functions Topic 5 Exponential Functions Topic 6 Trigonometric Functions Topic 7 Coordinate Geometry Topic 8 Geometric Constructions and Measurement Topic 9 Circles and Conics Copyright 2015 Pearson Education, Inc. or its affiliate(s). All rights reserved

4 A Correlation of - III Common Core to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Topic 1 Statistics Making Inferences and Justifying Conclusions (S IC): 1) Understand and evaluate random processes underlying statistical experiments. S IC 1: Understand statistics as a process SE: 1.3: for making inferences about population parameters based on a random sample from TG: 1.3: that population. S IC 1 - Core Math III Standard S IC 1 S IC 2: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question that model? SE: Activity Lab: Probably Distributions: TG: Activity Lab: Probably Distributions: MP.3 Construct viable arguments and critique the reasoning of others. S IC 2 - Core Math III Standard S IC 2 1

5 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s 2) Make inferences and justify conclusions from sample surveys, experiments, and observational studies. S IC 3: Recognize the purposes of and SE: 1.3: differences among sample surveys, experiments, and observational studies; TG: 1.3: explain how randomization relates to each. S IC 3 - Core Math III Standard S IC 3 MP.3 Construct viable arguments and critique the reasoning of others. S IC 4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. SE: Activity Lab: Margin of Error: TG: Activity Lab: Margin of Error: S IC 4 - Core Math III Standard S IC 4 2

6 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III S IC 5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. III Common Core SE: Activity Lab: Drawing Conclusions from Samples: TG: Activity Lab: Drawing Conclusions from Samples: Core Standards s S IC 5 - Core Math III Standard S IC 5 S IC 6: Evaluate reports based on data. SE: 1.1: 3-8, 1.2: 15-18, 1.3: TG: 1.1: 5-9, 1.2: 15-18, 1.3: S IC 6 - Core Math III Standard S IC 6 MP.8 Look for and express regularity in repeated reasoning. 3

7 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Interpreting Categorical and Quantitative Data (S ID): 3) Summarize, represent, and interpret data on a single count or measurement variable. S ID 4: Use the mean and standard SE: Lesson Lab: An Introduction to deviation of a data set to fit it to the normal Summation Notation: 13-14, 1.4: distribution and to estimate population percentages. Recognize that there are data TG: Lesson Lab: An Introduction to sets for which such a procedure is not Summation Notation: 13, 1.4: appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. S ID 4 - Core Math III Standard S ID 4 MP.3 Construct viable arguments and critique the reasoning of others. 4

8 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Topic 2 A Variety of Functions Seeing Structure in Expressions (A SSE): 4) Interpret the structure of expressions. A SSE 2: Use the structure of an expression to identify ways to rewrite it. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). SE: 3.3: 169, , , , 177, 3.5: , , , , 6.1: , , 6.2: , , 436, , , 6.3: , 443, , , 449, 6.4: , , 455, TG: 3.3: , 3.5: , 6.1: , 6.2: , 6.3: , 6.4: A SSE 2 - Core Math II-III Standard A SSE 2 MP.2 Reason abstractly and quantitatively. 5

9 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Creating Equations (A CED): 5) Create equations that describe numbers or relationships A CED 1: Create equations and inequalities SE: 2.1: 55-59, 2.2: 63-69, 3.5: , in one variable and use them to solve 3.6: , 5.7: , Technology problems. Include equations arising from Lab: Rational Inequalities: , linear and quadratic functions, and simple 6.5: , Lesson Lab: Exponential rational and exponential functions. and Logarithmic Inequalities: TG: 2.1: 53-57, 2.2: 60-64, 3.5: , 3.6: , 5.7: , Technology Lab: Rational Inequalities: , 6.5: , Lesson Lab: Exponential and Logarithmic Inequalities: A CED 1 - Core Math I-III Standard A CED 1 MP.2 Reason abstractly and quantitatively. MP.5 Use appropriate tools strategically. MP.8 Look for and express regularity in repeated reasoning. A CED 2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. SE: 2.3: 73-78, 2.7: , 3.2: , 5.4: , 7.1: TG: 2.3: 69-73, 2.7: , 3.2: , 5.4: , 7.1: A CED 2 - Core Math I-III Standard A CED 2 MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. 6

10 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Reasoning with Equations and Inequalities (A REI): 6) Understand solving equations as a process of reasoning and explain the reasoning. A REI 2: Solve simple rational and radical SE: 5.7: , 6.5: equations in one variable and give examples showing how extraneous solutions may arise. TG: 5.7: , 6.5: A REI 2 - Core Math III Standard A REI 2 MP.2 Reason abstractly and quantitatively. 7

11 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s 7) Represent and solve equations and inequalities graphically. A REI 11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. SE: 3.7: , 4.4: , 5.7: , Activity Lab: Systems with Rational Equations: , 6.5: , Lesson Lab: Exponential and Logarithmic Inequalities: TG: 3.7: , 4.4: , 5.7: , Activity Lab: Systems with Rational Equations: 399, 6.5: , Lesson Lab: Exponential and Logarithmic Inequalities: A REI 11 - Core Math I, III Standard A REI 11 MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically. 8

12 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Interpreting Functions (F IF): 8) Interpret functions that arise in applications in terms of the context. F IF 4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. SE: 2.3: 73-78, 3.1: , 4.1: , 4.9: , 5.5: , 5.6: , 6.8: , 8.1: TG: 2.3: 69-73, 3.1: , Chapter 3 Review: , 4.9: , 5.5: , 5.6: , 6.8: , 8.1: F IF 4 - Core Math I-III Standard F IF 4 MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. 9

13 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III F IF 6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. III Common Core SE: 3.1: , 3.2: , Lesson Lab: Identifying Quadratic Data: , 4.9: TG: 3.1: , 3.2: , Lesson Lab: Identifying Quadratic Data: 169, 4.9: Core Standards s F IF 6 - Core Math I-III Standard F IF 6 MP.5 Use appropriate tools strategically. 9) Analyze functions using different representations. F IF 7b: Graph square root, cube root, and This standard is addressed in Pearson piecewise-defined functions, including step Integrated - functions and absolute value functions. II Common Core, please see: SE: 14.2: , 14.3: TG: 14.2: , 14.3: F IF 7b - Core Math II Standard F IF 7b 10

14 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III F IF 9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. III Common Core SE: 3.2: , 4.10: , 5.6: , 6.8: TG: 3.2: , 4.10: , 5.6: , 6.8: Core Standards s F IF 9 - Core Math I-III Standard F IF 9 Building Functions (F BF): 10) Build a function that models a relationship between two quantities. F BF 1: Write a function that describes a This standard is addressed in Pearson relationship between two quantities. Integrated - I Common Core, please see: SE: 3-4: , 5-4: TG: 3-4: , 5-4: Also see - II Common Core: SE: 12.2: TG: 12.2: F BF 1 - Core Math I-II Standard F BF 1 11

15 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III F BF 1b: Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. III Common Core This standard is addressed in Pearson Integrated - II Common Core, please see: SE: 12.9: , 14.4: TG: 12.9: , 14.4: Core Standards s F BF 1b - Core Math II Standard F BF 1b MP.2 Reason abstractly and quantitatively. 11) Build new functions from existing functions. F BF 3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. SE: 2.4: 81-87, 2.5: 91-96, 3.1: , Technology Lab: Even and Odd Functions: , 4.10: , 8.7: TG: 2.4: 77-82, 2.5: 87-91, 3.1: , Technology Lab: Even and Odd Functions: 250, 4.10: , 8.7: F BF 3 - Core Math II-III Standard F BF 3 MP.5 Use appropriate tools strategically. 12

16 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s F BF 4: Find inverse functions. SE: 6.7: TG: 6.7: F BF 4 - Core Math III Standard F BF 4 MP.2 Reason abstractly and quantitatively. Topic 3 Polynomial Functions Seeing Structure in Expressions (A SSE): 12) Interpret the structure of expressions. A SSE 1: Interpret expressions that represent a quantity in terms of its context. This standard is addressed in - I Common Core, please see: SE: 1-1: 3-7, 1-9: 80-85, 5-1: TG: 1-1: 5-8, 1-9: 68-72, 5-1: Also see - II Common Core: SE: 12.9: TG: 12.9: A SSE 1 - Core Math I-II Standard A SSE 1 13

17 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III A SSE 1a: Interpret parts of an expression, such as terms, factors, and coefficients. A SSE 1b: Interpret complicated expression by viewing one or more of their parts as a single entity. For example, interpret P(1 + r) n as the product of P and a factor not depending on P. III Common Core This standard is addressed in Pearson Integrated - I Common Core, please see: SE: 1-1: 3-7, 2-5: , 2-7: , 5-1: , 5-7: TG: 1-1: 5-8, 2-5: , 2-7: , 5-1: , 5-8: This standard is addressed in Pearson Integrated - II Common Core, please see: SE: 7.5: , 11.5: , 11.6: , 11.7: , 11.8: TG: 7.5: , 11.5: , 11.6: , 11.7: , 11.8: Core Standards s A SSE 1a - Core Math I Standard A SSE 1a MP.2 Reason abstractly and quantitatively. A SSE 1b - Core Math II Standard A SSE 1b MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.8 Look for and express regularity in repeated reasoning. 14

18 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III A SSE 2: Use the structure of an expression to identify ways to rewrite it. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). III Common Core SE: 3.3: 169, , , , 177, 3.5: , , , , 6.1: , , 6.2: , , 436, , , 6.3: , 443, , , 449, 6.4: , , 455, TG: 3.3: , 3.5: , 6.1: , 6.2: , 6.3: , 6.4: Core Standards s A SSE 2 - Core Math III Standard A SSE 2 MP.2 Reason abstractly and quantitatively. Arithmetic with Polynomials and Rational Expressions (A APR): 13) Understand the relationship between zeros and factors of polynomials. A APR 2: Know and apply the Remainder SE: 4.3: , 4.5: Theorem: For a polynomial p(x) and a number a, the remainder on division by x a is p(a), TG: 4.3: , 4.5: so p(a) = 0 if and only if (x a) is a factor of p(x). A APR 2 - Core Math III Standard A APR 2 MP.5 Use appropriate tools strategically. 15

19 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III A APR 3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. III Common Core SE: 3.4: , 4.3: , 4.6: , 4.7: , Activity Lab: Mathematical Induction: 301 TG: 3.4: , 4.3: , 4.6: , 4.7: , Activity Lab: Mathematical Induction: Core Standards s A APR 3 - Core Math III Standard A APR 3 MP.2 Reason abstractly and quantitatively. MP.5 Use appropriate tools strategically. MP.8 Look for and express regularity in repeated reasoning. Arithmetic with Polynomials and Rational Expressions (A APR): 14) Use polynomial identities to solve problems. A APR 4: Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x 2 + y 2 ) 2 = (x 2 y 2 ) 2 + (2xy) 2 can be used to generate Pythagorean triples. SE: Lesson Lab: Using Polynomial Identities: , Lesson Lab: Mathematical Induction: TG: Lesson Lab: Using Polynomial Identities: , Lesson Lab: Mathematical Induction: A APR 4 - Core Math III Standard A APR 4 16

20 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Arithmetic with Polynomials and Rational Expressions (A APR): 15) Rewrite rational expressions. A APR 6: Rewrite simple rational SE: 4.5: , 5.1: expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), TG: 4.5: , 5.1: b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for more complicated examples, a computer algebra system. A APR 6 - Core Math III Standard A APR 6 17

21 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Reasoning with Equations and Inequalities (A REI): 16) Represent and solve equations and inequalities graphically. A REI 11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. SE: 3.7: , 4.4: , 5.7: , Activity Lab: Systems with Rational Equations: , 6.5: , Lesson Lab: Exponential and Logarithmic Inequalities: TG: 3.7: , 4.4: , 5.7: , Activity Lab: Systems with Rational Equations: 399, 6.5: , Lesson Lab: Exponential and Logarithmic Inequalities: A REI 11 - Core Math III Standard A REI 11 MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically. 18

22 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Interpreting Functions (F IF): 17) Interpret functions that arise in applications in terms of the context. F IF 4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. F IF 6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. SE: 2.3: 73-78, 3.1: , 4.1: , 4.9: , 5.5: , 5.6: , 6.8: , 8.1: TG: 2.3: 69-73, 3.1: , Chapter 3 Review: , 4.9: , 5.5: , 5.6: , 6.8: , 8.1: SE: 3.1: , 3.2: , Lesson Lab: Identifying Quadratic Data: , 4.9: TG: 3.1: , 3.2: , Lesson Lab: Identifying Quadratic Data: 169, 4.9: F IF 4 - Core Math III Standard F IF 4 MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. F IF 6 - Core Math III Standard F IF 6 MP.5 Use appropriate tools strategically. 19

23 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Interpreting Functions (F IF): 18) Analyze functions using different representations. F IF 7c: Graph polynomial functions, SE: 4.1: , 4.3: , Activity identifying zeros when suitable factorizations Lab: Mathematical Induction: 301, are available, and showing end behavior. 4.10: TG: 4.1: , 4.3: , Activity Lab: Mathematical Induction: 299, 4.10: F IF 7c - Core Math III Standard F IF 7c F IF 9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. SE: 3.2: , 4.10: , 5.6: , 6.8: TG: 3.2: , 4.10: , 5.6: , 6.8: MP.2 Reason abstractly and quantitatively. F IF 9 - Core Math I-III Standard F IF 9 20

24 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Building Functions (F BF): 19) Build a function that models a relationship between two quantities. F BF 1: Write a function that describes a This standard is addressed in Pearson relationship between two quantities. Integrated - I Common Core, please see: SE: 3-4: , 5-4: Building Functions (F BF): 20) Build new functions from existing functions. F BF 3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. TG: 3-4: , 5-4: Also see - II Common Core: SE: 12.2: TG: 12.2: SE: 2.4: 81-87, 2.5: 91-96, 3.1: , Technology Lab: Even and Odd Functions: , 4.10: , 8.7: TG: 2.4: 77-82, 2.5: 87-91, 3.1: , Technology Lab: Even and Odd Functions: 250, 4.10: , 8.7: F BF 1 - Core Math I-II Standard F BF 1 F BF 3 - Core Math II-III Standard F BF 3 MP.5 Use appropriate tools strategically. 21

25 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Topic 4 Rational Functions Arithmetic with Polynomials and Rational Expressions (A APR): 21) Rewrite rational expressions. A APR 6: Rewrite simple rational SE: 4.5: , 5.1: expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), TG: 4.5: , 5.1: b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for more complicated examples, a computer algebra system. A APR 6 - Core Math III Standard A APR 6 22

26 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Creating Equations (A CED): 22) Create equations that describe numbers or relationships A CED 1: Create equations and inequalities SE: 2.1: 55-59, 2.2: 63-69, 3.5: , in one variable and use them to solve 3.6: , 5.7: , Technology problems. Include equations arising from Lab: Rational Inequalities: , linear and quadratic functions, and simple 6.5: , Lesson Lab: Exponential rational and exponential functions. and Logarithmic Inequalities: TG: 2.1: 53-57, 2.2: 60-64, 3.5: , 3.6: , 5.7: , Technology Lab: Rational Inequalities: , 6.5: , Lesson Lab: Exponential and Logarithmic Inequalities: A CED 1 - Core Math I-III Standard A CED 1 MP.2 Reason abstractly and quantitatively. MP.5 Use appropriate tools strategically. MP.8 Look for and express regularity in repeated reasoning. 23

27 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III A CED 2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. III Common Core SE: 2.3: 73-78, 2.7: , 3.2: , 5.4: , 7.1: TG: 2.3: 69-73, 2.7: , 3.2: , 5.4: , 7.1: Core Standards s A CED 2 - Core Math I-III Standard A CED 2 MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. 24

28 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Reasoning with Equations and Inequalities (A REI): 23) Understand solving equations as a process of reasoning and explain the reasoning A REI 2: Solve simple rational and radical SE: 5.7: , 6.5: equations in one variable, and give examples showing how extraneous solutions may arise. TG: 5.7: , 6.5: A REI 2 - Core Math III Standard A REI 2 MP.2 Reason abstractly and quantitatively. 25

29 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Reasoning with Equations and Inequalities (A REI): 24) Represent and solve equations and inequalities graphically. A REI 11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. SE: 3.7: , 4.4: , 5.7: , Activity Lab: Systems with Rational Equations: , 6.5: , Lesson Lab: Exponential and Logarithmic Inequalities: TG: 3.7: , 4.4: , 5.7: , Activity Lab: Systems with Rational Equations: 399, 6.5: , Lesson Lab: Exponential and Logarithmic Inequalities: A REI 11 - Core Math I, III Standard A REI 11 MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically. 26

30 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Interpreting Functions (F IF): 25) Interpret functions that arise in applications in terms of the context. F IF 4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Interpreting Functions (F IF): 26) Analyze functions using different representations. F IF 9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. SE: 2.3: 73-78, 3.1: , 4.1: , 4.9: , 5.5: , 5.6: , 6.8: , 8.1: TG: 2.3: 69-73, 3.1: , Chapter 3 Review: , 4.9: , 5.5: , 5.6: , 6.8: , 8.1: SE: 3.2: , 4.10: , 5.6: , 6.8: TG: 3.2: , 4.10: , 5.6: , 6.8: F IF 4 - Core Math I-III Standard F IF 4 MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. F IF 9 - Core Math I-III Standard F IF 9 27

31 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Building Functions (F BF): 27) Build a function that models a relationship between two quantities. F BF 1: Write a function that describes a This standard is addressed in Pearson relationship between two quantities. Integrated - I Common Core, please see: SE: 3-4: , 5-4: Building Functions (F BF): 28) Build new functions from existing functions. F BF 3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. TG: 3-4: , 5-4: Also see - II Common Core: SE: 12.2: TG: 12.2: SE: 2.4: 81-87, 2.5: 91-96, 3.1: , Technology Lab: Even and Odd Functions: , 4.10: , 8.7: TG: 2.4: 77-82, 2.5: 87-91, 3.1: , Technology Lab: Even and Odd Functions: 250, 4.10: , 8.7: F BF 1 - Core I-II Standard F BF 1 F BF 3 - Core Math II-III Standard F BF 3 MP.5 Use appropriate tools strategically. 28

32 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Modeling Unit Project Topic 5 Exponential Functions Seeing Structure in Expressions (A SSE): 29) Write expressions in equivalent forms to solve problems. A SSE 3c: Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15 t can be rewritten as (1.15 1/12 ) 12t t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. This standard is addressed in Pearson Integrated - I Common Core, please see: SE: Lesson Lab: Using Properties of Exponents to Transform Functions: 319, TG: Lesson Lab: Using Properties of Exponents to Transform Functions: A SSE 3c - Core Math I Standard A SSE 3c A SSE 4*: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. SE: Activity Lab: Geometry and Infinite Series: , 9.5: TG: Activity Lab: Geometry and Infinite Series: 689, 9.5: A SSE 4 - Core Math III Standard A SSE 4 29

33 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Creating Equations (A CED): 30) Create equations that describe numbers or relationships A CED 1: Create equations and inequalities SE: 2.1: 55-59, 2.2: 63-69, 3.5: , in one variable and use them to solve 3.6: , 5.7: , Technology problems. Include equations arising from Lab: Rational Inequalities: , linear and quadratic functions, and simple 6.5: , Lesson Lab: Exponential rational and exponential functions. and Logarithmic Inequalities: TG: 2.1: 53-57, 2.2: 60-64, 3.5: , 3.6: , 5.7: , Technology Lab: Rational Inequalities: , 6.5: , Lesson Lab: Exponential and Logarithmic Inequalities: A CED 1 - Core Math I-III Standard A CED 1 MP.2 Reason abstractly and quantitatively. MP.5 Use appropriate tools strategically. MP.8 Look for and express regularity in repeated reasoning. 30

34 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III A CED 2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. III Common Core SE: 2.3: 73-78, 2.7: , 3.2: , 5.4: , 7.1: TG: 2.3: 69-73, 2.7: , 3.2: , 5.4: , 7.1: Core Standards s A CED 2 - Core Math I-III Standard A CED 2 MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. 31

35 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Reasoning with Equations and Inequalities (A REI): 31) Represent and solve equations and inequalities graphically. A REI 11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. SE: 3.7: , 4.4: , 5.7: , Activity Lab: Systems with Rational Equations: , 6.5: , Lesson Lab: Exponential and Logarithmic Inequalities: TG: 3.7: , 4.4: , 5.7: , Activity Lab: Systems with Rational Equations: 399, 6.5: , Lesson Lab: Exponential and Logarithmic Inequalities: Interpreting Functions (F IF): 32) Analyze functions using different representations. F IF 7e: Graph exponential and logarithmic SE: 7.1: , , , 511, functions, showing intercepts and end 7.2: , 515, , , 522- behavior. 524, 7.3: , 529, 530, , Technology Lab: Graphing Trigonometric Functions: TG: 7.1: , 7.2: , 7.3: , Technology Lab: Graphing Trigonometric Functions: A REI 11 - Core Math I, III Standard A REI 11 MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.5 Use appropriate tools strategically. F IF 7e - Core Math II-III Standard F IF 7e MP.4 Model with mathematics. 32

36 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III F IF 8b: Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02) t, y = (0.97) t, y = (1.01) 12t, y = (1.2) t/10, and classify them as representing exponential growth or decay. III Common Core This standard is addressed in Pearson Integrated - II Common Core, please see: SE: 14.1: TG: 14.1: Core Standards s F IF 8b - Core Math II Standard F IF 8b F IF 9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. SE: 3.2: , 4.10: , 5.6: , 6.8: TG: 3.2: , 4.10: , 5.6: , 6.8: F IF 9 - Core Math III Standard F IF 9 33

37 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Building Functions (F BF): 33) Build a function that models a relationship between two quantities. F BF 1: Write a function that describes a This standard is addressed in Pearson relationship between two quantities. Integrated - I Common Core, please see: SE: 3-4: , 5-4: TG: 3-4: , 5-4: Also see - II Common Core: SE: 12.2: TG: 12.2: F BF 1 - Core Math I-II Standard F BF 1 F BF 2*: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. This standard is addressed in Pearson Integrated - I Common Core, please see: SE: 2-7: , 5-6: TG: 2-7: , 5-6: F BF 2 - Core Math I Standard F BF 2 34

38 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Building Functions (F BF): 34) Build new functions from existing functions. F BF 4a: Solve a linear equation of the form SE: 6.7: , 7.3: f(x) = c for a simple function f that has an inverse and write an expression for the TG: 6.7: , 7.3: inverse. For example, f(x) = 2x 3 or f(x) = (x + 1)/(x 1) for x 1. F BF 4a - Core Math III Standard F BF 4a Linear, Quadratic, and Exponential Models (F LE): 35) Construct and compare linear, quadratic, and exponential models and solve problems. F LE 4: For exponential models, express as SE: 7.5: , 7.6: a logarithm the solution to ab ct = d where a, c, and d are numbers and the base b is 2, 10, TG: 7.5: , 7.6: or e; evaluate the logarithm using technology. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. F LE 4 - Core Math III Standard F LE 4 MP.5 Use appropriate tools strategically. 35

39 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Topic 6 Trigonometric Functions Interpreting Functions (F IF): 36) Interpret functions that arise in applications in terms of the context. F IF 4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. SE: 2.3: 73-78, 3.1: , 4.1: , 4.9: , 5.5: , 5.6: , 6.8: , 8.1: TG: 2.3: 69-73, 3.1: , Chapter 3 Review: , 4.9: , 5.5: , 5.6: , 6.8: , 8.1: F IF 4 - Core Math I-III Standard F IF 4 MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. 36

40 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Interpreting Functions (F IF): 37) Analyze functions using different representations. F IF 7e: Graph trigonometric functions, SE: 7.1: , , , 511, showing period, midline, and amplitude. 7.2: , 515, , , , 7.3: , 529, 530, , Technology Lab: Graphing Trigonometric Functions: TG: 7.1: , 7.2: , 7.3: , Technology Lab: Graphing Trigonometric Functions: F IF 7e - Core Math II-III Standard F IF 7e MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. 37

41 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Building Functions (F BF): 38) Build new functions from existing functions. F BF 3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. SE: 2.4: 81-87, 2.5: 91-96, 3.1: , Technology Lab: Even and Odd Functions: , 4.10: , 8.7: TG: 2.4: 77-82, 2.5: 87-91, 3.1: , Technology Lab: Even and Odd Functions: 250, 4.10: , 8.7: F BF 3 - Core Math II-III Standard F BF 3 MP.5 Use appropriate tools strategically. 38

42 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Trigonometric Functions (F TF): 39) Extend the domain of trigonometric function using the unit circle. F TF 1: Understand radian measure of an SE: 8.2: , 8.3: angle as the length of the arc on the unit circle subtended by the angle. TG: 8.2: , 8.3: F TF 1 - Core Math III Standard F TF 1 F TF 2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. SE: 8.2: , 8.3: , 8.4: , 8.5: , 8.6: , 8.8: TG: 8.2: , 8.3: , 8.4: , 8.5: , 8.6: , 8.8: F TF 2 - Core Math III Standard F TF 2 39

43 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Trigonometric Functions (F TF): 40) Model periodic phenomena with trigonometric functions. F TF 5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. SE: 8.4: , 8.5: , 8.6: , 8.7: , 8.8: TG: 8.4: , 8.5: , 8.6: , 8.7: , 8.8: F TF 5 - Core Math III Standard F TF 5 Trigonometric Functions (F TF): 41) Prove and apply trigonometric identities. F TF 8: Prove the Pythagorean identity SE: 8.9: 651, , 654, 654, sin 2 (ϴ) + cos 2 (ϴ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or TG: 8.9: tan(θ) and the quadrant of the angle. F TF 8 - Core Math III Standard F TF 8 MP.3 Construct viable arguments and critique the reasoning of others. 40

44 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Topic 7 Coordinate Geometry Geometry (G GPE): 42) Use coordinates to prove simple geometric theorems algebraically. G GPE 4: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2). SE: 3.8: , , , 220, 3.9: , 224, , 227, , 230, 11.4: , , 847, TG: 3.8: , 3.9: , 11.4: G GPE 4 - Core Math III Standard G GPE 4 G GPE 5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). SE: Activity Lab: Proving Slope Criteria for Parallel and Perpendicular Lines: TG: Activity Lab: Proving Slope Criteria for Parallel and Perpendicular Lines: G GPE 5 - Core Math III Standard G GPE 5 MP.2 Reason abstractly and quantitatively. 41

45 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III G GPE 6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio. III Common Core SE: Lesson Lab: Partitioning a Segment: TG: Lesson Lab: Partitioning a Segment: Core Standards s G GPE 6 - Core Math III Standard G GPE 6 G GPE 7*: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* SE: 11.1: , , , 815, , , 11.2: 823, , , TG: 11.1: , 11.2: G GPE 7 - Core Math III Standard G GPE 7 42

46 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Topic 8 Geometric Constructions and Measurement Congruence (G CO): 43) Make geometric constructions. G CO 12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. SE: 10.1: 737, , 740, , , TG: 10.1: G CO 12 - Core Math III Standard G CO 12 MP.4 Model with mathematics. G CO 13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. SE: 10.1: 737, , 740, , , TG: 10.1: G CO 13 - Core Math III Standard G CO 13 MP.4 Model with mathematics. 43

47 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III III Common Core - - Core Standards s Geometric Measurement and Dimension (G GMD): 44) Visualize relationships between two-dimensional and three-dimensional objects. G GMD 4: Identify the shapes of twodimensional cross-sections of three- SE: 10.5: , 10.7: dimensional objects, and identify threedimensional objects generated by rotations of TG: 10.5: , 10.7: two-dimensional objects. G GMD 4 - Core Math III Standard G GMD 4 MP.2 Reason abstractly and quantitatively. Topic 9 Circles and Conics Circles (G C): 45) Understand and apply theorems about circles. G C 1: Prove that all circles are similar. SE: 12.1: 855, 856, 857, , 860, 861, TG: 12.1: G C 1 - Core Math III Standard G C 1 44

48 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III G C 2: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. G C 3: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. III Common Core SE: 12.1: 855, 856, 857, , 860, 861, , 12.3: , 879, 880, , , 885, 12.4: , , 890, , , , 12.5: , 900, , , 12.6: , , , 914 TG: 12.1: , 12.3: , 12.4: , 12.5: , 12.6: SE: 10.1: 737, , 740, , , , 12.5: , 900, , TG: 10.1: , 12.5: Core Standards s G C 2 - Core Math III Standard G C 2 MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. G C 3 - Core Math III Standard G C 3 MP.4 Model with mathematics. 45

49 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III G C 5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. III Common Core SE: 12.1: 855, 856, 857, , 860, 861, , 12.2: , 867, 868, , , Activity Lab: Circles and Radians: 873, TG: 12.1: , 12.2: , Activity Lab: Circles and Radians: Core Standards s G C 5 - Core Math III Standard G C 5 MP.2 Reason abstractly and quantitatively. Expressing Geometric Properties with Equations (G GPE): 46) Translate between the geometric description and the equation for a conic section. G GPE 1: Derive the equation of a circle of SE: 3.9: , 224, , 227, 228- given center and radius using the 229, 230 Pythagorean Theorem; complete the square to find the center and radius of a circle given TG: 3.9: by an equation. G GPE 1 - Core Math III Standard G GPE 1 46

50 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III G GPE 2: Derive the equation of a parabola given a focus and directrix. Modeling Unit Project G MG 1*: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* III Common Core SE: 3.8: , , , 220 TG: 3.8: SE: 10.3: , 10.4: , 10.6: , 11.2: , 11.3: TG: 10.3: , 10.4: , 10.6: , 11.2: , 11.3: Core Standards s G GPE 2 - Core Math III Standard G GPE 2 G MG 1 - Core Math III Standard G MG 1 MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. 47

51 A Correlation of - III Common Core, to the CCSS III - - Core Standards and s III G MG 2*: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).* G MG 3*: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).* III Common Core SE: 10.2: , 10.3: , 10.6: TG: 10.2: , 10.3: , 10.6: SE: 10.2: , 10.3: , 10.6: TG: 10.2: , 10.3: , 10.6: Core Standards s G MG 2 - Core Math III Standard G MG 2 MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. G MG 3 - Core Math III Standard G MG 3 MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. 48