Prentice Hall Prentice Hall Algebra 2, Foundations Series 2011

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1 Prentice Hall Prentice Hall Algebra 2, Foundations Series 2011 C O R R E L A T E D T O Tennessee Mathematics Standards, Implementation, Algebra II

2 Tennessee Mathematics Standards Implementation Algebra II 3103 Standard 1 Mathematical Processes CLE Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning. CLE Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution. CLE Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of reasoning, logic, and intuition. CLE Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies. CLE Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies. CLE Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world. CLE Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models. SE/TE: 64 67, 70 71, 74 77, 88 90, 92 95, , , 137, , 238, , , , 510, , , 574 SE/TE: 64 67, 70 71, 74 77, 88 90, 92 95, , , 137, , 238, , , , 510, , , 574 SE/TE: 4 6, 34, 67, 88, 213, 312, 324, 346, , 491, 493, , , , 642, 686, 841 SE/TE: , , , , , , , , , , , 372, , , , , SE/TE: 28, 49, , 155, 164, 171, 180, , 247, 253, 262, 264, 315, , 419, 500, 530, 534, 543, 567, 616, , , 763 SE/TE: 6, 35, 115, 122, 158, 178, 186, 208, 233, 253, 263, 275, 315, 349, 384, 388, 397, 406, 494, 542, 550, 561, 566, 586, 602, , 691, 713, 795, 804, 853, 858 SE/TE: , 124, 147, 148, 164, 175, 188, 205, 212, 222, 244, 246, 247, 257, 264, 294, 305, 312, 314, 315, 337, 342, 353, 354, 355, 356, 443, 446, 465, 472, , , 493, 499, 503, 507, , 522, 527, 529, 534, 543, 568, 588, 640, 650, 668, 727, 733, 780, 790, 791, 794, 795, 796, 800, 805, , 854 1

3 Checks for Understanding (Formative/Summative Assessment): Create and analyze scatter-plots of non-linear and transcendental functions Compare and contrast sampling techniques and identify the best technique for a given situation Use calculators to identify regression equations for nonlinear data Identify the weaknesses of calculators and other technologies in representing non-linear data, such as graphs approaching vertical asymptotes, and use alternative techniques to identify these issues and correctly solve problems Determine the accuracy and reliability of a mathematical model Use graphical representations to perform operations on complex numbers Use the unit circle to determine the exact value of trigonometric functions for commonly used angles (0, 30, 45, 60 ) Understand and describe the inverse relationship between exponential and logarithmic functions Translate the syntax of technology to appropriate mathematical notation for non-linear and transcendental functions Interpret the results of mathematical modeling in various contexts to answer questions. State Performance Indicators: SPI Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic) of non-linear and transcendental functions to solve problems, to model mathematical ideas, and to communicate solution strategies. SPI Recognize and describe errors in data collection and analysis as well as identifying representations of data as being accurate or misleading. SPI Use technology tools to identify and describe patterns in data using non-linear and transcendental functions that approximate data as well as using those functions to solve contextual problems. SPI Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely to effectively communicate reasoning in the process of solving problems via mathematical modeling with both linear and non-linear functions. Standard 2 Number & Operations CLE Understand the hierarchy of the complex number system and relationships between the elements, properties and operations. SE/TE: , , , , , , , , , , , 372, , , , , SE/TE: , , 763 SE/TE: , 148, 222, , 372, , , 507 SE/TE: 64 67, 70 71, 74 77, 88 90, 92 95, , , 137, , 238, , , , 510, , , 574 SE/TE: 11 15, , 278, 284 2

4 CLE Connect numeric, analytic, graphical and verbal representations of both real and complex numbers. CLE Use appropriate technology (including graphing calculators and computer spreadsheets) to solve problems, recognize patterns and collect and analyze data. CLE Understand the capabilities and limitations of technology when performing operations, graphing, and solving equations involving complex numbers. Checks for Understanding (Formative/Summative Assessment): SE/TE: 11 15, 26 30, 44 45, 48 49, 54, 56, , 155, 164, , , , 256, , , , 278, , , , 328, 369, , , , , , 509, 512, , 573, 576 SE/TE: , 148, 175, 188, 222, 244, 246, 247, 264, 305, 315, 353, 354, 355, 356, 446, 465, , , 499, 503, 507, , 522, 527, 534, 543, 588, 727, 790, 791, 794, 795, 796, 805, 854 SE/TE: 124, 164, 175, 212, 244, 246, 257, 294, 312, 314, 342, 443, 472, , 493, 499, 503, 529, 534, 568, 640, 650, 668, 733, 780, 790, 791, 794, 795, 796, 800, 805, Understand that to solve certain problems and equations, the real number system needs to be extended from real numbers to complex numbers Define and give examples of each of the types of numbers in the complex number system Identify and apply properties of complex numbers (including simplification and standard form) Add and subtract complex numbers Multiply complex numbers Define and utilize the complex conjugates to write the quotient of two complex numbers in standard form Graph complex numbers in the complex plane and recognize differences and similarities with the graphical representations of real numbers graphed on the number line Solve quadratic equations over the complex number system Find and describe geometrically the absolute value of a complex number Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers over complex numbers Understand the capabilities and limitations of technology. Make estimations without a calculator to detect potential errors Select and use appropriate methods to make estimations without technology when solving contextual problems Analyze and evaluate contextual situations involving any type of number from the complex number system. State Performance Indicators: SPI Describe any number in the SE/TE: 11 12, , 284 complex number system. SPI Compute with all real and complex numbers. SE/TE: , 278 3

5 SPI Use the number system, from real to complex, to solve equations and contextual problems. Standard 3 Algebra CLE Understand and apply properties of rational exponents and perform basic operations to simplify algebraic expressions. CLE Understand, analyze, transform and generalize mathematical patterns, relations and functions using properties and various representations. CLE Analyze and apply various methods to solve equations, absolute values, inequalities, and systems of equations over complex numbers. CLE Graph and compare equations and inequalities in two variables. Identify and understand the relationships between the algebraic and geometric properties of the graph. CLE Use mathematical models involving equations and systems of equations to represent, interpret and analyze quantitative relationships, change in various contexts, and other real-world phenomena. SE/TE: 26 30, 44 45, 48 49, 54, 56, , 155, 164, , , , 256, , , , , , 328, 369, , , , , , 509, 512, , 573, 576 SE/TE: 21, 56, , , 329, , , 414, , , , , 872 SE/TE: 4 6, 64 67, 70, 82 84, 98 99, , , , , , , , , , , 372, , , , , , , , 511, 529, , , , SE/TE: 26 29, 33 36, 39 40, 43 45, 47 48, 56, , , , , 188, , 196, , , , 256, , , , , , 333, 335, , , 453, , , 512, , 576 SE/TE: 83 84, 92, 94 95, , 131, , , , 282, , 640, , 645, , , , SE/TE: 28, 49, , 155, 164, 171, 180, , 247, 253, 262, 264, 315, , 419, 500, 530, 534, 543, 567, 616 Checks for Understanding (Formative/Summative Assessment) Perform operations on algebraic expressions and justify the procedures Determine the domain of a function represented in either symbolic or graphical form Determine and graph the inverse of a function with and without technology Analyze the effect of changing various parameters on functions and their graphs Graph piece-wise and step functions Simplify expressions and solve equations containing radicals Solve quadratic equations by factoring, graphing, completing the square, extracting square roots and using the quadratic formula Solve a three by three system of linear equations algebraically and by using inverse matrices and determinants with and without technology Find an equation for a parabola when given its graph or when given its roots Given a quadratic equation use the discriminant to determine the nature of the roots Describe and articulate the characteristics and parameters of a parent function Understand the relationship between real zeros of a function and the x-intercepts of its graph. 4

6 Solve problems using exponential functions requiring the use of logarithms for their solutions Define and use arithmetic and geometric sequences and series including using sigma and pi notation Find the sum of an geometric series whose common ratio, r, is in the interval (-1,1) Prove basic properties of logarithms using properties of exponents and apply those properties to solve problems Know that the logarithm and exponential functions are inverses and use this information to solve real-world problems Solve compound inequalities involving disjunction and conjunction and linear inequalities containing absolute values Solve linear programming problems Understand the relationships between the equations of conic sections and their graphs Factor polynomials using a variety of methods including the factor theorem, synthetic division, long division, sums and differences of cubes, and grouping Determine the number and possible types of zeros for a polynomial function and find the rational roots Understand the connection between the roots, zeros, x-intercepts, factors of polynomials, and solutions of polynomial equations. State Performance Indicators SPI Add, subtract and multiply SE/TE: , , 329, 872 polynomials; divide a polynomial by a lower degree polynomial. SPI Solve quadratic equations and systems, and determine roots of a higher order polynomial. SPI Add, subtract, multiply, divide and simplify rational expressions including those with rational and negative exponents. SPI Use the formulas for the general term and summation of finite arithmetic and both finite and infinite geometric series. SPI Describe the domain and range of functions and articulate restrictions imposed either by the operations or by the contextual situations which the functions represent. SPI Combine functions (such as polynomial, rational, radical and absolute value expressions) by addition, subtraction, multiplication, division, or by composition and evaluate at specified values of their variables. SPI Identify whether a function has an inverse, whether two functions are inverses of each other, and/or explain why their graphs are reflections over the line y = x. SPI Solve systems of three linear equations in three variables. SE/TE: , , , 256, , , , , , 333, 335 SE/TE: , , , SE/TE: 585, 587, , , , , SE/TE: , 433, , , , , SE/TE: , 453 SE/TE: , , 454, 483 SE/TE: , 188, 193, 196 5

7 SPI Graph the solution set of two or three linear or quadratic inequalities. SPI Identify and/or graph a variety of functions and their transformations. SPI Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the standard form and the key characteristics of the graph. SPI Interpret graphs that depict realworld phenomena. SPI Solve contextual problems using quadratic, rational, radical and exponential equations, finite geometric series or systems of equations. SPI Solve problems involving the binomial theorem and its connection to Pascal s Triangle, combinatorics, and probability. Standard 4 Geometry & Measurement CLE Understand the trigonometric functions and their relationship to the unit circle. CLE Know and use the basic identities of sine, cosine, and tangent as well as their reciprocals. CLE Graph all six trigonometric functions and identify their key characteristics. CLE Know and use the Law of Sines to find missing sides and angles of a triangle, including the ambiguous case. CLE Use trigonometric concepts, properties and graphs to solve problems. SE/TE: , 172, 174, 175, 195 SE/TE: , , , , , , , , 372, , 454, , 511, 529, , SE/TE: , , , 282, , 640, , 645, , , , SE/TE: 146, 148, 164, 171, , , 530, 534, 543 SE/TE: , 155, 247, 253, 262, 264, 419, 500, 567, 616 SE/TE: , 371, , 763 SE/TE: , , 848, 852, 863 SE/TE: , 863 SE/TE: , 863 Checks for Understanding (Formative/Summative Assessment): Convert between radians and degrees and vice versa Determine the period and the amplitude of a periodic function. See Lesson 14-4 in Prentice Hall Algebra 2, Tennessee Edition 2012 ( ISBN-10: X). In spring 2011, this lesson will be available online at PowerAlgebra.com for students using Prentice Hall Algebra 2, Foundations Series SE/TE: , , 854, Extend the trigonometric functions to periodic functions on the real line by defining them as functions on the unit circle Understand the relationship between the radius, the central angle, and radian measure Determine the domain and range of the six trigonometric functions given a graph Know and be able to use the fundamental trigonometric identities, including the Pythagorean identities, reciprocal identities, sum of sine and cosine, and odd and even identities. State Performance Indicators: 6

8 SPI Exhibit knowledge of unit circle trigonometry. SE/TE: , , 848, 852, 863 SPI Match graphs of basic trigonometric functions with their equations. SPI Describe and articulate the characteristics and parameters of parent trigonometric functions to solve contextual problems. Standard 5 Data Analysis, Statistics, & Probability CLE Describe, interpret, and apply quantitative data. CLE Evaluate and critique various ways of collecting data and using information based on data published in the media. CLE Use data and statistical thinking to draw inferences, make predictions, justify conclusions and identify and explain misleading uses of data. CLE Develop an understanding of probability concepts in order to make informed decisions. SE/TE: , 863 SE/TE: 854, SE/TE: , , SE/TE: , , 763 Checks for Understanding (Formative/Summative Assessment): SE/TE: , 137, 222, , 372, , , , 763 SE/TE: , , , , , , , 761, Collect, represent and describe both linear and non-linear data developed from contextual situations Organize and display data using appropriate methods (including spreadsheets and technology tools) to detect patterns and departures from patterns Read and interpret data from a two-way table Understand the impact of various sampling methods and use them to draw valid conclusions Calculate measures of central tendency and spread (variance and standard deviation) Use technology to find the appropriate regression equation for both linear and non-linear data Recognize when the correlation coefficient measures goodness of fit and does not imply causation Know the Empirical Rule for one, two and three standard deviations for a normal distribution Use data to detect patterns Design simple experiments to collect data to answer questions of interest Evaluate published data by considering the source, the design of the study and the analysis and representation (or misrepresentation) of the data Investigate bias and the phrasing of questions during data acquisition to formulate reasonable conclusions Apply both theoretical and experimental probability to analyze the likelihood of an event. State Performance Indicators: 7

9 SPI Compute, compare and explain summary statistics for distributions of data including measures of center and spread. SE/TE: , , SPI Compare data sets using graphs and summary statistics. SPI Analyze patterns in a scatter-plot and describe relationships in both linear and non-linear data. SPI Apply the characteristics of the normal distribution. SPI Determine differences between randomized experiments and observational studies. SPI Find the regression curve that best fits both linear and non-linear data (using technology such as a graphing calculator) and use it to make predictions. SPI Determine/recognize when the correlation coefficient measures goodness of fit. SPI Apply probability concepts such as conditional probability and independent events to calculate simple probability. SE/TE: , 736 SE/TE: , , 222, 238, , 372, , SE/TE: , 764 SE/TE: , SE/TE: , 137, 222, 238, , 372, , SE/TE: , , 372 SE/TE: , , ,

10 Pearson Prentice Hall Algebra 2 Foundations Narrative Brief I. Orientation and Clarification Prentice Hall Algebra 2 Foundations is part of an integrated digital and print environment for the study of high school mathematics. It has been aligned to the Tennessee Mathematics Curriculum Framework Algebra 2 State Performance Indicators. This textbook is intended for use in Algebra Program Description Prentice Hall Algebra 2 Foundations was developed for the low-level or inclusive classroom by delivering comprehensive content in an accessible manner to all students. Simpler problems allow easier access to concepts and skills. Shorter Lessons and shorter chapters allow for more frequent assessments. More scaffolding in problems and exercises supports students at every step. Prentice Hall Algebra 2 Foundations teaches for understanding by incorporating an interwoven strand of thinking and reasoning into problem solving. This connects the math that the students learn, from the first lesson to the last. This focus on thinking, reasoning and problem solving prepares students for success in school, careers and life by creating a strong mathematical foundation. Math proficiency is developed through fluency, reasoning and application. This process is found throughout the text. Prentice Hall Algebra 2 Foundations begins by incorporating the Understanding by Design framework where students will develop answers to the Essential Questions posed and make connections to the Big Ideas. Visual Learning is incorporated throughout the series to aid students in clarifying important concepts, encouraging them to make connections with real-life situations and engaging them with visual representations of the mathematics. Problem solving strategies are embedded throughout each lesson. The worked-out problems model effective thinking and reasoning strategies to help foster students mathematical reasoning. The Think and Plan call-outs are a form of visual instruction that model the problem solving process, reveal Step Zero and provide additional support as they model the thinking behind each step. The Know-Need- Plan is another visual clue of the problem solving thought process which helps students to decode problems. These problem solving methods are modeled not only in the text, but online at PowerAlgebra.com with additional stepped out support and audio. Differentiating instruction helps all students develop conceptual understanding, foster mathematical reasoning and refine problem solving strategies. Response to

11 Intervention (RtI) is embedded into the Prentice Hall Program. RtI Tier 1 options are available to differentiate instruction at the start of each chapter (Getting Ready) and throughout the lessons (Got it? and Lesson Check). Data-Driven Differentiation is provided in the Lesson Resources following each lesson in the Teacher s Edition. This is RtI Tier 2 intervention. The Lesson Resources provide a detailed blueprint for instruction assessment and remediation that includes prescriptions for all levels of students from intervention to extension. RtI Tier 3 is available at the chapter level as part of the Mid-Chapter Quiz and Chapter Test. Remediation for these assessments is delivered through the MathXL for School component in the online digital path. 3. Research Prentice Hall Algebra 2 Foundations incorporates a variety of research-based methodology including: Understanding by Design, Teaching through Problem Solving, Visual Instruction and Differentiating Instruction. Initial efficacy studies, prepared by PRES Associates, showed significant learning gains for Algebra 1 students. Students also self-reported that the Pearson Prentice Hall Algebra 1 program helped them learn math, prepared them for future math courses and postsecondary education, and helped them mentally organize important algebraic concepts. 4. Assessment Assessment can be found throughout the Prentice Hall Algebra 2 Foundations program. Formative assessments include diagnostic tests and Getting Ready chapter assessments. During the lesson formative assessment takes the form of the Dynamic Activity online manipulative, Got It?, and Lesson Check. After the lesson the Lesson Quiz (also found online) indicates the needed remediation or enrichment for each student. Practice Level K was specifically designed for the Foundations student. Summative Assessments include fully editable Chapter Quizzes, Mid- Chapter tests and Chapter Tests available in print, DVD and online and additional assessments may be created using the ExamView Assessment Suite and Prentice Hall Math Art Gallery. Teachers may utilize Progress Monitoring Assessments in print or online to assess benchmarks, quarter, semester and final exams. If taken online, through the SuccessTracker Assessment system, instant grading takes place and remediation or enrichment is instantly assigned and reported. Teachers may also build their own assessments online within the SuccessTracker Assessment system.

Statewide Framework Document for:

Statewide Framework Document for: 270301 Standards may be added to this document prior to submission, but may not be removed from the framework to meet state credit equivalency requirements. Performance