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1 Prentice Hall University of Chicago School Mathematics Project: Advanced Algebra 2002 Delaware Mathematics Content Standards (Grades 910) STANDARD #1 Students will develop their ability to SOLVE PROBLEMS by engaging in developmentally appropriate problemsolving opportunities in which there is a need to use various approaches to investigate and understand mathematical concepts; to formulate their own problems; to find solutions to problems from everyday situations; to develop and apply strategies to solve a wide variety of problems; and to integrate mathematical reasoning, communication and connections. PERFORMANCE INDICATORS Through the investigation of meaningful problems, individually or in cooperative groups while using appropriate technology, all students in grades K10 will be able to: 1.01 persist and solve problems from start to finish; following are selected examples. 53, 59, 92, 126, 150, 178, 184, 237, 244, 249, 254, 259, 283, 329, 355, 368, 386, 406, 424, 436, 449, 482, 504, 508, 519, 561, 568, 580, 586, 609, 614, 620, 631, 650, 696, 753, 769, 792, 797, 815, 822 1
2 1.02 investigate and build their understanding of mathematical content; 1.03 formulate problems from everyday and mathematical situations; following are selected examples. 8, 12, 36, 62, 94, 99, 105, 140, 141, 240, 273, 305, 312, 351, 359, 418, 420, 440, 444, 541, 612, 718, 747, 765, 813, 826, 862 following are selected examples. 7, 10, 23, 28, 34, 57, 60, 72, 80, 86, 92, 102, 124, 143, 150, 154, 216, 271, , 313, 365, 419, 438, 442, 461, 517, 535, 564, 574, 614, 730, 857, 869, 871 2
3 1.04 develop and apply strategies to solve problems; 1.05 interpret results with respect to the original problem; following are selected examples. 14 Graphs of Functions 2429; 15 Solving Equations 3035; 27 Fitting a Model to Data I ; 610 Analyzing Solutions to Quadratic Equations ; 227, 232, 240, 312, 325, 382, 304, 611, 616, 623, 836 following pages for this standard: 4AD, 70A D; 202AD, 270AD, 344AD, 808AD; Lesson Masters A and B; Teaching Aid following are selected examples. 7, 21, 33, 79, 147, 273, 287, 332, 351, 353, 465, 497, 513, 578, 681, 706 3
4 1.06 generalize strategies and solutions to new problem situations. following are selected examples , STANDARD #2 Students will develop their ability to COMMUNICATE MATHEMATICALLY by solving problems in which there is a need to obtain information from the real world through reading, listening and observing; to translate this information into mathematical language and symbols; to process this information mathematically; and to present results in written, oral and visual formats. PERFORMANCE INDICATORS Through the investigation of meaningful problems, individually or in cooperative groups while using appropriate technology, all students in grades K10 will be able to: 2.01 model realworld situations using oral, written, concrete, pictorial, graphical and algebraic methods; following are selected examples. 7, 10, 23, 28, 34, 57, 60, 72, 80, 86, 92, 102, 124, 143, 150, 154, 216, 271, , 313, 365, 419, 438, 442, 461, 517, 535, 564, 574, 614, 730, 857, 869, 871 4
5 2.02 use reading, listening, viewing, speaking and writing to explain and develop mathematical ideas; 2.03 use mathematical notation and language to describe and discuss realworld situations; following are selected examples. 7, 9, 10, 14, 19, 22, 29, 33, 44, 73, 97, 112, 117, 176, 187, 189, 208, 210, 247, 313, 369, 443, 447, 454, 466, 506, 509, 552, 571, 577, 582, 591, 633, 678, 696, 704, 750, 766, 788,793, 824, 839, 841, 852, 867, 874 following are selected examples. 7, 10, 23, 28, 34, 57, 60, 72, 80, 86, 92, 102, 124, 143, 150, 154, 216, 271, , 313, 365, 419, 438, 442, 461, 517, 535, 564, 574, 614, 730, 857, 869, 871 5
6 2.04 read mathematics with understanding; following are selected examples. 7, 14, 19, 22, 44, 73, 97, 112, 117, 148, 176, 241, 247, 293, 313, 352, 369, 389, 419, 466, 491, 506, 547, 552, 558, 571, 624, 633, 718, 750, 766, 824, 841, develop common understandings of mathematical ideas and use generalizations discovered through investigations to formulate definitions; following are selected examples. 13, 20, 36, 72, 162, 232, 346, 370, 388, 418, , 558, 617, 640, 687, , ask questions to clarify the problem situation. following are selected examples. 17, 73, 172, 221, 253, 282, 367, 391, 423, 497, 566, 630, 683, 715, 755 6
7 STANDARD #3 Students will develop their ability to REASON MATHEMATICALLY by solving problems in which there is a need to investigate significant mathematical ideas in all content areas; to justify their thinking; to reinforce and extend their logical reasoning abilities; to reflect on and clarify their own thinking; to ask questions to extend their thinking; and to construct their own learning. PERFORMANCE INDICATORS Through the investigation of meaningful problems, individually or in cooperative groups while using appropriate technology, all students in grades K10 will be able to use inductive and deductive reasoning to: 3.01 formulate and test conjectures; following are selected examples Analyzing Solutions to Quadratic Equations ; 62 Chapter Planner of the TE. 344AD; Lesson Masters A and B; Teaching Aid Masters; Assessment Sourcebook; Technology Sourcebook; Answers Masters; Solution Manual 3.02 draw and then justify conclusions; following are selected examples. 33, 79, 153, 171, 188, 306, 351, 353, 363, 435, 558, 573, 589, 607, 624, 660, 681, 760, 790, 812, 837 7
8 3.03 construct and follow logical arguments; following are selected examples. 20, 85, 163, 181, 234, 236, 300, 348, 490, 496, 590, 616, use properties, models, known facts, and relationships to explain and defend their thinking following are selected examples. 66 Fitting a Quadratic Model to Data ; 94 Fitting Exponential Models to Data ; 31, 33, 85, 118, 222, 236, 281, 319, 348, 590, 681, 700 following pages for this standard: 344AD, 530AD; Lesson Masters A and B; Teaching Aid 8
9 STANDARD #4 Students will develop their ability to make MATHEMATICAL CONNECTIONS by solving problems in which there is a need to view mathematics as an integrated whole and to integrate mathematics with other disciplines, while allowing the flexibility to approach problems, from within and outside mathematics, in a variety of ways. PERFORMANCE INDICATORS Through the investigation of meaningful problems, individually or in cooperative groups while using appropriate technology, all students in grades K10 will be able to: 4.01 make connections linking conceptual and procedural knowledge; 4.02 integrate mathematical problemsolving with other curricular areas; following are selected examples. 22, 34, 75, 114, 144, 160, 212, 249, 303, 322, 368, 397, 399, 493, 508, 520, 561, 586, 593, 594, 609, 626, 650, 664, 665, 678, 704, 737, 762, 821, 875, 876 SE/TE: Application found in each lesson. Each chapter integrates interdisciplinary connections. A list of which lesson relates to which strand is on the TE page B of the chapter. Example: TE page 202B lists connections to Art, Science and Social Studies in lesson 48, as well as other connections in each of the lessons. 9
10 4.03 use connections among mathematical topics; SE/TE: Application found in each lesson. Each chapter integrates mathematical connections. A list of which lesson relates to which strand is on the TE page B of the chapter. Example: TE page 672B lists connections in lesson 115 to Number Sense, Algebra, Geometry, Measurement, Logic and Reasoning, and Patterns and Functions use various representations of the same concept; following are selected examples. 11 The Language of Algebra 611; 14 Graphs of Functions 2429; 17 Explicit Formulas for Sequences 4214; 27 Fitting a Model to Data I ; 28 Fitting a Model to Data II ; 36 Fitting a Line to Data ; 273 following pages for this standard: 4AD, 70A D; Lesson Masters A and B; Teaching Aid 10
11 4.05 make connections from manipulative solutions to algorithmic solutions to technological solutions; 4.06 determine the reasonableness of a mathematical solution as it applies in a realworld situation. following are selected examples. 14 Graphs of Functions 2429; 17 Explicit Formulas for Sequences 4214; 18 Recursive Formulas for Sequences 4854; 27 Fitting a Model to Data I ; 28 Fitting a Model to Data II ; 36 Fitting a Line to Data ; 273, 563, 723 following pages for this standard: 4AD, 70A D; Lesson Masters A and B; Teaching Aid following are selected examples. 7, 10, 19, 25, 72, 96, 112, 113, 126, 143, 154, 185, 280, 290, 313, 334, 367, 404, 438, 442, 484, 461, 517, 566, 589, 768, 869,
12 Standard #5 Students will develop an understanding of ESTIMATION, MEASUREMENT, and COMPUTATION by solving problems in which there is a need to measure to a required degree of accuracy by selecting appropriate tools and units; to develop computing strategies and select appropriate methods of calculation from among mental math, paper and pencil, calculators or computers; to use estimating skills to approximate an answer and to determine the reasonableness of results. PERFORMANCE INDICATORS: K10 Through the investigation of meaningful problems, individually or in cooperative groups while using appropriate technology, all students in grades 910, building upon the K8 expectations, will be able to: 5.90 compute permutations and combinations; SE/TE: 137 Subsets and Combinations ; 138 Probabilities and Combinations ; 826 following pages for this standard: 808AD; Lesson Masters A and B; Teaching Aid 5.91 compute areas and volumes by partitioning and indirect methods; Standard met in UCSMP Geometry and other UCSMP titles. 12
13 5.92 compute with real numbers; following are selected examples. 15 Solving Equations 3035; 16 Rewriting Formulas 3640; 21 Direct Variation 7277; Finding an Equation of a Line ; Chapter 14 Matrices ; 53 Solving Systems by Substitution ; 62 Absolute Value, Square Roots and Quadratic Equations ; 71 Power Functions ; 131 Arithmetic Series following pages for this standard: 4AD, 70A D, 138AD, 202AD, 270AD, 344AD, 416AD, 476AD, 530AD, 602AD, 672A D, 746AD, 808AD; Lesson Masters A and B; Teaching Aid Masters; Assessment 5.93 compute with matrices; SE/TE: Chapter 4 Matrices ; 305 following pages for this standard: 202AD; Lesson Masters A and B; Teaching Aid 13
14 5.94 extend computation procedures to algebraic procedures; following are selected examples. 15 Solving Equations 3035; 16 Rewriting Formulas 3640; 21 Direct Variation 7277; Finding an Equation of a Line ; Chapter 14 Matrices ; 53 Solving Systems by Substitution ; 62 Absolute Value, Square Roots and Quadratic Equations ; 71 Power Functions ; 131 Arithmetic Series following pages for this standard: 4AD, 70A D, 138AD, 202AD, 270AD, 344AD, 416AD, 476AD, 530AD, 602AD, 672A D, 746AD, 808AD; Lesson Masters A and B; Teaching Aid Masters; Assessment 5.95 determine if errors are within tolerance limits; Standard met in UCSMP Algebra and other UCSMP titles estimate and calculate derived measures; SE/TE: 14, 16, 38, 39, 60, 72, 126, 281, 345, 397, assess the error resulting from estimation and rounding; Standard met in UCSMP Algebra and other UCSMP titles. 14
15 5.98 estimate algebraic solutions on a graphics calculator. SE/TE: 50, 170, 177, 187, 298, 302, 352, 379, 434, 457, 496, 583, 605, 611, 833,
16 STANDARD #6 Students will develop NUMBER SENSE by solving problems in which there is a need to represent and model real numbers verbally, physically and symbolically; to use operations with understanding; to explain the relationships between numbers; to apply the concept of a unit; and to determine the relative magnitude of real numbers. PERFORMANCE INDICATORS: K10 Through the investigation of meaningful problems, individually or in cooperative groups while using appropriate technology, all students in grades 910, building upon the K8 expectations, will be able to:: 6.90 connect physical, verbal and symbolic representations of real numbers; 6.91 demonstrate an understanding of order relations for real numbers; following are selected examples. 11 The Language of Algebra 611; 15 Solving Equations 3035; 16 Rewriting Formulas 3640; 21 Direct Variation 7277; Finding an Equation of a Line ; Chapter 14 Matrices ; 51 Inequalities and Compound Sentences ; 62 Absolute Value, Square Roots and Quadratic Equations ; 71 Power Functions ; 84 Radical Notation for nth Roots ; 131 Arithmetic Series following pages for this standard: 4AD, 70A D, 138AD, 202AD, 270AD, 344AD, 416AD, 476AD, 530AD, 602AD, 672A D, 746AD, 808AD; Lesson Masters A and B; Teaching Aid Masters; Assessment SE/TE:
17 6.92 examine the relative effects of operations on real numbers; 6.93 recognize inverse operations: powers and roots. following are selected examples. 11 The Language of Algebra 611; 15 Solving Equations 3035; 16 Rewriting Formulas 3640; 21 Direct Variation 7277; Finding an Equation of a Line ; Chapter 14 Matrices ; 51 Inequalities and Compound Sentences ; 62 Absolute Value, Square Roots and Quadratic Equations ; 71 Power Functions ; 84 Radical Notation for nth Roots ; 131 Arithmetic Series following pages for this standard: 4AD, 70A D, 138AD, 202AD, 270AD, 344AD, 416AD, 476AD, 530AD, 602AD, 672A D, 746AD, 808AD; Lesson Masters A and B; Teaching Aid Masters; Assessment following are selected examples. 62 Absolute Value, Square Roots and Quadratic Equations ; Chapter 7 Powers ; Chapter 8 Inverses and Radicals ; 91 Exponential Growth ; 92 Exponential Decay following pages for this standard: 344AD, 416AD, 476AD, 530AD; Lesson Masters A 17
18 STANDARD #7 Students will develop an understanding of ALGEBRA by solving problems in which there is a need to progress from the concrete to the abstract using physical models, equations and graphs; to generalize number patterns; and to describe, represent and analyze relationships among variable quantities. PERFORMANCE INDICATORS: K10 Through the investigation of meaningful problems, individually or in cooperative groups while using appropriate technology, all students in grades 910, building upon the K8 expectations, will be able to: 7.90 model relationships among quantities using symbols and expressions; following are selected examples. 11 The Language of Algebra 611; 15 Solving Equations 3035; 16 Rewriting Formulas 3640; 21 Direct Variation 7277; Finding an Equation of a Line ; Chapter 14 Matrices ; 51 Inequalities and Compound Sentences ; 62 Absolute Value, Square Roots and Quadratic Equations ; 71 Power Functions ; 84 Radical Notation for nth Roots ; 131 Arithmetic Series following pages for this standard: 4AD, 70A D, 138AD, 202AD, 270AD, 344AD, 416AD, 476AD, 530AD, 602AD, 672A D, 746AD, 808AD; Lesson Masters A and B; Teaching Aid Masters; Assessment 18
19 7.91 develop appropriate symbol sense to use algebraic technology; 7.92 use tables and graphs to interpret expressions, equations and inequalities; following are selected examples. 11 The Language of Algebra 611; 15 Solving Equations 3035; 16 Rewriting Formulas 3640; 21 Direct Variation 7277; Finding an Equation of a Line ; Chapter 14 Matrices ; 51 Inequalities and Compound Sentences ; 62 Absolute Value, Square Roots and Quadratic Equations ; 71 Power Functions ; 84 Radical Notation for nth Roots ; 131 Arithmetic Series following pages for this standard: 4AD, 70A D, 138AD, 202AD, 270AD, 344AD, 416AD, 476AD, 530AD, 602AD, 672A D, 746AD, 808AD; Lesson Masters A and B; Teaching Aid Masters; Assessment following are selected examples. 14 Graphs of Functions 2429; Chapter 2 Variation and Graphs ; 52 Solving Systems Using Tables or Graphs ; , , , 648 following pages for this standard: 4AD, 70A D, 270AD, 344AD, 476AD; Lesson Masters A and B; Teaching Aid Masters; Assessment Sourcebook; Technology Sourcebook; Answers Masters; Solution Manual 19
20 7.93 describe relationships between variable quantities verbally, symbolically and graphically (including slope as a rate of change); 7.94 translate and make connections from narrative to table, graph and function; following are selected examples. 14 Graphs of Functions 2429; 17 Explicit Formulas for Sequences 4214; 18 Recursive Formulas for Sequences 4854; 27 Fitting a Model to Data I ;34 The Graph of Ax + By = C ; 36 Fitting a Line to Data ; 89, 90, 142, 148, 149, 253 following pages for this standard: 4AD, 70A D; Lesson Masters A and B; Teaching Aid following are selected examples. 14 Graphs of Functions 2429; 17 Explicit Formulas for Sequences 4214; 18 Recursive Formulas for Sequences 4854; 27 Fitting a Model to Data I ; 28 Fitting a Model to Data II ; 36 Fitting a Line to Data ; 273, 563, 723 following pages for this standard: 4AD, 70A D; Lesson Masters A and B; Teaching Aid 20
21 7.95 solve linear and quadratic algebraic problems using graphs, tables, equations, formulas and matrices; 7.96 solve systems of equations algebraically, graphically and with matrices; following are selected examples. Chapter 1 Functions 469; Chapter 2 Variation and Graphs ; Chapter 3 Linear Functions ; Chapter 4 Matrices ; Chapter 6 Quadratic Functions following pages for this standard: 4AD, 70A D, 138AD, 202AD, 344AD; Lesson Masters A and B; Teaching Aid Masters; Assessment Sourcebook; Technology Sourcebook; Answers Masters; Solution Manual following are selected examples. Chapter 5 Systems ; 791, 794, 789 following pages for this standard: 270AD; Lesson Masters A and B; Teaching Aid 21
22 7.97 solve inequalities graphically and symbolically; 7.98 explore algebraic relationships using technology. SE/TE: 51 Inequalities and Compound Sentences ; 57 Graphing Inequalities in the Coordinate Plane ; 58 Systems of Linear Inequalities ; Chapter Planner of the TE. 270AD; Lesson Masters A and B; Teaching Aid Masters; Assessment Sourcebook; Technology Sourcebook; Answers Masters; Solution Manual SE/TE: Introduction to Automatic Graphers 94; Automatic Graphers and Inverse Variation 103; 14, 15, 48, 50, 170, 177, 182, 187, 189, 217, 273, 298, 302, 352, 378, 379, 406, 420, 434, 443, 457, 496, 546, 553, 557, 583, 605, 611, 660, 689, 693, 695, 762, 815, 826, 833, 847, 858 following pages for this standard: 70AD; Lesson Masters A and B; Teaching Aid 22
23 STANDARD #8 Students will develop SPATIAL SENSE and an understanding of GEOMETRY by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships between, geometric figures. PERFORMANCE INDICATORS: K10 all students in grades 910, building upon the K8 expectations, will be able to: 8.90 explore, draw and construct three dimensional objects; 8.91 construct geometric figures on a coordinate plane; 8.92 identify congruent and similar figures using transformational, Euclidean, and coordinate geometries; 8.93 deduce properties of figures using coordinate and Euclidean geometries; Standard met in UCSMP Geometry and other UCSMP titles. SE/TE: 206, 376 SE/TE: 221, 223, 227, 232, 242, 256, 422 Standard met in UCSMP Geometry and other UCSMP titles. 23
24 8.94 explore geometric patterns and generalize results using algebraic expressions ; 8.95 apply similarity, congruence and proportionality; 8.96 use the properties and relationships in two and three dimensional figures including circles and spheres; SE/TE: 14, 16, 38, 39, 60, 72, 126, 281, 345, 397, 697 SE/TE: 221, 223, 227, 232, 242, 256, 422 SE/TE: 14, 16, 38, 39, 60, 72, 126, 281, 345, 397,
25 8.97 apply right triangle trigonometry and the Pythagorean Theorem to problem situations involving right triangles. SE/TE: Chapter 10 Trigonometry ; 400, 405 following pages for this standard: 602AD; Lesson Masters A and B; Teaching Aid STANDARD #9 Students will develop an understanding of STATISTICS AND PROBABILITY by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions; to present convincing arguments; and to model mathematical situations to determine the probability. PERFORMANCE INDICATORS: K10 all students in grades 910, building upon the K8 expectations, will be able to: 9.90 explore and analyze sampling methods to collect data; SE/TE: Polls and Sampling following pages for this standard: 808AD; Lesson Masters A and B; Teaching Aid 25
26 9.91 collect, explore, compare and interpret one or twovariable real world data; 9.92 use curvefitting to model and draw inferences from real life data; 9.93 summarize and interpret singlevariable data by exploring and choosing measures of central tendency and dispersion; SE/TE: 134 Descriptive Statistics ; Polls and Sampling following pages for this standard: 808AD; Lesson Masters A and B; Teaching Aid SE/TE: Binomial and Normal Distributions ; Polls and Sampling following pages for this standard: 808AD; Lesson Masters A and B; Teaching Aid SE/TE: Binomial and Normal Distributions ; Polls and Sampling following pages for this standard: 808AD; Lesson Masters A and B; Teaching Aid 26
27 9.94 analyze the validity of statistical conclusions and the use, misuse, and abuse of data caused by choices of scale, inappropriate choices of central tendency, incorrect curve fitting, or in appropriate use of control groups; 9.95 define a sample space using the fundamental counting principle; 9.96 compare and determine the reasonableness of outcomes; 9.97 model mathematical situations, using simulations or experiments, to determine probabilities of independent and dependent events. SE/TE: Binomial and Normal Distributions ; Polls and Sampling following pages for this standard: 808AD; Lesson Masters A and B; Teaching Aid Standard met in UCSMP Algebra and other UCSMP titles. SE/TE: 138 Probabilities and Combinations ; 139 Lotteries following pages for this standard: 808AD; Lesson Masters A and B; Teaching Aid SE/TE: 852, following pages for this standard: 808AD; Lesson Masters A and B; Teaching Aid 27
28 STANDARD #10 Students will develop an understanding of PATTERNS, RELATIONSHIPS AND FUNCTIONS by solving problems in which there is a need to recognize and extend a variety of patterns; and to analyze, represent, model and describe realworld functional relationships. PERFORMANCE INDICATORS: K10 Through the investigation of meaningful problems, individually or in cooperative groups while using appropriate technology, all students in grades 910, building upon the K8 expectations, will be able to: model realworld phenomena with appropriate functions; following are selected examples. 7, 10, 23, 28, 34, 57, 60, 72, 80, 86, 92, 102, 124, 143, 150, 154, 216, 271, , 313, 365, 419, 438, 442, 461, 517, 535, 564, 574, 614, 730, 857, 869,
29 10.91 search for and describe algebraic, geometric and statistical patterns using mathematical models; classify relationships between variable expressions as linear, quadratic, inverse, direct or exponential; following are selected examples. 12 What is a Function 1217; 17 Explicit Formulas for Sequences 4247; 31 ConstantIncrease or ConstantDecrease Situations ; 39 Step Functions ; 44 Matrices for Size Changes ; 91 Exponential Growth ; 92 Exponential Decay ; Binomial and Normal Distributions following pages for this standard: 4AD, 138AD, 202AD, 416AD, 530AD, 808A D; Lesson Masters A and B; Teaching Aid following are selected examples. 21 Direct Variation 7277;22 Inverse Variation 7882; 31 ConstantIncrease of ConstantDecrease Situations ; 36 Fitting a Line to Data ; 61 Quadratic Expressions, Rectangles and Squares ; 71 Power Functions ; 82 Inverses of Relations ; 91 Exponential Growth ; 92 Exponential Decay following pages for this standard: 70AD, 138AD, 344AD, 416AD, 476AD, 530A D; Lesson Masters A and B; Teaching Aid 29
30 10.93 use technology to explore transformations of functions caused by parameter changes; identify and interpret maximum and minimum values of functional relationships graphically. SE/TE: Introduction to Automatic Graphers 9495; Automatic Graphers and Inverse Variation 103 following pages for this standard: 70AD; Lesson Masters A and B; Teaching Aid SE/TE: 33 Linear Combination Situations ; 13, 25, 99, 480, 485 following pages for this standard: 138AD; Lesson Masters A and B; Teaching Aid 30
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