High School Algebra Indicator 1: Use procedures to transform algebraic expressions. 9-12.A.1.1. (Comprehension)Write equivalent forms of algebraic expressions using properties of the set of real numbers. SE/TE: 23-25, 26-28, 29, 36, 40-41, 46-49, 49-52, 58, 66, 70-71, 73, 75, 77, 87, 93, 94-97, 97-98, 100 Evaluate algebraic expressions. SE/TE: 12, 13-15, 22, 29, 34, 36, 41, 42-43, 58, 69, 71, 73, 74, 100, 108, 114, 199, 251, 273, 570-571, 571-573, 591, 593, 597, 700 Use laws of exponents. SE/TE: 414-416, 417-419, 425, 426-428, 429-431, 432, 433-436, 436-438, 439, 440-443, 443-446, 452, 464-465, 467, 468-469, 471 Use conventional order of operations, including grouping and exponents. 9-12.A.1.1A. (Application) Write equivalent forms of rational algebraic expressions using properties of real numbers. 9-12.A.1.2A. (Application) Extend the use of real number properties to expressions involving complex numbers. SE/TE: 11-12, 13-15, 22, 29, 36, 43, 69, 73, 74, 76, 87, 108, 114, 159, 170, 177, 229, 251 SE/TE: 652-654, 655-656, 658-661, 661-664, 671, 672-674, 675-677, 678, 685, 700, 704-705, 707, 709 Indicator 2: Use a variety of algebraic concepts and methods to solve equations and inequalities. 9-12.A.2.1. (Comprehension) Use algebraic properties to transform multi-step, single variable, and first-degree equations. 9-12.A.2.2. (Application) Use algebraic properties to transform multi-step, single variable, and first-degree inequalities and represent solutions using a number line. 9-12.A.2.1A. (Analysis) Determine solutions of quadratic equations. SE/TE: 81-84, 85-87, 88-90, 91-93, 94-97, 98-100, 101, 102-105, 105-108, 114, 117, 123, 129, 143, 153-154, 157, 159 SE/TE: 171-173, 174-177, 178-181, 181-183, 184, 185, 186-189, 189-192, 193, 195, 197, 199, 202, 204-206, 209-210, 211, 219, 223-226, 227 SE/TE: 548-550, 551-553, 554, 555-557, 558-559, 560, 561-563, 564-566, 567-571, 571-573, 580, 583-584, 585-586, 590-592, 593, 595, 618, 649 Use the quadratic formula. SE/TE: 567-571, 571-573, 580, 591, 593, 625, 756 Use the discriminant, b2-4ac, to describe the nature of the roots. 9-12.A.2.2A. (Application) Determine the solution of systems of equations and systems of inequalities. SE/TE: 570-571, 571-573, 591, 593, 597, 700 SE/TE: 360-362, 363-365, 366, 367, 368-370, 371-373, 374-377, 378-380, 381-382, 383-385, 386-388, 389, 395, 396-398, 399-400, 402, 403, 405-406, 407, 582-584, 585-586 1
9-12.A.2.3A. (Application) Determine solutions to absolute value statements. Indicator 3: Interpret and develop mathematical models. 9-12.A.3.1. (Application) Create linear models to represent problem situations. SE/TE: 207-210, 210-213, 220, 226, 227, 231, 259, 312, 318 SE/TE: 300-301, 302-304, 309, 311-312, 315-316, 317-318, 319, 322, 323-326, 330, 331, 334-336, 338-340, 341 Calculate and interpret slope. SE/TE: 292-294, 295-298, 299-300, 304, 307-309, 310-312, 313-315, 316-318, 319, 326, 328-330, 331-332, 335-336, 339, 341, 346, 350-351, 353 9-12.A.3.2. (Comprehension) Distinguish between linear and nonlinear models. 9-12.A.3.1A. (Analysis) Distinguish between linear, quadratic, inverse variations, and exponential models. 9-12.A.3.2A. (Synthesis) Create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential. 9-12.A.3.3A. (Analysis) Use sequences and series to model relationships. SE/TE: 246-249, 249-251, 252, 259, 283, 285, 288, 574-577, 578-580, 581, 587, 592 SE/TE: 574-577, 578-580, 581, 587, 592, 593, 688-689, 690-692 SE/TE: 300-301, 302-304, 309, 311-312, 315, 317-318, 322, 324, 451-452, 454, 456-458, 458-461, 466, 467, 686-687, 689, 690-692 SE/TE: 274-276, 277-279, 284, 285, 289, 298, 431, 453-454 Indicator 4: Describe and use properties and behaviors of relations, functions, and inverses. 9-12.A.4.1. (Application) Use graphs, tables, and equations to represent linear functions. 9-12.A.4.1A. (Analysis) Determine the domain, range, and intercepts of a function. 9-12.A.4.2A. (Analysis) Describe the behavior of a polynomial, given the leading coefficient, roots, and degree. 9-12.A.4.3A. (Analysis) Apply transformations to graphs and describe the results. SE/TE: 292-295, 296-297, 300-301, 302-303, 305, 306-309, 310-312, 313-316, 316-318, 319, 320-323, 324-326, 327-330, 330-332, 334-336, 340 SE/TE: 268-270, 271-272, 279, 284, 285, 298, 304, 306-307, 309, 310-311, 318, 319, 320-322, 324-325, 332, 449, 451, 535, 537, 538, 627, 628-629 SE/TE: 305, 306, 342-344, 345-346, 347, 352, 353, 447, 535-536, 537-539, 628, 629-630, 695-697, 698-700 Change coefficients and/or constants. SE/TE: 305, 306, 309, 327, 332, 342-344, 344-346, 347, 352, 353, 365 Graph the inverse of a function. 9-12.A.4.4A. (Application) Apply properties and definitions of trigonometric, exponential, and logarithmic expressions. 2
9-12.A.4.5A. (Analysis) Describe characteristics of nonlinear functions and relations. SE/TE: 447-449, 450-452, 455-458, 459-461, 463, 466, 467, 534-537, 537-539, 626-628, 628-630, 693-697, 698-699 Conic sections Trigonometric functions Exponential and logarithmic functions SE/TE: 447-449, 450-452, 455-458, 459-461, 463, 466, 467 9-12.A.4.6A. (Application) Graph solutions to linear inequalities. High School Geometry Logarithmic functions are addressed in Prentice Hall SE/TE: 164-167, 167-170, 171-173, 174-176, 179, 181, 193, 199, 200-203, 204-206, 209, 211-212, 222-224, 227, 229 Indicator 1: Use deductive and inductive reasoning to recognize and apply properties of geometric figures. 9-12.G.1.1. (Application) Apply the properties of triangles and quadrilaterals to find unknown parts. 9-12.G.1.2. (Application) Identify and apply relationships among triangles. Definitions and postulates Similarity theorems Congruence theorems 9-12.G.1.1A. (Evaluation) Justify properties of geometric figures. Write a direct proof. Make conjectures. 9-12.G.1.2A. (Application) Determine the values of the sine, cosine, and tangent ratios of right triangles. 9-12.G.1.3A. (Application) Apply properties associated with circles. 9-12.G.1.4A. (Analysis) Use formulas for surface area and volume to solve problems involving three-dimensional figures. SE/TE: 632, 633-636, 637-639, 644, 645, 657 3
Indicator 2: Use properties of geometric figures to solve problems from a variety of perspectives. 9-12.G.2.1. (Analysis) Recognize the relationship between a three-dimensional figure and its two-dimensional representation. Interpret floor plans Follow instructions for assembly of a product, e.g., some assembly required. 9-12.G.2.2. (Application) Reflect across vertical or horizontal lines, and translate twodimensional figures. Identify lines of symmetry. Use the coordinate plane. 9-12.G.2.3. (Application) Use proportions to solve problems. 9-12.G.2.1A. (Synthesis) Use Cartesian coordinates to verify geometric properties. High School Measurement Indicator 1: SE/TE: 124-126, 127-129, 131-133, 134-136, 137-138, 140, 141-142, 155, 157, 159, 229, 259, 298 Apply measurement concepts in practical applications. 9-12.M.1.1. (Comprehension) Choose appropriate unit label, scale, and precision. Determine appropriate scales for histograms, scatterplots, and other graphs. 9-12.M.1.2. (Comprehension) Use suitable units when describing rate of change. 9-12.M.1.3. (Application) Use formulas to find perimeter, circumference, and area to solve problems involving common geometric figures. Use algebraic expressions with geometric formulas. 9-12.M.1.1A. (Application) Use dimensional analysis to check answers and determine units of a problem solution. 9-12.M.1.2A. (Analysis) Use indirect measurement in problem situations that defy direct measurement. SE/TE: 292, 297, 309, 317, 319, 334, 337, 339 SE/TE: 334, 721, 748 SE/TE: 292, 297, 309, 317, 319, 337, 339 SE/TE: 486-488, 490-491, 492-493, 495-496, 498, 509, 514, 517, 520, 522, 527, 528-529, 550, 552-553, 557 SE/TE: 119-120, 122 SE/TE: 131-132, 134, 157, 159 4
High School Number Sense Indicator 1: Analyze the structural characteristics of the real number system and its various subsystems. Analyze the concept of value, magnitude, and relative magnitude of real numbers. 9-12.N.1.1. (Comprehension) Identify multiple representations of a real number. Given a real number identify the subset(s) of real numbers to which it belongs. Represent rational and irrational numbers in different forms. 9-12.N.1.2. (Comprehension) Apply the concept of place value, magnitude, and relative magnitude of real numbers. SE/TE: 16-17, 20, 28, 39, 42, 69, 73, 420-423, 423-425, 606-609, 610-612, 615, 616, 618, 619, 625, 639, 642, 645, 793 SE/TE: 18, 20-21, 29, 36, 70, 73 SE/TE: 16-17, 20, 28, 39, 42, 69, 73, 606-609, 610-612, 615, 616, 618, 619, 625, 639, 642, 645 SE/TE: 19, 20, 28, 29, 70, 73, 75, 420-423, 423-425, 428, 429-431, 436, 437, 439, 441, 444, 446, 462, 463-465, 467, 469, 510 Scientific notation SE/TE: 420-423, 423-425, 428, 429-431, 436, 437, 439, 441, 444, 446, 462, 463-465, 467, 469, 510 Infinitely many solutions SE/TE: 362, 363-365, 370, 371-372, 377, 378, 389, 405-406, 407 Completeness of the real numbers (density, i.e. between any two real numbers is another real number) 9-12.N.1.1A. (Comprehension) Describe the relationship of the real number system to the complex number system. 9-12.N.1.2A. (Application) Apply properties and axioms of the real number system to various subsets, e.g., axioms of order, closure. Indicator 2: The opportunity to address this standard can be found on page 18. SE/TE: 45 Apply operations within the set of real numbers. 9-12.N.2.1. (Comprehension) Add, subtract, multiply, and divide real numbers including integral exponents. 9-12.N.2.1A. (Application) Add, subtract, multiply, and divide real numbers including rational exponents. Simplify numeric expressions with radicals. SE/TE: 416, 419, 425, 426-428, 429-430, 436, 437, 439, 441, 443-444, 464-465, 467, 469 SE/TE: 606-609, 610-612, 613-615, 616-618, 619, 625, 639, 642-643, 645, 647, 657, 709, 782-783 5
Indicator 3: Develop conjectures, predictions, or estimations to solve problems and verify or justify the results. 9-12.N.3.1. (Analysis) Use estimation strategies in problem situations to predict results and to check the reasonableness of results. SE/TE: 17, 20, 55, 57, 70, 72, 122, 191, 465, 788 Use rounding as an estimation strategy. SE/TE: 17, 20, 70, 788 Use non-routine estimation strategies. SE/TE: 55, 57, 72 9-12.N.3.2. (Comprehension) Select alternative computational strategies and explain the chosen strategy. Use properties of numbers that allow operational shortcuts for computational procedures. SE/TE: 48, 50, 71, 137-139, 141-143, 150, 156, 157 SE/TE: 23-25, 26-28, 40-41, 44, 46-48, 50, 427-428, 429-430, 433-436, 437-438, 439, 441-442, 444-445 Note: Skills for this indicator have been subsumed within applications to advanced skills by the time students reach advanced high school mathematics. High School Statistics & Probability Indicator 1: conclusions. Use statistical models to gather, analyze, and display data to draw 9-12.S.1.1. (Analysis) Draw conclusions from a set of data. Determine and use appropriate statistical values. Determine which questions can or cannot be answered from a given data set. 9-12.S.1.2. (Comprehension) Compare multiple one-variable data sets, using range, interquartile range, mean, mode, and median. 9-12.S.1.3. (Analysis) Represent a set of data in a variety of graphical forms and draw conclusions. Make a scatterplot to draw a regression line and make predictions. Make a box-and-whisker plot to model a set of one-variable data. Make a histogram from a frequency distribution. 9-12.S.1.1A. (Evaluation) Analyze and evaluate the design of surveys and experiments. 9-12.S.1.2A. (Evaluation) Analyze and evaluate graphical displays of data. SE/TE: 716, 717-718, 722, 724, 727, 731, 736, 738-739, 748 SE/TE: 726-729, 730-732, 733, 734-737, 737-739, 749, 762, 776, 779 SE/TE: 739 SE/TE: 728, 730-731, 736, 737-739, 776 SE/TE: 720-722, 723-725, 730-732, 734-737, 737-739, 746, 748, 749, 775-776, 779, 782 SE/TE: 333-337, 337-340, 341, 346, 348, 352, 353, 574-577, 578-580, 581, 587, 592 739 SE/TE: 734-737, 737-739, 749, 776, 779, 782 SE/TE: 721-722, 723-725, 732, 749, 773, 775, 779, 785 SE/TE: 740, 741-744, 744-747, 749, 756, 770, 772, 773, 777, 779 SE/TE: 721-722, 723, 725, 736, 737-739, 748, 749, 773, 775-776, 779, 785 6
9-12.S.1.3A. (Analysis) Compare multiple onevariable data sets, using standard deviation and variance. Calculate the standard deviation and variance of a data set. 9-12.S.1.4A. (Application) Describe the normal curve and use it to make predictions. 9-12.S.1. 5A. (Application) Use scatterplots, best-fit lines, and correlation coefficients to model data and support conclusions. Indicator 2: problems. SE/TE: 733 SE/TE: 333-337, 337-340, 341, 346, 348, 352, 353, 574-577, 578-580, 581, 587, 592 739 Apply the concepts of probability to predict events/outcomes and solve 9-12.S.2.1. (Knowledge) Distinguish between experimental and theoretical probability. 9-12.S.2.2. (Comprehension) Predict outcomes of simple events using given theoretical probabilities. Determine the sample space of an experiment. 9-12.S.2.1A. (Application) Use probabilities to solve problems. SE/TE: 757-760, 774, 778 SE/TE: 760, 761, 784 SE/TE: 757, 765 SE/TE: 758-760, 761-762, 763, 765-767, 768-770, 771-772, 778, 779 Compute combinations, permutations. SE/TE: 750-753, 754-756, 762, 777, 779 Interpret tables. SE/TE: 761, 769, 771, 783 Create and use tree diagrams. SE/TE: 765, 772, 786 9-12.S.2.2A. (Application) Determine probability of compound, complementary, independent, and mutually exclusive events. 9-12.S.2.3A. (Analysis) Generate data and use the data to estimate empirical probabilities. SE/TE: 758, 760-761, 763, 764-767, 768-770, 771-772, 778, 779 SE/TE: 763, 772 7