A Correlation of 2018 To the North Carolina Standard Course of Study for Mathematics High School Math 1
Table of Contents Standards for Mathematical Practice... 1 Number and Quantity... 8 Algebra... 9 Functions... 15... 21 Statistics and Probability... 23 Copyright 2017 Pearson Education, Inc. or its affiliate(s). All rights reserved
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, 327-328, 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, 195-197, 216, 248-250, 256-257, 275-276, 293-294, 366, 398-399, 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, 124-126, 209, 221, 244-245, 262, 271, 373-375, 381-382, 391, 399, 407-408, 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
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, 166-172, 173-180, 226-232, 233-238, 245-251, 271-278, 317-323, 333-339, 345-353, 361-366, 374-379, 393-399, 425, 433, 537-543 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, 122-123, 126, 207-208, 304, 331, 347, 363, 373, 375, 380-381, 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
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, 207-208, 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, 166-172, 173-180, 230-231, 259-260, 271-278, 317-323, 377-378, 393-399, 432-433, 448-449, 456-457, 468-469, 484-485, 519-520, 534-535 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, 362-363, 373-374, 380-381, 389-390, 397-398, 405, 421 TE: 9, 56B, 81, 91, 98, 111, 183, 194, 211, 224, 247B, 263B, 360, 415, 437, 452, 493, 565B, 637, 645 3
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, 169-170, 189, 209, 230, 259, 266, 274, 290, 343, 350, 362, 375, 403-404 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, 142-142B, 153, 166-166B, 201B, 217-217B, 252-252B, 332-332B, 350, 357, 373-373B, 392-392B, 419B, 435-435B, 475, 479-479B, 514-514B SE: 11-12, 22, 30, 38-39, 64, 101, 123, 209, 223, 271, 313, 381-382, 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
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, 138-139, 145, 166, 174, 184, 198, 208, 225, 237, 244, 250, 272-273, 276-277, 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
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, 133-134, 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, 214-215, 381, 383B, 409, 421, 431, 449B, 454-455, 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
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, 111-112, 127, 137, 156, 178, 230, 232, 251, 261, 322-323, 339, 360, 397, 434, 449-450, 458 TE: 51B, 105B, 115, 125, 130, 137, 149B, 210, 220, 271, 280, 286B, 335, 388, 394, 401-402, 436B, 444B, 465B, 480B SE: 11, 13, 15, 21, 35, 38, 99, 118, 124, 177, 215, 217, 245, 362-363, 374, 390, 393, 398, 405-406, 408 TE: 8, 15, 26, 31B, 97, 120, 148, 179B, 213, 217B, 322, 357B, 365B, 377, 388, 402, 417, 427, 442, 463B 7
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, 132-133, 148, 155, 168, 175, 195, 201, 210, 219, 228, 236, 305, 340-341, 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, 111-112, 124, 135, 164, 167-172, 208, 223-224, 293, 310-316, 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, 362-363, 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. Number and Quantity NC.M1.N-RN.2 Rewrite algebraic expressions with integer exponents using the properties of exponents. SE: 217-223 TE: 217A-223B SE: 247-248, 252-253 TE: 247B, 247-248, 252-253, 254B 8
Algebra Seeing Structure in Expressions Interpret the structure of expressions. NC.M1.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 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.M1.A-SSE.1a Identify and interpret parts of a linear, exponential, or quadratic expression, including terms, factors, coefficients, and exponents. SE: 11-17, 24-29, 37-42, 57-62, 63-68, 69-74, 76-82, 95-101, 102-108, 143-149, 224-230, 246-251, 259-266, 287-293, 295-300, 301-306, 315-321, 322-328, 329-335, 344-350 TE: 11A-17B, 24A-29B, 37A-42B, 57A-62B, 63A- 68B, 69A-74B, 76A-82B, 95A-101B, 102A-108B, 143A-149B, 224A-230B, 246A-251B, 259A-266B, 287A-293B, 295A-300B, 301A-306B, 315A-321B, 322A-328B, 329A-335B, 344A-350B SE: 5-12, 13-22, 31-39, 40-46, 47-54, 73-79, 80-87, 88-94, 103-109, 110-116, 117-123, 297-304, 305-312, 313, 333-339, 340-348 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, 313-313B, 333A-339B, 340A-348B 9
NC.M1.A-SSE.1b Interpret a linear, exponential, or quadratic expression made of multiple parts as a combination of entities to give meaning to an expression. SE: 17, 29, 42, 62, 68, 74, 82, 101, 108, 149, 230, 231-238, 251, 266, 293, 300, 306, 321, 336-342, 350 TE: 17B, 29B, 42B, 62B, 68B, 74B, 82B, 101B, 108B, 149B, 230B, 231A-238, 251B, 266B, 293B, 300B, 306B, 321B, 336A-342B, 350B SE: 5-12, 13-22, 31-39, 40-46, 47-54, 73-79, 80-87, 88-94, 103-109, 110-116, 117-123, 297-304, 305-312, 313, 333-339, 340-348 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, 313-313B, 333A-339B, 340A-348B Write expressions in equivalent forms to solve problems. NC.M1.A-SSE.3 Write an equivalent form of a quadratic expression 2 + x+, where a is an integer, by factoring to reveal the solutions of the equation or the zeros of the function the expression defines. SE: 287-293, 295-300, 301-306, 363-369 TE: 287A-293B, 295A-300B, 301A-306B, 363A- 369B SE: 407-412 TE: 407-412B SE: 73-79, 80-87, 88-94 TE: 73A-79B, 80A-87B, 88A-94B Arithmetic with Polynomial Expressions Perform arithmetic operations on polynomials. NC.M1.A-APR.1 Build an understanding that operations with polynomials are comparable to operations with integers by adding and subtracting quadratic expressions and by adding, subtracting, and multiplying linear expressions. SE: 259-266, 267-274, 275-280 TE: 259A-266B, 267A-274B, 275A-280B SE: 139-145, 146-153, 154-161 TE: 139A-145B, 146A-153B, 154A-161B 10
Understand the relationship between zeros and factors of polynomials. NC.M1.A-APR.3 Understand the relationships among the factors of a quadratic expression, the solutions of a quadratic equation, and the zeros of a quadratic function. SE: 357-362, 363-369 TE: 357A-362B, 363A-369B Students graph and write equations for parabolas in the coordinate plane. SE: 407-412 TE: 407-412B SE: 73-79, 88-94, 103-109, 110-116, 131-138, 162-169, 171-178 TE: 73A-79B, 88A-94B, 103A-109B, 110A-116B, 131A-138B, 162A-169B, 171A-178B Creating Equations Create equations that describe numbers or relationships. NC.M1.A-CED.1 Create equations and inequalities in one variable that represent linear, exponential, and quadratic relationships and use them to solve problems. SE: 11-17, 18, 20-23, 30, 32-33, 35, 37, 39-42, 43-49, 233-235, 237-238, 362, 364, 368-369, 378, 381, 384, 388, 391, 395 TE: 11B-17B, 18B, 20-23B, 30B, 32-33, 35-35B, 37B, 39-42B, 43B, 44-49B, 233-235, 237-238, 362, 364, 368-369, 378, 381, 384, 388, 391, 395 SE: 5-12, 13-22, 31-39, 40-46, 47-54, 73-79, 80-87, 88-94, 103-109, 110-116, 117-123, 297-304, 305-312, 313, 333-339, 340-348 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, 313-313B, 333A-339B, 340A-348B 11
NC.M1.A-CED.2 Create and graph equations in two variables to represent linear, exponential, and quadratic relationships between quantities. SE: 57-62, 63-68, 76-82, 89-94, 95-101, 102-108, 118-125, 126-134, 143-149, 164-169, 71-176, 183-189, 191-196, 197-202, 203-209, 224-230, 246-251, 315-321, 322-328, 357-362 TE: 57A-62B, 63A-68B, 76A-82B, 89A-94B, 95A- 101B, 102A-108B, 118A-125B, 126A-134B, 143A- 149B, 164A-169B, 171A-176B, 183A-189B, 191A- 196B, 197A-202B, 203A-209B, 224A-230B, 246A- 251B, 315A-321B, 322A-328B, 357A-362B SE: 5-12, 13-22, 31-39, 40-46, 47-54, 73-79, 80-87, 88-94, 103-109, 110-116, 117-123, 297-304, 305-312, 313, 333-339, 340-348 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, 313-313B, 333A-339B, 340A-348B NC.M1.A-CED.3 Create systems of linear equations and inequalities to model situations in context. SE: 143-149, 150-156, 157-163, 164-169, 170, 171-176 TE: 143A-149B, 150A-156B, 157A-163B, 164A- 169B, 170A-170B, 171A-176B SE: 47-54, 55, 56-64 TE: 47A-54B, 55-55B, 56A-64B 12
NC.M1.A-CED.4 Solve for a quantity of interest in formulas used in science and mathematics using the same reasoning as in solving equations. SE: 24-29 TE: 24A-29B Students use a variety of formulas with mathematical and real-world applications, including formulas for arithmetic and geometric sequences and series, exponential growth and decay, the quadratic formula, the Law of Sines and the Law of Cosines, and Permutations and Combinations. These formulas have multiple parameters, and various mathematical and realworld problems require students to solve for any of those variables. SE: 31-39, 110-116, 305-312, 340-348, 424-432, 621-627 TE: 31A-39B, 110A-116B, 305A-312B, 340A-348B, 424A-432B, 621A-627B Reasoning with Equations and Inequalities Understand solving equations as a process of reasoning and explain the reasoning. NC.M1.A-REI.1 Justify a chosen solution method and each step of the solving process for linear and quadratic equations using mathematical reasoning. SE: 11-17, 18-23, 357-362, 363-369, 376-381, 382-388, 389-395 TE: 11A-17B, 18A-23B, 357A-362B, 363A-369B, 376A-381B, 382A-388B, 389A-395B SE: 40-46, 103-109, 110-116 TE: 40A-46B, 103A-109B, 110A-116B Solve equations and inequalities in one variable. NC.M1.A-REI.3 Solve linear equations and inequalities in one variable. SE: 11-17, 18-23, 30-35, 37-42 TE: 11A-17B, 18A-23B, 30A-35B, 37A-42B SE: 40-46 TE: 40A-46B 13
NC.M1.A-REI.4 Solve for the real solutions of quadratic equations in one variable by taking square roots and factoring. SE: 363-369, 376-381 TE: 363A-369B, 376A-381B SE: 88-94, 103-109, 110-116 TE: 88A-94B, 103A-109B, 110A-116B Solve systems of equations. NC.M1.A-REI.5 Explain why replacing one equation in a system of linear equations by the sum of that equation and a multiple of the other produces a system with the same solutions. SE: 157-163 TE: 157A-163B SE: 47-54, 56-64 TE: 47A-54B, 56A-64B NC.M1.A-REI.6 Use tables, graphs, or algebraic methods (substitution and elimination) to find approximate or exact solutions to systems of linear equations and interpret solutions in terms of a context. SE: 143-149, 150-156, 157-163 TE: 143A-149B, 150A-156B, 157A-163B SE: 47-54, 56-64 TE: 47A-54B, 56A-64B Represent and solve equations and inequalities graphically NC.M1.A-REI.10 Understand that the graph of a two variable equation represents the set of all solutions to the equation. SE: 57-62, 63-68, 143-149 TE: 57A-62B, 63A-68B, 143A-149B SE: 92-98, 400-405, 406-412 TE: 92A-98B, 400A-405B, 406A-412B SE: 40-46, 73-79, 131-138, 179-186, 201-209, 255-262, 383-391, 393-399, 463-471, 472-478, 480-488, 489-497 TE: 40A-46B, 73A-79B, 131A-138B, 179A-186B, 201A-209B, 255A-262B, 383A-391B, 393A-399B, 463A-471B, 472A-478B, 480A-488B, 489A-497B 14
NC.M1.A-REI.11 Build an understanding of why the x-coordinates of the points where the graphs of two linear, exponential, and/or quadratic equations = ( ) and = ( ) intersect are the solutions of the equation ( ) = ( ) and approximate solutions using graphing technology or successive approximations with a table of values. SE: 143-149, 235, 330, 361, 398 TE: 143A-149B, 235, 330, 354A, 361, 397-398 SE: 40-46 TE: 40A-46B NC.M1.A-REI.12 Represent the solutions of a linear inequality or a system of linear inequalities graphically as a region of the plane. SE: 164-169, 171-176 TE: 164A-169B, 171A-176B SE: 40-46, 47-54 TE: 40A-46B, 47A-54B Functions Interpreting Functions Interpret functions that arise in applications in terms of the context. NC.M1.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: intercepts; intervals where the function is increasing, decreasing, positive, or negative; and maximums and minimums. SE: 89-94, 95-101, 102-108, 118-125, 126-134, 183-189, 191-196, 197-202, 203-209, 224-230, 246-251, 315-321, 357-362 TE: 89A-94B, 95A-101B, 102A-108B, 118A-125B, 126A-134B, 183A-189B, 191A-196B, 197A-202B, 203A-209B, 224A-230B, 246A-251B, 315A-321B, 357A-362B SE: 5-12, 13-22, 31-39, 40-46, 47-54, 73-79, 80-87, 88-94, 103-109, 110-116, 117-123, 297-304, 305-312, 313, 333-339, 340-348 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, 313-313B, 333A-339B, 340A-348B 15
NC.M1.F-IF.5 Interpret a function in terms of the context by relating its domain and range to its graph and, where applicable, to the quantitative relationship it describes. SE: 89-94, 95-101, 102-108, 118-125, 126-134, 183-189, 191-196, 197-202, 203-209, 224-230, 246-251, 315-321, 357-362 TE: 89A-94B, 95A-101B, 102A-108B, 118A-125B, 126A-134B, 183A-189B, 191A-196B, 197A-202B, 203A-209B, 224A-230B, 246A-251B, 315A-321B, 357A-362B SE: 5-12, 13-22, 31-39, 40-46, 47-54, 73-79, 80-87, 88-94, 103-109, 110-116, 117-123, 297-304, 305-312, 313, 333-339, 340-348 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, 313-313B, 333A-339B, 340A-348B NC.M1.F-IF.6 Calculate and interpret the average rate of change over a specified interval for a function presented numerically, graphically, and/or symbolically. SE: 196, 202, 235, 237, 253, 318, 319, 320, 321, 346, 348, 413, 415-417, 421-423 TE: 189B, 197A, 202A-B, 238A, 321A-B, 350A-B, 411A-B, 418A, 424A-B, 439 SE: 11-12, 133, 137, 138, 301, 303, 323, 325, 390 TE: 5B, 5, 9, 12A, 31B, 304A, 326A-B, 383A, 391A-B Analyze functions using different representations. NC.M1.F-IF.7 Analyze linear, exponential, and quadratic 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; rate of change; intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; and end behavior. SE: 89-94, 95-101, 102-108, 118-125, 126-134, 183-189, 191-196, 197-202, 203-209, 224-230, 246-251, 315-321, 357-362 TE: 89A-94B, 95A-101B, 102A-108B, 118A-125B, 126A-134B, 183A-189B, 191A-196B, 197A-202B, 203A-209B, 224A-230B, 246A-251B, 315A-321B, 357A-362B 16
(Continued) NC.M1.F-IF.7 Analyze linear, exponential, and quadratic 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; rate of change; intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; and end behavior NC.M1.F-IF.8 Use equivalent expressions to reveal and explain different properties of a function. SE: 5-12, 13-22, 31-39, 40-46, 47-54, 73-79, 80-87, 88-94, 103-109, 110-116, 117-123, 297-304, 305-312, 313, 333-339, 340-348 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, 313-313B, 333A-339B, 340A-348B SE: 89-94, 95-101, 102-108, 118-125, 126-134, 183-189, 191-196, 197-202, 203-209, 224-230, 246-251, 315-321, 357-362 TE: 89A-94B, 95A-101B, 102A-108B, 118A-125B, 126A-134B, 183A-189B, 191A-196B, 197A-202B, 203A-209B, 224A-230B, 246A-251B, 315A-321B, 357A-362B SE: 5-12, 13-22, 31-39, 40-46, 47-54, 73-79, 80-87, 88-94, 103-109, 110-116, 117-123, 297-304, 305-312, 313, 333-339, 340-348 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, 313-313B, 333A-339B, 340A-348B NC.M1.F-IF.8a Rewrite a quadratic function to reveal and explain different key features of the function SE: 351-321, 322-328, 329-335 TE: 351A-321B, 322A-328B, 329A-335B SE: 73-79, 80-87, 88-94 TE: 73A-79B, 80A-87B, 88A-94B NC.M1.F-IF.8b Interpret and explain growth and decay rates for an exponential function SE: 224-230, 231-238 TE: 224A-230B, 231A-238B 17 SE: 297-304, 305-312, 313 TE: 297A-304B, 305A-312B, 313-313B
NC.M1.F-IF.9 Compare key features of two functions (linear, quadratic, or exponential) each with a different representation (symbolically, graphically, numerically in tables, or by verbal descriptions). SE: 95-101, 102-108, 224-230, 246-251, 315-321, 344-350 TE: 95A-101B, 102A-108B, 224A-230B, 246A-251B, 315A-321B, 344A-350B SE: 5-12, 13-22, 31-39, 40-46, 47-54, 73-79, 80-87, 88-94, 103-109, 110-116, 117-123, 297-304, 305-312, 313, 333-339, 340-348 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, 313-313B, 333A-339B, 340A-348B Building Functions Build a function that models a relationship between two quantities. NC.M1.F.BF.1 Write a function that describes a relationship between two quantities. SE: 95-101, 102-108, 118-125, 126-134, 183-189, 191-196, 197-202, 203-209, 224-230, 246-251, 315-321, 357-362 TE: 95A-101B, 102A-108B, 118A-125B, 126A-134B, 183A-189B, 191A-196B, 197A-202B, 203A-209B, 224A-230B, 246A-251B, 315A-321B, 357A-362B SE: 5-12, 13-22, 31-39, 40-46, 47-54, 73-79, 80-87, 88-94, 103-109, 110-116, 117-123, 201-209, 255-262, 297-304, 305-312, 313, 321-326, 333-339, 340-348, 383-391 TE: 5A-12B, 13A-22B, 31A-39B, 40A-46B, 47A-54B, 73A-79B, 80A-87B, 88A-94B, 103A-109B, 110A- 116B, 117A-123B, 201A-209B, 255A-262B, 297A- 304B, 305A-312B, 313-313B, 321A-326B, 333A- 339B, 340A-348B, 383A-391B NC.M1.F-BF.1a Build linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two ordered pairs (include reading these from a table). SE: 95-101, 102-108, 110-117, 118-125, 126-134, 224-230, 231-238, 239-245, 246-251 TE: 95A-101B, 102A-108B, 110A-117B, 118A-125B, 126A-134B, 224A-230B, 231A-238B, 239A-245B, 246A-251B 18
(Continued) NC.M1.F-BF.1a Build linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two ordered pairs (include reading these from a table). Students apply trigonometric functions using the Law of Sines and the Law of Cosines to solve problems. They write equations of linear functions for parallel and perpendicular lines and quadratic equations to represent circles and parabolas in the coordinate plane. SE: 92-98, 354-360, 361-366, 367-372, 374-379, 400-405, 406-412 TE: 92A-98B, 354A-360B, 361A-366B, 367A-372B, 374A-379B, 400A-405B, 406A-412B SE: 5-12, 13-22, 31-39, 297-304, 305-312, 313, 340-348 TE: 5A-12B, 13A-22B, 31A-39B, 297A-304B, 305A- 312B, 313-313B, 340A-348B NC.M1.F.BF.1b Build a function that models a relationship between two quantities by combining linear, exponential, or quadratic functions with addition and subtraction or two linear functions with multiplication. SE: 445-450 TE: 445A-450B SE: 95-98, 407-412 TE: 95-98B, 407-412B SE: 273-280 TE: 273A-280B NC.M1.F-BF.2 Translate between explicit and recursive forms of arithmetic and geometric sequences and use both to model situations. SE: 110-117, 239-245 TE: 110A-117B, 239A-245B Students explore arithmetic and geometric sequences in and. SE: 31-39, 340-348 TE: 31A-39B, 340A-348B 19
Linear, Quadratic, and Exponential Models Construct and compare linear and exponential models and solve problems. NC.M1.F-LE.1 Identify situations that can be modeled with linear and exponential functions, and justify the most appropriate model for a situation based on the rate of change over equal intervals. SE: 95-101, 102-108, 110-117, 118-125, 126-134, 224-230, 231-238, 239-245, 246-251, 344-350 TE: 95A-101B, 102A-108B, 110A-117B, 118A-125B, 126A-134B, 224A-230B, 231A-238B, 239A-245B, 246A-251B, 344A-350B SE: 5-12, 13-22, 31-39, 297-304, 305-312, 313, 340-348 TE: 5A-12B, 13A-22B, 31A-39B, 297A-304B, 305A- 312B, 313-313B, 340A-348B NC.M1.F-LE.3 Compare the end behavior of linear, exponential, and quadratic functions using graphs and tables to show that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically. SE: 344-350 TE: 344A-350B SE: 92-98, 406-412 TE: 92A-98B, 406A-412B SE: 5-12, 13-22, 31-39, 40-46, 47-54, 73-79, 80-87, 88-94, 103-109, 110-116, 117-123, 297-304, 305-312, 313, 333-339, 340-348 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, 313-313B, 333A-339B, 340A-348B Interpret expressions for functions in terms of the situation they model. NC.M1.F-LE.5 Interpret the parameters and in a linear function ( ) = + or an exponential function ( ) = x. in terms of a context. SE: 95-101, 102-108, 118-125, 126-134, 224-230, 231-238, 246-251 TE: 95A-101B, 102A-108B, 118A-125B, 126A-134B, 224A-230B, 231A-238B, 246A-251B SE: 92-98 TE: 92A-98B 20
(Continued) NC.M1.F-LE.5 Interpret the parameters and in a linear function ( ) = + or an exponential function ( ) = x. in terms of a context. SE: 5-12, 13-22, 31-39, 297-304, 305-312, 313, 340-348 TE: 5A-12B, 13A-22B, 31A-39B, 297A-304B, 305A- 312B, 313-313B, 340A-348B Expressing Geometric Properties with Equations Use coordinates to prove simple geometric theorems algebraically. NC.M1.G-GPE.4 Use coordinates to solve geometric problems involving polygons algebraically SE: 61, 73, 156 TE: 61, 73, 156, 166 SE: 107-108, 110-111, 113-114, 116, 118-120, 122, 127, 129-135, 385-391, 393-399 TE: 113B, 118-120B, 128A, 129A-135B, 385A-391B, 393A-399B Use coordinates to compute perimeters of polygons and areas of triangles and rectangles. students use quadratic functions to model the area of a rectangle with variable side lengths. SE: 340-341 TE: 166, 340-341 SE: 120, 385, 388-390, 399, 413 TE: 22, 120, 382C, 385B, 391A-B, 415A-C TE: 547D Use coordinates to verify algebraically that a given set of points produces a particular type of triangle or quadrilateral. SE: 61, 73, 156 TE: 61, 73, 156, 166 SE: 393-399 TE: 393A-399B 21
NC.M1.G-GPE.5 Use coordinates to prove the slope criteria for parallel and perpendicular lines and use them to solve problems. SE: 76-82 TE: 76A-82B SE: 92-98, 99 TE: 92A-98B, 99-99B SE: 14, 52, 444 TE: 47B, 235A Determine if two lines are parallel, perpendicular, or neither. SE: 76-82 TE: 76A-82B SE: 92-98, 99 TE: 92A-98B, 99-99B SE: 52, 444 TE: 47B, 235A Find the equation of a line parallel or perpendicular to a given line that passes through a given point. SE: 76-82 TE: 76A-82B SE: 92-98, 99 TE: 92A-98B, 99-99B NC.M1.G-GPE.6 Use coordinates to find the midpoint or endpoint of a line segment. SE: 22, 25-27, 385, 389-390, 394-399, 401, 403, 408 TE: 22, 25-27B, 198B, 382A, 382C-E, 385A-B, 391B, 392A, 394-399, 399B SE: 441-442, 446-448, 459, 474-476, 480, 498 TE: 186B, 441A, 448A-B, 471B, 480B 22
Statistics and Probability Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a single count or measurement variable. NC.M1.S-ID.1 Use technology to represent data with plots on the real number line (histograms, and box plots). SE: 465-471, 472-479, 480-486 TE: 465A-471B, 472A-479B, 480A-486B SE: 551, 556-557, 563, 565, 568-572, 582-584, 586-587, 592, 595 TE: 551B, 565B, 573B, 581B, 588B, 597B NC.M1.S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Interpret differences in shape, center, and spread in the context of the data sets. SE: 472-479, 480-486, 487-494, 495-500 TE: 472A-479B, 480A-486B, 487A-494B, 495A- 500B SE: 551-557, 565-572 TE: 551A-557B, 565A-572B NC.M1.S-ID.3 Examine the effects of extreme data points (outliers) on shape, center, and/or spread. SE: 465, 472-473, 476 TE: 465A-B, 471A-B, 472A-B, 487B, 501B SE: 572, 580 SE: 572, 580 NC.M1.S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. SE: 118-125, 126-134 TE: 118A-125B, 126A-134B SE: 30, 309, 404, 552, 556 SE: 30, 309, 404, 552, 556 NC.M1.S-ID.6a Fit a least squares regression line to linear data using technology. Use the fitted function to solve problems. SE: 118-125, 126-134 TE: 118A-125B, 126A-134B SE: 84-86 TE: 87A, 127A-B 23
NC.M1.S-ID.6b Assess the fit of a linear function by analyzing residuals. SE: 118-125, 126-134 TE: 118A-125B, 126A-134B SE: 84-86 TE: 87A, 127A-B NC.M1.S-ID.6c Fit a function to exponential data using technology. Use the fitted function to solve problems. SE: 309-311, 313, 414 TE: 305A, 312A, 313A-B, 333B Interpret linear models. NC.M1.S-ID.7 Interpret in context the rate of change and the intercept of a linear model. Use the linear model to interpolate and extrapolate predicted values. Assess the validity of a predicted value. SE: 118-125, 126-134 TE: 118A-125B, 126A-134B SE: 84-86, 309-311, 313, 414 TE: 87A, 127A-B, 305A, 312A, 313A-B, 333B NC.M1.S-ID.8 Analyze patterns and describe relationships between two variables in context. Using technology, determine the correlation coefficient of bivariate data and interpret it as a measure of the strength and direction of a linear relationship. Use a scatter plot, correlation coefficient, and a residual plot to determine the appropriateness of using a linear function to model a relationship between two variables. NC.M1.S-ID.9 Distinguish between association and causation. SE: 118-125, 126-134 TE: 118A-125B, 126A-134B SE: 84-86, 309-311, 313, 414 TE: 87A, 127A-B, 305A, 312A, 313A-B, 333B SE: 131, 133 TE: 126A-B, 131, 133 24