Pearson Integrated High School Mathematics Mathematics II

A Correlation of

Pearson Integrated High School Mathematics Mathematics II Common Core

©2014

To the

Columbus City Schools High School CCSS Mathematics II - High School

PARRC Model Content Frameworks Mathematics - Core Standards And Math Practices

A Correlation of Pearson Integrated High School Mathematics - Mathematics II Common Core, ©2014 to the Columbus City Schools High School CCSS Mathematics II - High School

PARRC Model Content Frameworks Mathematics - Core Standards and Math Practices

Copyright ©2015 Pearson Education, Inc. or its affiliate(s). All rights reserved

Introduction

This document demonstrates how Pearson Integrated High School Mathematics - Mathematics II Common Core ©2014 meets the standards of the Columbus City Schools High School CCSS Mathematics II - High School and the Common Core State Standards for Mathematics within the PARRC Model Content Frameworks Mathematics Core Math II. Correlation references are to the pages of the Student and Teacher’s Editions. Pearson Integrated High School Mathematics ©2014, fully aligned to the Common Core State Standards for Mathematics, 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 Mathematics, Mathematics II Common Core.



Copyright ©2015 Pearson Education, Inc. or its affiliate(s). All rights reserved

Table of Contents

Topic 1 – Similarity ................................................................................................................................ 1 Topic 2 – Trigonometric Ratios .............................................................................................................. 5 Topic 3 – Other Types of Functions ........................................................................................................ 6 Topic 4 – Comparing Functions and Different Representations of Quadratic ........................................ 15 Topic 5–Quadratic Functions – Solving by factoring ............................................................................. 24 Topic 6– Quadratic Functions – Completing the Square/Quadratic Formula ......................................... 29 Topic 7 –Probability ............................................................................................................................. 35 Topic 8 – Geometric Measurement ....................................................................................................... 39 Geometric and Modeling Project ......................................................................................................... 40



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SE = Student Edition TG = Teacher’s Guide * = indicates modeling standards

Columbus City Schools High School

Common Core State Standards Mathematics II

Pearson Integrated High School Mathematics

Mathematics II Common Core ©2014

Common Core State Standards for Mathematics - High School

PARRC Model Content Frameworks Mathematics - Core Standards

Math Practices

Topic 1 – Similarity Geometry (G – SRT): 1) Similarity, Right Triangles, and Trigonometry: Understand similarity in terms of similarity transformations. G – SRT 1: Verify experimentally the properties of dilations given by a center and a scale factor.

SE: Activity Lab: Exploring Dilations: 390-392 TG: Activity Lab: Exploring Dilations: 392-393

Common Core State Standards for Mathematics G – SRT 1 PARRC Model Content Frameworks Mathematics - Core Math II Standard G – SRT 1 Math Practice MP.3 Construct viable arguments and critique the reasoning of others.

G – SRT 1a: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

SE: Activity Lab: Exploring Dilations: 390-392, 6.6: 393-397 TG: Activity Lab: Exploring Dilations: 392-393, 6.6: 394-397

Common Core State Standards for Mathematics G – SRT 1a PARRC Model Content Frameworks Mathematics - Core Math II Standard G – SRT 1a Math Practice MP.3 Construct viable arguments and critique the reasoning of others.



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Math Practices

G – SRT 1b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

SE: Activity Lab: Exploring Dilations: 390-392, 6.6: 393-397 TG: Activity Lab: Exploring Dilations: 392-393, 6.6: 394-397

Common Core State Standards for Mathematics G – SRT 1b PARRC Model Content Frameworks Mathematics - Core Math II Standard G – SRT 1b Math Practice MP.3 Construct viable arguments and critique the reasoning of others.

G – SRT 2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

SE: 6.7: 401-406 TG: 6.7: 402-406




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Math Practices

G – SRT 3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

SE: 6.7: 401-406 TG: 6.7: 402-406


Geometry (G – SRT): 2) Similarity, Right Triangles, and Trigonometry: Prove theorems involving similarity. G – SRT 4: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

SE: Technology Lab: Exploring Proportions in Triangles: 378-380, 6.5: 381-385, 7.1: 415-421 TG: Technology Lab: Exploring Proportions in Triangles: 383, 6.5: 384-387, 7.1: 419-423

Common Core State Standards for Mathematics G – SRT 4 PARRC Model Content Frameworks Mathematics - Core Math II Standard G – SRT 4 Math Practice MP.1 Make sense of problems and persevere in solving them. MP.5 Use appropriate tools strategically.



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Math Practices

G – SRT 5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

SE: 3.1: 121-125, 3.2: 129-133, 3.3: 138-144, 3.4: 148-150, 3.5: 156-160, 3.6: 165-170, 3.7: 173-179, 4.1: 199-203, 4.2: 207-211, 4.4: 223-227, 5.1: 263-266, 5.2: 270-277, 5.4: 289-293, 5.5: 298-301, 5.6: 306-312, 6.1: 337-343, 6.2: 348-353, 6.3: 358-364, 6.4: 369-373 TG: 3.1: 127-131, 3.2: 135-139, 3.3: 144-148, 3.4: 152-154, 3.5: 160-164, 3.6: 169-173, 3.7: 177-181, 4.1: 205-208, 4.2: 212-216, 4.4: 230-233, 5.1: 273-276, 5.2: 280-285, 5.4: 297-301, 5.5: 306-309, 5.6: 314-318, 6.1: 349-353, 6.2: 357-361, 6.3: 366-371, 6.4: 375-379

Common Core State Standards for Mathematics G – SRT 5 PARRC Model Content Frameworks Mathematics - Core Math II Standard G – SRT 5 Math Practice MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.



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Math Practices

Topic 2 – Trigonometric Ratios Geometry (G – SRT): 3) Similarity, Right Triangles, and Trigonometry: Define trigonometric ratios and solve problems involving right triangles G – SRT 6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

SE: Technology Lab: Exploring Trigonometric Ratios: 435-437 TG: Technology Lab: Exploring Trigonometric Ratios: 436

Common Core State Standards for Mathematics G – SRT 6 PARRC Model Content Frameworks Mathematics - Core Math II Standard G – SRT 6 Math Practice MP.5 Use appropriate tools strategically.

G – SRT 7: Explain and use the relationship between the sine and cosine of complementary angles.

SE: 7.3: 438-442 TG: 7.3: 437-440

Common Core State Standards for Mathematics G – SRT 7 PARRC Model Content Frameworks Mathematics - Core Math II Standard G – SRT 7 Math Practice MP.6 Attend to precision.



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Math Practices

G – SRT 8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

SE: 7.1: 415-421, 7.2: 426-432, 7.3: 438-442, 7.4: 447-450 TG: 7.1: 419-423, 7.2: 428-432, 7.3: 437-440, 7.4: 445-448

Common Core State Standards for Mathematics G – SRT 8 PARRC Model Content Frameworks Mathematics - Core Math II Standard G – SRT 8 Math Practice MP.1 Make sense of problems and persevere in solving them. MP.6 Attend to precision.

Topic 3 – Other Types of Functions Creating Equations (A – CED): 4) Create equations that describe numbers or relationships A – CED 1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

SE: 12.4: 740-743, 12.5: 750-756, 12.7: 768-774, Lesson Lab: Quadratic Inequalities: 809-811, Lesson Lab: Solving Exponential Equations and Inequalities: 915-918 TG: 12.4: 717-720, 12.5: 725-729, 12.7: 741-745, Lesson Lab: Quadratic Inequalities: 776-777, Lesson Lab: Solving Exponential Equations and Inequalities: 882-883

Common Core State Standards for Mathematics A – CED 1 PARRC Model Content Frameworks Mathematics - Core Math I-III Standard A – CED 1 Math Practice MP.3 Construct viable arguments and critique the reasoning of others. MP.8 Look for and express regularity in repeated reasoning.



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Math Practices

A – CED 4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.

SE: Lesson Lab: Formulas With Quadratic Expressions: 748-749 TG: Lesson Lab: Formulas With Quadratic Expressions: 724

Common Core State Standards for Mathematics A – CED 4 PARRC Model Content Frameworks Mathematics - Core Math I-II Standard A – CED 4 Math Practice MP.1 Make sense of problems and persevere in solving them.

Reasoning with Equations and Inequalities (A – REI): 5) Understand solving equations as a process of reasoning and explain the reasoning. A – REI 1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

SE: 12.4: 740-743, 744-745, 12.5: 750, 751-756, 757, 758, 759, 12.6: 760, 761-763, 764-765, 766-767 TG: 12.4: 717-723, 12.5: 725-732, 12.6: 733-740

Common Core State Standards for Mathematics A – REI 1 PARRC Model Content Frameworks Mathematics - Core Math II-III Standard A – REI 1 Math Practice MP.1 Make sense of problems and persevere in solving them.



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Math Practices

The Real Number System (N – RN): 6) Extend the properties of exponents to rational exponents. N – RN 1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.

SE: 10.1: 595-603, 10.2: 606-612, 10.3: 615-619, 10.4: 624-628 TG: 10.1: 585-590, 10.2: 593-597, 10.3: 600-603, 10.4: 608-611

Common Core State Standards for Mathematics N – RN 1 PARRC Model Content Frameworks Mathematics - Core Math II Standard N – RN 1 Math Practice MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.6 Attend to precision.

N – RN 2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.

SE: 10.4: 624-628 TG: 10.4: 608-611

Common Core State Standards for Mathematics N – RN 2 PARRC Model Content Frameworks Mathematics - Core Math II Standard N – RN 2 Math Practice MP.6 Attend to precision.



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Math Practices

The Real Number System (N – RN): 7) Use properties of rational and irrational numbers. N – RN 3: Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

SE: Activity Lab: Operations With Rational and Irrational Numbers: 631-633 TG: Activity Lab: Operations With Rational and Irrational Numbers: 614

Common Core State Standards for Mathematics N – RN 3 PARRC Model Content Frameworks Mathematics - Core Math II Standard N – RN 3 Math Practice MP.2 Reason abstractly and quantitatively.

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: 12.1: 707-712, 12.3: 732-735, 14.1: 905-911, 14.2: 919-926, 14.3: 930-934 TG: 12.1: 687-691, 12.3: 710-713, 14.1: 873-878, 14.2: 884-889, 14.3: 893-898

Common Core State Standards for Mathematics F – IF 4 PARRC Model Content Frameworks Mathematics - Core Math I-III Standard F – IF 4 Math Practice MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.7 Look for and make use of structure.



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Math Practices

Interpreting Functions (F – IF): 9) Analyze functions using different representations. F – IF 7b: Graph square root, cube root, and absolute value functions.

SE: 14.2: 919-928, 14.3: 930-934 TG: 14.2: 884-889, 14.3: 893-898

Common Core State Standards for Mathematics F – IF 7b PARRC Model Content Frameworks Mathematics - Core Math II Standard F – IF 7b Math Practice MP.1 Make sense of problems and persevere in solving them.

F – IF 7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

SE: 14.1: 905, 906-909, 911-912, 913-914 TG: 14.1: 873-881

Common Core State Standards for Mathematics F – IF 7e PARRC Model Content Frameworks Mathematics - Core Math II-III Standard F – IF 7e Math Practice MP.7 Look for and make use of structure.



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Math Practices

F – IF 8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

SE: 12.6: 760-764, 14.2: 919-926 TG: 12.6: 733-736, 14.2: 884-889

Common Core State Standards for Mathematics F – IF 8 PARRC Model Content Frameworks Mathematics - Core Math II Standard F – IF 8 Math Practice MP.1 Make sense of problems and persevere in solving them.

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.

SE: 14.1: 905-911 TG: 14.1: 873-878

Common Core State Standards for Mathematics F – IF 8b PARRC Model Content Frameworks Mathematics - Core Math II Standard F – IF 8b Math Practice MP.6 Attend to precision.



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Math Practices

Building Functions (F – BF): 10) Build a function that models a relationship between two quantities. F – BF 1: Write a function that describes a relationship between two quantities.

SE: 12.2: 720-722 TG: 12.2: 699-702

Common Core State Standards for Mathematics F – BF 1 PARRC Model Content Frameworks Mathematics - Core Math I-II Standard F – BF 1 Math Practice MP.1 Make sense of problems and persevere in solving them.

F – BF 1a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

SE: 12.2: 720-722, 15.1: 955-959, 15.2: 964-967, 15.3: 971-975, 15.4: 979-984 TG: 12.2: 699-702, 15.1: 921-925, 15.2: 929-932, 15.3: 936-939, 15.4: 943-947

Common Core State Standards for Mathematics F – BF 1a PARRC Model Content Frameworks Mathematics - Core Math I-II Standard F – BF 1a Math Practice MP.1 Make sense of problems and persevere in solving them. MP.6 Attend to precision. MP.7 Look for and make use of structure.



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Math Practices

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.

SE: 12.9: 791-795, 14.4: 938-941 TG: 12.9: 759-763, 14.4: 902-905

Common Core State Standards for Mathematics F – BF 1b PARRC Model Content Frameworks Mathematics - Core Math II Standard F – BF 1b Math Practice MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively.

Building Functions (F – BF): 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: Technology Lab: Families of Quadratic Functions: 716-719, 14.1: 905-911, 14.2: 919-926, 14.3: 930-934 TG: Technology Lab: Families of Quadratic Functions: 697-698, 14.1: 873-878, 14.2: 884-889, 14.3: 893-898

Common Core State Standards for Mathematics F – BF 3 PARRC Model Content Frameworks Mathematics - Core Math II-III Standard F – BF 3 Math Practice MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.



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Math Practices

Seeing Structure in Expressions (A – SSE): 12) Interpret the structure of expressions. A – SSE 1b: Interpret complicated expressions 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.

SE: 7.5: 454-457, 11.5: 671-674, 11.6: 678-681, 11.7: 685-690, 11.8: 694-697 TG: 7.5: 452-455, 11.5: 651-654, 11.6: 658-660, 11.7: 664-668, 11.8: 672-674

Common Core State Standards for Mathematics A – SSE 1b PARRC Model Content Frameworks Mathematics - Core Math I-II Standard A – SSE 1b Math Practice 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.

Quantities (NQ): 13) Reason quantitatively and use units to solve problems. N – Q 2: Define appropriate quantities for the purpose of descriptive modeling.

SE: 6.1: 337, 338-340, 342-343, 346-347, 9.1: 537-541, 542-544, 545-548, 9.2: 549-550, 551-554 TG: 6.1: 349-356, 9.1: 535-544, 9.2: 545-553

Common Core State Standards for Mathematics N – Q 2 PARRC Model Content Frameworks Mathematics - Core Math I-III Standard N – Q 2 Math Practice MP.6 Attend to precision.



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Math Practices

Topic 4 – Comparing Functions and Different Representations of Quadratic Interpreting Functions (F – IF): 14) 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: 12.1: 707-712, 12.3: 732-735, 14.1: 905-911, 14.2: 919-926, 14.3: 930-934 TG: 12.1: 687-691, 12.3: 710-713, 14.1: 873-878, 14.2: 884-889, 14.3: 893-898

Common Core State Standards for Mathematics F – IF 4 PARRC Model Content Frameworks Mathematics - Core Math I-III Standard F – IF 4 Math Practice MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

F – IF 5*: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*

SE: 12.1: 707-712, 12.3: 732-735 TG: 12.1: 687-691, 12.3: 710-713

Common Core State Standards for Mathematics F – IF 5 PARRC Model Content Frameworks Mathematics - Core Math I-II Standard F – IF 5 Math Practice MP.4 Model with mathematics.



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Math Practices

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: Activity Lab: Rates of Increase: 727-730 TG: Activity Lab: Rates of Increase: 707-708

Common Core State Standards for Mathematics F – IF 6 PARRC Model Content Frameworks Mathematics - Core Math I-III Standard F – IF 6 Math Practice MP.8 Look for and express regularity in repeated reasoning.

Interpreting Functions (F – IF): 15) Analyze functions using different representations. F – IF 7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

SE: Technology Lab: Families of Quadratic Functions: 716-719 TG: Technology Lab: Families of Quadratic Functions: 697-698

Common Core State Standards for Mathematics F – IF 7 PARRC Model Content Frameworks Mathematics - Core Math I-III Standard F – IF 7 Math Practice MP.5 Use appropriate tools strategically.



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Math Practices

F – IF 7a*: Graph linear and quadratic functions and show intercepts, maxima, and minima.*

SE: 12.1: 707-712, 12.2: 720-722, 12.4: 740-743 TG: 12.1: 687-691, 12.2: 699-702, 12.4: 717-720

Common Core State Standards for Mathematics F – IF 7a PARRC Model Content Frameworks Mathematics - Core Math I-II Standard F – IF 7a Math Practice MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics.

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: 12.2: 720-722 TG: 12.2: 699-702

Common Core State Standards for Mathematics F – IF 9 PARRC Model Content Frameworks Mathematics - Core Math I-III Standard F – IF 9 Math Practice MP.1 Make sense of problems and persevere in solving them.



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Math Practices

Creating Equations (A – CED): 16) Create equations that describe numbers of relationships. A – CED 1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.


Common Core State Standards for Mathematics A – CED 1 PARRC Model Content Frameworks Mathematics - Core Math I-III Standard A – CED 1 Math Practice MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. 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: 12.1: 707-712 TG: 12.1: 687-691

Common Core State Standards for Mathematics A – CED 2 PARRC Model Content Frameworks Mathematics - Core Math I-III Standard A – CED 2 Math Practice MP.4 Model with mathematics.



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Math Practices

Building Functions (F – BF): 17) Build a function that models a relationship between two quantities. F – BF 1: Write a function that describes a relationship between two quantities.

SE: 12.2: 720-722 TG: 12.2: 699-702

Common Core State Standards for Mathematics F – BF 1 PARRC Model Content Frameworks Mathematics - Core Math I-II Standard F – BF 1 Math Practice MP.1 Make sense of problems and persevere in solving them.

F – BF 1a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

SE: 12.2: 720-722, 15.1: 955-959, 15.2: 964-967, 15.3: 971-975, 15.4: 979-984 TG: 12.2: 699-702, 15.1: 921-925, 15.2: 929-932, 15.3: 936-939, 15.4: 943-947

Common Core State Standards for Mathematics F – BF 1a PARRC Model Content Frameworks Mathematics - Core Math I-II Standard F – BF 1a Math Practice MP.1 Make sense of problems and persevere in solving them. MP.6 Attend to precision. MP.7 Look for and make use of structure.



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Math Practices

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.

SE: 12.9: 791-795, 14.4: 938-941 TG: 12.9: 759-763, 14.4: 902-905

Common Core State Standards for Mathematics F – BF 1b PARRC Model Content Frameworks Mathematics - Core Math II Standard F – BF 1b Math Practice MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively.

Building Functions (F – BF): 18) 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: Technology Lab: Families of Quadratic Functions: 716-719, 14.1: 905-911, 14.2: 919-926, 14.3: 930-934 TG: Technology Lab: Families of Quadratic Functions: 697-698, 14.1: 873-878, 14.2: 884-889, 14.3: 893-898

Common Core State Standards for Mathematics F – BF 3 PARRC Model Content Frameworks Mathematics - Core Math II-III Standard F – BF 3 Math Practice MP.1 Make sense of problems and persevere in solving them. MP.5 Use appropriate tools strategically. MP.7 Look for and make use of structure.



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Math Practices

Linear and Exponential Models (F – LE): 19) Construct and compare linear and exponential models and solve problems. F- LE 3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

This standard is addressed in Pearson Integrated High School Mathematics - Mathematics I Common Core, please see: SE: 5-3: 301-304 TG: 5-3: 290-293

Common Core State Standards for Mathematics F- LE 3 PARRC Model Content Frameworks Mathematics - Core Math I Standard F- LE 3 Math Practice MP.4 Model with mathematics.

Quantities (N-Q): 20) Reason quantitatively and use units to solve problems. N – Q 2: Define appropriate quantities for the purpose of descriptive modeling.

SE: 6.1: 337, 338-340, 342-343, 346-347, 9.1: 537-541, 542-544, 545-548, 9.2: 549-550, 551-554 TG: 6.1: 349-356, 9.1: 535-544, 9.2: 545-553

Common Core State Standards for Mathematics N – Q 2 PARRC Model Content Frameworks Mathematics - Core Math I-III Standard N – Q 2 Math Practice MP.6 Attend to precision.



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Math Practices

Interpreting Categorical and Quantitative Data (S – ID): 21) Summarize, represent, and interpret data on two categorical and quantitative variables. S – ID 6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models.

SE: 12.3: 732, 734, 735, 12.9: 791-794, 795-799 TG: 12.3: 710-716, 12.9: 759-766

Common Core State Standards for Mathematics S – ID 6a PARRC Model Content Frameworks Mathematics - Core Math I-III Standard S – ID 6a Math Practice MP.1 Make sense of problems and persevere in solving them. MP.4 Model with mathematics.

S – ID 6b: Informally assess the fit of a function by plotting and analyzing residuals.

SE: Lesson Lab: Analyzing Residual Plots: 800-801 TG: Lesson Lab: Analyzing Residual Plots: 767-768

Common Core State Standards for Mathematics S – ID 6b PARRC Model Content Frameworks Mathematics - Core Math II-III Standard S – ID 6b Math Practice MP.5 Use appropriate tools strategically.



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Math Practices

Reasoning with Equations and Inequalities (A – REI): 22) Solve systems of equations. A – REI 7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x2 + y2 = 3.

SE: 12.10: 802-805 TG: 12.10: 769-772

Common Core State Standards for Mathematics A – REI 7 PARRC Model Content Frameworks Mathematics - Core Math II Standard A – REI 7 Math Practice MP.1 Make sense of problems and persevere in solving them.



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Math Practices

Modeling Unit and Project Topic 5–Quadratic Functions – Solving by factoring Arithmetic with Polynomials and Rational Expressions (A – APR): 23) Perform arithmetic operations on polynomials. A – APR 1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

SE: 11.1: 639-643, 11.2: 646-649, 11.3: 653-658, 11.4: 662-667 TG: 11.1: 623-627, 11.2: 630-633, 11.3: 636-640, 11.4: 643-647

Common Core State Standards for Mathematics A – APR 1 PARRC Model Content Frameworks Mathematics - Core Math II Standard A – APR 1 Math Practice MP.2 Reason abstractly and quantitatively. MP.6 Attend to precision. MP.8 Look for and express regularity in repeated reasoning.



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Reasoning with Equations and Inequalities (A – REI): 24) Understand solving equations as a process of reasoning and explain the reasoning. A – REI 1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

SE: 12.4: 740-743, 744-745, 12.5: 750, 751-756, 757, 758, 759, 12.6: 760, 761-763, 764-765, 766-767 TG: 12.4: 717-723, 12.5: 725-732, 12.6: 733-740


Reasoning with Equations and Inequalities (A – REI): 25) Solve equations and inequalities in one variable. A – REI 4b: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

SE: 12.4: 740-743, 12.5: 750-756, 12.6: 760-764, 12.7: 768-774, 12.8: 778-787 TG: 12.4: 717-720, 12.5: 725-729, 12.6: 733-736, 12.7: 741-745, 12.8: 749-754

Common Core State Standards for Mathematics A – REI 4b PARRC Model Content Frameworks Mathematics - Core Math II Standard A – REI 4b Math Practice MP.1 Make sense of problems and persevere in solving them. MP.6 Attend to precision.



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Interpreting Functions (F – IF): 26) Analyze functions using different representations. F – IF 8a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

SE: 12.5: 750-756, 12.6: 760-764 TG: 12.5: 725-729, 12.6: 733-736

Common Core State Standards for Mathematics F – IF 8a PARRC Model Content Frameworks Mathematics - Core Math II Standard F – IF 8a Math Practice MP.1 Make sense of problems and persevere in solving them.



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Seeing Structure in Expressions (A – SSE): 28) Interpret the structure of expressions. A – SSE 1b: Interpret complicated expressions 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 factor not depending on P.

SE: 7.5: 454-457, 11.5: 671-674, 11.6: 678-681, 11.7: 685-690, 11.8: 694-697 TG: 7.5: 452-455, 11.5: 651-654, 11.6: 658-660, 11.7: 664-668, 11.8: 672-674

Common Core State Standards for Mathematics A – SSE 1b PARRC Model Content Frameworks Mathematics - Core Math I-II Standard A – SSE 1b Math Practice MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.



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Seeing Structure in Expressions (A – SSE): 29) Write expressions in equivalent forms to solve problems. A – SSE 3a: Factor a quadratic expression to reveal the zeros of the function it defines.

SE: 12.5: 750-756 TG: 12.5: 725-729

Common Core State Standards for Mathematics A – SSE 3a PARRC Model Content Frameworks Mathematics - Core Math II Standard A – SSE 3a Math Practice MP.1 Make sense of problems and persevere in solving them.

Topic 6– Quadratic Functions – Completing the Square/Quadratic Formula Reasoning with Equations and Inequalities (A – REI): 30) Understand solving equations as a process of reasoning and explain the reasoning. A – REI 1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

SE: 12.4: 740-743, 744-745, 12.5: 750, 751-756, 757, 758, 759, 12.6: 760, 761-763, 764-765, 766-767 TG: 12.4: 717-723, 12.5: 725-732, 12.6: 733-740




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Reasoning with Equations and Inequalities (A – REI): 31) Solve equations and inequalities in one variable. A – REI 4: Solve quadratic equations in one variable.

SE: 12.7: 768-774 TG: 12.7: 741-745

Common Core State Standards for Mathematics A – REI 4 PARRC Model Content Frameworks Mathematics - Core Math II Standard A – REI 4 Math Practice MP.8 Look for and express regularity in repeated reasoning.

A – REI 4a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.

SE: 12.6: 760-764, 12.7: 768-774 TG: 12.6: 733-736, 12.7: 741-745

Common Core State Standards for Mathematics A – REI 4a PARRC Model Content Frameworks Mathematics - Core Math II Standard A – REI 4a Math Practice MP.1 Make sense of problems and persevere in solving them. MP.8 Look for and express regularity in repeated reasoning.



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A – REI 4b: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

SE: 12.4: 740-743, 12.5: 750-756, 12.6: 760-764, 12.7: 768-774, 12.8: 778-787 TG: 12.4: 717-720, 12.5: 725-729, 12.6: 733-736, 12.7: 741-745, 12.8: 749-754

Common Core State Standards for Mathematics A – REI 4b PARRC Model Content Frameworks Mathematics - Core Math II Standard A – REI 4b Math Practice MP.1 Make sense of problems and persevere in solving them. MP.6 Attend to precision.

Seeing Structure in Expressions (A – SSE): 32) Write expressions in equivalent forms to solve problems. A – SSE 3b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

SE: 12.6: 760-764 TG: 12.6: 733-736

Common Core State Standards for Mathematics A – SSE 3b PARRC Model Content Frameworks Mathematics - Core Math II Standard A – SSE 3b Math Practice MP.1 Make sense of problems and persevere in solving them.



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Interpreting Functions (F – IF): 33) Analyze functions using different representations. F – IF 8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

SE: 12.6: 760-764, 14.2: 919-926 TG: 12.6: 733-736, 14.2: 884-889

Common Core State Standards for Mathematics F – IF 8 PARRC Model Content Frameworks Mathematics - Core Math II Standard F – IF 8 Math Practice MP.1 Make sense of problems and persevere in solving them.

F – IF 8a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

SE: 12.5: 750-756, 12.6: 760-764 TG: 12.5: 725-729, 12.6: 733-736

Common Core State Standards for Mathematics F – IF 8a PARRC Model Content Frameworks Mathematics - Core Math II Standard F – IF 8a Math Practice MP.1 Make sense of problems and persevere in solving them.



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The Complex Number System (N – CN): 35) Perform arithmetic operations with complex numbers. N – CN 1: Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.

SE: 12.8: 778-787 TG: 12.8: 749-754

Common Core State Standards for Mathematics N – CN 1 PARRC Model Content Frameworks Mathematics - Core Math II Standard N – CN 1 Math Practice MP.6 Attend to precision.

N – CN 2: Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

SE: 12.8: 778-787 TG: 12.8: 749-754




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Math Practices

The Complex Number System (N – CN): 36) Use complex numbers in polynomial identities and equations. N – CN 7: Solve quadratic equations with real coefficients that have complex solutions.

SE: 12.8: 778-787 TG: 12.8: 749-754


Topic 7 –Probability Conditional Probability and the Rules of Probability (S – CP): 37) Understand independence and conditional probability and use them to interpret data. S – CP 1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

SE: 13.1: 841-844, 13.4: 865-870 TG: 13.1: 809-812, 13.4: 832-836

Common Core State Standards for Mathematics S – CP 1 PARRC Model Content Frameworks Mathematics - Core Math II Standard S – CP 1 Math Practice MP.3 Construct viable arguments and critique the reasoning of others. MP.6 Attend to precision.



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S – CP 2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

SE: 13.4: 865-870 TG: 13.4: 832-836

Common Core State Standards for Mathematics S – CP 2 PARRC Model Content Frameworks Mathematics - Core Math II Standard S – CP 2 Math Practice MP.3 Construct viable arguments and critique the reasoning of others.

S – CP 3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

SE: 13.6: 880-886 TG: 13.6: 848-852

Common Core State Standards for Mathematics S – CP 3 PARRC Model Content Frameworks Mathematics - Core Math II Standard S – CP 3 Math Practice MP.2 Reason abstractly and quantitatively.



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Math Practices

S – CP 4: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from you school will favor science given that the student is in the tenth grade. Do the same for other subjects and compare the results.

SE: 13.2: 848-851, 13.5: 873-876, 13.6: 880-886 TG: 13.2: 816-819, 13.5: 840-843, 13.6: 848-852

Common Core State Standards for Mathematics S – CP 4 PARRC Model Content Frameworks Mathematics - Core Math II Standard S – CP 4 Math Practice MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively.

S – CP 5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

SE: 13.2: 848-851, 13.4: 865-870, 13.6: 880-886 TG: 13.2: 816-819, 13.4: 832-836, 13.6: 848-852

Common Core State Standards for Mathematics S – CP 5 PARRC Model Content Frameworks Mathematics - Core Math II Standard S – CP 5 Math Practice MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others.



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Conditional Probability and the Rules of Probability (S – CP): 38) Use the rules of probability to compute probabilities of compound events in a uniform probability model. S – CP 6: Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

SE: 13.4: 865-870 TG: 13.4: 832-836

Common Core State Standards for Mathematics S – CP 6 PARRC Model Content Frameworks Mathematics - Core Math II Standard S – CP 6 Math Practice MP.3 Construct viable arguments and critique the reasoning of others.

S – CP 7: Apply the Addition Rule, P (A or B) = P(B) – P(A and B), and interpret the answer in terms of the model.

For related content, please see: SE: 13.6: 880-884 TG: 13.6: 848-852

Common Core State Standards for Mathematics S – CP 7 PARRC Model Content Frameworks Mathematics - Core Math II Standard S – CP 7 Math Practice MP.2 Reason abstractly and quantitatively.



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Topic 8 – Geometric Measurement Geometric Measurement and Dimension (G – GMD): 39) Explain volume formulas and use them to solve problems. G – GMD 1: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

SE: Activity Lab: Exploring the Circumference and Area of a Circle: 533-536, 9.3: 559-565, Activity Lab: Finding Volume: 569-571, 9.4: 572-576 TG: Activity Lab: Exploring the Circumference and Area of a Circle: 533-534, 9.3: 554-558, Activity Lab: Finding Volume: 562, 9.4: 563-566

Common Core State Standards for Mathematics G – GMD 1 PARRC Model Content Frameworks Mathematics - Core Math II Standard G – GMD 1 Math Practice MP.3 Construct viable arguments and critique the reasoning of others. MP.6 Attend to precision. MP.7 Look for and make use of structure.



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G – GMD 3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

SE: 9.3: 559-565, 9.4: 572-576, 9.5: 581-586 TG: 9.3: 554-558, 9.4: 563-566, 9.5: 570-574

Common Core State Standards for Mathematics G – GMD 3 PARRC Model Content Frameworks Mathematics - Core Math II Standard G – GMD 3 Math Practice MP.4 Model with mathematics. MP.6 Attend to precision.

Geometric and Modeling Project *Modeling with Geometry (G – MG): 40) Apply geometric concepts in modeling situations. 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).*

This standard is addressed in Pearson Integrated High School Mathematics - Mathematics III Common Core, please see: SE: 10.3: 755-760, 10.4: 765-769, 10.6: 785-789, 11.2: 823-827, 11.3: 832-835 TG: 10.3: 724-727, 10.4: 731-734, 10.6: 746-749, 11.2: 782-786, 11.3: 790-792

Common Core State Standards for Mathematics G – MG 1 PARRC Model Content Frameworks Mathematics - Core Math III Standard G – MG 1 Math Practice MP.4 Model with mathematics. MP.6 Attend to precision. MP.7 Look for and make use of structure.



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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).*

This standard is addressed in Pearson Integrated High School Mathematics - Mathematics III Common Core, please see: SE: 10.2: 747-750, 10.3: 755-760, 10.6: 785-789 TG: 10.2: 717-720, 10.3: 724-727, 10.6: 746-749

Common Core State Standards for Mathematics G – MG 2 PARRC Model Content Frameworks Mathematics - Core Math III Standard G – MG 2 Math Practice MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

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).*

This standard is addressed in Pearson Integrated High School Mathematics - Mathematics III Common Core, please see: SE: 10.2: 747-750, 10.3: 755-760, 10.6: 785-789 TG: 10.2: 717-720, 10.3: 724-727, 10.6: 746-749

Common Core State Standards for Mathematics G – MG 3 PARRC Model Content Frameworks Mathematics - Core Math II Standard G – MG 3 Math Practice MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.7 Look for and make use of structure.

Documents

Pearson Integrated High School Mathematics Mathematics II