Prentice Hall Prentice Hall Algebra 1, Foundations Series 2011

Prentice Hall Prentice Hall Algebra 1, Foundations Series 2011 C O R R E L A T E D T O Tennessee Mathematics Standards, 2009-2010 Implementation, Algebra I

Tennessee Mathematics Standards 2009-2010 Implementation Algebra I 3102 Standard 1 Mathematical Processes Course Level Expectations: CLE 3102.1.1 Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning. CLE 3102.1.2 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 3102.1.3 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 3102.1.4 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 3102.1.5 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 3102.1.6 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 3102.1.7 Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models. Checks for Understanding (Formative/Summative Assessment): 3102.1.1 Develop meaning for mathematical vocabulary. 3102.1.2 Use the terminology of mathematics correctly. SE/TE: 4 7, 28 29, 33, 69 71, 76, 78, 97, 210 213, 230 233, 255 258, 262 265, 295 298, 304 306, 751 753 SE/TE: 62, 90, 96, 102, 111, 119, 127, 132 133, 139, 144 146, 150 154, 158 160, 164 166, 280 282, 306, 321 324, 335, 342, 352, 360, 383, 392, 397, 408 409, 483 486, 494, 575 576, 579, 582, 588, 610, 614, 694 SE/TE: 6 7, 26 29, 34, 39 40, 47 48, 52 54, 56 57, 69 71, 77 78, 87 90, 97, 101 103, 105 106, 137, 197, 210 213, 230 233, 256, 264, 295 298 SE/TE: 70 71, 78, 230 233, 262 265, 270 273, 280 282, 305 306, 321 324, 328, 329 330, 334 335, 338 339, 341 342, 349 353, 357 360, 374, 408 409, 477, 482, 483 486, 567 569, 573 576, 610 SE/TE: 70 71, 271 273, 280 282, 314 316, 321 324, 335, 342, 352, 360, 407 409, 477, 482, 483 486, 494, 569, 575 576 SE/TE: 18, 31, 42, 55, 92, 160, 187, 295 296, 333, 402, 428, 480, 489, 519, 543, 549, 571, 576, 579, 605, 611, 630, 651, 682, 683, 719, 721, 736 SE/TE: 67, 278 279, 328, 355, 388, 431, 568, 571, 575, 577, 614 3102.1.3 Understand and use mathematical symbols, notation, and common mathematical abbreviations correctly. 3102.1.4 Write a rule with variables that expresses a pattern. 3102.1.5 Use formulas, equations, and inequalities to solve real-world problems including time/rate/distance, percent increase/decrease, ratio/proportion, and mixture problems. 1

3102.1.6 Use a variety of strategies to estimate and compute solutions, including real-world problems. 3102.1.7 Identify missing or irrelevant information in problems. 3102.1.8 Recognize and perform multiple steps in problem solving when necessary. 3102.1.9 Identify and use properties of the real numbers (including commutative, associative, distributive, inverse, identity element, closure, reflexive, symmetric, transitive, operation properties of equality). 3102.1.10 Use algebraic properties to develop a valid mathematical argument. 3102.1.11 Use manipulatives to model algebraic concepts. 3102.1.12 Create and work flexibly among representations of relations (including verbal, equations, tables, mappings, graphs). 3102.1.13 Change from one representation of a relation to another representation, for example, change from a verbal description to a graph. 3102.1.14 Apply graphical transformations that occur when changes are made to coefficients and constants in functions. 3102.1.15 Apply arithmetic concepts in algebraic contexts. 3102.1.16 Understand and express the meaning of the slope and y-intercept of linear functions in real-world contexts. 3102.1.17 Connect the study of algebra to the historical development of algebra. 3102.1.18 Translate syntax of technology to appropriate mathematical notation. 3102.1.19 Recognize and practice appropriate use of technology in representations and in problem solving. 3102.1.20 Estimate solutions to evaluate the reasonableness of results and to check technological computation. State Performance Indicators: SPI 3102.1.1 Interpret patterns found in sequences, tables, and other forms of quantitative information using variables or function notation. SPI 3102.1.2 Write an equation symbolically to express a contextual problem. SPI 3102.1.3 Apply properties to evaluate expressions, simplify expressions, and justify solutions to problems. SPI 3102.1.4 Translate between representations of functions that depict real-world situations. SPI 3102.1.5 Recognize and express the effect of changing constants and/or coefficients in problem solving. SE/TE: 6 7, 69 71, 78, 255 258, 262 265, 295 298, 304 306 SE/TE: 62, 90, 96, 102, 111, 119, 127, 139, 144 146, 150 154, 164 166, 280 282, 306, 321 324, 335, 342, 352, 360, 383, 392, 397, 408 409, 483 486, 494, 575 576, 579, 582, 588, 610, 614, 694 SE/TE: 26 29, 34, 39 40, 47 48, 52 54, 56 57, 76 77, 87 90, 97, 101 103, 105 106, 125 127, 131 133, 137 139, 144 146, 164 165, 197 SE/TE: 70 71, 78, 271 273, 280 282, 305 306, 329, 335, 338, 342, 349, 352, 408 409, 477, 482, 483 486, 494, 569, 573, 575 576 SE/TE: 321 324, 328, 330, 357 360, 374, 483 486, 491, 494, 567 568, 573 574 2

SPI 3102.1.6 Determine and interpret slope in multiple contexts including rate of change in real-world problems. Standard 2 Number & Operations Grade Level Expectations: CLE 3102.2.1 Understand computational results and operations involving real numbers in multiple representations. CLE 3102.2.2 Understand properties of and relationships between subsets and elements of the real number system. Checks for Understanding (Formative/Summative Assessment): 3102.2.1 Recognize and use like terms to simplify expressions. SE/TE: 314 317, 321 324, 328, 329 331, 334 335, 338 339, 341 342, 345 346, 357 360, 373 374 SE/TE: 11 13, 15 16, 19 20, 26 29, 33 34, 37 40, 45 49, 52 54, 56 57, 76 77, 457 458, 469, 627, 631, 632 634, 636 638, 640 643, 654 656 SE/TE: 20 22, 26 29, 34, 39 40, 47 48, 52 54, 56 57, 76 77 3102.2.2 Apply the order of operations to simplify and evaluate algebraic expressions. 3102.2.3 Operate with and simplify radicals (index 2, 3, n) and radical expressions including rational numbers and variables in the radicand. 3102.2.4 Operate efficiently with both rational and irrational numbers. 3102.2.5 Perform operations with numbers in scientific notation (multiply, divide, powers). 3102.2.6 Use appropriate technologies to apply scientific notation to real-world problems. 3102.2.7 Identify the subsets in the real number system and understand their relationships. 3102.2.8 Use multiple strategies to approximate the value of an irrational number including irrational square roots and including location on the real number line. State Performance Indicators: SPI 3102.2.1 Operate (add, subtract, multiply, divide, simplify, powers) with radicals and radical expressions including radicands involving rational numbers and algebraic expressions. SPI 3102.2.2 Multiply, divide, and square numbers expressed in scientific notation. SPI 3102.2.3 Describe and/or order a given set of real numbers including both rational and irrational numbers. Standard 3 Algebra Grade Level Expectations: CLE 3102.3.1 Use algebraic thinking to analyze and generalize patterns. CLE 3102.3.2 Understand and apply properties in order to perform operations with, evaluate, simplify, and factor expressions and polynomials. SE/TE: 19 20, 627, 631, 632 634, 636 638, 640 643, 654 656 SE/TE: 457 458, 469 SE/TE: 21 22, 34, 81 SE/TE: 6 7, 16, 70 71, 78, 255 258, 262 265, 295 298, 303 306, 324, 342, 475 477, 481 482, 491, 494, 608 610, 614, 616, 618 SE/TE: 11 13, 15 16, 26 28, 33 34, 52 54, 56 57, 76 77, 442 445, 455 458, 461 464, 468 471, 491 493, 503 505, 508 510, 513, 514 515, 517 519, 522 525, 528 529, 532, 533 535, 539 541, 545 548, 551 553, 557 558, 632 634, 636 637, 640 643, 654 656, 678, 679 681, 701 3

CLE 3102.3.3 Understand and apply operations with rational expressions and equations. CLE 3102.3.4 Solve problems involving linear equations and linear inequalities. CLE 3102.3.5 Manipulate formulas and solve literal equations. CLE 3102.3.6 Understand and use relations and functions in various representations to solve contextual problems. CLE 3102.3.7 Construct and solve systems of linear equations and inequalities in two variables by various methods. CLE 3102.3.8 Solve and understand solutions of quadratic equations with real roots. CLE 3102.3.9 Understand and use exponential functions to solve contextual problems. SE/TE: 664 667, 671 674, 685 688, 692 696, 700 702 SE/TE: 87, 90, 94, 96, 101 102, 110 111, 164, 184, 186, 193, 199 200, 216, 218, 222 223, 227 SE/TE: 117 119, 127, 162, 311, 342 SE/TE: 248 251, 280 282, 286, 289, 292, 303 304, 306, 321, 323, 329, 335, 338, 342, 349, 352, 360, 475 477, 482, 483 486, 491, 494, 566, 569, 573, 575 576, 579 SE/TE: 382 385, 388, 389, 390 393, 396 397, 399 402, 405 406, 407 409, 412 413, 425 427, 431, 433 434 SE/TE: 580 582, 586 588, 592, 595 598, 601 605, 616 617 SE/TE: 475 477, 483 486, 491, 494 Checks for Understanding (Formative/Summative Assessment): 3102.3.1 Recognize and extend arithmetic and geometric sequences. 3102.3.2 Explore patterns including Pascal s Triangle and the Fibonacci sequence. 3102.3.3 Justify correct results of algebraic procedures using extension of properties of real numbers to algebraic expressions. 3102.3.4 Simplify expressions using exponent rules including negative exponents and zero exponents. 3102.3.5 Add, subtract, and multiply polynomials including squaring a binomial. 3102.3.6 Find the quotient of a polynomial and a monomial. 3102.3.7 Use various models (including area models) to represent products of polynomials. 3102.3.8 Find the GCF of the terms in a polynomial. 3102.3.9 Find two binomial factors of a quadratic expression. 3102.3.10 Add, subtract, multiply, and divide rational expressions and simplify results. 3102.3.11 Solve multi-step linear equations with one variable. 3102.3.12 Recognize and articulate when an equation has no solution, a single solution, or all real numbers as solutions. 3102.3.13 Solve multi-step linear inequalities with one variable and graph the solution on a number line. 3102.3.14 Solve absolute value equations and inequalities (including compound inequalities) with one variable and graph their solutions on a number line. 3102.3.15 Determine domain and range of a relation and articulate restrictions imposed either by the operations or by the real life situation that the function represents. 3102.3.16 Determine if a relation is a function from its graph or from a set of ordered pairs. 3102.3.17 Recognize families of functions. 3102.3.18 Analyze the characteristics of graphs of basic linear relations and linear functions including constant function, direct variation, identity function, vertical lines, absolute value of linear functions. Use technology where appropriate. 4

3102.3.19 Explore the characteristics of graphs of various nonlinear relations and functions including inverse variation, quadratic, and square root function. Use technology where appropriate. 3102.3.20 Understand that a linear equation has a constant rate of change called slope and represent slope in various forms. 3102.3.21 Determine the equation of a line using given information including a point and slope, two points, a point and a line parallel or perpendicular, graph, intercepts. 3102.3.22 Express the equation of a line in standard form, slope-intercept, and point-slope form. 3102.3.23 Determine the graph of a linear equation including those that depict contextual situations. 3102.3.24 Interpret the changes in the slope-intercept form and graph of a linear equation by looking at different parameters, m and b in the slope-intercept form. 3102.3.25 Find function values using f(x) notation or graphs. 3102.3.26 Graph linear inequalities on the coordinate plane and identify regions of the graph containing ordered pairs in the solution. 3102.3.27 Determine the number of solutions for a system of linear equations (0, 1, or infinitely many solutions). 3102.3.28 Solve systems of linear equations graphically, algebraically, and with technology. 3102.3.29 Solve contextual problems involving systems of linear equations or inequalities and interpret solutions in context. 3102.3.30 Solve quadratic equations using multiple methods: factoring, graphing, quadratic formula, or square root principle. 3102.3.31 Determine the number of real solutions for a quadratic equation including using the discriminant and its graph. 3102.3.32 Recognize the connection among factors, solutions (roots), zeros of related functions, and x-intercepts in equations that arise from quadratic functions. 3102.3.33 Recognize data that can be modeled by an exponential function. 3102.3.34 Graph exponential functions in the form y = a(bx) where b 0. 3102.3.35 Apply growth/decay and simple/compound interest formulas to solve contextual problems. State Performance Indicators: SPI 3102.3.1 Express a generalization of a pattern in various representations including algebraic and function notation. SPI 3102.3.2 Operate with polynomials and simplify results. SE/TE: 6 7, 16, 70 71, 78, 255 258, 262 265, 295 298, 303 306, 324, 342, 475 477, 481 482, 491, 494, 608 610, 614, 616, 618 SE/TE: 503 505, 508, 513, 514 515, 517 519, 522 525, 528 529, 678, 679 681, 701 SPI 3102.3.3 Factor polynomials. SE/TE: 509 510, 532, 533 535, 539 541, 545 548, 551 553, 557 558 SPI 3102.3.4 Operate with, evaluate, and simplify rational expressions including determining restrictions on the domain of the variables. SPI 3102.3.5 Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value. SE/TE: 664 667, 671 674, 685 688, 700 702 SE/TE: 101 103, 105 106, 109, 110 113, 126 127, 164, 174 176, 178 180, 184 187, 191 194, 198, 199 202, 206 207, 216 219, 222 224, 226 228, 238 240 5

SPI 3102.3.6 Interpret various relations in multiple representations. SPI 3102.3.7 Determine domain and range of a relation, determine whether a relation is a function and/or evaluate a function at a specified rational value. SPI 3102.3.8 Determine the equation of a line and/or graph a linear equation. SPI 3102.3.9 Solve systems of linear equation/inequalities in two variables. SPI 3102.3.10 Find the solution of a quadratic equation and/or zeros of a quadratic function. SPI 3102.3.11 Analyze nonlinear graphs including quadratic and exponential functions that model a contextual situation. Standard 4 Geometry & Measurement Grade Level Expectations: CLE 3102.4.1 Use algebraic reasoning in applications involving geometric formulas and contextual problems. CLE 3102.4.2 Apply appropriate units of measure and convert measures in problem solving situations. SE/TE: 248 251, 303 304, 321 324, 328, 329 331, 334 335, 338 339, 341 342, 346, 349 353, 357 360, 373 374 SE/TE: 286 289, 291 292, 303, 306 Checks for Understanding (Formative/Summative Assessment) SE/TE: 322 324, 328, 329 331, 334 335, 338 339, 341 342, 346, 349 353, 357 360, 373 374 SE/TE: 382 385, 388, 389, 390 393, 396 397, 399 402, 405 406, 407 409, 412 413, 425 427, 431, 433 434 SE/TE: 580 582, 586 588, 592, 595 598, 601 604, 616 617 SE/TE: 262 264, 303, 305, 475, 483, 485, 488, 566 569, 573 576, 579, 608 610, 614, 616, 618 SE/TE: 17, 118 119, 123 124, 127, 143 146, 165, 200, 203, 275, 282, 404, 465, 520, 527, 535, 540, 551, 626 628, 631, 634, 650, 651, 655, 656, 667, 680, 683 SE/TE: 17, 123 124, 130 133, 159, 161, 165, 195, 222 223, 227, 457, 465 3102.4.1 Using algebraic expressions solve for measures in geometric figures as well as for perimeter, area, and volume. 3102.4.2 Use the Pythagorean Theorem to find the missing measure in a right triangle including those from contextual situations. 3102.4.3 Understand horizontal/vertical distance in a coordinate system as absolute value of the difference between coordinates; develop the distance formula for a coordinate plane using the Pythagorean Theorem. 3102.4.4 Develop the midpoint formula for segments on a number line or in the coordinate plane. 3102.4.5 Use dimensional analysis to convert rates and measurements both within a system and between systems and check the appropriateness of the solution. State Performance Indicators: SPI 3102.4.1 Develop and apply strategies to estimate the area of any shape on a plane grid. SPI 3102.4.2 Solve contextual problems using the Pythagorean Theorem. SPI 3102.4.3 Solve problems involving the distance between points or midpoint of a segment. SE/TE: 626 627, 634 SE/TE: 631 SPI 3102.4.4 Convert rates and measurements. SE/TE: 130 133, 165 6

Standard 5 Data Analysis, Statistics, & Probability Grade Level Expectations: CLE 3102.5.1 Describe and interpret quantitative information. CLE 3102.5.2 Use statistical thinking to draw conclusions and make predictions. CLE 3102.5.3 Understand basic counting procedures and concepts of probability. Checks for Understanding (Formative/Summative Assessment): 3102.5.1 Identify patterns or trends in data. SE/TE: 363 367, 371, 373 374, 716 719, 730 733, 744, 746 747 SE/TE: 363 367, 371, 373 374, 722 725, 729, 760 761, 773 SE/TE: 750 753, 757 761, 764, 765 769, 773 775 3102.5.2 Develop a meaning for and identify outliers in a data set and verify. 3102.5.3 When a set of data is changed, identify effects on measures of central tendency, range, and inter-quartile range. 3102.5.4 Explore quartiles, deciles, and percentiles of a distribution. 3102.5.5 Construct and interpret various forms of data representations, (including line graphs, bar graphs, circle graphs, histograms, scatter-plots, box-and-whiskers, stem-and-leaf, and frequency tables). 3102.5.6 Draw qualitative graphs of functions and describe a general trend or shape. 3102.5.7 Compare two data sets using graphs and descriptive statistics. 3102.5.8 Examine real-world graphical relationship (including scatter-plots) to determine type of relationship (linear or nonlinear) and any association (positive, negative or none) between the variables of the data set. 3102.5.9 Determine an equation for a line that fits real-world linear data; interpret the meaning of the slope and y-intercept in context of the data. 3102.5.10 Using technology with a set of contextual linear data to examine the line of best fit; determine and interpret the correlation coefficient. 3102.5.11 Use an equation that fits data to make a prediction. 3102.5.12 Use techniques (Venn Diagrams, tree diagrams, or counting procedures) to identify the possible outcomes of an experiment or sample space and compute the probability of an event. 3102.5.13 Determine the complement of an event and the probability of that complement. 3102.5.14 Determine if two events are independent or dependent. 3102.5.15 Explore joint and conditional probability. 3102.5.16 Identify situations for which the Law of Large Numbers applies. 3102.5.17 Perform simulations to estimate probabilities. 3102.5.18 Make informed decisions about practical situations using probability concepts. State Performance Indicators: SPI 3102.5.1 Interpret displays of data to answer questions about the data set(s) (e.g., identify pattern, trends, and/or outliers in a data set). SPI 3102.5.2 Identify the effect on mean, median, mode, and range when values in the data set are changed. SE/TE: 363 366, 371, 373 374, 717 718, 731 732, 744 SE/TE: 723 725 7

SPI 3102.5.3 Using a scatter-plot, determine if a linear relationship exists and describe the association between variables. SPI 3102.5.4 Generate the equation of a line that fits linear data and use it to make a prediction. SPI 3102.5.5 Determine theoretical and/or experimental probability of an event and/or its complement including using relative frequency. SE/TE: 363 364, 371, 374, 377 SE/TE: 364 366, 371, 373 374 SE/TE: 757 761, 764, 765 769, 773, 775 8

Pearson Prentice Hall Algebra 1 Foundations Narrative Brief I. Orientation and Clarification Prentice Hall Algebra 1 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 1 State Performance Indicators. This textbook is intended for use in Algebra 1. 2. Program Description Prentice Hall Algebra 1 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 1 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 1 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

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 1 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 1 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.