Prentice Hall Mathematics:,, & 2004 Kansas Curricular Standards for Mathematics (By the end of Grade 10) STANDARD 1: NUMBER AND COMPUTATION The student uses numerical and computational concepts and procedures in a variety of situations. Benchmark 1: Number Sense The student demonstrates number sense for real numbers and algebraic expressions in a variety of situations 1. The student uses appropriate representations of real numbers and algebraic expressions to formulate and solve real-world problems. 2. The student determines reasonableness of solutions to problems involving real numbers and/or algebraic expression. SE/TE: 6, 11, 18, 26, 34, 103-107 SE/TE: 52, 57, 146, 212, 358, 367-369, 440 SE/TE: 6, 13, 36, 842 SE/TE: 76, 82, 97, 154, 349, 354, 537, 673 SE/TE: 264 Benchmark 2: Number Systems and Their Properties The student demonstrates an understanding of the real number system, recognizes, applies, and explains its properties, and extends these properties to algebraic expressions. 1. The student uses properties of the real number system to formulate and solve real-world problems. 2. The student uses real number properties to perform various computational procedures and explains how they are used. SE/TE: 48, 55, 76, 82, 89, 103-107, 142, 148 SE/TE: 89-91, 134, 212, 358, 367-369, 434-435, 441, 447, 608, 610 SE/TE: 20-21, 28-29 SE/TE: 9-12, 48-49, 56, 83 SE/TE: 118, 124, 132, 251, 290, 314, 358, 367-369, 434-435, 440, 447, 608-609, 610, 691, 716-720 SE/TE: 12-14, 18-21, 26-29 1
Prentice Hall Mathematics:,, & 2004 Benchmark 3: Estimation The student uses numerical estimation with real numbers in a variety of situations. 1. The student uses estimation to check reasonableness of results, and makes predictions in situations involving real numbers and algebraic expressions. 2. The student adjusts original rational number estimates based on additional information (estimation from a frame of reference). 3. The student explains the impact of rounding errors on numerical results. 4. The student determines if a problem calls for an exact or approximate answer and performs the appropriate computation. SE/TE: 76, 78, 82, 97, 154, 199, 218, 354, 445, 537, 673, 723 SE/TE: 32, 56, 383, 458, 547, 723 SE/TE: 238, 628, 745-746, 747 #44, 701 #33, 727 SE/TE: 78, 86, 149, 199, 250, 350, 521 SE/TE: 32, 56, 383, 458 SE/TE: 205-206, 628 SE/TE: 710-711 SE/TE: 18, 205-206 Benchmark 4: Computation The student explains and performs computation with real numbers and algebraic expressions in a variety of situations. 1. The student uses arithmetic operations and inverse relationships to formulate and solve real-world problems involving real numbers and algebraic expressions with special emphasis on topics such as: Finding the volume and surface area when formulas are given. SE/TE: 13, 14, 113, 114, 116-117, 465, 532, 567, 610 SE/TE: 527, 536, 544-547, 551-554, 579, 558-560 SE/TE: 847 2
Prentice Hall Mathematics:,, & 2004 Applications from business, economics, chemistry, and physics (avoiding logarithms). Probabilities and exponential growth and decay. SE/TE: 8, 29, 93, 97, 99, 130-131, 157, 159, 162, 244, 245, 264, 265, 283, 288, 322, 358, 363, 366, 376, 382, 383, 408, 413, 428, 438-439, 456, 521, 555, 586, 603, 677 SE/TE: 6, 21, 336 SE/TE: 15, 61, 103, 112-113, 119, 176, 181, 212, 214, 230-231, 237, 244, 245, 266, 267, 290, 291, 358-359, 440, 459, 474-475, 495, 584-585 SE/TE: 210-213, 219-221, 437-441 SE/TE: 402-404 SE/TE: 422-426 STANDARD 2: ALGEBRA The student uses algebraic concepts and procedures in a variety of situations. Benchmark 1: Patterns The student recognizes, describes, extends, develops, analyzes and gives the general rule of patterns from a variety of situations involving tenth grade content. 1. The student recognizes the generalization of a pattern using symbolic notation to represent the nth term in an explicit form. 2. The student recognizes the generalization of a pattern using symbolic notation to represent the nth term in a recursive form. 3. The student recognizes the same general pattern presented in different representations. 4. The student generalizes a pattern using a written description. SE/TE: 268-270, 424-427 SE/TE: 594-595, 600-602 SE/TE: 272 SE/TE: 590, 595, 601 SE/TE: 282-285, 291-292, 306-307 SE/TE: 72-74, 78-80, 538 SE/TE: 37, 306, 318-319, 326-327, 394, 411, 428, 716 3
Prentice Hall Mathematics:,, & 2004 Benchmark 2: Variables, Equations, and Inequalities The student uses variables, symbols, real numbers, and algebraic expressions to solve equations and inequalities in a variety of situations. 1. The student uses symbols, variables, expressions, inequalities, equations, and simple systems of linear equations to represent problem situations, which involve variable quantities. 2. The student formulates and solves problems involving symbols, percents, variables, expressions, inequalities, equations, and simple systems. SE/TE: 4-6, 103-107, 136, 142, 362-365 SE/TE: 25-29, 118, 132, 145-146, 209, 422, 615-617, 722 SE/TE: 20-21, 26-29, 78-80, 116-118, 123-125 SE/TE: 197-200, 204-206 SE/TE: 110-111, 238-239, 344-345, 466-467, 578-579, 688-689, 723 SE/TE: 112-113, 230-231, 842 Benchmark 3: Functions The student analyzes functions in a variety of situations. 1. The student moves between symbolic, numerical, and graphical representations of functions with fluency and accuracy. 2. The student analyses the effects of parameter changes on the appearance of a function s graph such as scale changes or restricted domains 3. The student analyzes how changes in constants and/or slopes within a linear function affect the appearance of a graph. 4. The student analyzes how changes in constants and/or coefficients within quadratic and absolute value functions affect the appearance of the graph. 5. The student interprets the meaning of points on a graph in the context of a real-world situation. SE/TE: 247-249, 253 SE/TE: 62-67, 234-235 SE/TE: 122, 358-359, 407, 555, 772, 777 SE/TE: 291-293 SE/TE: 151-154, 158-161 SE/TE: 62-67 SE/TE: 249, 325-327, 510-513, 647 SE/TE: 86-88, 91-95, 241-243, 248-251 SE/TE: 61-62, 248 SE/TE: 44 SE/TE: 78-85 4
Prentice Hall Mathematics:,, & 2004 6. The student examines a situation and extracts from it quantities the vary directly and indirectly and represent that variation in a graph, in a table, or in an equation SE/TE: 261-264, 636-639 SE/TE: 72-74, 478-480 Benchmark 4: Models The student develops and uses models to represent and justify mathematical relationships found in a variety of situations involving tenth grade knowledge and skills. 1. uses the mathematical modeling process to make inferences about real-world situations. SE/TE: 255, 561-566, 440-441 SE/TE: 78-80, 108, 302, 308 STANDARD 3: GEOMETRY The student uses geometric concepts and procedures in a variety of situations. Benchmark 1: Geometric Figures and their Properties The student recognizes geometric figures, and applies, compares, and justifies the properties of geometric figures in a variety of situations. 1. The student uses definitions, axioms, theorems and deductive reasoning to justify the following a. parallel line properties including angle relationships created by a transversal. b. angle relationships in triangles such as base angles of an isosceles triangle are equal or the sum of the angles in a triangle equals 180. 2. The student formulates and solves real-world problems by applying properties or geometric figures. SE/TE: 114-118 SE/TE: 131-134, 211-212 SE/TE: 14, 97, 103, 112, 375, 470, 494, 515, 532, 545 SE/TE: 110-111, 238-239, 344-345, 466-467, 578-579, 688-689 SE/TE: 42, 43, 389, 436, 590, 592, 613, 739, 784 3. The student uses definitions, axioms, theorems, and deductive reasoning to justify the following properties of geometric figures. a. congruence properties of triangles (SSS, ASA, AAS, and HL) SE/TE: 186-188, 194-196 5
Prentice Hall Mathematics:,, & 2004 b. ratios in special right triangles. SE/TE: 598-599 SE/TE: 366-369 SE/TE: 703 c. central and inscribed angles. SE/TE: 386, 598-601 SE/TE: 712 4. The student understands the concepts of and develops both formal and informal proof through understanding of the difference between a statement verified by mathematical proof (i.e., theorem) and a statement verified by using examples. SE/TE: 56, 83, 173, 268 SE/TE: 4-9, 82-84 Benchmark 2: Measurement and Estimation The student estimates, measures and uses geometric formulas in a variety of situations. 1. The student formulates and solves real-world problems by applying measurements and measurement formulas. 2. The student uses estimation to check reasonableness of measurements and calculations and/or adjusts original measurements based on additional information (estimation from a frame of reference). 3. The student uses indirect measurements to measure inaccessible objects. SE/TE: 232-233, 336-337, 591-596, 608 SE/TE: 297, 315, 321, 483, 578-579 SE/TE: 81, 112-113, 418, 584-585, 713-715, 791, 856 SE/TE: 205-206, 232-233, 602, 615 SE/TE: 710-711 SE/TE: 628, 701, 727, 746 SE/TE: 191 SE/TE: 245, 434-435, 482-483 SE/TE: 75, 778-781 6
Prentice Hall Mathematics:,, & 2004 Benchmark 3: Transformational The student recognizes and applies transformation of twoand three-dimensional figures in a variety of situations. 1. The student uses a variety of scales to view and analyze two-and three- dimensional figures. 2. The student uses visualization and spatial reasoning to represent, formulate, and solve realworld problems. 3. The student represents geometric transformations using sketches, coordinate systems, vectors, or matrices. 4. The student analyzes the impact of the transformations on area and perimeter of triangles and circles and on volume of cylinders and rectangular prisms. 5. The student analyzes the impact of transformations on geometric figures within the coordinate plane. 6. The student describes and draws threedimensional shapes as they would appear after undergoing two specified transformations without actually performing the transformations with concrete objects. SE/TE: 191, 255, 414, 528, 591-593 SE/TE: 43-45, 48, 51, 244, 250, 551, 553, 528-531, 544-545 SE/TE: 534, 692-693 SE/TE: 522, 688-689 SE/TE: 325-327, 732-734 SE/TE: 634-636, 641-643, 647-649 SE/TE: 186-191 SE/TE: 454, 532, 634, 674-675 SE/TE: 188-189 SE/TE: 636, 642, 656, 674-675 SE/TE: 186-189 SE/TE: 688-689 Benchmark 4: from An Algebraic Perspective The student uses an algebraic perspective to analyze the geometry of two- and three- dimensions in a variety of situations. 1. The student analyzes how changes in constants and/or coefficients within the equation of a line or parabola changes the appearance of the graph of the equation. SE/TE: 290, 510-513 SE/TE: 152-154 SE/TE: 62-67, 241-243, 248-251 7
Prentice Hall Mathematics:,, & 2004 2. The student translates between the algebraic representation of a problem and the geometric representation of a problem. 3. The student represents, formulates, and solves distance and geometry problems using the language and symbols of algebra and the coordinate plane. 4. The student recognizes and explains the effects of scale changes on the appearance of the graph of an equation or inequality involving a line or parabola. SE/TE: 462, 467, 474 SE/TE: 51, 131, 243, 356, 373, 395, 544, 551, 598 SE/TE: 78-80, 85, 236, 240, 302, 551, 644 SE/TE: 591-593 SE/TE: 43-45, 615-617 SE/TE: 62, 78-80, 86, 142-144, 422, 440, 535-538, 546, 550, 557, 564, 720, 856 SE/TE: 674-675, 678, 683 STANDARD 4: DATA The student uses concept and procedures of Data Analysis in a variety of situations. Benchmark 1: Probability The student applies probability theory to analyze the validity of arguments, draw conclusions, and make decisions in a variety of situations. 1. The student uses theoretical or experimental probability to make predictions about real-world events such as work in economics, quality control, genetics, meteorology, and other areas of science, games, and situations involving geometric probability. 2. The student conducts experiments and/or simulations, records the results in charts, tables, or graphs, and uses the results to draw conclusions and make predictions. 3. The student compares theoretical (expected) results with empirical (experimental) results. 4. The student uses conditional probabilities to make decisions. SE/TE: 211-216 SE/TE: 402-404, 724 SE/TE: 39-42, 519 SE/TE: 218 SE/TE: 59, 171, 406 #46, 502 #34, 536, 704 SE/TE: 40, 519, 638-639 SE/TE: 211-213 E/TE: 39-42 SE/TE: 642-644, 647 Benchmark 2: Statistics The student generates, organizes, and interprets real number and other data in a variety of situations. 8
Prentice Hall Mathematics:,, & 2004 1. The student determines or explains appropriate sampling techniques for gathering data for a given situation (observation, survey, census of total population, random sampling, sampling of specific groups, etc.). 2. The student uses data analysis to make accurate inferences, decisions/predictions, and to develop convincing arguments from data displayed in a variety of formats (see listing of graphical displays). 3. The student recognizes or explains the effects of scale and/or interval changes on graphs of data sets. 4. The student determines the advantages and disadvantages of using various statistical measures to describe a data set. 5. The student analyzes the effects of data transformations on various statistical measures. 6. The student uses properties of the normal curve to make inferences about data sets that are assumed to be normally distributed. SE/TE: 225 SE/TE: 663-666, 670 SE/TE: 61, 118-121, 318-320, 735-740 SE/TE: 69, 269, 292, 671, 713-714 SE/TE: 648-652, 656-660, 857-858 SE/TE: 737 SE/TE: 118-121 SE/TE: 712 SE/TE: 654 #20 SE/TE: 118-121 SE/TE: 712 SE/TE: 653 #13 SE/TE: 678-680 9