# Prentice Hall Algebra Correlated to: South Dakota Mathematics Standards, (Grades 9-12)

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1 High School Algebra Indicator 1: Use procedures to transform algebraic expressions 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, , , 591, 593, 597, 700 Use laws of exponents. SE/TE: , , 425, , , 432, , , 439, , , 452, , 467, , 471 Use conventional order of operations, including grouping and exponents A.1.1A. (Application) Write equivalent forms of rational algebraic expressions using properties of real numbers 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: , , , , 671, , , 678, 685, 700, , 707, 709 Indicator 2: Use a variety of algebraic concepts and methods to solve equations and inequalities A.2.1. (Comprehension) Use algebraic properties to transform multi-step, single variable, and first-degree equations A.2.2. (Application) Use algebraic properties to transform multi-step, single variable, and first-degree inequalities and represent solutions using a number line A.2.1A. (Analysis) Determine solutions of quadratic equations. SE/TE: 81-84, 85-87, 88-90, 91-93, 94-97, , 101, , , 114, 117, 123, 129, 143, , 157, 159 SE/TE: , , , , 184, 185, , , 193, 195, 197, 199, 202, , , 211, 219, , 227 SE/TE: , , 554, , , 560, , , , , 580, , , , 593, 595, 618, 649 Use the quadratic formula. SE/TE: , , 580, 591, 593, 625, 756 Use the discriminant, b2-4ac, to describe the nature of the roots A.2.2A. (Application) Determine the solution of systems of equations and systems of inequalities. SE/TE: , , 591, 593, 597, 700 SE/TE: , , 366, 367, , , , , , , , 389, 395, , , 402, 403, , 407, ,

2 9-12.A.2.3A. (Application) Determine solutions to absolute value statements. Indicator 3: Interpret and develop mathematical models A.3.1. (Application) Create linear models to represent problem situations. SE/TE: , , 220, 226, 227, 231, 259, 312, 318 SE/TE: , , 309, , , , 319, 322, , 330, 331, , , 341 Calculate and interpret slope. SE/TE: , , , 304, , , , , 319, 326, , , , 339, 341, 346, , A.3.2. (Comprehension) Distinguish between linear and nonlinear models A.3.1A. (Analysis) Distinguish between linear, quadratic, inverse variations, and exponential models A.3.2A. (Synthesis) Create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential A.3.3A. (Analysis) Use sequences and series to model relationships. SE/TE: , , 252, 259, 283, 285, 288, , , 581, 587, 592 SE/TE: , , 581, 587, 592, 593, , SE/TE: , , 309, , 315, , 322, 324, , 454, , , 466, 467, , 689, SE/TE: , , 284, 285, 289, 298, 431, Indicator 4: Describe and use properties and behaviors of relations, functions, and inverses A.4.1. (Application) Use graphs, tables, and equations to represent linear functions A.4.1A. (Analysis) Determine the domain, range, and intercepts of a function A.4.2A. (Analysis) Describe the behavior of a polynomial, given the leading coefficient, roots, and degree A.4.3A. (Analysis) Apply transformations to graphs and describe the results. SE/TE: , , , , 305, , , , , 319, , , , , , 340 SE/TE: , , 279, 284, 285, 298, 304, , 309, , 318, 319, , , 332, 449, 451, 535, 537, 538, 627, SE/TE: 305, 306, , , 347, 352, 353, 447, , , 628, , , Change coefficients and/or constants. SE/TE: 305, 306, 309, 327, 332, , , 347, 352, 353, 365 Graph the inverse of a function A.4.4A. (Application) Apply properties and definitions of trigonometric, exponential, and logarithmic expressions. 2

3 9-12.A.4.5A. (Analysis) Describe characteristics of nonlinear functions and relations. SE/TE: , , , , 463, 466, 467, , , , , , Conic sections Trigonometric functions Exponential and logarithmic functions SE/TE: , , , , 463, 466, A.4.6A. (Application) Graph solutions to linear inequalities. High School Geometry Logarithmic functions are addressed in Prentice Hall SE/TE: , , , , 179, 181, 193, 199, , , 209, , , 227, 229 Indicator 1: Use deductive and inductive reasoning to recognize and apply properties of geometric figures G.1.1. (Application) Apply the properties of triangles and quadrilaterals to find unknown parts 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 G.1.2A. (Application) Determine the values of the sine, cosine, and tangent ratios of right triangles G.1.3A. (Application) Apply properties associated with circles G.1.4A. (Analysis) Use formulas for surface area and volume to solve problems involving three-dimensional figures. SE/TE: 632, , , 644, 645, 657 3

4 Indicator 2: Use properties of geometric figures to solve problems from a variety of perspectives 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 G.2.2. (Application) Reflect across vertical or horizontal lines, and translate twodimensional figures. Identify lines of symmetry. Use the coordinate plane G.2.3. (Application) Use proportions to solve problems G.2.1A. (Synthesis) Use Cartesian coordinates to verify geometric properties. High School Measurement Indicator 1: SE/TE: , , , , , 140, , 155, 157, 159, 229, 259, 298 Apply measurement concepts in practical applications M.1.1. (Comprehension) Choose appropriate unit label, scale, and precision. Determine appropriate scales for histograms, scatterplots, and other graphs M.1.2. (Comprehension) Use suitable units when describing rate of change 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 M.1.1A. (Application) Use dimensional analysis to check answers and determine units of a problem solution 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: , , , , 498, 509, 514, 517, 520, 522, 527, , 550, , 557 SE/TE: , 122 SE/TE: , 134, 157, 159 4

5 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 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 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, , , , , 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, , , 615, 616, 618, 619, 625, 639, 642, 645 SE/TE: 19, 20, 28, 29, 70, 73, 75, , , 428, , 436, 437, 439, 441, 444, 446, 462, , 467, 469, 510 Scientific notation SE/TE: , , 428, , 436, 437, 439, 441, 444, 446, 462, , 467, 469, 510 Infinitely many solutions SE/TE: 362, , 370, , 377, 378, 389, , 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 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 N.2.1. (Comprehension) Add, subtract, multiply, and divide real numbers including integral exponents N.2.1A. (Application) Add, subtract, multiply, and divide real numbers including rational exponents. Simplify numeric expressions with radicals. SE/TE: 416, 419, 425, , , 436, 437, 439, 441, , , 467, 469 SE/TE: , , , , 619, 625, 639, , 645, 647, 657, 709,

6 Indicator 3: Develop conjectures, predictions, or estimations to solve problems and verify or justify the results 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, 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, , , 150, 156, 157 SE/TE: 23-25, 26-28, 40-41, 44, 46-48, 50, , , , , 439, , 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 S.1.2. (Comprehension) Compare multiple one-variable data sets, using range, interquartile range, mean, mode, and median 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 S.1.1A. (Evaluation) Analyze and evaluate the design of surveys and experiments S.1.2A. (Evaluation) Analyze and evaluate graphical displays of data. SE/TE: 716, , 722, 724, 727, 731, 736, , 748 SE/TE: , , 733, , , 749, 762, 776, 779 SE/TE: 739 SE/TE: 728, , 736, , 776 SE/TE: , , , , , 746, 748, 749, , 779, 782 SE/TE: , , 341, 346, 348, 352, 353, , , 581, 587, SE/TE: , , 749, 776, 779, 782 SE/TE: , , 732, 749, 773, 775, 779, 785 SE/TE: 740, , , 749, 756, 770, 772, 773, 777, 779 SE/TE: , 723, 725, 736, , 748, 749, 773, , 779, 785 6

7 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 S.1.4A. (Application) Describe the normal curve and use it to make predictions 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: , , 341, 346, 348, 352, 353, , , 581, 587, Apply the concepts of probability to predict events/outcomes and solve 9-12.S.2.1. (Knowledge) Distinguish between experimental and theoretical probability S.2.2. (Comprehension) Predict outcomes of simple events using given theoretical probabilities. Determine the sample space of an experiment S.2.1A. (Application) Use probabilities to solve problems. SE/TE: , 774, 778 SE/TE: 760, 761, 784 SE/TE: 757, 765 SE/TE: , , 763, , , , 778, 779 Compute combinations, permutations. SE/TE: , , 762, 777, 779 Interpret tables. SE/TE: 761, 769, 771, 783 Create and use tree diagrams. SE/TE: 765, 772, S.2.2A. (Application) Determine probability of compound, complementary, independent, and mutually exclusive events S.2.3A. (Analysis) Generate data and use the data to estimate empirical probabilities. SE/TE: 758, , 763, , , , 778, 779 SE/TE: 763, 772 7

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