A Correlation of. To the. North Carolina Standard Course of Study for Mathematics High School Math 2

Transcription

1 A Correlation of 2018 To the North Carolina Standard Course of Study for Mathematics High School Math 2

2 Table of Contents Standards for Mathematical Practice... 1 Number and Quantity... 8 Algebra... 9 Functions Statistics and Probability Copyright 2017 Pearson Education, Inc. or its affiliate(s). All rights reserved

3 Standards for Mathematical Practice Make sense of problems and persevere in solving them. The envision A G A program fosters the development of mathematical practices and habits of mind by providing opportunities for students to carefully read and effectively analyze problems and devise and implement meaningful solution strategies. Sample references are cited here. SE: 10, 35, 52, 74, 116, 123, 133, 179, 186, 228, 244, 265, , 373, 381, 407, 459, 479, 500, 505 TE: 5B, 11A-B, 18B, 24A, 30A-B, 37B, 43A, 143B, 157A, 164B, 197B, 224B, 231B, 344A-B, 363B, 397A, 418B, 432A, 472B, 495B SE: 13-14, 34, 58, 78, 101, 106, 123, 165, 187, , 216, , , , , 366, , 469, 513, 536 TE: 14B, 58A-B, 71A, 78A-B, 167B, 174A-B, 182B, 188A-B, 245A-B, 262A-B, 317B, 361A-B, 385B, 393B, 406A-B, 444A-B, 451A-B, 487A-B, 515B, 537A-B SE: 12, 28, 39, 64, 116, , 209, 221, , 262, 271, , , 391, 399, , 411, 545, 556, 598 TE: 7, 27, 36, 103B, 106, 181, 205, 228, 242, 248, 369, 378, 394, 400B, 433B, 445, 484, 503B, 523, 551B 1

4 Reason abstractly and quantitatively The envision A G A program incorporates mathematical practices and habits of mind by requiring students to reason abstractly (using variables, expressions, and equations to solve problems) and to reason quantitatively (comparing and using numbers, measurements, and data to solve problems). In geometry, emphasis on proof requires entire lessons to focus on the development of abstract reasoning. Higher Order Thinking problems are included in many of the problem sets throughout the series. Sample references are cited here. SE: 9, 22, 34, 61, 73, 100, 116, 133, 163, 188, 208, 229, 244, 265, 292, 327, 341, 380, 405, 449 TE: 5A, 18A, 69A, 110A, 118A, 143A, 150A, 183A, 246A, 259A, 295A, 301A, 354D, 363A, 376A-B, 438A, 451A, 462D, 472A, 495A SE: 28-34, 44-50, 51-57, 58-63, 78-84, , , , , , , , , , , , , 425, 433, TE: 5A, 22A, 51A, 58A, 78A, 92A, 105A, 129A, 149A, 182A, 201A, 233A, 301A, 333A, 361A, 367A, 393A, 419A, 427A, 465A SE: 11, 20, 30, 64, , 126, , 304, 331, 347, 363, 373, 375, , 389, 397, 406, 411, 425 TE: 13B, 24, 117B, 210B, 220, 224B, 225, 251, 298, 314B, 358, 372, 383B, 393B, 436, 467, 475, 489B, 511B, 521 2

5 Construct viable arguments and critique the reasoning of others The envision A G A program incorporates mathematical practices and habits of mind by challenging students to construct viable arguments to justify their own reasoning and conclusions, and to critique the reasoning of others by finding their errors or explaining their reasoning. In geometry, emphasis on proof requires entire lessons to focus on the construction of viable arguments. Construct Arguments and Error Analysis problems are included in many of the problem sets throughout the series and ask students to critique the reasoning of others. Sample references are cited here. SE: 8, 51, 73, 92, 99, 133, 148, 162, 175, 194, , 222, 243, 265, 292, 305, 340, 368, 441, 500 TE: 5A-B, 24B, 30A, 63A-B, 102B, 157A-B, 197B, 217A-B, 259A, 301B, 322B, 329A, 357A, 376B, 382A-B, 418A-B, 432B, 465A-B, 472B, 487A SE: 28-34, 44-50, 51-57, 58-63, 78-84, , , , , , , , , , , , , , , TE: 8, 15, 31, 47, 54, 79, 105, 150, 178, 218B, 253B, 279B, 328, 345B, 368, 396, 429, 472, 531, 539 SE: 10-11, 20-21, 26, 29, 37, 38, 39, 99, 121, 207, 253, 261, 302, , , , , , 405, 421 TE: 9, 56B, 81, 91, 98, 111, 183, 194, 211, 224, 247B, 263B, 360, 415, 437, 452, 493, 565B, 637, 645 3

6 Model with mathematics The envision A G A program incorporates mathematical practices and habits of mind by encouraging students to model problem situations using equations and inequalities, tables and graphs, and drawings and physical manipulatives. Mathematical Modeling in 3 Acts activities are included within each topic. Sample references are cited here. SE: 23-24, 35-36, 42-43, 51-53, 83-84, 125, 134, , 189, 209, 230, 259, 266, 274, 290, 343, 350, 362, 375, TE: 24A-B, 37B, 43A-B, 57A, 76A, 95A, 110B, 143B, 171A, 183B, 203A, 231B, 259B, 281A, 321A, 322A, 336A, 418A, 425A, 443A SE: 35, 50, 77, 99, 120, 142, 181, 216, 225, 238, 252, 309, 320, 332, 373, 392, 435, 443, 479, 514 TE: 22B, 35-35B, 92B, 99-99B, B, 153, B, 201B, B, B, B, 350, 357, B, B, 419B, B, 475, B, B SE: 11-12, 22, 30, 38-39, 64, 101, 123, 209, 223, 271, 313, , 391, 407, 409, 422, 448, 458, 471, 478 TE: 17, 55A-B, 84, 91, 102A-B, 170A-B, 203, 232A-B, 258, 272A-B, 281B, 313A-B, 392A-B, 404, 423A-B, 449B, 479A-B, 544A-B, 597A-B, 620A-B 4

7 Use appropriate tools strategically. The envision A G A program incorporates mathematical practices and habits of mind by asking students to use appropriate tools strategically. These tools include different forms of technology (e.g., drawing and graphing software, spreadsheet, calculator) and measuring instruments (e.g., rulers, protractors). Sample references are cited here. SE: 20, 29, 71, 91, 104, 129, , 145, 166, 174, 184, 198, 208, 225, 237, 244, 250, , , 282 TE: 91, 104, 118A-B, 126A, 145, 150B, 166, 172, 191B, 197A, 225, 239B, 287A, 330, 389B, 397B, 411A, 445A, 465A-B, 488 SE: 16, 20, 57, 85, 204, 220, 269, 277, 291, 357, 378, 391, 450, 469, 477, 478, 487, 517, 540, 541 TE: 10, 14A, 22B, 35A-B, 52, 113B, 174A, 181, 201B, 246, 271A, 271B, 310B, 319, 324A-B, 374A-B, 385A, 400B, 427A-B, 481 SE: 18, 62-63, 110, 114, 215, 219, 231, 241, 345, 351, 418, 453, 456, 487, 531, 575, 583, 591, 623, 647 TE: 34, 40A, 43, 113, 135, 169A-B, 171A, 239A, 330, 333B, 339B, 343, 365A, 369, 415A, 429, 453, 544B, 596B, 627B 5

8 Attend to precision. The envision A G A program incorporates mathematical practices and habits of mind by requiring students to attend to precision by using precise mathematical vocabulary, accurate computation, and estimation to verify the reasonableness of answers or when an exact answer is unattainable or inappropriate for the situation. Sample references are cited here. SE: 67, 122, 126, , 139, 143, 146, 151, 155, 186, 189, 234, 251, 330, 339, 344, 358, 410, 421, 480 TE: 11, 39, 57A, 63A, 78, 95A, 110A, 114, 127, 134B, 143A, 160, 165, 191A, 197A, 411A, 425A, 438A SE: 6, 21, 22, 39, 41, 66, 67, 77, 78, 110, 120, 123, 128, 278, 296, 308, 381, 410, 457, 528 TE: 14B, 22B, 39, 58B, 105B, 113A-B, 114, 121B, 129B, 136B, 205, 212, 233B, 258, 313, 328, 347, 375, 385B, 409 SE: 5, 12, 28-29, 37, 44, 52-53, 63, 206, 208, , 381, 383B, 409, 421, 431, 449B, , 481, 495, 594 TE: 23B, 95, 110B, 155, 197, 216, 227, 243, 255B, 315, 361, 396, 434, 441B, 450, 466, 506, 524, 528B, 554 6

9 Look for and make use of structure. The envision A G A program incorporates mathematical practices and habits of mind by encouraging students to look for and make use of structure to relate mathematical concepts and procedures, thereby promoting deeper mathematical understanding and efficient and effective problem solving. Sample references are cited here. SE: 16, 48, 51-52, 61, 66, 72, 101, 107, 116, 162, 207, 222, 233, 278, 309, 320, 326, 369, 401, 423 TE: 11A, 57A, 76A, 89B, 102A, 110B, 143A, 150A, 164A, 171A, 203A, 227, 247, 289, 297, 302, 332, 370A, 397A, 445B SE: 26, 48, 57, 90, , 127, 137, 156, 178, 230, 232, 251, 261, , 339, 360, 397, 434, , 458 TE: 51B, 105B, 115, 125, 130, 137, 149B, 210, 220, 271, 280, 286B, 335, 388, 394, , 436B, 444B, 465B, 480B SE: 11, 13, 15, 21, 35, 38, 99, 118, 124, 177, 215, 217, 245, , 374, 390, 393, 398, , 408 TE: 8, 15, 26, 31B, 97, 120, 148, 179B, 213, 217B, 322, 357B, 365B, 377, 388, 402, 417, 427, 442, 463B 7

10 Look for and express regularity in repeated reasoning. The envision A G A program incorporates mathematical practices and habits of mind by challenging students to look for and express regularity in repeated reasoning as they gain experience with mathematical algorithms. Students Look for Relationships to make generalizations and solve related problems. Sample references are cited here. SE: 21, 40-41, 124, , 148, 155, 168, 175, 195, 201, 210, 219, 228, 236, 305, , 352, 386, 422, 489 TE: 14, 37A, 46, 57B, 76A-B, 89A, 96, 126A, 150B, 157A, 164A, 193, 217A, 239A, 275A, 315A, 344A, 418A, 480A, 487A SE: 28-34, 49, 59, 71-77, , 124, 135, 164, , 208, , 293, , 331, 337, 358, 371, 426, 460, 519 TE: 28A, 71A, 167A, 183, 190, 226B, 234, 310A, 361B, 386, 453, 499B, 507B, 518, 522B, 525 SE: 26, 107, 111, 125, 215, 231, 242, 270, 279, 316, 319, , 374, 381, 398, 406, 421, 431, 439, 447 TE: 19, 96, 212, 240, 297B, 305, 307, 309, 323, 327B, 386, 419, 468, 485, 494, 504, 531, 539, 581B, 606 Number and Quantity The Real Number System Extend the properties of exponents to rational exponents. NC.M2.N-RN.1 Explain how expressions with rational exponents can be rewritten as radical expressions. SE: TE: 217A-223B SE: , TE: 239A-246B, 247A-254B 8

11 NC.M2.N-RN.2 Rewrite expressions with radicals and rational exponents into equivalent expressions using the properties of exponents. SE: TE: 217A-223B SE: , TE: 239A-246B, 247A-254B Use properties of rational and irrational numbers. NC.M2.N-RN.3 Use the properties of rational and irrational numbers to explain why: the sum or product of two rational numbers is rational; SE: 5-10 TE: 5A-10B the sum of a rational number and an irrational number is irrational; SE: 5-10 TE: 5A-10B the product of a nonzero rational number and an irrational number is irrational. SE: 5-10 TE: 5A-10B The Complex Number System Defining complex numbers. NC.M2.N-CN.1 Know there is a complex number i such that 2 = 1, and every complex number has the form + where and are real numbers. SE: , , TE: 95A-101B, 441A-448B, 449A-456B Algebra Seeing Structure in Expressions Interpret the structure of expressions. NC.M2.A-SSE.1 Interpret expressions that represent a quantity in terms of its context. SE: 11-13, 25, 30-31, 39, 46, 101, 154, 189, 209, 219, 242, 259, 263, 271, 277, 290, 302, 325, 372, 378 TE: 2A, 11A, 17B, 30B, 18B, 23B, 43A, 109A-B, 143B, 150B, 164B, 259B, 274B, 295B, 306B, 311B, 342B, 363B, 397B, 418A 9

12 (Continued) NC.M2.A-SSE.1 Interpret expressions that represent a quantity in terms of its context. SE: 23, 26, 89, 164, 179, 215, 335, 347, 353, 360, 366, 369, 372, 423, 430, 455, 492, 505 TE: 23, 26, 89, 164, 179, 215, 335, 347, 353, 360, 366, 369, 372, 423, 435B, 455, 492, 505 SE: 39, 54, 64, 87, 102, 109, 116, 145, 161, 169, 200, 216, 231, 254, 271, 289, 313, 326, 339, 382 TE: 23B, 88B, 110B, 146B, 162B, 171B, 193B, 217B, 224B, 263B, 273B, 305B, 321B, 375B, 424B, 463B, 480B, 511B, 518B, 589B NC.M2.A-SSE.1a Identify and interpret parts of a quadratic, square root, inverse variation, or right triangle trigonometric expression, including terms, factors, coefficients, radicands, and exponents. SE: , , , , , , , TE: 287A-293B, 295A-300B, 301A-306B, 315A-321B, 322A-328B, 329A-335B, 344A-350B, 411A-417B SE: 73-79, 80-87, 88-94, , , , , , , TE: 73A-79B, 80A-87B, 88A-94B, 193A-200B, 239A- 246B, 247A-254B, 255A-262B, 357A-364B, 365A- 374B, 375A-382B NC.M2.A-SSE.1b Interpret quadratic and square root expressions made of multiple parts as a combination of single entities to give meaning in terms of a context. SE: , , , , , , , TE: 287A-293B, 295A-300B, 301A-306B, 315A-321B, 322A-328B, 329A-335B, 344A-350B, 411A-417B SE: 73-79, 80-87, 88-94, , TE: 73A-79B, 80A-87B, 88A-94B, 239A-246B, 247A- 254B 10

13 NC.M2.A-SSE.3 Write an equivalent form of a quadratic expression by completing the square, where is an integer of a quadratic expression, 2 + +, to reveal the maximum or minimum value of the function the expression defines. SE: TE: 382A-388B SE: TE: 406A-412B SE: TE: 103A-109B Arithmetic with Polynomial and Rational Expressions Perform arithmetic operations on polynomials NC.M2.A-APR.1 Extend the understanding that operations with polynomials are comparable to operations with integers by adding, subtracting, and multiplying polynomials. SE: , , TE: 259A-266B, 267A-274B, 275A-280B SE: , , TE: 139A-145B, 146A-153B, 154A-161B Creating Equations Create equations that describe numbers or relationships. NC.M2.A-CED.1 Create equations and inequalities in one variable that represent quadratic, square root, inverse variation, and right triangle trigonometric relationships and use them to solve problems. SE: 362, 364, , 378, 381, 384, 388, 391, 395 TE: 362, 364, , 378, 381, 384, 388, 391, 395 SE: 5-12, 13-22, 31-39, 40-46, 47-54, 73-79, 80-87, 88-94, , , , , , 313, , TE: 5A-12B, 13A-22B, 31A-39B, 40A-46B, 47A-54B, 73A-79B, 80A-87B, 88A-94B, 103A-109B, 110A- 116B, 117A-123B, 297A-304B, 305A-312B, B, 333A-339B, 340A-348B 11

14 NC.M2.A-CED.2 Create and graph equations in two variables to represent quadratic, square root and inverse variation relationships between quantities. SE: , , , TE: 315A-321B, 322A-328B, 357A-362B, 411A-417B SE: , TE: 400A-405B, 406A-412B SE: 5-12, 13-22, 31-39, 40-46, 47-54, 73-79, 80-87, 88-94, , , , , , 313, , TE: 5A-12B, 13A-22B, 31A-39B, 40A-46B, 47A-54B, 73A-79B, 80A-87B, 88A-94B, 103A-109B, 110A- 116B, 117A-123B, 297A-304B, 305A-312B, B, 333A-339B, 340A-348B NC.M2.A-CED.3 Create systems of linear, quadratic, square root, and inverse variation equations to model situations in context. SE: , , , TE: 143A-149B, 150A-156B, 157A-163B, 397A-402B SE: 47-54, 55, 56-64, TE: 47A-54B, 55-55B, 56A-64B, 117A-123B Reasoning with Equations and Inequalities Understand solving equations as a process of reasoning and explain the reasoning. NC.M2.A-REI.1 Justify a chosen solution method and each step of the solving process for quadratic, square root and inverse variation equations using mathematical reasoning. SE: , , , , TE: 357A-362B, 363A-369B, 376A-381B, 382A-388B, 389A-395B SE: , , , TE: 103A-109B, 110A-116B, 224A-231B, 263A-271B NC.M2.A-REI.2 Solve and interpret one variable inverse variation and square root equations arising from a context, and explain how extraneous solutions may be produced. SE: , 232, , 272 TE: 224A-231B, B, 263A-271B, B 12

15 Reasoning with Equations and Inequalities Solve equations and inequalities in one variable. NC.M2.A-REI.4 Solve for all solutions of quadratic equations in one variable. SE: , , , , TE: 357A-362B, 363A-369B, 376A-381B, 382A-388B, 389A-395B SE: , TE: 103A-109B, 110A-116B NC.M2.A-REI.4a Understand that the quadratic formula is the generalization of solving by using the process of completing the square. SE: TE: 389A-395B SE: , TE: 103A-109B, 110A-116B NC.M2.A-REI.4b Explain when quadratic equations will have non-real solutions and express complex solutions as ± for real numbers and. SE: , TE: 103A-109B, 110A-116B Solve systems of equations. NC.M2.A-REI.7 Use tables, graphs, and algebraic methods to approximate or find exact solutions of systems of linear and quadratic equations, and interpret the solutions in terms of a context. SE: , , , TE: 143A-149B, 150A-156B, 157A-163B, 397A-402B SE: 47-54, 56-64, TE: 47A-54B, 56A-64B, 117A-123B Represent and solve equations and inequalities graphically. NC.M2.A-REI.11 Extend the understanding that the -coordinates of the points where the graphs of two square root and/or inverse variation equations = ( ) and = ( ) intersect are the solutions of the equation ( ) = ( ) and approximate solutions using graphing technology or successive approximations with a table of values. Students in explore this strategy with linear, exponential, and quadratic equations. SE: , 235, 330, 361, 398 TE: 143A-149B, 235, 330, 354A, 361, SE: TE: 40A-46B 13

16 Functions Interpreting Functions Understand the concept of a function and use function notation. NC.M2.F-IF.1 Extend the concept of a function to include geometric transformations in the plane by recognizing that: the domain and range of a transformation function f are sets of points in the plane; the image of a transformation is a function of its pre-image. SE: , , , , , , , TE: 102A-108B, 203A-209B, 246A-251B, 315A-321B, 322A-328B, 425A-431B, 432A-437B, 438A-443B SE: , , , , , TE: 107A-112B, 113A-120B, 121A-128B, 129A-135B, 301A-309B, 310A-316B SE: 5-12, 13-22, 73-79, , , , , , , , TE: 5A-12B, 13A-22B, 73A-79B, 131A-138B, 179A- 186B, 201A-209B, 255A-262B, 297A-304B, 383A- 391B, 393A-399B, 400A-407B NC.M2.F-IF.2 Extend the use of function notation to express the image of a geometric figure in the plane resulting from a translation, rotation by multiples of 90 degrees about the origin, reflection across an axis, or dilation as a function of its preimage. SE: , , , , , TE: 107A-112B, 113A-120B, 121A-128B, 129A-135B, 301A-309B, 310A-316B 14

17 Interpret functions that arise in applications in terms of the context. NC.M2.F-IF.4 Interpret key features of graphs, tables, and verbal descriptions in context to describe functions that arise in applications relating two quantities, including: domain and range, rate of change, symmetries, and end behavior. SE: , , , , , , , , , , , , TE: 95A-101B, 102A-108B, 183A-189B, 191A-196B, 197A-202B, 203A-209B, 224A-230B, 246A-251B, 315A-321B, 322A-328B, 425A-431B, 432A-437B, 438A-443B SE: 5-12, 13-22, 73-79, , , , , , , , TE: 5A-12B, 13A-22B, 73A-79B, 131A-138B, 179A- 186B, 201A-209B, 255A-262B, 297A-304B, 383A- 391B, 393A-399B, 400A-407B Analyze functions using different representations. NC.M2.F-IF.7 Analyze quadratic, square root, and inverse variation functions by generating different representations, by hand in simple cases and using technology for more complicated cases, to show key features, including: domain and range; intercepts; intervals where the function is increasing, decreasing, positive, or negative; rate of change; maximums and minimums; symmetries; and end behavior. SE: , , , , , TE: 315A-321B, 322A-328B, 329A-335B, 336A-342B, 411A-417B, 425A-431B SE: 73-79, , TE: 73A-79B, 179A-186B, 255A-262B NC.M2.F-IF.8 Use equivalent expressions to reveal and explain different properties of a function by developing and using the process of completing the square to identify the zeros, extreme values, and symmetry in graphs and tables representing quadratic functions, and interpret these in terms of a context. SE: , , , , TE: 315A-321B, 322A-328B, 329A-335B, 382A-388B, 425A-431B SE: 5-12, 13-22, 73-79, , , , , , , , TE: 5A-12B, 13A-22B, 73A-79B, 131A-138B, 179A- 186B, 201A-209B, 255A-262B, 297A-304B, 383A- 391B, 393A-399B, 400A-407B 15

18 NC.M2.F-IF.9 Compare key features of two functions (linear, quadratic, square root, or inverse variation functions) each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions). SE: , , , , TE: 95A-101B, 102A-108B, 315A-321B, 344A-350B, 411A-417B SE: 5-12, 13-22, 73-79, , TE: 5A-12B, 13A-22B, 73A-79B, 179A-186B, 255A- 262B Building Functions Build a function that models a relationship between two quantities. NC.M2.F-BF.1 Write a function that describes a relationship between two quantities by building quadratic functions with real solution(s) and inverse variation functions given a graph, a description of a relationship, or ordered pairs (include reading these from a table). SE: , , , , 343, TE: 315A-321B, 322A-328B, 329A-335B, 336A-342B, B, 357A-362B SE: 73-79, TE: 73A-79B, 179A-186B Build new functions from existing functions. NC.M2.F-BF.3 Understand the effects of the graphical and tabular representations of a linear, quadratic, square root, and inverse variation function f with ( ), ( ) +, ( + ) for specific values of (both positive and negative). SE: , , , , , TE: 102A-108B, 315A-321B, 322A-328B, 425A-431B, 432A-437B, 438A-443B SE: 5-12, 13-22, 73-79, , TE: 5A-12B, 13A-22B, 73A-79B, 179A-186B, 255A- 262B 16

19 Congruence Experiment with transformations in the plane. NC.M2.G-CO.2 Experiment with transformations in the plane. Represent transformations in the plane. Compare rigid motions that preserve distance and angle measure (translations, reflections, rotations) to transformations that do not preserve both distance and angle measure (e.g. stretches, dilations). Understand that rigid motions produce congruent figures while dilations produce similar figures. In, students apply transformations to graphs of functions. SE: , , , , , , , TE: 102A-108B, 203A-209B, 246A-251B, 315A-321B, 322A-328B, 425A-431B, 432A-437B, 438A-443B SE: , , , , , , TE: 107A-112B, 113A-120B, 121A-128B, 129A-135B, 149A-156B, 301A-309B, 310A-316B In, students transform graphs of functions. SE: 5-12, 13-22, 73-79, , , , , , , , TE: 5A-12B, 13A-22B, 73A-79B, 131A-138B, 179A- 186B, 201A-209B, 255A-262B, 297A-304B, 383A- 391B, 393A-399B, 400A-407B NC.M2.G-CO.3 Given a triangle, quadrilateral, or regular polygon, describe any reflection or rotation symmetry i.e., actions that carry the figure onto itself. Identify center and angle(s) of rotation symmetry. Identify line(s) of reflection symmetry. SE: , , TE: 107A-112B, 121A-128B, 136A-141B NC.M2.G-CO.4 Verify experimentally properties of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. SE: , , , , TE: 107A-112B, 113A-120B, 121A-128B, 129A-135B, 136A-141B 17

20 NC.M2.G-CO.5 Given a geometric figure and a rigid motion, find the image of the figure. Given a geometric figure and its image, specify a rigid motion or sequence of rigid motions that will transform the pre-image to its image. SE: , , , TE: 107A-112B, 113A-120B, 121A-128B, 129A-135B Understand congruence in terms of rigid motions. NC.M2.G-CO.6 Determine whether two figures are congruent by specifying a rigid motion or sequence of rigid motions that will transform one figure onto the other. SE: , , , , TE: 107A-112B, 113A-120B, 121A-128B, 129A-135B, 149A-156B NC.M2.G-CO.7 Use the properties of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. SE: , , , , TE: 107A-112B, 113A-120B, 121A-128B, 129A-135B, 149A-156B NC.M2.G-CO.8 Use congruence in terms of rigid motion. Justify the ASA, SAS, and SSS criteria for triangle congruence. Use criteria for triangle congruence (ASA, SAS, SSS, HL) to determine whether two triangles are congruent. SE: , , , , TE: 149A-156B, 167A-173B, 174A-181B, 182A-187B, 188A-193B Prove geometric theorems. NC.M2.G-CO.9 Prove theorems about lines and angles and use them to prove relationships in geometric figures including: Vertical angles are congruent. SE: 51-52, TE: 51-52, 54-57B When a transversal crosses parallel lines, alternate interior angles are congruent. SE: TE: 71A-77B When a transversal crosses parallel lines, corresponding angles are congruent. SE: TE: 71A-77B Points are on a perpendicular bisector of a line segment if and only if they are equidistant from the endpoints of the segment. SE: , , 217 TE: 201A-208B, B, B 18

21 Use congruent triangles to justify why the bisector of an angle is equidistant from the sides of the angle. SE: , TE: B, 209A-216B NC.M2.G-CO.10 Prove theorems about triangles and use them to prove relationships in geometric figures including: The sum of the measures of the interior angles of a triangle is 180º. SE: 77 TE: 77 Students apply this property when solving triangles using trigonometry. SE: TE: 424A-432B An exterior angle of a triangle is equal to the sum of its remote interior angles. SE: TE: 87-91B The base angles of an isosceles triangle are congruent. SE: TE: 157A-165B The segment joining the midpoints of two sides of a triangle is parallel to the third side and half the length. SE: TE: B Similarity, Right Triangles, and Trigonometry Understand similarity in terms of similarity transformations. NC.M2.G-SRT.1 Verify experimentally the properties of dilations with given center and scale factor: SE: TE: 301A-309B NC.M2.G-SRT.1a When a line segment passes through the center of dilation, the line segment and its image lie on the same line. When a line segment does not pass through the center of dilation, the line segment and its image are parallel. SE: TE: 301A-309B NC.M2.G-SRT.1b The length of the image of a line segment is equal to the length of the line segment multiplied by the scale factor. SE: TE: 301A-309B 19

22 NC.M2.G-SRT.1c The distance between the center of a dilation and any point on the image is equal to the scale factor multiplied by the distance between the dilation center and the corresponding point on the pre-image. SE: TE: 301A-309B NC.M2.G-SRT.1d Dilations preserve angle measure. SE: TE: 301A-309B NC.M2.G-SRT.2 Understand similarity in terms of transformations. SE: , TE: 301A-309B, 310A-316B a. Determine whether two figures are similar by specifying a sequence of transformations that will transform one figure into the other. SE: TE: 310A-316B b. Use the properties of dilations to show that two triangles are similar when all corresponding pairs of sides are proportional and all corresponding pairs of angles are congruent. SE: , TE: 301A-309B, 310A-316B NC.M2.G-SRT.3 Use transformations (rigid motions and dilations) to justify the AA criterion for triangle similarity. SE: , , TE: 301A-309B, 310A-316B, 317A-323B Prove theorems involving similarity. NC.M2.G-SRT.4 Use similarity to solve problems and to prove theorems about triangles. Use theorems about triangles to prove relationships in geometric figures. A line parallel to one side of a triangle divides the other two sides proportionally and its converse. SE: , , , 332, TE: 310A-316B, 317A-323B, 324A-331B, B, 333A-339B SE: TE: 333A-339B 20

23 The Pythagorean Theorem SE: 369, 378 TE: 369, 378 SE: TE:345A-353B SE: , , 431, 443, 472, 475, 482, 483, 519, 521 TE: 357A-364B, 424A-B, 472A-B Define trigonometric ratios and solve problems involving right triangles. NC.M2.G-SRT.6 Verify experimentally that the side ratios in similar right triangles are properties of the angle measures in the triangle, due to the preservation of angle measure in similarity. Use this discovery to develop definitions of the trigonometric ratios for acute angles. SE: , TE: 345A-353B, 354A-360B SE: , , TE: 357A-364B, 365A-374B, 375A-382B NC.M2.G-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve problems involving right triangles in terms of a context. SE: , TE: 345A-353B, 354A-360B SE: , , TE: 357A-364B, 365A-374B, 375A-382B NC.M2.G-SRT.12 Develop properties of special right triangles ( and ) and use them to solve problems. SE: TE: 345A-353B 21

24 Statistics and Probability Making Inference and Justifying Conclusions Understand and evaluate random processes underlying statistical experiments. NC.M2.S-IC.2 Use simulation to determine whether the experimental probability generated by sample data is consistent with the theoretical probability based on known information about the population. SE: 398 TE: 398 SE: , , , 595, 604 TE: 588B, 589A, 596A-B, 605A Conditional Probability and the Rules for Probability Understand independence and conditional probability and use them to interpret data. NC.M2.S-CP.1 Describe events as subsets of the outcomes in a sample space using characteristics of the outcomes or as unions, intersections and complements of other events. SE: TE: 499A-506B SE: , , TE: 551A-557B, 558A-564B, 605A-612B NC.M2.S-CP.3 Develop and understand independence and conditional probability. SE: , TE: 499A-506B, 507A-513B SE: , TE: 605A-612B, 613A-619B NC.M2.S-CP.3a Use a 2-way table to develop understanding of the conditional probability of A given B (written P(A B)) as the likelihood that A will occur given that B has occurred. That is, P(A B) is the fraction of event B s outcomes that also belong to event A. SE: TE: 507A-513B SE: TE: 613A-619B 22

25 NC.M2.S-CP.3b Understand that event A is independent from event B if the probability of event A does not change in response to the occurrence of event B. That is P(A B)=P(A). SE: , TE: 499A-506B, 507A-513B SE: , TE: 605A-612B, 613A-619B NC.M2.S-CP.4 Represent data on two categorical variables by constructing a two-way frequency table of data. Interpret the two-way table as a sample space to calculate conditional, joint and marginal probabilities. Use the table to decide if events are independent. Students construct two-way frequency tables in. SE: TE: 495A-500B SE: TE: 507A-513B SE: , TE: 605A-612B, 613A-619B NC.M2.S-CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. SE: , TE: 499A-506B, 507A-513B SE: , TE: 605A-612B, 613A-619B Use the rules of probability to compute probabilities of compound events in a uniform probability model. NC.M2.S-CP.6 Find the conditional probability of A given B as the fraction of B s outcomes that also belong to A, and interpret the answer in context. SE: TE: 507A-513B SE: TE: 613A-619B 23

26 NC.M2.S-CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) P(A and B), and interpret the answer in context. The "Addition Rule" is not formally stated, but the textbook includes examples of mutually exclusive events whose probabilities can be added. SE: TE: 499A-506B The "Addition Rule" is not formally stated, but the textbook includes examples of mutually exclusive events whose probabilities can be added. SE: TE: 605A-612B NC.M2.S-CP.8 Apply the general Multiplication Rule P(A and B) = P(A)P(B A) = P(B)P(A B), and interpret the answer in context. Include the case where A and B are independent: P(A and B) = P(A) P(B). The "Multiplication Rule" is not formally stated, but the textbook includes examples of independent events whose probabilities can be multiplied. SE: TE: 499A-506B The "Multiplication Rule" is not formally stated, but the textbook includes examples of independent events whose probabilities can be multiplied. SE: TE: 605A-612B 24