1. Mathematics Content/Alignment with the Standards Correlation to California Algebra Readiness Standards

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1 PROGRAM DESCRIPTION The goal of Prentice Hall Connecting to Algebra is to fully prepare students for success in Algebra 1 by thoroughly covering the Algebra Readiness standards outlined by the California Framework and providing complete support for the necessary foundational standards. Connecting to Algebra provides opportunities to build conceptual understanding and develop proficiency with mathematical skills. 1. Mathematics Content/Alignment with the s Prentice Hall Connecting to Algebra is aligned with and addresses 100% of the California Mathematics s outlined for Algebra Readiness. To help acquaint teachers with the program and the way it assures complete and through mastery of the s, the following features are in included in the Implementation Guide: o Correlation to California Algebra Readiness s - This correlation chart shows the complete list of the California Algebra Readiness s and the Foundational Skills and Concepts, with clear identification of the lesson in which the standard is addressed. o Pacing and Differentiated Instruction Guide for California - This chart is provided as a guide to help teachers customize instruction and provide universal access. It lists each Unit of Connecting to Algebra, with a correlation to the standard covered. It also suggests pacing options for core and advanced instruction. 2. Program Organization The Connecting to Algebra Student Edition includes 7 primary Units of Instruction. Each Unit is organized around an important mathematical idea. The format of the student book promotes an in-depth understanding of important mathematical concepts and proficiency in related procedures and skills. The format of the Teacher s Guides supports systematic instruction: Unit Opener - Each Unit opens with a set of three focusing questions that reflect the major standards-based mathematical goals of the units. The Unit Opener also provides a set of goals, or Mathematical Highlights, that preview the important ideas of the unit. The highlights help students track their progress through the unit. Investigations The standards-aligned Investigations form the core of each Connecting to Algebra unit. It is through the Investigations that the students develop conceptual understanding, reasoning, and procedural skill. Each unit includes three to five Investigations with the following key elements: o Problem An Investigation includes two to five carefully sequenced problems. Each problem is launched by the teacher through systematic

2 direct instruction; then the students explore the problem individually, in groups, or as a whole class. Teachers direct a systematic summary at the end of each problem, and students are able to explicitly describe the mathematics of the problem. o Getting Ready This feature occurs occasionally before a problem. It is intended to be used as a part of the launch for the problem. It reviews or introduces the mathematical ideas needed in the problem. o Applications Connections Extensions (ACE) Exercises The problems in each Investigation are followed by a set of homework exercises to be used at the end of each problem. Applications Exercises help students solidify their understanding by providing practice with strategies that were in the Investigation. Connections Exercises provide continued review of previously learned concepts and skills and connects to prior knowledge. Extension Exercises provide a challenge for students to extend their learning. o Mathematical Reflections At the end of each Investigation, students are asked to articulate what they have learned. A set of questions helps students summarize important concepts, strategies, and strategies. 3. Assessment Connecting to Algebra provides teachers with the assessment tools needed to inform instruction and document student progress. Formative Assessments - Checkpoints Connecting to Algebra includes assessment tools such as ACE assignments, Mathematical Reflections, and Unit Reviews give teachers and students an opportunity to check student understanding at key points in the unit. Checkpoints help students solidify their understanding, determine the areas that need further attention, and help teachers make instructional decisions. Summative Assessments The Assessment Resources provide support for assessing student progress. It includes quizzes, multiple-choice items, self-assessments, and unit tests. These assessments provide teachers with a broad view of student knowledge both during a unit and at the end of a unit. ExamView Test Generator Technology, such as the ExamView CD-ROM, allows teachers to create customized assessment, with all test items correlated to the California Algebra Readiness or Foundational s California s Review and Preparation Workbook This resource contains review lessons and multiple-choice practice items for each of the California Math Content s, providing regular assessment and monitoring of standards mastery.

3 4. Universal Access Connecting to Algebra provides complete support for meeting the needs of every student in the classroom. The Connecting to Algebra Implementation Guide provides comprehensive and detailed professional development for meeting the needs of English Learners, Special Needs Students, and Gifted Students. The Connecting to Algebra Special Needs Handbook provides suggestions for adapting instruction and modifying instruction. It also includes ready-to-use blackline masters for supporting Special Needs students. Daily support is provided in each Connecting to Algebra Teacher s Guide for adapting instruction and modifying homework assignments. 5. Instructional Planning and Support Connecting to Algebra provides complete support for teachers to plan effective instruction. The principal teacher planning tool is the Teacher s Guide for each unit. The features and organization of the Teacher s Guide are described below. Unit Introduction Teachers can use the material in the Unit Introduction to prepare for teaching the unit. The following features are included in this section: o Unit Introduction - Goals of the Unit, Developing Students Mathematical Habits o The Mathematics in the Unit Overview, Summary of the Investigations, and Mathematical Background (A detailed description designed to assist teachers in understanding the content) o Planning for the Unit - Pacing Suggestions and Materials, Vocabulary o Program Resources o Assessment Summary o Launching the Unit Using the Unit Opener, Using the Mathematical Highlights, Introducing the Unit Project Teaching Notes Detailed teaching notes included for every problem provide support for direct, standards-based instruction. Included are: o Specific Mathematical and Problem-Solving Goals o Detailed Teaching Notes Includes problem-by-problem discussions with examples of the instructional role of the teacher, as well as sample student responses to questions. Provides detailed support for instruction, with a systematic approach for teachers. o Check for Understanding The summary section ends with questions for the teacher to use to check students understanding o Lesson At a Glance A one-page lesson guide for each problem is provided.

4 In addition to the Teacher s Guide for each unit, there are several resources that are designed to assist teachers. o Teaching Transparencies support problems from the student book. o Parent Materials for Connecting to Algebra include a parent letter for each unit with the goals of the unit and examples of worked out problems, as well as a website for parents to help with homework for each unit o Special Needs Handbook for teachers includes suggestions for adapting instruction, exercises, and assessments o Assessment Resources include blackline masters quizzes, tests, multiple-choice items, and self-assessments o Additional Practice and Skills Workbook for each grade level provides practice exercises for each investigation as well as additional skills practice to reinforce student learning o TeacherExpress CD-ROM includes lesson planning software, the Teacher s Guide pages and all the teaching resources o ExamView Test Generator includes all the items from the Assessment Resources and the Additional Practice and Skills Workbook in both English and Spanish. Items can be edited electronically and saved. Many items are dynamic and can be used to create multiple versions of practice sheets. o Companion Website grants instant access to a wealth of resources to support learning including online homework help, multiple-choice practice, Active Math Online, Vocabulary Quizzes, and California s Tutorials.

5 Program Title: California Grade Grade Level(s): Grade 6 STANDARDS MAP for a Basic Grade-Level Program Grade 6 Mathematics Language NUMBER SENSE 1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages: 1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line. 1.2 Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations (a/b, a to b, a:b). 1.3 Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/ 21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. 1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips. Publisher SE/TE: 78-81, 89-91, 93-96, 134, , , , , SE/TE: 78-81, 86, 89-91, SE/TE: , , SE/TE: , 207, , , , , SE/TE: , , , , 263, SE/TE: 242, 512 SE/TE: 85, 92, 493, 494, 512 SE/TE: , 201, 498, 499 SE/TE: , SE/TE: 262, 309, , , Students calculate and solve problems SE/TE: 30-34, SE/TE: 17, California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 1

6 Program Title: California Grade Grade Level(s): Grade 6 Language involving addition, subtraction, multiplication, and division: 2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation. 2.2 Explain the meaning of multiplication and division of positive fractions and perform the calculations (e.g., 5/8 15/16 = 5/8 x 16/15 = 2/3). 2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. 2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction). ALGEBRA AND FUNCTIONS 1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results: 1.1 Write and solve one-step linear equations in one variable. Publisher 36-39, , , , , 134 SE/TE: , , , 128, SE/TE: 121, , 128, SE/TE: 30-34, 36-39, 40-43, 152, 153 SE/TE: 66, 68-70, 72-73, 75-76, , SE/TE: , , , , , , SE/TE: , , , , , 121, 128, , 524 SE/TE: 111, , , 128, SE/TE: 494, 495 SE/TE: 35, 375, , , 494, 495 SE/TE: 67, 71, 93, 494 SE/TE: , 381, , SE/TE: 164, 175, , 182, California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 2

7 Program Title: California Grade Grade Level(s): Grade 6 Language 1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables. 1.3 Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process. 1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator. 2.0 Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions: 2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches). 2.2 Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity. 2.3 Solve problems involving rates, average speed, distance, and time. 3.0 Students investigate geometric patterns and describe them algebraically: 3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = 1/2bh, C = (pi)d the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). 3.2 Express in symbolic form simple relationships arising from geometry. MEASUREMENT AND GEOMETRY 1.0 Students deepen their understanding of the measurement of plane and solid shapes and Publisher SE/TE: 134, 150, SE/TE: 9-10, 13, 15, 40-43, SE/TE: 40-43, 61-63, 64 SE/TE: 206, SE/TE: 21-24, , 140, 200 SE/TE: , 201, 206 SE/TE: 37-39, 171, 206, 207, 381 SE/TE: 373, SE/TE: , , , SE/TE: , SE/TE: , , SE/TE: 134, 381, 496, 497 SE/TE: 44 SE/TE: SE/TE: , 368, 374 SE/TE: , SE/TE: 207, SE/TE: 18-19, 173, 175, 368, SE/TE: 328, 333, 377 SE/TE: 336, 350, , SE/TE: , SE/TE: 336, , 502- California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 3

8 Program Title: California Grade Grade Level(s): Grade 6 Language use this understanding to solve problems: , , , Understand the concept of a constant such as (pi); know the formulas for the circumference and area of a circle. 1.2 Know common estimates of π (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements. 1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base x height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid. 2.0 Students identify and describe the properties of two-dimensional figures: 2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms. 2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. 2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle). Publisher SE/TE: 337, , 353 SE/TE: , 353 SE/TE: SE/TE: , , , , , SE/TE: 285, 287, 288 SE/TE: , , SE/TE: 294, , SE/TE: 337 SE/TE: 350, 359, SE/TE: , 504, 505 SE/TE: 304, 315, 502, 503 SE/TE: SE/TE: 294, 304, 502, 503 SE/TE: 315, 391 STATISTICS, DATA ANALYSIS, AND PROBABILITY 1.0 Students compute and analyze statistical SE/TE: 45-49, SE/TE: 51, California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 4

9 Program Title: California Grade Grade Level(s): Grade 6 Publisher Language measurements for data sets: 50, , Compute the range, mean, median, and mode of data sets. 1.2 Understand how additional data added to data sets may affect these computations. 1.3 Understand how the inclusion or exclusion of outliers affects these computations. 1.4 Know why a specific measure of central tendency (mean, median) provides the most useful information in a given context. 2.0 Students use data samples of a population and describe the characteristics and limitations of the samples: 2.1 Compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use a sample. 2.2 Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population. 2.3 Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why the way in which the results were displayed might have influenced the conclusions reached. 2.4 Identify data that represent sampling errors and explain why the sample (and the display) might be biased. SE/TE: 45-49, 432 SE/TE: 50, 435 SE/TE: 45, 47, 50 SE/TE: 50, , 433, 435 SE/TE: SE/TE: 418, SE/TE: SE/TE: , 415, , 423, , SE/TE: SE/TE: 50, 51, SE/TE: 434 SE/TE: 432 SE/TE: 432 SE/TE: , 434, SE/TE: 508, 509 SE/TE: 309, , 410, 437, 508, 509 SE/TE: California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 5

10 Program Title: California Grade Grade Level(s): Grade 6 Language 2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims. 3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events: 3.1 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome. 3.2 Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven). 3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1- P is the probability of an event not occurring. 3.4 Understand that the probability of either of two disjoint events occurring is the sum of the two individual probabilities and that the probability of one event following another, in independent trials, is the product of the two probabilities. 3.5 Understand the difference between independent and dependent events. Publisher SE/TE: , SE/TE: , , , SE/TE: , 465 SE/TE: , 461, SE/TE: , , , SE/TE: 463, , SE/TE: 462, SE/TE: 427, 431, 437 SE/TE: 451, , SE/TE: 462, 467, 475, 510, 511 SE/TE: 210, 475 SE/TE: , 462, SE/TE: 462, 510, 511 SE/TE: 510, 511 MATHEMATICAL REASONING 1.0 Students make decisions about how to approach problems: (Grade 6, AF 2.1) SE/TE: 22-23; (Grade 6, NS 2.2) SE/TE: 131; SE: CA40- CA49 California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 6

11 Program Title: California Grade Grade Level(s): Grade 6 Language 1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns. 1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed. Publisher (Grade 6, MG 2.2) SE/TE: 286; (Grade 6, SDAP 3.4) SE/TE: 465 (Grade 6, NS 2.0) SE/TE: 17; (Grade 6, NS 2.3) SE/TE: 35; (Grade 6, AF 2.2) SE/TE: 201; (Grade 6, MG 2.2) SE/TE: 286; (Grade 6, AF 3.0) SE/TE: ; (Grade 6, SDAP 2.3) SE/TE: 415; (Grade 6, SDAP 3.3) SE/TE: (Grade 6, AF 2.0) SE/TE: 215; (Grade 6, MG 2.3) SE/TE: 289; (Grade 6, MG 1.1) SE/TE: 337; (Grade 6, SE: CA40- CA49 (Grade 6, NS 2.4) SE/TE: 65; (Grade 6, NS 2.4) SE/TE: 71 California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 7

12 Program Title: California Grade Grade Level(s): Grade 6 Language 1.3 Determine when and how to break a problem into simpler parts. 2.0 Students use strategies, skills, and concepts in finding solutions: Publisher MG 3.0) SE/TE: 373 (Grade 6, NS 1.4) SE/TE: 244; (Grade 6, NS 1.4) SE/TE: 263; (Grade 6, NS 2.7) SE/TE: 41; (Grade 6, NS 2.7) SE/TE: ; (Grade 6, MG 2.2) SE/TE: 301; (Grade 6, AF 1.3) SE/TE: 336; (Grade 6, SDAP 3.4) SE/TE: 465 (Grade 6, AF 1.3) SE/TE: 41; (Grade 6, NS 2.2) SE/TE: ; (Grade 6, NS 1.3) SE/TE: 217; (Grade 6, NS 1.4) SE/TE: ; (Grade 6, MG 2.2) SE/TE: SE: CA47 SE: CA40- CA49 California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 8

13 Program Title: California Grade Grade Level(s): Grade 6 Language 2.1 Use estimation to verify the reasonableness of calculated results. 2.2 Apply strategies and results from simpler problems to more complex problems. 2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques. Publisher ; (Grade 6, AF 1.0) SE/TE: 386; (Grade 6, SDAP 3.4) SE/TE: (Grade 6, AF 2.3) SE/TE: 18; (Grade 6, NS 2.1) SE/TE: ; (Grade 6, AF 1.4) SE/TE: 180; (Grade 6, NS 2.2) SE/TE: 123; (Grade 6, NS 1.0) SE/TE: 239 (Grade 6, AF 152; (Grade 6, NS 1.4) SE/TE: 262 (Grade 6, AF 2.0) SE/TE: 206; (Grade 6, AF 2.0) SE/TE: 370- (Grade 6, NS 2.1) SE/TE: 112; (Grade 6, MG 1.3) SE/TE: (Grade 6, NS 2.2) SE/TE: ; (Grade 6, AF 3.1) SE/TE: 336; (Grade 6, SDAP 3.2) SE/TE: 461 (Grade 6, NS 1.3) SE/TE: 214; (Grade 6, AF 1.0) SE/TE: 380 California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 9

14 Program Title: California Grade Grade Level(s): Grade 6 Publisher Language Use a variety of methods, such as words, (Grade 6, AF SE: CA40- numbers, symbols, charts, graphs, tables, 2.3) SE/TE: CA49 diagrams, and models, to explain mathematical 18; (Grade 6, reasoning. NS 2.1) SE/TE: 111; (Grade 6, NS 2.2) SE/TE: 121; (Grade 6, AF 1.1) SE/TE: ; (Grade 6, NS 1.4) SE/TE: 313; (Grade 6, AF 1.1) SE/TE: Express the solution clearly and logically by (Grade 6, NS SE: CA40- using the appropriate mathematical notation and 1.3) SE/TE: CA49 terms and clear language; support solutions with ; evidence in both verbal and symbolic work. (Grade 6, MG 2.2) SE/TE: ; (Grade 6, MG 1.0) SE/TE: 349; (Grade 6, SDAP 1.4) SE/TE: ; (Grade 6, SDAP 3.2) SE/TE: Indicate the relative advantages of exact and (Grade 6, AF (Grade 6, MG California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 10

15 Program Title: California Grade Grade Level(s): Grade 6 Language approximate solutions to problems and give answers to a specified degree of accuracy. 2.7 Make precise calculations and check the validity of the results from the context of the problem. 3.0 Students move beyond a particular problem by generalizing to other situations: Publisher 1.1) SE/TE: 164; (Grade 6, MG 1.2) SE/TE: 339; (Grade 6, MG ; (Grade 6, MG 353; (Grade 6, MG 1.2) SE/TE: (Grade 6, AF 2.3) SE/TE: 171; (Grade 6, AF 1.1) SE/TE: 175; (Grade 6, NS 1.0) SE/TE: 242 (Grade 6, AF 1.1) SE/TE: ; (Grade 6, NS 1.4) SE/TE: ; (Grade 6, AF 1.0) SE/TE: ; (Grade 6, SDAP 2.3) SE/TE: SE: CA40- CA49 (Grade 6, NS 1.4) SE/TE: 261 California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 11

16 Program Title: California Grade Grade Level(s): Grade 6 Language 3.1 Evaluate the reasonableness of the solution in the context of the original situation. 3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems. 3.3 Develop generalizations of the results obtained and the strategies used and apply them in new problem situations. Publisher 431 (Grade 6, AF 1.1) SE/TE: 175; (Grade 6, NS 1.0) SE/TE: 242; (Grade 6, AF 2.3) SE/TE: 171 (Grade 6, NS 2.4) SE/TE: 72-73; (Grade 6, AF 1.1) SE/TE: ; (Grade 6, SDAP 3.4) SE/TE: (Grade 6, NS 1.1) SE/TE: 82-85; (Grade 6, AF 1.1) SE/TE: ; (Grade 6, NS 1.3) SE/TE: ; (Grade 6, MG 2.2) SE/TE: ; (Grade 6, MG 1.3) SE/TE: ; (Grade 6, (Grade 6, NS 1.4) SE/TE: ; (Grade 6, AF 3.0) SE/TE: 374 (Grade 6, NS 1.4) SE/TE: ; (Grade 6, MG 1.0) SE/TE: SE: CA42- CA49 California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 12

17 Program Title: California Grade Grade Level(s): Grade 6 Appendix Language Publisher SDAP 1.4) SE/TE: California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 13

18 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 STANDARDS MAP for a Basic Grade-Level Program Grade 7 Mathematics Language NUMBER SENSE 1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms: 1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) compare rational numbers in general. 1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. Publisher SE/TE: 24-28, 30-34, 44-49, , , , 197, , , , , , , , , , , , , 259, 267, , 315, SE/TE: 126, 198, , 232, 325 SE/TE: 24-28, 30-34, 44-49, , , , , , , , , , SE/TE: 8-12, 57, , , , 236, 257, , , , 662, , 680, 682, 683, 685, 687, 688, 689, 690, 691, 692, 693, 696, 697, 698 SE/TE: 662, 680, 685, 698 SE/TE: 8-12, 57, , , , 236, 257, , , , , 682, 683, 687, 688, California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 1

19 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language 1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. 1.4 Differentiate between rational and irrational numbers. Publisher , 690, 691, 692, 693, 696, 697 SE/TE: , 259, 267, , 315 SE/TE: 197, SE/TE: , SE/TE: 597, Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions. 1.6 Calculate the percentage of increases and decreases of a quantity. 1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest. 2.0 Students use exponents, powers, and roots and use exponents in working with fractions: 2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base. 2.2 Add and subtract fractions by using factoring to find common denominators. 2.3 Multiply, divide, and simplify rational numbers by using exponent rules. SE/TE: , SE/TE: , SE/TE: , SE/TE: , , , , , SE/TE: , SE/TE: SE/TE: , , SE/TE: 197, 276, 664, 676 SE/TE: 337, SE/TE: , 324, 362, SE/TE: 213, , , , 578, , 593, , SE/TE: 213, SE/TE: , , SE/TE: , California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 2

20 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language 2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why. 2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers. ALGEBRA AND FUNCTIONS 1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs: 1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A). Publisher SE/TE: , SE/TE: , 578, , 593, SE/TE: SE/TE: 25-26, 29, SE/TE: 5-7, 15-17, 68-72, 73-77, 82-84, , , , , , , , 408, , SE/TE: 5-7, 15-17, 82-84, , , , SE/TE: 8-11, 79, 80-81, 84-85, 91-92, 94, 96-97, , 111, , , 258, , , , 362, , 398, , 411 SE/TE: 91-92, 94, 96-97, , 111, , 258, , , 362, , 411, 416, Use the correct order of operations to evaluate SE/TE: 14-17, SE/TE: 8-11, California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 3

21 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language algebraic expressions such as 3(2x + 5) , SE/TE: 24, 57, 68-72, 73-77, Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used. 1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly. 1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph. 2.0 Students interpret and evaluate expressions involving integer powers and simple roots: 2.1 Interpret positive whole-number powers as repeated multiplication and negative wholenumber powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents. 2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent. 3.0 Students graph and interpret linear and some nonlinear functions: 3.1 Graph functions of the form y = nx 2 and y = nx 3 and use in solving problems. Publisher SE/TE: 4-5, 50, 78-79, 82-83, 102, SE/TE: , , 408 SE/TE: , , , , 590 SE/TE: , , , SE/TE: , , , 590 SE/TE: , 398, , , SE/TE: , SE/TE: 79, 88-92, 94-97, , SE/TE: 6-7, 80-81, 84-85, 176 SE/TE: 398, , 416, 421 SE/TE: 177, SE/TE: 177, SE/TE: SE/TE: 402, 405, , , SE/TE: , California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 4

22 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language Publisher 3.2 Plot the values from the volumes of threedimensional shapes for various values of the edge lengths (e.g., cubes with varying edge lengths or a triangle prism with a fixed height and an equilateral triangle base of varying lengths). 3.3 Graph linear functions, noting that the vertical change (change in y- value) per unit of horizontal change (change in x- value) is always the same and know that the ratio ("rise over run") is called the slope of a graph. 3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities. 4.0 Students solve simple linear equations and inequalities over the rational numbers: 4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. 4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation. MEASUREMENT AND GEOMETRY 1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems: SE/TE: 592 SE/TE: 595 SE/TE: , SE/TE: 398, 400, SE/TE: , , SE/TE: , , SE/TE: , , , , 409 SE/TE: , 247, , 251, , SE/TE: 398, 405, 407 SE/TE: 402, SE/TE: , , SE/TE: , , SE/TE: , 333, SE/TE: 161, , 252, , California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 5

23 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language 1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters). 1.2 Construct and read drawings and models made to scale. Publisher SE/TE: , , 251, , SE/TE: , SE/TE: 161, 252, , SE/TE: 300, Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer. 2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale: 2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic threedimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. SE/TE: 248, SE/TE: , 465, , , , , , 536, , 543, SE/TE: , 465, , , , , , 543 SE/TE: , , , 536 SE/TE: 250, 251, 326, 328 SE/TE: 141, , , 367, 369, , , 504, , 512, 533, , , 585, SE/TE: 141, 367, 369, , , 504, , 533, , , 585 SE/TE: 512, 538, Estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking the figures down into more basic geometric objects. 2.3 Compute the length of the perimeter, the surface SE/TE: 525- SE/TE: 674- California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 6

24 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language area of the faces, and the volume of a threedimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor. 2.4 Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches or [1 ft 2 ] = [144 in 2 ], 1 cubic inch is approximately cubic centimeters or [1 in 3 ] = [16.38 cm 3 ]). 3.0 Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures: 3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, mid-points, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge. 3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections. 3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the Publisher 526, 539, SE/TE: , SE/TE: 52-56, 436, 453, , , 463, , 469, 476, 483, 518, , , , , SE/TE: 436, 453, , , 469, SE/TE: 52-56, 476, 483, SE/TE: , , 675 SE/TE: , SE/TE: , , 453, , , 486, 488, 501, , , 585, , , SE/TE: , , 453, 501, SE/TE: , , , , SE/TE: 585, California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 7

25 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement. 3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures. 3.5 Construct two-dimensional patterns for threedimensional models, such as cylinders, prisms, and cones. Publisher 579 SE/TE: , 463 SE/TE: 518, SE/TE: 476, 478, 483, 484, 486, 488 SE/TE: , Identify elements of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect). STATISTICS, DATA ANALYSIS, AND PROBABILITY 1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program: 1.1 Know various forms of display for data sets, including a stem-and-leaf plot or box-andwhisker plot; use the forms to display a single set of data or to compare two sets of data. 1.2 Represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two SE/TE: , 442, , 524 SE/TE: , 611, , 616, , , , , 639 SE/TE: 611, , 616, , , , SE/TE: , , 639 SE/TE: , , SE/TE: 51, 136, 187, , , 615, 627, 634, SE/TE: 51, 136, 187, , 627, 634 SE/TE: 634, California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 8

26 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language variables (e.g., between time spent on homework and grade level). 1.3 Understand the meaning of, and be able to compute, the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set. MATHEMATICAL REASONING 1.0 Students make decisions about how to approach problems: Publisher SE/TE: , ; (Grade 7, SE/TE: 40-43; ; 2.1) SE/TE: 177; (Grade 7, MG 2.1) SE/TE: 504; 1.4) SE/TE: ; 4.1) SE/TE: ; ; 4.2) SE/TE: ; (Grade 7, MG SE/TE: , 615, ; (Grade 7, AF 1.4) SE/TE: ; (Grade 7, AF 4.1) SE/TE: ; (Grade 7, MG 3.1) SE/TE: ; (Grade 7, AF 4.1) SE/TE: ; (Grade 7, SDAP 1.1) SE/TE: 172; (Grade 7, MG 2.1) SE/TE: 10; (Grade 7, MG 2.2) SE/TE: ; (Grade 7, MG 2.2) SE/TE: 536, 538 California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 9

27 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language 1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns. 1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed. Publisher 3.1) SE/TE: ; (Grade 7, SE/TE: 40-43; ; 2.1) SE/TE: 177; (Grade 7, MG 2.1) SE/TE: 504; 1.4) SE/TE: ; 4.1) SE/TE: ) SE/TE: 29; (Grade 7, SE/TE: 35-39; ; 2.1) SE/TE: 177; (Grade 7, 101; (Grade 7, AF 1.4) SE/TE: ; (Grade 7, AF 4.1) SE/TE: ; (Grade 7, MG 3.1) SE/TE: ; (Grade 7, AF 4.1) SE/TE: ; (Grade 7, SDAP 1.1) SE/TE: ; (Grade 7, SE/TE: ; (Grade 7, MG 3.6) SE/TE: 442; (Grade 7, MG 2.1) SE/TE: 543; (Grade 7, SDAP 1.2) California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 10

28 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language 1.3 Determine when and how to break a problem into simpler parts. 2.0 Students use strategies, skills, and concepts in finding solutions: Publisher SE/TE: 204 SE/TE: (Grade 7, MG 2.1) SE/TE: ; 10; (Grade 7, MG 2.2) 4.2) SE/TE: SE/TE: ; 516; (Grade 7, (Grade 7, MG MG 2.2) 3.1) SE/TE: SE/TE: 536, ; (Grade 7, SE/TE: ; (Grade 7, SE/TE: 236; 2.1) SE/TE: 201; (Grade 7, NS 2.1) SE/TE: 205; 1.3) SE/TE: 267; (Grade 7, NS 2.4) SE/TE: 578; (Grade 7, MG 2.1) SE/TE: 585; (Grade 7, AF 3.3) 136; (Grade 7, SE/TE: 308; 359; (Grade 7, SE/TE: ; (Grade 7, AF 4.2) SE/TE: 333; 4.1) SE/TE: ; (Grade 7, MG 3.1) SE/TE: 453; (Grade 7, MG 2.1) SE/TE: ; (Grade 7, California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 11

29 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Publisher Language SE/TE: 394; SDAP 1.1) SE/TE: 51; 3.1) SE/TE: ; 3.3) SE/TE: (Grade 7, 396; (Grade 7, SDAP 1.2) SDAP 1.1) SE/TE: 628; SE/TE: 614- (Grade 7, 615; (Grade 7, SDAP 1.2) SDAP 1.2) SE/TE: 634; SE/TE: 639; (Grade 7, SDAP 1.2) 1.1) SE/TE: SE/TE: ; (Grade 7, 638; 1.2) AF 1.3) SE/TE: 40-45; SE/TE: 57; 101; (Grade 7, 35-39; (Grade MG 2.4) 7, AF 2.1) SE/TE: 505- SE/TE: 177; Use estimation to verify the reasonableness of calculated results. 128; (Grade 7, 136; (Grade 7, SE/TE: 130- SE/TE: 308; 134; (Grade 7, SE/TE: Apply strategies and results from simpler California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 12

30 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language problems to more complex problems. 2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques. 2.4 Make and test conjectures by using both inductive and deductive reasoning. Publisher 2.1) SE/TE: 201; (Grade 7, NS 2.1) SE/TE: 205; 1.3) SE/TE: 267; (Grade 7, NS 2.4) SE/TE: 578; (Grade 7, MG 2.1) SE/TE: ) SE/TE: 394; (Grade 7, AF 3.1) SE/TE: ; (Grade 7, SDAP 1.2) SE/TE: 628; (Grade 7, SDAP 1.2) SE/TE: 634; (Grade 7, SDAP 1.2) SE/TE: ) SE/TE: 57; (Grade 7, SE/TE: 35-39; ; 4.2) SE/TE: 333; (Grade 7, AF 4.1) SE/TE: ; (Grade 7, MG 3.1) SE/TE: 453; (Grade 7, MG 2.1) SE/TE: (Grade 7, SDAP 1.1) SE/TE: 51; 3.3) SE/TE: 396; (Grade 7, SDAP 1.1) SE/TE: ; (Grade 7, SDAP 1.2) SE/TE: ) SE/TE: 15; (Grade 7, SE/TE: 40-45; California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 13

31 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language 2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning. 2.6 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work. Publisher 2.1) SE/TE: 177; (Grade 7, SE/TE: ) SE/TE: 18-21; (Grade 7, SE/TE: 24-29; 30-33; (Grade 7, MG 1.1) SE/TE: ; (Grade 7, AF 4.2) SE/TE: ; (Grade 7, AF 4.1) SE/TE: ; (Grade 7, MG 3.1) SE/TE: ) SE/TE: 57; (Grade 7, AF 1.3) SE/TE: 68-72; 1.1) SE/TE: 101; (Grade 7, MG 2.4) SE/TE: ; (Grade 7, SE/TE: 36-39; 44; (Grade 7, AF 1.3) SE/TE: 73-76; (Grade 7, SDAP 1.1) SE/TE: 187; AND MG 3.1) SE/TE: 37; (Grade 7, NS 2.1) SE/TE: ; (Grade 7, California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 14

32 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language 2.7 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. 2.8 Make precise calculations and check the validity of the results from the context of the problem. Publisher ; 4.1) SE/TE: ; (Grade 7, MG 3.4) SE/TE: ; (Grade 7, SDAP 1.3) SE/TE: ; (Grade 7, SDAP 1.3) SE/TE: ; ; ; (Grade 7, MG 1.1) SE/TE: ; (Grade 7, SE/TE: 132; 1.2 AND MG 1.1) SE/TE: MG 3.2) SE/TE: ; (Grade 7, SE/TE: 94-95; 98-99; (Grade California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 15

33 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language 3.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations: Publisher 161; (Grade 7, AF 4.1) SE/TE: 364; 3.3) SE/TE: 408; (Grade 7, MG 1.3) SE/TE: ; (Grade 7, SE/TE: 132; 1.2 AND MG 1.1) SE/TE: 161; (Grade 7, AF 4.1) SE/TE: 364; 3.3) SE/TE: 408; (Grade 7, MG 1.3) SE/TE: 251; 1.3) SE/TE: 57; (Grade 7, MG 2.1) SE/TE: 141; (Grade 7, MG 1.3) SE/TE: 251; (Grade 7, NS 1.7) 7, MG 1.1) SE/TE: ; (Grade 7, AF 1.1) SE/TE: ; (Grade 7, SE/TE: 94-95; 98-99; (Grade 7, MG 1.1) SE/TE: ; (Grade 7, AF 1.1) SE/TE: 422; 13; (Grade 7, SE/TE: 192; 4.1) SE/TE: 359; (Grade 7, F 4.2) SE/TE: 409; (Grade 7, AF 4.2) SE/TE: 333; California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 16

34 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language 3.1 Evaluate the reasonableness of the solution in the context of the original situation. 3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems. Publisher SE/TE: 321; 2.4) SE/TE: 578; (Grade 7, SE/TE: 98-99; (Grade 7, MG 3.6) SE/TE: 442; (Grade 7, MG 2.1) SE/TE: ; (Grade 7, SE/TE: 132; 1.2 AND MG 1.1) SE/TE: 161; (Grade 7, AF 4.1) SE/TE: 364; 3.3) SE/TE: 408; (Grade 7, MG 1.3) SE/TE: ) SE/TE: 57; (Grade 7, MG 2.1) SE/TE: 141; (Grade 7, MG 4.1) SE/TE: 359; (Grade 7, AF 4.1) SE/TE: ; (Grade 7, SE/TE: 94-95; 98-99; (Grade 7, MG 1.1) SE/TE: ; (Grade 7, AF 1.1) SE/TE: ; (Grade 7, SE/TE: 192; California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 17

35 Program Title: California Pre-Algebra 2009 Grade Level(s): 7 Language 3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations. Appendix Publisher 1.3) SE/TE: 251; (Grade 7, NS 1.7) SE/TE: 321; 2.4) SE/TE: ; (Grade 7, MG 3.6) SE/TE: 442; (Grade 7, MG 2.1) SE/TE: ) SE/TE: 359; (Grade 7, F 4.2) SE/TE: ) SE/TE: 333; (Grade 7, AF 4.1) SE/TE: 359; 4.1) SE/TE: California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 18

36 Program Title: California Algebra Grade Level(s): 8 STANDARDS MAP for a Basic Grade-Level Program Grade Eight Mathematics (Algebra I) Language ALGEBRA I 1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable: 1.1 Students use properties of numbers to demonstrate whether assertions are true or false. 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. 3.0 Students solve equations and inequalities involving absolute values. Publisher SE/TE: 17-22, 24-30, 32-36, 37-44, 45-50, 52-56, 57, 75 SE/TE: 19-21, 24-30, 32-36, 37-44, 45-50, SE/TE: 20-23, 40-44, 78-81, , , , , 358, , , 492, SE/TE: SE/TE: 9-15, SE/TE: SE/TE: 26-30, 32-36, , , , , 513 SE/TE: 20-23, Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = Students solve multistep problems, including word problems, involving linear equations and SE/TE: 76-81, 86-88, SE/TE: 69-74, 76-82, 83, 84- SE/TE: 46-50, , SE/TE: 90-91, California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 1

37 Program Title: California Algebra Grade Level(s): 8 Language linear inequalities in one variable and provide justification for each step. 6.0 Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4). 7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula. 8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point. 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques Students apply basic factoring techniques to second-and simple third-degree polynomials. These techniques include finding a common Publisher 89, 93-98, 99, , , , , SE/TE: , , , 253, 255, 257, SE/TE: , , 265 SE/TE: SE/TE: , , , 301, SE/TE: 46-50, , , , , , 380, , 387, , SE/TE: , 394, , , SE/TE: , , SE/TE: , , 258 SE/TE: SE/TE: SE/TE: , 556 SE/TE: , 416, 595 California Department of Education Basic Grade-Level Program s Map SBE Approved November 2006 Page 2