Utah Core Curriculum for Mathematics, Processes of Teaching and Learning Mathematics and Intermediate Algebra Standards (Grades 9-12) MATHEMATICS Problem Solving 1. Select and use appropriate methods for computing, e.g., mental computation, estimation, paper and pencil, and calculator or computer. 2. Propose, critique, and value alternative approaches to solving problems. 3. Extend mathematical knowledge by considering the thinking strategies of others. 4. Reflect and evaluate mathematical thinking processes used in solving problems. SE/TE: 1-3: Solving Equations, 18-24; 1-4: Solving Inequalities, 26-31; 1-5: Absolute Value Equations and Inequalities, 33-37; 3-2: Solving Systems Algebraically, 123-128; 4-2: Adding and Subtracting Matrices, 170-176; 4-3: Matrix Multiplication, 178-184; 6-4: Solving Polynomial Equations, 321-326; 7-2: Multiplying and Dividing Radical Expressions, 368-373; 7-5: Solving Radical Equations, 385-390; 9-5: Adding and Subtracting Rational Expressions, 504-509; 9-6: Solving Rational Equations, 512-517; 14-2: Solving Trigonometric Equations Using Inverses, 769-776 SE/TE: Problem Solving Strategies: Draw a Diagram, 352, 588, 836; Look For a Pattern, 838; Make a Table, 838; Solve a Simpler Problem, 83; Try, Test, and Revise, 837; Use Logical Reasoning, 840; Work Backward, 841; Writing Equations, 20-21 SE/TE: Cooperative Learning: 4, 11, 25, 39, 64, 71, 85, 99, 112-113, 116, 122, 128, 135, 141, 177, 180, 187, 208-209, 230-231, 240, 248, 255, 269, 277, 300, 306, 328, 335, 346, 358-359, 388, 400, 407, 424, 430, 446, 452, 461, 474-475, 484, 504, 511, 519, 534, 542, 555, 562, 570, 577, 584-585, 588, 599, 600, 607, 613, 620-621, 622, 647, 656, 671, 685, 692-693, 696, 706, 711, 728, 764, 777-778, 793, 820-821 SE/TE: Problem Solving Strategies: Draw a Diagram, 352, 588, 836; Look For a Pattern, 838; Make a Table, 838; Solve a Simpler Problem, 83; Try, Test, and Revise, 837; Use Logical Reasoning, 840; Work Backward, 841; 1
4. Reflect and evaluate mathematical thinking processes used in solving problems. 5. Utilize different problem solving strategies including: a. Drawing a picture or diagram b. Looking for a pattern. c. Identifying counterexamples. d. Choosing an appropriate operation. e. Guessing and checking. f. Making a list, table, graph, or equation. g. Working backwards. h. Eliminating possibilities. i. Making a model or simulation. j. Solving a simpler or related problem. k. Checking the reasonableness of results. l. Using proportional reasoning. 6. Develop clarification and understanding of new mathematical concepts, processes, and vocabulary by reflecting upon and answering such questions as: a. What made you think of that? b. Did anyone think about this in a different way? c. How are these ideas related? d. Where have we seen a problem like this before? e. How does today s work relate to what we have done in earlier units of study? 7. Solve a variety of multi- step, nonroutine, complex problems including puzzles, applications, patterning, and open- ended or extended problemsolving projects. SE/TE: Writing Equations, 20-21; Real-World Snapshots: 112-113, 230-231, 474-475, 584-585, 692-693, 820-821 SE/TE: Real-World Snapshots: 112-113, 230-231, 474-475, 584-585, 692-693, 820-821; Problem Solving Strategies: Draw a Diagram, 352, 588, 836; Look For a Pattern, 838; Make a Table, 838; Solve a Simpler Problem, 83; Try, Test, and Revise, 837; Use Logical Reasoning, 840; Work Backward, 841; Writing Equations, 20-21; Real World Connections: 13, 15, 21, 22, 24, 37, 41, 58, 61, 73, 77, 78, 82, 112-113, 117, 131, 133, 134, 138, 143, 147, 175, 189, 205, 207, 214, 222, 230-231, 236, 243, 245, 247, 250, 260, 264, 302, 320, 325, 340, 343, 350, 358-359, 366, 380, 383, 386, 394, 405, 406, 426, 432, 436, 438, 463, 467, 474-475, 479, 486, 495, 505, 509, 513, 525, 5541, 545, 547, 551, 572, 575, 584-585, 604, 605, 608, 610, 615, 616, 617, 637, 642, 649, 664, 668, 669, 692-693, 699, 700, 702, 705, 715, 738, 745, 774, 779, 781, 789, 798, 799, 820-821 SE/TE: Writing: 10, 11, 17, 25, 30, 37, 44, 50, 60, 71, 76, 77, 83, 85, 89, 96, 103, 110, 120, 122, 127, 133, 139, 145, 154, 160, 167, 176, 184, 185, 192, 193, 200, 206, 209, 213, 222, 228, 238, 246, 253, 260, 267, 274, 282, 290, 296, 304, 312, 319, 326, 334, 338, 343, 344, 345, 350, 356, 362, 367, 372, 377, 383, 389, 396, 397, 405, 407, 412, 418, 419, 429, 430, 435, 442, 450, 457, 460, 461, 466, 472, 482, 487, 489, 496, 502, 508, 516, 530, 539, 542, 547, 553, 555, 560, 566, 574, 577, 582, 592, 597, 603, 605, 611, 618, 622, 626, 629, 630, 632, 640, 645, 647, 653-655, 661, 662, 667, 675, 680, 681, 690, 700, 709, 718, 726, 728, 733, 739, 747, 754, 760, 767, 774, 775, 791, 793, 798, 805, 810, 816 SE/TE: Problem Solving Strategies: Draw a Diagram, 352, 588, 836; Look For a Pattern, 838; Make a Table, 838; Solve a Simpler Problem, 83; Try, Test, and Revise, 837; Use Logical Reasoning, 840; Work Backward, 841 2
7. Solve a variety of multi- step, nonroutine, complex problems including puzzles, applications, patterning, and open- ended or extended problemsolving projects. 8. Estimate solutions to problems and determine the reasonableness of answers by relating them to the estimates. SE/TE: Writing Equations, 20-21; Real-World Snapshots: 112-113, 230-231, 474-475, 584-585, 692-693, 820-821; Real World Connections: 13, 15, 21, 22, 24, 37, 41, 58, 61, 73, 77, 78, 82, 112-113, 117, 131, 133, 134, 138, 143, 147, 175, 189, 205, 207, 214, 222, 230-231, 236, 243, 245, 247, 250, 260, 264, 302, 320, 325, 340, 343, 350, 358-359, 366, 380, 383, 386, 394, 405, 406, 426, 432, 436, 438, 463, 467, 474-475, 479, 486, 495, 505, 509, 513, 525, 5541, 545, 547, 551, 572, 575, 584-585, 604, 605, 608, 610, 615, 616, 617, 637, 642, 649, 664, 668, 669, 692-693, 699, 700, 702, 705, 715, 738, 745, 774, 779, 781, 789, 798, 799, 820-821 SE/TE: estimation: 168, 238, 628, 701, 727, 746, 747 Reasoning and Proof 1. Link problem solving to the sequence of steps in a proof and draw reasonable conclusions. 2. Explain and justify problem-solving procedures. 3. Examine patterns and note regularities and irregularities in various types of problems. 4. Make and investigate mathematical conjectures. SE/TE: Reasoning: 9, 79, 120, 175, 241, 284, 318-319, 343, 346, 383, 450, 497, 547, 553, 576, 607, 615, 667, 705, 718, 720, 737, 753, 754, 755, 778, 783, 792, 804, 805 SE/TE: Problem Solving Strategies: Draw a Diagram, 352, 588, 836; Look For a Pattern, 838; Make a Table, 838; Solve a Simpler Problem, 83; Try, Test, and Revise, 837; Use Logical Reasoning, 840; Work Backward, 841; Writing Equations, 20-21; Real-World Snapshots: 112-113, 230-231, 474-475, 584-585, 692-693, 820-821 SE/TE: Problem Solving Strategies: Look For a Pattern, 838; 11-1: Mathematical Patterns, 588-593; 11-2: Arithmetic Sequences, 594-598; 11-3: Geometric Sequences, 600-604; 11-4: Arithmetic Series, 607-613; 11-5: Geometric Series, 614-618 SE/TE: Make a Conjecture: 186, 201, 277, 313, 334, 413, 446, 539, 562, 567, 599, 613, 705, 755, 764, 778 3
5. Formulate counterexamples. SE/TE: Reasoning: 9, 79, 120, 175, 241, 284, 318-319, 343, 346, 383, 450, 497, 547, 553, 576, 607, 615, 667, 705, 718, 720, 737, 753, 754, 755, 778, 783, 792, 804, 805 6. Use a variety of formal and informal proofs appropriate to the course. 7. Identify information as necessary, sufficient, or extraneous and conclusions as valid or invalid. 8. Realize that observing a pattern and stating a conjecture related to the pattern does not constitute a proof. SE/TE: Reasoning: 9, 79, 120, 175, 241, 284, 318-319, 343, 346, 383, 450, 497, 547, 553, 576, 607, 615, 667, 705, 718, 720, 737, 753, 754, 755, 778, 783, 792, 804, 805 SE/TE: Problem Solving Strategies: Look For a Pattern, 838; 11-1: Mathematical Patterns, 588-593; 11-2: Arithmetic Sequences, 594-598; 11-3: Geometric Sequences, 600-604; 11-4: Arithmetic Series, 607-613; 11-5: Geometric Series, 614-618 SE/TE: Problem Solving Strategies: Look For a Pattern, 838; 11-1: Mathematical Patterns, 588-593; 11-2: Arithmetic Sequences, 594-598; 11-3: Geometric Sequences, 600-604; 11-4: Arithmetic Series, 607-613; 11-5: Geometric Series, 614-618 Communication 1. Express mathematical ideas coherently and clearly to peers, teachers, and others.. 2. Employ the precise language and notation of mathematics to clearly express mathematical ideas. SE/TE: Writing: 10, 11, 17, 25, 30, 37, 44, 50, 60, 71, 76, 77, 83, 85, 89, 96, 103, 110, 120, 122, 127, 133, 139, 145, 154, 160, 167, 176, 184, 185, 192, 193, 200, 206, 209, 213, 222, 228, 238, 246, 253, 260, 267, 274, 282, 290, 296, 304, 312, 319, 326, 334, 338, 343, 344, 345, 350, 356, 362, 367, 372, 377, 383, 389, 396, 397, 405, 407, 412, 418, 419, 429, 430, 435, 442, 450, 457, 460, 461, 466, 472, 482, 487, 489, 496, 502, 508, 516, 530, 539, 542, 547, 553, 555, 560, 566, 574, 577, 582, 592, 597, 603, 605, 611, 618, 622, 626, 629, 630, 632, 640, 645, 647, 653-655, 661, 662, 667, 675, 680, 681, 690, 700, 709, 718, 726, 728, 733, 739, 747, 754, 760, 767, 774, 775, 791, 793, 798, 805, 810, 816 SE/TE: Writing: 10, 11, 17, 25, 30, 37, 44, 50, 60, 71, 76, 77, 83, 85, 89, 96, 103, 110, 120, 122, 127, 133, 139, 145, 154, 160, 167, 176, 184, 185, 192, 193, 200, 206, 209, 213, 222, 228 4
2. Employ the precise language and notation of mathematics to clearly express mathematical ideas. 3. Organize and consolidate mathematical thinking using communication methods, e.g., class and group discussion, journals, portfolios, oral presentations, and written reports. SE/TE: Writing: 238, 246, 253, 260, 267, 274, 282, 290, 296, 304, 312, 319, 326, 334, 338, 343, 344, 345, 350, 356, 362, 367, 372, 377, 383, 389, 396, 397, 405, 407, 412, 418, 419, 429, 430, 435, 442, 450, 457, 460, 461, 466, 472, 482, 487, 489, 496, 502, 508, 516, 530, 539, 542, 547, 553, 555, 560, 566, 574, 577, 582, 592, 597, 603, 605, 611, 618, 622, 626, 629, 630, 632, 640, 645, 647, 653-655, 661, 662, 667, 675, 680, 681, 690, 700, 709, 718, 726, 728, 733, 739, 747, 754, 760, 767, 774, 775, 791, 793, 798, 805, 810, 816 SE/TE: Real-World Snapshots: 112-113, 230-231, 474-475, 584-585, 692-693, 820-821; Cooperative Learning: 4, 11, 25, 39, 64, 71, 85, 99, 112-113, 116, 122, 128, 135, 141, 177, 180, 187, 208-209, 230-231, 240, 248, 255, 269, 277, 300, 306, 328, 335, 346, 358-359, 388, 400, 407, 424, 430, 446, 452, 461, 474-475, 484, 504, 511, 519, 534, 542, 555, 562, 570, 577, 584-585, 588, 599, 600, 607, 613, 620-621, 622, 647, 656, 671, 685, 692-693, 696, 706, 711, 728, 764, 777-778, 793, 820-821 Connections 1. Formulate real- world situations that require extended investigations, solve them, and justify answers. 2. Establish connections among mathematical expressions, physical models, pictorial representations, and real- world situations. SE/TE: Real-World Snapshots: 112-113, 230-231, 474-475, 584-585, 692-693, 820-821; Real World Connections: 13, 15, 21, 22, 24, 37, 41, 58, 61, 73, 77, 78, 82, 112-113, 117, 131, 133, 134, 138, 143, 147, 175, 189, 205, 207, 214, 222, 230-231, 236, 243, 245, 247, 250, 260, 264, 302, 320, 325, 340, 343, 350, 358-359, 366, 380, 383, 386, 394, 405, 406, 426, 432, 436, 438, 463, 467, 474-475, 479, 486, 495, 505, 509, 513, 525, 5541, 545, 547, 551, 572, 575, 584-585, 604, 605, 608, 610, 615, 616, 617, 637, 642, 649, 664, 668, 669, 692-693, 699, 700, 702, 705, 715, 738, 745, 774, 779, 781, 789, 798, 799, 820-821 SE/TE: Problem Solving Strategies: Draw a Diagram, 352, 588, 836; Make a Table, 838; Real- World Snapshots: 112-113, 230-231, 474-475, 584-585, 692-693, 820-821 5
2. Establish connections among mathematical expressions, physical models, pictorial representations, and real- world situations. 3. Find applications of mathematical concepts in newspapers, magazines, television, radio, or other sources. 4. Explore historical and multicultural contributions to mathematics. 5. Recognize and apply mathematical ideas and relationships in areas outside the mathematics classroom, e.g., art, science, other curricular areas, and everyday life. SE/TE: 2-4: Using Linear Models, 78-84; 5-1: Modeling Data with Quadratic Functions, 234-239; 8-1: Exploring Exponential Models, 422-429 SE/TE: Real World Connections: 13, 15, 21, 22, 24, 37, 41, 58, 61, 73, 77, 78, 82, 112-113, 117, 131, 133, 134, 138, 143, 147, 175, 189, 205, 207, 214, 222, 230-231, 236, 243, 245, 247, 250, 260, 264, 302, 320, 325, 340, 343, 350, 358-359, 366, 380, 383, 386, 394, 405, 406, 426, 432, 436, 438, 463, 467, 474-475, 479, 486, 495, 505, 509, 513, 525, 5541, 545, 547, 551, 572, 575, 584-585, 604, 605, 608, 610, 615, 616, 617, 637, 642, 649, 664, 668, 669, 692-693, 699, 700, 702, 705, 715, 738, 745, 774, 779, 781, 789, 798, 799, 820-821 SE/TE: Point in Time: 207, 467, 541, 605, 702 SE/TE: Real-World Snapshots: 112-113, 230-231, 474-475, 584-585, 692-693, 820-821; Real World Connections: 13, 15, 21, 22, 24, 37, 41, 58, 61, 73, 77, 78, 82, 112-113, 117, 131, 133, 134, 138, 143, 147, 175, 189, 205, 207, 214, 222, 230-231, 236, 243, 245, 247, 250, 260, 264, 302, 320, 325, 340, 343, 350, 358-359, 366, 380, 383, 386, 394, 405, 406, 426, 432, 436, 438, 463, 467, 474-475, 479, 486, 495, 505, 509, 513, 525, 5541, 545, 547, 551, 572, 575, 584-585, 604, 605, 608, 610, 615, 616, 617, 637, 642, 649, 664, 668, 669, 692-693, 699, 700, 702, 705, 715, 738, 745, 774, 779, 781, 789, 798, 799, 820-821 Representation 1. Use a variety of visual representations (e.g., patty paper, dot paper, graph paper, models, manipulatives, nets, and technology) to explore and formulate conjectures related to mathematical concepts being studied. SE/TE: Technology: 25, 85, 141, 177, 240, 407, 430, 452, 461, 484, 542, 622, 685, 728; number cubes: 519; tiles: 277 6
2. Represent mathematical concepts using physical models, visualizations, and appropriate symbolic notations. 3. Represent problem situations verbally, numerically, graphically, geometrically, or algebraically. SE/TE: Problem Solving Strategies: Draw a Diagram, 352, 588, 836; Make a Table, 838; Real- World Snapshots: 112-113, 230-231, 474-475, 584-585, 692-693, 820-821; 2-4: Using Linear Models, 78-84; 5-1: Modeling Data with Quadratic Functions, 234-239; 8-1: Exploring Exponential Models, 422-429 SE/TE: Problem Solving Strategies: Draw a Diagram, 352, 588, 836; Look For a Pattern, 838; Make a Table, 838; Solve a Simpler Problem, 83; Try, Test, and Revise, 837; Use Logical Reasoning, 840; Work Backward, 841; Writing Equations, 20-21; Real-World Snapshots: 112-113, 230-231, 474-475, 584-585, 692-693, 820-821 INTERMEDIATE ALGEBRA Standard 1: Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1: Compute fluently and make reasonable estimates. 1. Simplify numerical expressions with rational exponents. 2. Add, subtract, and multiply complex numbers. 3. Add, subtract, and multiply matrices using paper and pencil for simple cases and technology for more complicated cases. 4. Find the multiplicative inverse of a matrix using paper and pencil for a 2 2 and technology for larger matrices. SE/TE: 7-4: Rational Exponents, 379-384; 9-4: Rational Expressions, 499-503; 9-5: Adding and Subtracting Rational Expressions, 504-509 SE/TE: 6-3: Dividing Polynomials, 314-319; 7-2: Multiplying and Dividing Radical Expressions, 368-373; 9-5: Adding and Subtracting Rational Expressions, 504-509 SE/TE: 4-2: Adding and Subtracting Matrices, 170-176; 4-3: Matrix Multiplication, 178-184 SE/TE: 4-5: 2 2 Matrices, Determinants, and Inverses, 195-201; 4-6: 3 3 Matrices, Determinants, and Inverses, 202-206 Objective 1.2: Represent complex numbers in a variety of ways. 7
1. Extend the number system to include complex numbers in the form a + bi. 1. Extend the number system to include complex numbers in the form a + bi. 2. Identify the need for the square root of a negative number and define the imaginary number I = -1. SE/TE: 6-1: Polynomial Functions, 300-305; 6-2: Polynomials and Linear Factors, 307-313; 6-3: Dividing Polynomials, 314-319 SE/TE: 6-4: Solving Polynomial Equations, 321-326; 6-5: Theorems about Roots of Polynomials, 329-334; 6-8: The Binomial Theorem, 347-351 SE/TE: 6-5: Theorems about Roots of Polynomials, 329-334; 7-1: Roots and Radical Expressions, 363-367 3. Simplify expressions involving radical expressions including square roots of negative numbers. SE/TE: 7-1: Roots and Radical Expressions, 363-367; 7-2: Multiplying and Dividing Radical Expressions, 368-373; 7-3: Binomial Radical Expressions, 374-377 Objective 1.3: Identify relationships among real numbers and operations involving these numbers. 1. Identify matrices that can be added, subtracted, or multiplied. 2. Demonstrate that matrix multiplication is not commutative. 3. Identify additive and multiplicative identities and inverses of a matrix when they exist. SE/TE: 4-2: Adding and Subtracting Matrices, 170-176; 4-3: Matrix Multiplication, 178-184 SE/TE: 4-3: Matrix Multiplication, 178-184 SE/TE: 4-2: Adding and Subtracting Matrices, 170-176; 4-3: Matrix Multiplication, 178-184 Standard 2: Students will represent and analyze mathematical situations and properties using patterns, relations, functions, and algebraic symbols. Objective 2.1 Use patterns, relations, and functions to represent mathematical situations. 1. Compare and contrast relations and functions. SE/TE: 7-7: Inverse Relations and Functions, 400-406; 7-8: Graphing Radical Functions, 408-413; 8-2: Properties of Exponential Functions, 431-436; 9-3: Rational Functions and Their Graphs, 491-497 8
2. Identify the domain and range of the absolute value, quadratic, radical, sine, and cosine functions. SE/TE: 2-5: Absolute Value Functions and Graphs, 86-90; 5-1: Modeling Data with Quadratic Functions, 234-239; 7-6: Function Operations, 392-397; 7-8: Graphing Radical Functions, 408-413; 13-4: The Sine Function, 720-727; 13-5: The Cosine Function, 729-734 3. Use function notation. SE/TE: 2-1: Relations and Functions, 55-61; 2-5: Absolute Value Functions and Graphs, 86-90; 5-1: Modeling Data with Quadratic Functions, 234-239; 6-1: Polynomial Functions, 300-305; 7-6: Function Operations, 392-397; 7-7: Inverse Relations and Functions, 400-406; 7-8: Graphing Radical Functions, 408-413; 8-2: Properties of Exponential Functions, 431-436; 8-3: Logarithmic Functions as Inverses, 438-444; 9-3:Rational Functions and Their Graphs, 491-497; 13-4: The Sine Function, 720-727; 13-5: The Cosine Function, 729-734; 13-6: The Tangent Function, 735-740; 13-7: Translating Sine and Cosine Functions, 742-747; 13-8: Reciprocal Trigonometric Functions, 749-755 4. Find the compositions or combinations of two simple functions. 5. Find the inverse of a function by interchanging the values of domain and range, reflecting across the line y = x or by using algebra. 6. Relate the sine, cosine, tangent, cosecant, secant, and cotangent to the unit circle. 7. Express angle measure in degrees or radians when given the trigonometric value. SE/TE: 7-6: Function Operations, 392-397 SE/TE: 7-7: Inverse Relations and Functions, 400-406; 8-3: Logarithmic Functions as Inverses, 438-444; 9-1: Inverse Variation, 478-483; 9-2: Graphing Inverse Variations, 485-490 SE/TE: 12-2: Angles and the Unit Circle, 704-711; 13-4: The Sine Function, 720-727; 13-5: The Cosine Function, 729-734; 13-6: The Tangent Function, 735-740; 13-7: Translating Sine and Cosine Functions, 742-747 SE/TE: 12-2: Angles and the Unit Circle, 704-711; 12-3: Radian Measure, 712-718 Objective 2.2: Evaluate, solve, and analyze mathematical situations using algebraic properties and symbols. 9
1. Solve quadratic equations. SE/TE: 5-5: Quadratic Equations, 263-268; 5-6: Complex Numbers, 270-275; 5-7: Completing the Square, 278-283; 5-8: The Quadratic Formula, 285-291 2. Solve first-degree absolute value equations. SE/TE: 1-5: Absolute Value Equations and Inequalities, 33-37 3. Solve radical equations including those with extraneous roots. 4. Solve single-variable quadratic and absolute value inequalities. 5. Write a quadratic equation when given the rational roots or zeroes of the function. 6. Solve systems of equations with no more than three variables using technology. 7. Solve and graph systems of linear inequalities. 8. Add, subtract, multiply, and divide simple rational expressions and solve simple rational equations. 9. Recognize that a -n is defined as the reciprocal of a n. SE/TE: 7-5: Solving Radical Equations, 385-390; 7-6: Function Operations, 392-397; 7-7: Inverse Relations and Functions, 400-406; 7-8: Graphing Radical Functions, 408-413 SE/TE: 1-5: Absolute Value Equations and Inequalities, 33-37 SE/TE: 5-5: Quadratic Equations, 263-268; 5-6: Complex Numbers, 270-275; 5-7: Completing the Square, 278-283; 5-8: The Quadratic Formula, 285-291 SE/TE: 3-1: Graphing Systems of Equations, 116-121; 3-2: Solving Systems Algebraically, 123-128; 3-6: Systems with Three Variables, 148-155; 4-7: Inverse Matrices and Systems, 210-215; 4-8: Augmented Matrices and Systems, 217-223 SE/TE: 3-3: Systems of Inequalities, 130-133 SE/TE: 9-1: Inverse Variation, 478-483; 9-2: Graphing Inverse Variations, 485-490; 9-3: Rational Functions and Their Graphs, 491-497; 9-4: Rational Expressions, 499-503; 9-5: Adding and Subtracting Rational Expressions, 504-509; 9-6: Solving Rational Equations, 512-517; 9-7: Probability of Multiple Events, 519-525 SE/TE: 5-5: Quadratic Equations, 263-268; 5-6: Complex Numbers, 270-275 10
10. Recognize that rational exponents are used to represent radicals. 11. Represent intervals with correct symbolic notation; e.g., a < x < b, (a, b), [a, b]. SE/TE: 7-4: Rational Exponents, 379-384 SE/TE: 1-4: Solving Inequalities, 26-31; 1-5: Absolute Value Equations and Inequalities, 33-37; 3-3: Systems of Inequalities, 130-133 Objective 2.3: Represent quantitative relationships using mathematical models and symbols. 1. Interpret rates of change by analyzing graphical and numerical data for quadratic and radical functions. 2. Find the vertex, maximum or minimum values, intercepts, and axis of symmetry of a quadratic or absolute value functions, algebraically, graphically, and numerically. 3. Write the equation of a parabola in the form y = a(x h) 2 + k and a circle in the form y = a(x-h) 2 + (y k) 2 = r 2 by completing the square. SE/TE: 5-1: Modeling Data with Quadratic Functions, 234-239; 5-2: Properties of Parabolas, 241-247; 5-3: Translating Parabolas, 248-253; 7-6: Function Operations, 392-397; 7-7: Inverse Relations and Functions, 400-406; 7-8: Graphing Radical Functions, 408-413 SE/TE: 2-5: Absolute Value Functions and Graphs, 86-90; -1: Modeling Data with Quadratic Functions, 234-239; 5-2: Properties of Parabolas, 241-247; 5-3: Translating Parabolas, 248-253 SE/TE: 5-2: Properties of Parabolas, 241-247; 5-3: Translating Parabolas, 248-253; 5-7: Completing the Square, 278-283; 10-3: Circles, 549-553 Standard 3: Students will solve problems using spatial and logical reasoning, applications of geometric principles, and modeling. Objective 3.2: Specify locations and describe spatial relationships using coordinate geometry. 1. Sketch the graph of a quadratic and absolute value function. 2. Sketch the solutions of absolute value and quadratic inequalities of one variable on a number line. SE/TE: 2-5: Absolute Value Functions and Graphs, 86-90; -1: Modeling Data with Quadratic Functions, 234-239; 5-2: Properties of Parabolas, 241-247; 5-3: Translating Parabolas, 248-253 SE/TE: 1-5: Absolute Value Equations and Inequalities, 33-37; Extension: Quadratic Inequalities, 269 11
3. Sketch the solutions of absolute value and quadratic inequalities of two variables on a Cartesian coordinate system. 4. Sketch the graph of a square root function. 5. Write an equation of a parabola in the form y = a( x - h) 2 + k when given a graph. SE/TE: 1-5: Absolute Value Equations and Inequalities, 33-37; Extension: Quadratic Inequalities, 269 SE/TE: 7-8: Graphing Radical Functions, 408-413 SE/TE: 5-2: Properties of Parabolas, 241-247; 5-3: Translating Parabolas, 248-253; 10-2: Parabolas, 543-548 6. Graph sine and cosine functions. SE/TE: 13-4: The Sine Function, 720-727; 13-5: The Cosine Function, 729-734 7. Perform the transformations of stretching, shifting, and reflecting the graphs of linear, absolute value, quadratic, and radical functions. 8. Perform transformation on the sine and cosine functions involving amplitude, period, phase shift, vertical shift, and reflections. SE/TE: 2-6: Vertical and Horizontal Translations, 91-97; 4-4: Geometric Transformations with Matrices, 187-194; 5-3: Translating Parabolas, 248-253; 10-6: Translating Conic Sections, 570-576 SE/TE: 13-7: Translating Sine and Cosine Functions, 742-747 Objective 3.3: Solve problems using visualization, spatial reasoning, and geometric modeling. 1. Solve problems involving absolute value and quadratic functions algebraically and graphically. 2. Solve problems using graphs of sine and cosine functions. SE/TE: 2-5: Absolute Value Functions and Graphs, 86-90; -1: Modeling Data with Quadratic Functions, 234-239; 5-2: Properties of Parabolas, 241-247; 5-3: Translating Parabolas, 248-253 SE/TE: 13-4: The Sine Function, 720-727; 13-5: The Cosine Function, 729-734; 13-7: Translating Sine and Cosine Functions, 742-747 Standard 4: Students will understand and apply measurement tools, formulas, and techniques. Objective 4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement. 1. Convert angle measurements between radians and degrees. SE/TE: 12-3: Radian Measure, 712-718 12
2. Calculate the exact values of the sine, cosine, and tangent functions for the special angles of the unit circle. SE/TE: 12-2: Angles and the Unit Circle, 704-711; 13-4: The Sine Function, 720-727; 13-5: The Cosine Function, 729-734; 13-6: The Tangent Function, 735-740 Objective 4.2: Determine measurements using appropriate techniques, tools, and formulas. 1. Find the length of an arc using radian measure. 2. Find the area of a sector in a circle using radian measure. SE/TE: 12-3: Radian Measure, 712-718 SE/TE: 12-3: Radian Measure, 712-718 Standard 5: Students will draw conclusions using concepts of probability after collecting, organizing, and analyzing a data set. Objective 5.1: Formulate and answer questions by collecting, organizing, and analyzing data. 1. Determine the quadratic regression equation for a given set of bivariate data using technology. 2. Analyze the meaning of the maximum or minimum and intercepts of the regression equation as they relate to a given set of bivariate data. 3. Make predictions and estimations and determine their reasonableness using a regression equation. SE/TE: 5-1: Modeling Data with Quadratic Functions, 234-239 SE/TE: 5-1: Modeling Data with Quadratic Functions, 234-239 SE/TE: 5-1: Modeling Data with Quadratic Functions, 234-239 Objective 5.2: Apply basic concepts of probability. 1. Identify the difference between a permutation and a combination. 2. Calculate a probability using the Fundamental Counting Principle. SE/TE: 6-7: Permutations and Combination, 339-344 SE/TE: 6-7: Permutations and Combination, 339-344 13
3. Calculate simple combinations and permutations of n objects taken r at a time. SE/TE: 6-7: Permutations and Combination, 339-344 14