Prentice Hall Mathematics, Algebra 1 Program Organization Prentice Hall Mathematics supports student comprehension of the mathematics by providing well organized sequence of the content, structure of the daily lesson, systematic direct instruction, and teacher support provided for each lesson. Content Sequence - Prentice Hall is organized with the goal of addressing all of the mathematics mtandards through direct and effective instruction, building concept upon concept, skill upon skill in an order that is pedagogically sound. The Table of Contents shows the smooth flow of the book, with prerequisite skills and concepts presented before the more complex topics that depend on them. Starting the Chapter - Every chapter begins by reviewing the previous standards that have been learned and overviewing the standards that will be covered in the chapter. New Vocabulary is identified to prepare students for the chapter. Finally, Check Your Readiness questions assess student understanding of necessary prerequisite skills and identifies which lesson they can go to for any necessary remediation. Lesson Organization - The daily lesson is structured and presented in a consistent format that enables teachers to effectively present the content and monitor student understanding. The Instant Check System is a system of assessments that helps ensure standards mastery. It is comprised of assessments to use before, during, and after instruction so teachers can easily and effectively monitor student understanding. o Each lesson begins with Check Skills You ll Need to ensure students have the necessary prerequisite skills for success in the lesson. A Go for Help reference directs them to a previous lesson if remediation is necessary. o Check Skills questions after every single example provide a way to check student o understanding during instruction. Finally, Checkpoint Quizzes occur after instruction to continually monitor student progress. Daily Standards Practice is provided with a comprehensive exercise set following every lesson. Each exercise set is leveled to ensure a variety of practice. Test Prep and Mixed Review ensures students also have a daily opportunity to practice concepts and skills previously mastered. Concluding the Chapter - The following features conclude each chapter, providing opportunities for students to review all standards and demonstrate mastery. This part of the systematic instruction provides regular opportunities for review and practice and ensures focus on and mastery of the Standards. Chapter Review The Chapter Review serves as a chapter study guide for students by reviewing the key concepts covered in each lesson and providing an opportunity to practice. In addition, key vocabulary is reviewed. Chapter Test Students demonstrate their understanding of the entire chapter by completing this practice chapter test. Standardized Test Prep Cumulative Practice This provides a regular opportunity for students to practice and demonstrate mastery of all the standards that have been covered. If remediation is necessary, students are directed to a previous lesson where each concept was taught. 1
Assessment Prentice Hall Mathematics provides teachers with the assessment tools needed to inform instruction and document student progress. The Progress Monitoring Assessments contains all the program assessments needed to evaluate student understanding, monitor student progress, and inform future instruction. The following assessments are included: Formative Assessments o Screening Test check student readiness at the beginning of the school year o Benchmark Tests monitor student progress o Test-Taking Strategy Practice Masters provide opportunities to improve problemsolving skills Summative Assessments All the summative assessments are provided in two forms onlevel and basic versions. Both forms fully assess student progress on the course content, but the basic versions have been modified for special needs students. o Quarter Tests on-level and basic versions o Mid-Course Tests on-level and basic versions o Final Tests on-level and basic versions The Test Preparation Workbook contains review lessons and multiple-choice practice tests. Technology, such as the ExamView CD-ROM, allows teachers to create customized assessment, with all test items correlated to state standards. Universal Access Prentice Hall Mathematics provides better solutions for meeting the needs of every student in the classroom. Universal Access can be fostered by modifying instruction to address individual needs, and provided adapted resources when appropriate. Prentice Hall uses a systematic method for labeling and identifying resources and instructional support. This consistency helps teachers easily identify and choose the appropriate support for specific populations of students. The Teacher s Edition provides universal access strategies in detailed daily lesson plans, and daily teaching notes to help differentiate the lesson for all learners, including special needs, below level, advanced and English Language Learners. Chapter-level support pages provide teachers with an easy-to-read overview of the chapter resources available and suggest ways in the instructional lesson to use the resources. Key ancillaries to support universal access include the All-in-One Teaching Resources and the All-in-One Student Workbooks. The Teaching Resources include leveled practice for every lesson and daily activity labs. The All-in-One Student Workbook, available as both on-level and adapted for special needs, includes daily notetaking, daily practice, daily guided problem solving, and vocabulary support. Instructional Planning and Support Prentice Hall Mathematics is designed to provide teachers the tools needed to effectively and easily implement the program in the classroom. A Road Map for Planning the Year - A Leveled Pacing Chart is provided in the Teacher s Edition that lays out a plan for teaching all the mathematics content standards. It suggests time to spend on each Chapter, and offers support for adjusting the instruction to meeting the pacing needs of all students. Planning a Chapter - The Teacher s Edition begins each chapter with a series of planning pages. These pages provide an overview of the chapter and make it easy to determine how to individualize lessons for specific students. Planning Daily Instruction - Teachers can use a variety of program materials to organize their teaching. The primary planning tools are the Teacher s Edition and the Teacher Center Planning CD- 2
ROM. The Teacher s Edition includes step-by-step, daily support for directing instruction. Support is organized systematically around a 4-step teaching plan of Plan, Teach, Practice, and Assess/Reteach. Instructional Tools to Plan, Teach, and Assess: Core Components o Student Edition Thorough coverage of the standards, with built-in assessments and ongoing student support o Teacher s Edition Provides comprehensive support for planning, teaching, and providing Universal Access Teacher Support o All-in-One Teaching Resources - All teaching resources are in one convenient place. Includes leveled practice, chapter projects, alternative assessments, cumulative reviews, guided problem solving masters, and vocabulary support. o Progress Monitoring Assessments Provides support for formative and summative assessment, with comprehensive resources for monitoring progress on the standards. o Test Preparation Workbook Provides instruction and practice on specific test taking strategies. o Teacher Center CD-ROM The one-stop solution for planning, teaching, and assessing. The following resources are part of the Teacher Center: Planning CD-ROM Powerful lesson planning software, Teacher s Edition, and Teaching Resources. Presentation CD-ROM Complete support for digital presentations of lessons including videos, activities, stepped-out examples, quick check assessments, and online active math MindPoint Quiz Show Animated game show review for chapter level mathematics o ExamView Test Generator CD-ROM Allows teachers to quickly and easily generate tests correlated to the standards. Student Support o All-in-One Student Workbook Structured daily notetaking pages for every lesson Practice for every lesson Guided problem solving pages for every lesson with scaffolded questions Vocabulary and study skills focusing on key mathematical vocabulary o All-in-One Student Workbook, Adapted Version Adapted for special needs students. Includes all the resources in the regular All-in-One Student Workbooks, in an adapted form. o Student Center Online Complete interactive textbook with videos built-in at pointof-use, digital activities, stepped-out examples, vocabulary support and more. Also includes the All-in-One Student Workbooks. o Companion Websites - Grants instant access to a wealth of resources to support learning including vocabulary quizzes, lesson quizzes, data updates, tutorials, chapter tests, and homework video tutors. Transparency Package o Classroom Aid Transparencies - Full-color multi-use transparencies such as graphs, fraction strips, and manipulatives o Additional Examples on Transparencies o Daily Skills Check and Lesson Quiz Transparencies o Standards Review Transparencies o Student Edition Answers on Transparencies 3
Algebra 1 A1.1. Core Content: Solving problems (Algebra) Students learn to solve many new types of problems in Algebra 1, and this first core content area highlights the types of problems students will be able to solve after they master the concepts and skills in this course. Students are introduced to several types of functions, including exponential and functions defined piecewise, and they spend considerable time with linear and quadratic functions. Each type of function included in Algebra 1 provides students a tool to solve yet another class of problems. They learn that specific functions model situations described in word problems, and so functions are used to solve various types of problems. The ability to determine functions and write equations that represent problems is an important mathematical skill in itself, Many problems that initially appear to be very different from each other can actually be represented by identical equations. Students encounter this important and unifying principle of algebra that the same algebraic techniques can be applied to a wide variety of different situations. A1.1.A Select and justify functions and equations to model and solve problems. A1.1.B Solve problems that can be represented by linear functions, equations, and inequalities. A1.1.C Solve problems that can be represented by a system of two linear equations or inequalities. A1.1.D Solve problems that can be represented by quadratic functions and equations. A1.1.E Solve problems that can be represented by exponential functions and equations. SE/TE: 270-274, 324-329, 468-474, 597-604, 466-467 SE/TE: 158-165, 270-276, 277-283, 219-224, 227-231 SE/TE: 396-401, 411-417, 149-154, 374-379, 382-385, 387-393 SE/TE: 557-562, 565-569, 577, 597-604, 585-590, 592-596 SE/TE: 468-474. 475-482, 597-604, 460-465, 466-467 A1.2. Core Content: Numbers, expressions, and operations (Numbers, Operations, Algebra) Students see the number system extended to the real numbers represented by the number line. They work with integer exponents, scientific notation, and radicals, and use variables and expressions to solve problems from purely mathematical as well as applied contexts. They build on their understanding of computation using arithmetic operations and properties and expand this understanding to include the symbolic language of algebra. Students demonstrate this ability to write and manipulate a wide variety of algebraic expressions throughout high school mathematics as they apply algebraic procedures to solve problems. A1.2.A Know the relationship between real SE/TE: 17-22, 176-179, 436-440 numbers and the number line, and compare and order real numbers with and without the number line. A1.2.B Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. A1.2.C Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions. SE/TE: 4-8, 27-31, 158-165, 12-13, 69-75, 140-141, 433, 470-472 SE/TE: 176-179, 4430-435, 441-451, 453-459, 616-621 4
A1.2.D Determine whether approximations or exact values of real numbers are appropriate, depending on the context, and justify the selection. A1.2.E Use algebraic properties to factor and combine like terms in polynomials. A1.2.F Add, subtract, multiply, and divide polynomials. SE/TE: 176-179 SE/TE: 518, 519-523, 524-527, 528-533, 534-539 SE/TE: 494-499, 500-504, 505-509, 512-517, 677-680, 682-685 A1.3. Core Content: Characteristics and behaviors of functions (Algebra) Students formalize and deepen their understanding of functions, the defining characteristics and uses of functions, and the mathematical language used to describe functions. They learn that functions are often specified by an equation of the form y = f(x), where any allowable x-value yields a unique y-value. While Algebra 1 has a particular focus on linear and quadratic equations and systems of equations, students also learn about exponential functions and those that can be defined piecewise, particularly step functions and functions that contain the absolute value of an expression. Students learn about the representations and basic transformations of these functions and the practical and mathematical limitations that must be considered when working with functions and when using functions to model situations. A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent dependent variables. A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. A1.3.C Evaluate f(x) at a (i.e., f(a)) and solve for x in the equation f(x) = b. SE/TE: 257-261, 358-363, 571-575, 592-595, 638-643, 26-31 SE/TE: 284-291, 336-341, 468-472, 557-563, 638-643, 27-37, 125, 270-275, 263-269, 605 SE/TE: 257-261, 468-472, 673 A1.4. Core Content: Linear functions, equations, and inequalities (Algebra) Students understand that linear functions can be used to model situations involving a constant rate of change. They build on the work done in middle school to solve sets of linear equations and inequalities in two variables, learning to interpret the intersection of the lines as the solution. While the focus is on solving equations, students also learn graphical and numerical methods for approximating solutions to equations. They use linear functions to analyze relationships, represent and model problems, and answer questions. These algebraic skills are applied in other Core Content areas across high school courses. A1.4.A Write and solve linear equations and inequalities in one variable. A1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. A1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. SE/TE: 134-138, 212-217, 219-225, 227-223, 235-240, 126-131 SE/TE: 308-315, 317-323, 324-329, 330-334, 336-341 SE/TE: 308-315, 317-323, 324-329, 343-348, 357 5
A1.4.D Write and solve systems of two linear equations and inequalities in two variables. A1.4.E Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent. A1.5. Core Content: Quadratic functions and equations (Algebra) SE/TE: 374-380, 381-386, 387-393, 396-401, 411-419 SE/TE: 358, 359-363, 367, 667 Students study quadratic functions and their graphs, and solve quadratic equations with real roots in Algebra 1. They use quadratic functions to represent and model problems and answer questions in situations that are modeled by these functions. Students solve quadratic equations by factoring and computing with polynomials. The important mathematical technique of completing the square is developed enough so that the quadratic formula can be derived. A1.5.A Represent a quadratic function with a SE/TE: 557-564, 565-569, 577, 592-595 symbolic expression, as a graph, in a table, and with a description, and make connections among the representations. A1.5.B Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the x-intercepts as solutions to a quadratic equation. A1.5.C Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers. A1.5.D Solve quadratic equations that have real roots by completing the square and by using the quadratic formula. SE/TE: 550-556, 557-564, 565-569, 571 SE/TE: 572-575, 577, 608, 742 SE/TE: 579-584, 585-591, 592-595 A1.6. Core Content: Data and distributions (Data/Statistics/Probability) Students select mathematical models for data sets and use those models to represent, describe, and compare data sets. They analyze data to determine the relationship between two variables and make and defend appropriate predictions, conjectures, and generalizations. Students understand limitations of conclusions based on results of a study or experiment and recognize common misconceptions and misrepresentations in interpreting conclusions. A1.6.A Use and evaluate the accuracy of summary statistics to describe and compare data sets. A1.6.B Make valid inferences and draw conclusions based on data. A1.6.C Describe how linear transformations affect the center and spread of univariate data. A1.6.D Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions. SE/TE: 38-39, 40-45, 52-53, 546-547 Data Analysis and Probability Workbook: 8, 23 SE/TE: 38-39, 52-53, 304-305, 426-427 Data Analysis and Probability Workbook: 21 SE/TE: 350-356, 547 6
A1.6.E Describe the correlation of data in scatterplots in terms of strong or weak and positive or negative. A1.7. Additional Key Content (Algebra) SE/TE: 34-37 Data Analysis and Probability Workbook: 26, 27, 30 Students develop a basic understanding of arithmetic and geometric sequences and of exponential functions, including their graphs and other representations. They use exponential functions to analyze relationships, represent and model problems, and answer questions in situations that are modeled by these nonlinear functions. Students learn graphical and numerical methods for approximating solutions to exponential equations. Students interpret the meaning of problem solutions and explain limitations related to solutions. A1.7.A Sketch the graph for an exponential SE/TE: 466-467, 468-473, 474, 481, 482 function of the form y = abn where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions. A1.7.B Find and approximate solutions to exponential equations. A1.7.C Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence. A1.7.D Solve an equation involving several variables by expressing one variable in terms of the others. SE/TE: 466-467, 468-473, 474, 475-482 SE/TE: 292-297, 460-465 A1.8. Core Processes: Reasoning, problem solving, and communication SE/TE: 140-141; This concept is applied on: 142-148 Students formalize the development of reasoning in Algebra 1 as they use algebra and the properties of number systems to develop valid mathematical arguments, make and prove conjectures, and find counterexamples to refute false statements, using correct mathematical language, terms, and symbols in all situations. They extend the problem-solving practices developed in earlier grades and apply them to more challenging problems, including problems related to mathematical and applied situations. Students formalize a coherent problem-solving process in which they analyze the situation to determine the question(s) to be answered, synthesize given information, and identify implicit and explicit assumptions that have been made. They examine their solution(s) to determine reasonableness, accuracy, and meaning in the context of the original problem. The mathematical thinking, reasoning, and problem-solving processes students learn in high school mathematics can be used throughout their lives as they deal with a world in which an increasing amount of information is presented in quantitative ways and more and more occupations and fields of study rely on mathematics. A1.8.A Analyze a problem situation and represent it mathematically. follow: 8 (#43-44), 148 (#64), 417 (#38-41) 7
A1.8.B Select and apply strategies to solve problems. A1.8.C Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem. A1.8.D Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems. A1.8.E Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics. A1.8.F Summarize mathematical ideas with precision and efficiency for a given audience and purpose. A1.8.G Synthesize information to draw conclusions, and evaluate the arguments and conclusions of others. A1.8.H Use inductive reasoning about algebra and the properties of numbers to make conjectures, and use deductive reasoning to prove or disprove conjectures. follow: 131 (#67), 147 (#56), 364 follow: 261 (#41), 315 (#74), 321 #(57) follow: 267 (#39, 40), 322 (#65), 587 follow: 597-604, 231 (#46) follow: 130 (#53), 147 (#52), 502 (#41) follow: 354, 130 (#51), 291, 356 (#23) follow: 292-296, 460-465, 13 (#49), 261 (#47), 267 (#41) 8