A Correlation of to the Mathematics Standards Approved July 30, 2010 Bid Category 13-130-10
A Correlation of, to the Mathematics Standards Mathematics Standards I. Ways of Looking: Revisiting Concepts Students learn mathematics best by being introduced to concepts that they have previously studied in a new approach. The concepts in this section appear in a manner that emphasizes their basic definition. This presentation of each concept is based upon the format that would be a best practice of introducing the particular concept. 3181.1.1 Diagrammatic Mathematics 3181.1.1.1 Identify the graph of a linear inequality on the number line. SE: Section 36: 503-507, 523, 528-531, Section 37: 535-540 3181.1.1.2 Create and use absolute value functions to model and solve problems in common settings. 3181.1.1.3 Given an equation of a line, write an accurate definition of a line by determining the unique characteristics that define it (i.e. slope and intercepts). SE: Section 36: 516-518, 525-531 SE: Section 29: 394-395, Section 30: 406, 408-410, 417-422, 426-429, Section 31: 440-445 3181.1.1.4 Compute the perimeter of simple composite geometric figures with unknown side lengths. 3181.1.1.5 Apply a variety of strategies to determine the circumference and the area for circles. SE: Section 16: 222-223 SE: Section 17: 233-236, Section 18: 241, 243-245 3181.1.1.6 Investigate the area of a sector and the arc length of a circle. SE: Section 17: 235-236, Section 21: 307-313, 317-319 3181.1.2 Verbal Mathematics 3181.1.2.1 Understand that a line parallel to one side of a triangle divides the other two proportionally, and conversely. 3181.1.2.2 Apply similar triangles to solve problems, such as finding heights and distances. 3181.1.2.3 Use several angle properties to find an unknown angle measure (i.e. supplementary, complementary, vertical, angles along a transversal, and sum of angles in a polygon). SE: Section 20: 260-261, 284 SE: Section 19: 249-253, Section 20: 259-261, 268-272, 274-277, 280-282, 285-288 SE: Section 15: 215-218, Section 16: 223-225, Section 19: 252-253, Section 20: 274-277, 281-282, 285-288 SE = Student Edition 1
A Correlation of, to the Mathematics Standards Mathematics Standards 3181.1.2.4 Describe, compare, and contrast plane and solid figures using their attributes. SE: Section 14: 210, Section 15: 213-218, Section 16: 222-225, Section 17: 230-236, Section 18: 241-245, Section 19: 249-253 3181.1.2.5 Multiply, divide and simplify radicals. SE: Section 2: 17, 19-24, Section 5: 62-66, Section 10: 163-167 3181.1.2.6 Use mathematical grammar and appropriate mathematical symbols to represent contextual situations. SE: Section 2: 24, Section 4: 36, Section 9: 148-150, 151-157, Section 12: 176-181, Section 19: 249-253, Section 25: 345-351, Section 26: 354-361, Section 29: 395-398, Section 32: 451-455, Section 41: 591-596, Section 42: 602-607, Section 47: 667-669, Section 48: 673-677, Section 58: 765-767 3181.1.3 Symbolic Mathematics 3181.1.3.1 Operations with numbers expressed in scientific notation. SE: Section 13: 197-203 3181.1.3.2 Develop a thorough understanding of both rational and irrational numbers: make both historical and concrete connections between irrational numbers and the real world. 3181.1.3.3 Use mathematical symbols and variables to express a relationship between quantities. SE: Section 1: 3-14, Section 2: 17-24, Section 3: 28-32, Section 6: 84-85 SE: Section 6: 72, 75-78, 83-88, 94-97, Section 7: 113-117, 130-136, Section 9: 148-150, 151-157, Section 12: 176-181, Section 20: 285-288, Section 21: 300-303, Section 30: 426-429, Section 46: 657-662 3181.1.3.4 Model a variety of problem situations with expressions. SE: Section 4: 36, Section 6: 83-88, 94-97, Section 7: 113-117, Section 9: 148-150, 151-157, Section 11: 170-174, Section 12: 176-181, Section 19: 249-253, Section 20: 285-288, Section 29: 397-399, Section 32: 451-461, Section 49: 681-682 SE = Student Edition 2
A Correlation of, to the Mathematics Standards Mathematics Standards 3181.1.3.5 Skillfully manipulate formulas involving exponents. 3181.1.3.6 Understand how mathematical properties yield equivalent equations and can be used in determining if two expressions are equivalent. SE: Section 9: 150, 151-157, Section 10: 160-167, Section 12: 176-181, Section 22: 327-328, Section 49: 682 SE: Section 3: 30-32, Section 4: 36, Section 5: 63, 69-70, Section 7: 130-136, Section 10: 163-167, Section 28: 378-384, Section 29: 388-399, Section 40: 577-583, Section 44: 636-637 3181.1.3.7 Perform polynomial arithmetic, including addition, subtraction, multiplying, dividing, factoring, and simplifying results. SE: Section 7: 117-120, 130-136, Section 40: 576-583 3181.1.3.8 Demonstrate fluency with techniques needed to simplify radical expressions and calculate with them, including addition, subtraction, and multiplication. 3181.1.3.9 Rationalize denominators in order to perform division with radicals. SE: Section 2: 19-24, Section 5: 50-56, 62-66, Section 10: 163-167 SE: Section 2: 22-23 3181.1.4 Graphic Mathematics 3181.1.4.1 Understand that a linear function models a situation in which a quantity changes at a constant rate, m, relative to another. 3181.1.4.2 Graph quadratic equations and identify key characteristics of the function. SE: Section 29: 394-395, Section 30: 405-411, 417-422, 426-429, Section 31: 439-445, Section 32: 453-454 SE: Section 8: 140, 143-144, Section 32: 458-461, Section 38: 546-552, 556-563, Section 39: 569-573, Section 40: 586, Section 50: 691-693 3181.1.4.3 Find the solution of a quadratic equation and/or zeros of a quadratic function. SE: Section 8: 140-141, 143-145, Section 32: 459-461, Section 38: 547, 556, 559, 562-563, Section 39: 569-573, Section 40: 581-587 3181.1.4.4 Operate (add, subtract, multiply, and divide) with and evaluate rational expressions. SE: Section 4: 38-39, Section 28: 378-384, Section 43: 620-625, Section 44: 633-637 SE = Student Edition 3
A Correlation of, to the Mathematics Standards Mathematics Standards 3181.1.4.5 Operate (add, subtract, multiply, divide, simplify, powers) with radicals and radical expressions including radicands involving rational numbers and algebraic expressions. 3181.1.4.6 Identify and calculate the measures of central tendency and spread in a set of data. 3181.1.4.7 Understand the correlation coefficient and its role in measuring the goodness of fit for a model for a data set. 3181.1.4.8 Analyze data to make predictions based on an understanding of the data set, for example, use a scatter-plot to determine if a linear relationship exists and describe the association between the variables. 3181.1.4.9 Use algebra and geometry to solve problems involving midpoints and distances (i.e. geometric figures). 3181.1.5 Numeric Mathematics 3181.1.5.1 Understand that there are numbers that are not rational numbers, called irrational numbers, e.g., π, e, and 2, which together with the rational numbers form the real number system that satisfies the laws of arithmetic. 3181.1.5.2 Apply and use elementary number concepts and number properties to model and solve nonroutine problems that involve new ideas. SE: Section 2: 19-24, Section 4: 38-39, Section 5: 48-56, 62-66, Section 10: 162-167 SE: Section 56: 743-752, Section 57: 756-761 SE: Section 33: 467-473 SE: Section 30: 426-429, Section 31: 432-436, Section 32: 451-461, Section 33: 466-473, Section 45: 641-645, Section 46: 657, Section 50: 691-693, Section 52: 702-703 SE: Section 20: 258, 268-272, 280-282 SE: Section 2: 17-24, Section 3: 28-32, Section 6: 84-85, Section 32: 454-455 SE: Section 1: 7-8, Section 2: 17-24, Section 22: 327-328, Section 23: 330-335, Section 24: 338-342, Section 53: 714-717, Section 54: 725-727 3181.1.5.3 Determine if a data set represents a line through numerically analyzing slope calculations. If appropriate, interpret the slope in terms of a rate. 3181.1.5.4 Find the probability of simple events, disjoint events, compound events, and independent events in a variety of settings using a variety of counting techniques. SE: Section 30: 426-429, Section 31: 432-436, Section 32: 453-454, Section 33: 466-473 SE: Section 22: 324, Section 25: 345-351, Section 26: 354-361 SE = Student Edition 4
A Correlation of, to the Mathematics Standards Mathematics Standards 3181.1.5.5 Develop fluency with the basic operations of complex numbers. SE: Section 8: 140-145 II. Making Connections Making connections allows those concepts that need a more complex look to be studied through two different modalities. This allows connections to be made between the concepts, and allows for a more in-depth understanding of the topics supporting the foundation for problem solving application. In addition, building topics in this manner helps students work problems of a higher depth of knowledge level. 3181.2.1 Symbolic & Diagrammatic Mathematics 3181.2.1.1 Use the laws of exponents to simplify and interpret expressions for exponential functions, recognizing positive rational exponents as indicating roots of the base and negative exponents as indicating the reciprocal of a power. SE: Section 10: 160-167, Section 12: 176-181, Section 13: 198-203, Section 32: 451-455, Section 41: 591-596, Section 42: 603, 606-607, Section 47: 666-668, Section 48: 673-677, Section 49: 681-682, Section 58: 765-767 3181.2.1.2 Solve a linear inequality and provide an interpretation of the solution. SE: Section 36: 503-507, 523, 528-531, Section 37: 535-540 3181.2.1.3 Recognize special products and factors of polynomials to facilitate problem solving with polynomials; in particular, find the zeros of a quadratic polynomial. SE: Section 7: 130-136, Section 32: 459-461, Section 38: 547, 560-562, Section 39: 569-573, Section 40: 581-587, Section 47: 668 3181.2.1.4 Investigate the properties of plane figures, developing precise mathematical descriptions of geometric shapes, both in the plane and in space. 3181.2.1.5 Apply a variety of strategies using relationships between perimeter, area, and volume to calculate desired measures in composite figures. 3181.2.2 Symbolic & Verbal Mathematics 3181.2.2.1 Explain, solve, and/or draw conclusions for complex problems using relationships and elementary number concepts. SE: Section 7: 130-132, Section 14: 205-211, Section 15: 213-218, Section 16: 222-225, Section 17: 229-236, Section 19: 249-253, Section 20: 258-264, 268-272, 274-277, 280-282 SE: Section 7: 130-132, 134, Section 14: 205-211, Section 16: 222-225, Section 17: 229-236, Section 18: 241-245 SE: Section 2: 23-24, Section 8: 141-145, Section 53: 710-717, Section 54: 721-727 SE = Student Edition 5
A Correlation of, to the Mathematics Standards Mathematics Standards 3181.2.2.2 Solve simple rational and radical equations in one variable, noting and explaining extraneous solutions. 3181.2.2.3 Write ratios, proportions, and solve proportions in a contextual setting for an unknown value. SE: Section 4: 37-38, Section 5: 62-66, Section 44: 633-637 SE: Section 19: 249-253, Section 25: 345-351, Section 26: 354-361, Section 29: 395-398 3181.2.2.4 Solve literal equations for any variable; interpret the results based on units. SE: Section 4: 36, Section 5: 63, 69-70, Section 44: 636-637 3181.2.3 Symbolic & Numeric Mathematics 3181.2.3.1 In the context of exponential models, solve equations of the form SE: Section 9: 148-150, 151-157, Section 12: 176-181, Section 32: 451-455, Section 41: 591-596, Section 42: 602-607, Section 47: 667-669, Section 48: 673-677 a b ct = d where a, c, and d are specific numbers and the base b is 2, 10, or e. SE: Section 9: 150, 151-157, Section 12: 176-181, Section 32: 451-455, Section 41: 591-596, Section 42: 602-607, Section 47: 667-669, Section 48: 673-677 3181.2.3.2 Use the rules of exponents to develop an understanding of the difference between the rational and real numbers. SE: Section 10: 160-163, 165-167, Section 32: 454-455, Section 49: 681-682 3181.2.3.3 Recognize functions as mappings of an independent variable into a dependent variable. SE: Section 5: 48-55, Section 6: 72, 75-78, 83-88, 94-97, 103-112, Section 7: 113-120, 125-129, Section 9: 148-150, 151-157, Section 21: 300-303, 307-313, Section 28: 382-384, Section 30: 405-411, Section 31: 439-445, Section 32: 451-461, Section 41: 591-596 3181.2.3.4 Evaluate polynomial and exponential functions that use function notation. SE: Section 7: 113-117, Section 9: 148-150, 151-157, Section 32: 451-455, 458-461, Section 40: 586-587, Section 41: 591-596, Section 42: 602-607, Section 47: 667-669, Section 51: 697-699, Section 58: 765-767 SE = Student Edition 6
A Correlation of, to the Mathematics Standards Mathematics Standards 3181.2.3.5 Recognize composite functions as an application of substitution and use this understanding to write expressions for and evaluate composite functions. 3181.2.4 Symbolic & Graphic Mathematics 3181.2.4.1 Graphically represent the solution to a linear equation and the solution to a system of linear equations in two variables. SE: Section 10: 160-162, 164-165, 167 SE: Section 6: 85-88, Section 29: 394-395, Section 30: 419-421, Section 31: 440, 443-445, Section 34: 477-480, 484-487, Section 59: 776-777, 779-781, Section 60: 788 3181.2.4.2 Graphically represent the solution to a linear inequality and the solution to a system of linear inequalities in two variables. 3181.2.4.3 Relate the basic definitions of the trigonometric ratios to the right triangle. SE: Section 35: 491-497, Section 36: 502-507, 514-516, 523, 528-531, Section 37: 535-540 SE: Section 19: 249-253, Section 20: 258-265, 268-272, 274-277, 280-282, 285-288, Section 21: 307 3181.2.4.4 Identify the graphs of basic trigonometric functions and shifts of those graphs. 3181.2.4.5 Solve a simple system consisting of one linear equation and one quadratic equation in two variables; for example, find points of intersection between the line y = 3x and the circle x 2 + y 2 = 3. Illustrate the solution graphically. 3181.2.5 Numeric & Graphic Mathematics 3181.2.5.1 Given a variety of appropriate information, determine the equation of a line. 3181.2.5.2 Use appropriate technology to generate the equation of a line from a set of data and if appropriate, use it to make a prediction. 3181.2.5.3 Use appropriate technology to find the mathematical model for a set of non-linear data. SE: Section 21: 300-303, 307-313, 317-319, Section 52: 702-703 SE: Section 39: 571-573 SE: Section 30: 405-410, 417-422, 426-429, Section 31: 439-445 SE: Section 30: 420-421, 426-429, Section 31: 432-436, Section 33: 466-473, Section 45: 641-645 SE: Section 31: 432-433, Section 45: 642-645, Section 50: 691-693, Section 51: 697-699, Section 52: 702-703, Section 58: 765-769 SE = Student Edition 7
A Correlation of, to the Mathematics Standards Mathematics Standards 3181.2.5.4 Compare measures of central tendency and spread for a single data set along with its graph and summary statistics. SE: Section 56: 743-752, Section 57: 756-761 3181.2.5.5 Compare data sets using graphs and summary statistics, and measures of central tendency and spread. 3181.2.5.6 Examine radical and rational equations, both graphically and numerically, to determine restrictions on the domain of the variables. SE: Section 55: 730-738, Section 56: 743-752, Section 57: 756-761 SE: Section 4: 36-38, Section 28: 380-384, Section 43: 620-626, Section 44: 633-637 3181.2.5.7 Apply special right-triangle properties and the Pythagorean Theorem to solve congruent, similar shape, and contextual problems. SE: Section 19: 249-253, Section 20: 258-265, 268-272, 274-277, 280-282 3181.2.6 Numeric & Diagrammatic Mathematics 3181.2.6.1 Understand and use basic SE: Section 22: 324-328, Section 23: 330- counting techniques in contextual settings. 335, Section 24: 338-342, Section 26: 357-361 3181.2.6.2 Use counting techniques to calculate probabilities for conditional and independent events. SE: Section 26: 357-361 3181.2.6.3 Compare a theoretical probability model to an experimental probability model for the same process. SE: Section 25: 349-351 III. Applications: Ways of Looking at the World Students are confronted with different ways to look at the world. Here students look at multiple representations of concepts, blend their new understanding of topics with applications, and have the opportunity to model contextual situations. Various applications should be addressed each week, throughout the course to support theoretical learning and increased complexity. 3181.3.1 Applications with Numbers 3181.3.1.1 Solve problems using scientific notation. SE: Section 13: 197-203 SE = Student Edition 8
A Correlation of, to the Mathematics Standards Mathematics Standards 3181.3.1.2 Solve problems involving percent of increase or decrease, for example mark-ups and mark-downs. SE: Section 9: 148-150, 151-157, Section 11: 170-174, Section 12: 176-181, Section 27: 369-375, Section 28: 378-379, Section 29: 397-398 3181.3.1.3 Solve rate, distance, and work problems using proportions and percentages. SE: Section 29: 397-398 3181.3.1.4 Solve problems involving evaluation of exponential functions, for example applications involving simple and compound interest. 3181.3.2 Applications with Geometry 3181.3.2.1 Solve problems involving ratios in geometric settings, such as similar figures and right triangle distance problems. 3181.3.2.2 Solve problems involving finding missing dimensions given area or perimeter of the figure. 3181.3.2.3 Solve problems involving surface areas and volumes of 3-dimensional figures, including maximization, scale, and increment problems. 3181.3.2.4 Solve problems involving angles of elevation and angles of declination. 3181.3.2.5 Solve problems requiring the interpretation of polynomial, rational, and exponential graphs that depict real-world phenomena, including identification of max/min and end behavior of functions. 3181.3.3 Applications with Functions 3181.3.3.1 Solve problems involving applications of linear equations. SE: Section 9: 148-150, 151-157, Section 11: 170-174, Section 12: 176-181, Section 32: 451-455, Section 41: 591-596, Section 42: 602-607, Section 58: 765-767 SE: Section 13: 187-194, Section 17: 233-236, Section 19: 249-253, Section 20: 258-265, 268-272, 274-277, 280-282, Section 21: 307-313 SE: Section 17: 235-236, Section 19: 251-253 SE: Section 7: 130-132, 134, Section 14: 208-211, Section 18: 241-245 SE: Section 19: 252-253, Section 20: 280-282 SE: Section 7: 117, 130-132, 134, Section 9: 148-150, Section 28: 383, Section 38: 546-548, 550-551, 556, Section 39: 569-572, Section 41: 591-596, Section 42: 602-607, Section 43: 620-626, Section 44: 635, Section 47: 667-669, Section 51: 697-699, Section 58: 765-767 SE: Section 6: 83, 85-87, 95-97, Section 29: 388-399, Section 30: 417-421, 426-429, Section 31: 439-445 SE = Student Edition 9
A Correlation of, to the Mathematics Standards Mathematics Standards 3181.3.3.2 Solve problems involving direct and inverse variations, such as frequency, interest, and pressure. 3181.3.3.3 Solve problems involving systems of equations such as mixture problems. SE: Section 11: 170-174, Section 28: 378-384, Section 43: 620-626, Section 44: 633-637 SE: Section 34: 477-480, 484-487, Section 39: 571-573, Section 59: 775-782, Section 60: 788-792 3181.3.3.4 Solve problems involving quadratic equations such as area and gravity; additionally examine the fact that quadratic functions have maximum or minimum values and can be used to model problems with optimum solutions. 3181.3.3.5 Solve problems involving radical equations, such as wind chill and body mass index. 3181.3.3.6 Solve problems involving rational equations such as work problems. SE: Section 6: 93-94, Section 32: 458-460, Section 38: 546-548, 550-551, 556, Section 39: 569-572, Section 50: 691-693 SE: Section 2: 24, Section 5: 64-66 SE: Section 4: 36-38, Section 28: 378-384, Section 43: 620-626, Section 44: 633-637 3181.3.3.7 Solve problems involving exponential applications such as half-life and continuous interest. SE: Section 9: 148-150, 151-157, Section 12: 176-181, Section 32: 451-455, Section 41: 591-596, Section 42: 602-607, Section 47: 667-669, Section 48: 673-677, Section 58: 765-767 3181.3.4 Applications with Data 3181.3.4.1 Solve problems involving constructing and interpreting pie charts. 3181.3.4.2 Solve problems that use the construction and interpretation of Venn diagrams to analyze the attributes of a set of data, for example logic and counting problems. SE: Section 17: 236 Related material: SE: Section 53: 708-720 3181.3.4.3 Solve problems involving geometric probabilities. SE: Section 25: 352-353, Section 26: 362 SE = Student Edition 10