CHICAGO PUBLIC SCHOOLS (ILLINOIS) MATH & SCIENCE INITIATIVE COURSE FRAMEWORK FOR ALGEBRA Course Framework: Algebra


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1 Chicago Public Schools (Illinois) Math & Science Initiative Course Framework for Algebra Course Framework: Algebra Central Concepts and Habits of Mind The following concepts represent the big ideas or driving intellectual processes that describe the discipline of algebra. They should not be taught in isolation, but should be integrated throughout the curriculum structure. Problem Solving and Mathematical Reasoning Solving problems using generalized reasoning skills rather than with a memorized set of detailed and specific algorithms Solving multistep problems and practical problems that occur in everyday life Using inquiry as a means of understanding concepts and solving problems in mathematics SE/TE: See Critical Thinking on page T798 of Index; OpenEnded on page T804 of Index SE/TE: See Connections: Careers, Interdisciplinary, Mathematics, and RealWorld on pages T797, T798 of Index SE/TE: See Critical Thinking on page T798 of Index; Make a Conjecture on page T803 of index Algebraic Skills and Tools Demonstrating fluency with numerical calculations and symbolic manipulation Selecting appropriate computational methods (egg. mental, pencil and paper, graphical, calculatorbased, softwarebased, etc.) Thinking about computations independently from the particular numbers that are used Working backwards from the answer to the starting point of a problem Recognizing patterns and organizing data using well defined rules (i.e. building rules to represent functions) SE/TE: 944, 50, 56, 63, , 136, 156, 349, , 493, 532, 556 SE/TE: See Mental Math on page T803 of Index; Graph(s) on page T801 of Index; Graphing calculator on page T801 of Index SE/TE: See OpenEnded on page T804 of Index; Error Analysis on page T799 of Index SE/TE: 208, 209, 375, 446, 608, 719 SE/TE: 37, 42, 43, 96, 185, 187, 209, 250, , 306, 308, 318, 319, 325, 329, 394, 397, 411, 428, 429, 434, 584, 621, 665, 716 1
2 Mathematical Communication Demonstrating fluency with multiple mathematical representations including symbols, tables, graphs, and expressions Understanding and describing mathematical concepts through reading, writing, listening, and speaking Sharing mathematical ideas in a variety of settings, including cooperative groups, whole class discussions, individual work, etc. SE/TE: See Symbol(s) on page T808 of Index; Tables on page T808 of Index; Graph(s) on page T801 of Index; Expressions on page T800 of Index SE/TE: See Reading Math on page T806 of Index; Writing on page T809 of Index SE/TE: RealWorld Snapshots on pages , , , , , Major Curriculum Structure The course will be structured in a series of units that addresses major topics in algebra. While the storyline of these units will be driven by the algebra content, a major emphasis will be on developing abilities to understand concepts and solve problems. The following list of units represents an approximation of expected emphases and time allocations for key topics. The sequence may vary depending on the instructional materials being used, but the course should cover all topics indicated. These units should also incorporate concepts in geometry and measurement to integrate all ILS goals into the curriculum. Number and Operation Concepts (4 weeks) Representing quantities using variables and basic expressions SE/TE: 48, 15, 23, 36, 53, 58, 68, 70, 180, 702 TR: Practice, Reteaching, Enrichment 11; Practice Workbook 11; Spanish Practice Workbook 11; Reading and Math Literacy 1A; Spanish Reading and Math Literacy 1A; Basic Algebra Planning Guide 11; Transparencies [Check Skills You ll Need 11; Additional Examples 11; Student Edition Answers 11; Lesson Quiz 11]; PH Presentation Pro CD 11 Puzzles pp. 24, 29; Selfgrading Lesson Quiz]; Teacher Center [Lesson 2
3 Simplifying and evaluating numerical and algebraic expressions using order of operations Representing and translating of these concepts between symbols, words, different types of graphs (histogram, bar, circle, Cartesian, etc.), or diagrams as appropriate SE/TE: 915, 23, 30, 44, 4752, 58, 65, 6970, 80, 145, 180, 392, , 447, 450, 454, 508, 528, 702 TR: Practice, Reteaching, Enrichment 12, 17; Practice Workbook 12, 17; Spanish Practice Workbook 12, 17; HandsOn Activities 3; Basic Algebra Planning Guide 12, 17; Transparencies [Check Skills You ll Need 12, 17; Additional Examples 12, 17; Student Edition Answers 12, 17; Lesson Quiz 12, 17]; PH Presentation Pro CD 12, 17 Puzzles pp. 2, 25, 28; Graphing Calculator, procedure 1; Selfgrading Lesson Quiz]; Teacher Center [Lesson SE/TE: 5964, 6970, 80, 280, 702 TR: Practice, Reteaching, Enrichment 19; Practice Workbook 19; Spanish Practice Workbook 19; Basic Algebra Planning Guide 19; Transparencies [Check Skills You ll Need 19; Additional Examples 19; Student Edition Answers 19; Lesson Quiz 19]; PH Presentation Pro CD 19 Puzzles pp. 61, 62; Graphing Calculator, procedure 20; Selfgrading Lesson Quiz]; Teacher Center [Lesson 3
4 Substituting numbers for unknown quantities to evaluate expressions SE/TE: 915, 23, 2829, 3435, 4142, 44, 68, 70, 392, , 447, 450, 508, 528 TR: Practice, Reteaching, Enrichment 12; Practice Workbook 12; Spanish Practice Workbook 12; Basic Algebra Planning Guide 12; Transparencies [Check Skills You ll Need 12; Additional Examples 12; Student Edition Answers 12; Lesson Quiz 12]; PH Presentation Pro CD 12 Puzzles pp. 2, 25; Graphing Calculator, procedure 1; Selfgrading Lesson Quiz]; Teacher Center [Lesson Linear Functions and Inequalities (6 weeks) Solving routine and contextualbased firstdegree equations and inequalities SE/TE: 7480, 8186, 8894, , , 115, 123, , 132, , , , 166, 172, 176, 178, 180, 188, 195, 202, 209, 240, 267, 280, 289, 324, 338, 359, 703, 704 TR: Practice, Reteaching, Enrichment 21 to 25, 32 to 34; Practice Workbook 21 to 25, 32 to 34; Spanish Practice Workbook 21 to 25, 32 to 34; Reading and Math Literacy 2A, 2B, 3B; Spanish Reading and Math Literacy 2A, 2B, 3B; Technology Activities 16; Hands On Activities 4, 5; Basic Algebra Planning Guide 21 to 25, 32 to 34; Transparencies [Check Skills You ll Need 21 to 25, 32 to 34; Additional Examples 21 to 25, 32 to 34; Student Edition Answers 21 to 25, 32 to 34; Lesson Quiz 21 to 25, 32 to 34]; PH Presentation Pro CD 21 to 25, 32 to 34 Puzzles pp , 46, 55, 56, 58; Graphing Calculator, procedures 7, 9 ; Selfgrading 4
5 Recognizing patterns and developing linear models to describe them Developing linear functions and proportional relations SE/TE: , 571, 583, 711 TR: Practice, Reteaching, Enrichment 109; Practice Workbook 109; Spanish Practice Workbook 109; Technology Activities 9; HandsOn Activities 25; Basic Algebra Planning Guide 109; Transparencies [Check Skills You ll Need 109; Additional Examples 109; Student Edition Answers 109; Lesson Quiz 109]; PH Presentation Pro CD 109 [Teacher Web Code: aek5500; Updated Data; Selfgrading Lesson Quiz]; Teacher Center [Lesson SE/TE: , 202, 228, 230, 246, 252, , 273, , 429, 705, 706 TR: Practice, Reteaching, Enrichment 42, 55; Practice Workbook 42, 55; Spanish Practice Workbook 42, 55; Reading and Math Literacy 4B, 5C; Spanish Reading and Math Literacy 4B, 5C; Basic Algebra Planning Guide 42, 55; Transparencies [Check Skills You ll Need 42, 55; Additional Examples 42, 55; Student Edition Answers 42, 55; Lesson Quiz 42, 55]; PH Presentation Pro CD 42, 55 [Teacher Web Code: aek5500; Updated Data; Reasoning & Puzzles p. 87; Selfgrading 5
6 Representing these concepts through graphs, symbols, diagrams, or words as appropriate Solving rate of change, equations (simple and twostep), and inequalities SE/TE: , 175, , , , 317, , , 338, 399, 495, 704, 707 TR: Practice, Reteaching, Enrichment 31, 62 to 64, 66; Practice Workbook 31, 62 to 64, 66; Spanish Practice Workbook 31, 62 to 64, 66; Reading and Math Literacy 3A, 6B, 6C; Spanish Reading and Math Literacy 3A, 6B, 6C; Technology Activities 2, 6, 20; HandsOn Activities 7, 14, 19; Basic Algebra Planning Guide 31, 62 to 64, 66; Transparencies [Check Skills You ll Need 31, 62 to 64, 66; Additional Examples 31, 62 to 64, 66; Student Edition Answers 31, 62 to 64, 66; Lesson Quiz 31, 62 to 64, 66]; PH Presentation Pro CD 31, 62 to 64, 66 Puzzles pp. 57, 64; Updated Data; Graphing Calculator, procedures 5, 8, 22; Selfgrading SE/TE: 7480, 8186, 8894, , 123, , 128, 132, , , , 166, 172, 176, 178, 180, 188, 195, 202, 209, 240, 267, 280, , 297, 324, 331, 334, 338, 359, 368, 416, 703, 704, 707 TR: Practice, Reteaching, Enrichment 21 to 24, 32 to 34, 61; Practice Workbook 21 to 24, 32 to 34, 61; Spanish Practice Workbook 21 to 24, 32 to 34, 61; Reading and Math Literacy 2A, 2B, 3B, 6A; Spanish Reading and Math Literacy 2A, 2B, 3B, 6A; Technology Activities 1, 16; HandsOn Activities 4, 5, 13; Basic Algebra Planning Guide 21 to 24, 32 to 34, 61; Transparencies [Check Skills You ll Need 21 to 24, 32 to 34, 61; Additional Examples 21 to 24, 32 to 34, 61; Student Edition Answers 21 to 24, 32 to 34, 61; Lesson Quiz 21 to 24, 32 to 34, 61]; PH Presentation Pro CD 21 to 24, 32 to 34, 61 6
7 Solving rate of change, equations (simple and twostep), and inequalities Translating back and forth between algebraic sentences, equations, and words Puzzles pp , 55, 56, 58, 63, 64, 108; Graphing Calculator, procedure 5, 7, 9; Selfgrading Lesson Quiz]; Teacher Center [Lesson SE/TE: 48, 72, 9293, , , 234, , , 702 TR: Practice, Reteaching, Enrichment 11, 25, 63; Practice Workbook 11, 25, 63; Spanish Practice Workbook 11, 25, 63; Reading and Math Literacy 1A, 6B; Spanish Reading and Math Literacy 1A, 6B; Basic Algebra Planning Guide 11, 25, 63; Transparencies [Check Skills You ll Need 11, 25, 63; Additional Examples 11, 25, 63; Student Edition Answers 11, 25, 63; Lesson Quiz 11, 25, 63]; PH Presentation Pro CD 11, 25, 63 Puzzles pp. 24, 29, 38, 39, 46; Graphing Calculator, procedure 5; Selfgrading Lesson Quiz]; Teacher Center [Lesson Planner; Resources] Systems of Linear Equations (4 weeks) Using multiple strategies for solving two equations with two unknowns SE/TE: , , , , , 376, , 390, 416, 423, 465, 485, 501, 708 TR: Practice, Reteaching, Enrichment 71 to 74; Practice Workbook 71 to 74; Spanish Practice Workbook 71 to 74; Reading and Math Literacy 7A, 7B; Spanish Reading and Math Literacy 7A, 7B; Technology Activities 4, 21; Basic Algebra Planning Guide 71 to 74; Transparencies [Check Skills You ll Need 71 to 74; Additional Examples 71 to 74; Student Edition Answers 71 to 74; Lesson Quiz 71 to 74]; PH Presentation Pro CD 71 to 74 7
8 Using multiple strategies for solving two equations with two unknowns Interpreting the contextual meaning of systems with zero, one, or infinitely many solutions Puzzles pp. 68, 69, 71, 72; Selfgrading SE/TE: , 387, 390 TR: Practice, Reteaching, Enrichment 71; Practice Workbook 71; Spanish Practice Workbook 71; Reading and Math Literacy 7A; Spanish Reading and Math Literacy 7A; Technology Activities 4; Basic Algebra Planning Guide 71; Transparencies [Check Skills You ll Need 71; Additional Examples 71; Student Edition Answers 71; Lesson Quiz 71]; PH Presentation Pro CD 71 Puzzles p. 68; Selfgrading Lesson Quiz]; Teacher Center [Lesson Solving linear systems of inequalities SE/TE: , , 399, 410, 708 TR: Practice, Reteaching, Enrichment 76; Practice Workbook 76; Spanish Practice Workbook 76; HandsOn Activities 17; Basic Algebra Planning Guide 76; Transparencies [Check Skills You ll Need 76; Additional Examples 76; Student Edition Answers 76; Lesson Quiz 76]; PH Presentation Pro CD 76 [Teacher Web Code: aek5500; Selfgrading 8
9 Statistics and Probability Concepts (5 weeks) Organizing and applying singlevariable data, frequency distributions, graphs, and histograms Identifying and understanding the significance of basic statistical quantities such as mean, median, mode, range, standard deviation, etc Understanding concepts of basic probability, such as equally likely, sample space, outcomes, counting principles, and analysis of events involving chance SE/TE: , 217, 246, 703 TR: Practice, Reteaching, Enrichment 27; Practice Workbook 27; Spanish Practice Workbook 27; Basic Algebra Planning Guide 27; Transparencies [Check Skills You ll Need 27; Additional Examples 27; Student Edition Answers 27; Lesson Quiz 27]; PH Presentation Pro CD 27 [Teacher Web Code: aek5500; Graphing Calculator, procedure 21; Selfgrading Lesson Quiz]; Teacher Center [Lesson Planner; Resources] SE/TE: , 139, 217, 576, 703 TR: Practice, Reteaching, Enrichment 27; Practice Workbook 27; Spanish Practice Workbook 27; Basic Algebra Planning Guide 27; Transparencies [Check Skills You ll Need 27; Additional Examples 27; Student Edition Answers 27; Lesson Quiz 27]; PH Presentation Pro CD 27 [Teacher Web Code: aek5500; Graphing Calculator, procedure 21; Selfgrading Lesson Quiz]; Teacher Center [Lesson Planner; Resources] SE/TE: , , , 240, 289, 303, 359, 634, 705 TR: Practice, Reteaching, Enrichment 45, 46; Practice Workbook 45, 46; Spanish Practice Workbook 45, 46; Reading and Math Literacy 4C; Spanish Reading and Math Literacy 4C; HandsOn Activities 10; Basic Algebra Planning Guide 45, 46; Transparencies [Check Skills You ll Need 45, 46; Additional Examples 45, 46; Student Edition Answers 45, 46; Lesson Quiz 45, 46]; PH Presentation Pro CD 45, 46 9
10 Understanding concepts of basic probability, such as equally likely, sample space, outcomes, counting principles, and analysis of events involving chance [Teacher Web Code: aek5500; Graphing Calculator, procedure 15; Selfgrading Lesson Quiz]; Teacher Center [Lesson Planner; Resources] Using an area model to describe probability SE/TE: 655, 660 Polynomials: Operations and Concepts (7 weeks) Solving quadratic equations by various methods (graphing, factoring, quadratic formula, etc.) Using a quadratic model to describe and solve geometric problems involving area Identifying and describing patterns which can be represented by quadratic functions and higher degree polynomials SE/TE: , , , , 558, , 597, 612, 619, 671, 677, 685, 691, 711 TR: Practice, Reteaching, Enrichment 104 to 107; Practice Workbook 104 to 107; Spanish Practice Workbook 104 to 107; Reading and Math Literacy 10B; Spanish Reading and Math Literacy 10B; Technology Activities 7, 24; HandsOn Activities 23; Basic Algebra Planning Guide 104 to 107; Transparencies [Check Skills You ll Need 104 to 107; Additional Examples 104 to 107; Student Edition Answers 104 to 107; Lesson Quiz 104 to 107]; PH Presentation Pro CD 104 to 107 Puzzles pp. 84, 9699; Selfgrading Lesson Quiz]; Teacher Center [Lesson Planner; Resources] SE/TE: 477, , , 551 SE/TE: , 523, , 567, 569, 571, 583, 711 TR: Practice, Reteaching, Enrichment 101, 109; Practice Workbook 101, 109; Spanish Practice Workbook 101, 109; Reading and Math Literacy 10A; Spanish Reading and Math Literacy 10A; Technology Activities 9; HandsOn Activities 25; Basic Algebra Planning Guide 101, 109; Transparencies 10
11 Identifying and describing patterns which can be represented by quadratic functions and higher degree polynomials Applying rules of exponents to solve problems in context Using basic functions (addition, subtraction, multiplication, and division) with polynomials TR: [Check Skills You ll Need 101, 109; Additional Examples 101, 109; Student Edition Answers 101, 109; Lesson Quiz 101, 109]; PH Presentation Pro CD 101, 109 [Teacher Web Code: aek5500; Updated Data; Reasoning & Puzzles p. 88; Selfgrading SE/TE: , 404, , , , 429, 444, 448, 450, 454, 461, 465, 472, 501, 528, 546, 634, 709 TR: Practice, Reteaching, Enrichment 81, 83 to 85; Practice Workbook 81, 83 to 85; Spanish Practice Workbook 81, 83 to 85; Reading and Math Literacy 8A, 8B; Spanish Reading and Math Literacy 8A, 8B; Basic Algebra Planning Guide 81, 83 to 85; Transparencies [Check Skills You ll Need 81, 83 to 85; Additional Examples 81, 83 to 85; Student Edition Answers 81, 83 to 85; Lesson Quiz 81, 83 to 85]; PH Presentation Pro CD 81, 83 to 85 Puzzles pp. 10, 30, 78; Graphing Calculator, procedure 17; Selfgrading Lesson Quiz]; Teacher Center [Lesson SE/TE: , , , , 506, 516, 523, 583, 590, 597, , 671, 694, 696, 710, 713 TR: Practice, Reteaching, Enrichment 91 to 93, 125; Practice Workbook 91 to 93, 125; Spanish Practice Workbook 91 to 93, 125; Reading and Math Literacy 9A, 9B; Spanish Reading and Math Literacy 9A, 9B; Technology Activities 23; HandsOn Activities 20, 21; Basic Algebra Planning Guide 91 to 93, 125; Transparencies [Check Skills You ll Need 91 to 93, 125; Additional Examples 91 to 93, 125; Student 11
12 Using basic functions (addition, subtraction, multiplication, and division) with polynomials TR: Edition Answers 91 to 93, 125; Lesson Quiz 91 to 93, 125]; PH Presentation Pro CD 91 to 93, 125 Puzzles pp , 78, 95; Selfgrading Rational and Irrational Expressions: Operations and Concepts (6 weeks) Performing basic operations and solving equations with rational (fractional) expressions SE/TE: , , 666, , , 685, 691, , 713 TR: Practice, Reteaching, Enrichment 123, 124, 126, 127; Practice Workbook 123, 124, 126, 127; Spanish Practice Workbook 123, 124, 126, 127; Reading and Math Literacy 12B; Spanish Reading and Math Literacy 12B; HandsOn Activities 29; Basic Algebra Planning Guide 123, 124, 126, 127; Transparencies [Check Skills You ll Need 123, 124, 126, 127; Additional Examples 123, 124, 126, 127; Student Edition Answers 123, 124, 126, 127; Lesson Quiz 123, 124, 126, 127]; PH Presentation Pro CD 123, 124, 126, 127 Puzzles pp. 32, 33, 36; Selfgrading Lesson Quiz ]; Teacher Center [Lesson Planner; Resources] SE/TE: , 650, 693, 713 TR: Practice, Reteaching, Enrichment 121; Practice Workbook 121; Spanish Practice Workbook 121; Reading and Math Literacy 12A; Spanish Reading and Math Literacy 12A; Basic Algebra Planning Guide 121; Transparencies [Check Skills You ll Need 121; Additional Examples 121; Student Edition Answers 121; Lesson Quiz 121]; PH Presentation Pro CD
13 Identifying and describing inverse variations Performing basic operations and solving equations with irrational expressions (ie). Roots and rational exponents) Using rational and irrational expressions to solve applicationbased problems [Teacher Web Code: aek5500; Selfgrading SE/TE: , 534, 576, , , , , , 619, , 631, 634, 642, 661, 666, 671, 691, 711, 712 TR: Practice, Reteaching, Enrichment 103, 111 to 115; Practice Workbook 103, 111 to 115; Spanish Practice Workbook 103, 111 to 115; Reading and Math Literacy 11A, 11B; Spanish Reading and Math Literacy 11A, 11B; Technology Activities 25; HandsOn Activities 26, 27; Basic Algebra Planning Guide 103, 111 to 115; Transparencies [Check Skills You ll Need 103, 111 to 115; Additional Examples 103, 111 to 115; Student Edition Answers 103, 111 to 115; Lesson Quiz 103, 111 to 115]; PH Presentation Pro CD 103, 111 to 115 Puzzles pp. 90, 91, 94; Graphing Calculator, procedure 19; Selfgrading Lesson Quiz]; Teacher Center [Lesson SE/TE: , , , , , 606, , , , 660, 661, 666, TR: Practice, Reteaching, Enrichment 112, 113, 115; Practice Workbook 112, 113, 115; Spanish Practice Workbook 112, 113, 115; Reading and Math Literacy 11B; Spanish Reading and Math Literacy 11B; Technology Activities 25; HandsOn Activities 26, 27; Basic Algebra Planning Guide 112, 113, 115; Transparencies [Check Skills You ll Need 112, 113, 115; Additional Examples 112, 113, 115; Student Edition Answers 112, 113, 115; Lesson Quiz 112, 113, 115]; PH Presentation Pro CD 112, 113,
14 Using rational and irrational expressions to solve applicationbased problems Puzzles pp. 94; Graphing Calculator, procedure 19; Selfgrading Lesson Quiz]; Teacher Center [Lesson Determining when an expression is undefined Exponentials and Other NonLinear Functions (5 weeks) Solving simple exponential equations Applying realworld problems and making predictions using exponential models Using technology such as a graphing calculator to represent and analyze nonlinear functions and their graphs. SE/TE: , , 461, 558, 709 TR: Practice, Reteaching, Enrichment 88; Practice Workbook 88; Spanish Practice Workbook 88; Technology Activities 8; HandsOn Activities 19; Basic Algebra Planning Guide 88; Transparencies [Check Skills You ll Need 88; Additional Examples 88; Student Edition Answers 88; Lesson Quiz 88]; PH Presentation Pro CD 88 [Teacher Web Code: aek5500; Selfgrading SE/TE: TR: Practice, Reteaching, Enrichment 122; Practice Workbook 122; Spanish Practice Workbook 122; Technology Activities 26; Basic Algebra Planning Guide 122; Transparencies [Check Skills You ll Need 122; Additional Examples 122; Student Edition Answers 122; Lesson Quiz 122]; PH Presentation Pro CD 122 [Teacher Web Code: aek5500; Selfgrading Reference: 14
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