correlated to the Ohio Academic Content Standards with Indicators Mathematics Grade 9
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1 correlated to the Ohio Academic Content Standards with Indicators Mathematics Grade 9
2 McDougal Littell Algebra correlated to the Ohio Academic Content Standards with Indicators Mathematics, Grade 9 Number, Number Sense and Operations Standard Students demonstrate number sense including an understanding of number systems and operations, and how they relate to one another. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods. Number and Number Systems 1. Identify and justify whether properties (closure, identity, inverse, commutative and associative) hold for a given set and operations; e.g., even integers and multiplication. 75 (Key Concept, Properties of Addition), 76 (Example 3, Guided Practice 8-10), 77 (#26-31), 83 (#40), 84 (#53-56), 89, 90 (Example 3, Guided Practice #10-12), 91 (#19-36), 103 (Key Concept, Inverse Property of Multiplication), 107 (#48), 120 (Big Idea 2), 129 (#6), 938 (#32-37), Compare, order and determine equivalent forms for rational and irrational numbers. 62 (#4-7), 64, 65 (Example 3, Guided Practice 4-7), 67 (#5-13), 68 (#14-22), 69 (#53-54, 69), 70 (#59-60), 76 (Example 4, Guided Practice 11), 78 (#55c, 56), 79 (#57a), 84 (#1), 86 (#1, 6), 107 (#54b), 108 (#57b), , 112 (Example 4, Guided Practice 9), 113 (#3-14), 114 (#15-29), 121 (Example 2.1, #7-8), 124 (Example 2.7, #50-59), 125 (#5-6), 128 (#1b, 3), 129 (#5), 130 (#7-10), 159 (#56-59), 909, 912, 913,
3 Meaning of Operations 3. Explain the effects of operations such as multiplication or division, and of computing powers and roots on the magnitude of quantities. 73 (#9-14), 77 (#2), 82 (#2, 38), 83 (#41), 87 (#1), 88 (Key Concept), 89 (Key Concept), 92 (#45-49), 104 (Key Concept), 103 (Key Concept, Inverse Property of Multiplication), 105 (Concept Summary), 106 (#1-2), 107 (#49), 120 (Big Idea 1-2) Computation and Estimation 4. Demonstrate fluency in computations using real numbers. 73 (#1-8), 74-75, 76 (Example 4, Guided Practice 5-7, 11), 77 (#3-25, 32-37), 78 (#53-54, 55a-55b, 56), 79 (#57, 58a, 59), 80-81, 82 (#3-16, 26-31), 83 (#39, 42-44, 46a), 84 (#48, Quiz #2-7), 86 (#2-5), 87, 88, 90 (Example 4, Guided Practice 13), 91 (#3-18), 92 (#50-53), 93 (#54-56, 61-64), 101 (#56-67, Quiz #1-4), , 106 (#11-22, 24-32), 107 (#53, 54a), 108 (#55-56, 58), 109 (#1, 3), 122 (Example 2.2, #13-19, Example 2.3, #20-25), 123 (Example 2.4, #29-31), 124 (Example 2.6, #43-46), 125 (#7-18, 29-30, 32), 914, 915, 939 (#8-23, 28-31, 46-53) 5. Estimate the solutions for problem situations involving square and cube roots. 111, 114 (#15-23), 115 (#48), 124 (#54-57), 939 (#58-61) Measurement Standard Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools and technologies. Measurement Units 1. Convert rates within the same measurement system; e.g., miles per hour to feet per second; kilometers per hour to meters per second. Opportunities to address this standard can be found on the following pages: 17 (Example 4), 146 (#45), 152 (#40-41), 159 (#53), 200 (#5) 2
4 Use Measurement Techniques and Tools 2. Use unit analysis to check computations involving measurement. 17 (Example 5), 185 (Example 3b), 237 (Example 5), 285 (Example 5), 289 (#52b), 508 (#56b) 3. Use the ratio of lengths in similar two-dimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively. Opportunities to address this standard can be found on the following pages: Use scale drawings and right triangle trigonometry to solve problems that include unknown distances and angle measures. 170, 172 (#35-41), 195 (#52), 197 (#36), 200 (#8), 736 (#6), , 740 (#3-22), 741 (#29, 32-33), 742 (#36-37, 38a), 750 (Quiz #1-6), 752 (#1a, 2a, 3), 753 (Big Idea 3), 756 (Example 11.4, #23-29), 757 (#17-19, 26-27), 759 (Problem 2, Method 1), 761 (#11-13), 907 (#49), 948 (#42-47) 5. Solve problems involving unit conversion for situations involving distances, areas, volumes and rates within the same measurement system. 929 (#4-7, 9-12, 14, 16-20) Geometry and Spatial Sense Standard Students identify, classify, compare and analyze characteristics, properties and relationships of one-, two-, and three-dimensional geometric figures and objects. Students use spatial reasoning, properties of geometric objects and transformations to analyze mathematical situations and solve problems. Characteristics and Properties 1. Define the basic trigonometric ratios in right triangles: sine, cosine and tangent. This standard is taught in McDougal Littell Geometry. 2. Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures
5 Visualization and Geometric Models 3. Analyze two-dimensional figures in a coordinate plane; e.g., use slope and distance formulas to show that a quadrilateral is a parallelogram. 210 (#28), 749 (#51) Patterns, Functions and Algebra Standard Students use patterns, relations and functions to model, represent and analyze problem situations that involve variable quantities. Students analyze, model and solve problems using various representations such as tables, graphs and equations. Use Patterns, Relations and Functions 1. Define function with ordered pairs in which each domain element is assigned exactly one range element. 35, 36 (Example 2, Guided Practice 2-3), 38 (#6-10), 40 (#27), 49, 50 (Example 2, #1-6), 51 (#1b), 57 (#16a), 60 (#6b-6c) 2. Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations. 283 (Example 2), 284 (Example 3, Guided Practice 3), 286 (#10-15, 16), 287 (#18-23, 41-42), 289 (#50b), 296 (#17-22), 299 (#53a-53b, 54a), 303 (Example 3), 304 (Example 5), 305 (Guided Practice 5), 306 (#20-22, 29-34), 307 (#41b), 311 (Example 2), 312 (Example 3-4), 313 (Example 5a-5b), 315 (#41), 316 (Quiz #10), 317 (#3b), 323 (#32a-32b), 331 (#25-27), , 524 (#4-7, 9-20, 22-34), 527 (#60-61), , 535 (#3-31), 536 (#32-34, 38-40), 538 (Quiz #1-6), 539 (Example 2), 540 (#10), 541 (#2a, 5a-5b, 6b), 545 (Example 8.5, #35-39), 546 (Example 1, #40-41), , 632 (#3-21, 23), 633 (#24-32, 41a), 634 (#43a, 44a-44b), 636, 638 (#15-27), , 941 (#9-26, 41-44, 56-59), 945 (#52-68), 947 (#1-14, 45-48) 4
6 3. Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations. 221 (#40), 230 (#44), 259 (#45), 285 (Example 5a, Guided Practice 6a), 288 (#45a, 46-47, 48a, 49), 289 (#50b, 51a, 52a), 298 (#50b, 51b, 52b), 299 (#53a-53b, 54a), , 304 (Example 4), 305 (Guided Practice 4a, 5), 307 (#37a, 39, 40a, 41b), 313, 315 (#38, 39b, 40-41, 42a), 316 (#43, 44a), 317 (#1b, 2a, 4, 5b, 6), 323 (#33a), 346 (#14), 347 (#17), 349 (#17), 522 (Example 4a), 525 (#39a, 40a, 41), 527 (#51), 534 (Example 5a), 537 (#47, 48b, 50), 538 (#53a-53b, Quiz #7), 546 (#42), 547 (#40a), 579 (#52a, 55a), 580 (#57a, 58a-58b), 589 (#64a-64b), , 595 (Example 4a), 598 (#62), 599 (#25a), 604 (#48a, 50a), 621 (#32a, 33a), 634 (#42a), 648 (#52a), 649 (#54a), 654 (Example 5), 658 (#62a-62b), 668 (#48a, 50a), 675 (#48a) 4. Demonstrate the relationship among zeros of a function, roots of equations, and solutions of equations graphically and in words. 337 (Key Concept), 345 (#3), 639 (#38a), 641 (Example 1), , 647 (#3-46), 649 (#16-18), 652 (Key Concept), 654 (Example 4), 679 (Example 3), 697 (Example 10.3, #11-13), 698 (Example 10.4) 5. Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum. 235 (Key Concept), 263 (Key Concept), 264 (Concept Summary), 271 (#1), 520, 524 (#8), 533 (Concept Summary), 543 (#2), 628 (Key Concept), 630 (Key Concept), 632 (#1), 635 (Key Concept), 636 (Key Concept), 638 (#1), 644 (Key Concept), 651 (#15-16), 652 (Key Concept), 684 (Key Concept), 685 (Differences and Ratios), 695 (Big Idea 1, 3) 5
7 Use Algebraic Representations 6. Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope-intercept form , 187 (#3-26), 188 (#27-28, 30-34), 189 (#36a-36b, 37, Quiz #8), 196 (Example 3.8, #58-61), 311 (Example 1, Guided Practice 1), 314 (#5-10), 344 (Big Idea 1), 381 (Example 3, Guided Practice 4-6), 388, , 392 (Example 5, Guided Practice 7), 393 (#3-21, 25, 27-29, 31, 33-36), , 401 (#3-20, 23-28), 402 (#33, 37, 38b), 403 (#39b, 40b, 41), 412 (#1-6), 414 (Big Idea 2), 417 (Example 6.5, #24-29), 418 (Example 6.6, #31-36), 419 (#20-22, 24), 433 (#43-48), 441 (#45-50), 465 (#54-55), 940 (#51-56), 941 (#37-40), 943 (#43, 45-48, 50-52, 54-66) 7. Use formulas to solve problems involving exponential growth and decay. 522, 523 (Example 5, Guided Practice 5-6), 524 (#21), 525, 526 (#44-45, 46b), 527 (Example, #47-51), , 535 (#19), 536 (#32-40), 537, 538 (#53-54, Quiz #7), 541 (#2-7), 546, 547 (#40-41), 551 (#14, 17-18, 20), 707 (#60) 8. Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point. 293 (Example 2, Guided Practice 2), 296 (#11-22), 299 (#63-64), 308 (#56-57), 311 (Example 2, Guided Practice 2), 314 (#17-22), 316 (Quiz #4-9), 319, 321 (Example 4, Guided Practice 4), 322 (#3-11, 18-26), 323 (#27-29), 324 (#42), 331 (#25-27), 341 (Quiz #1-4), 346 (Example 5.3, #11-13), 347 (#16, Example 5.5, #18-20), 349 (#7-9, 11-14), 353 (#9), 395 (#51-53), 448 (#34c), 658 (#71-73), 942 (#16-18, 22-27) 6
8 9. Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology , 429 (Guided Practice 4-5), 430 (Example 4, Guided Practice 6), 431 (#8-26, 28), 432 (#29b, 30-31, 33), 433 (#34, 35a, 36), 434, , 439 (#3-17, 19-28), 440 (#31-34), 441 (#35-38, Quiz #1-9), 443, , 447 (Guided Practice 7, #3-14, 16-21), 448 (#23-33, 34b, 35), 449 (#39-41, 42a), 450 (#43b, 44-45, 50-52), , 454 (#3-8), 455 (#9-17, 19-32, 33a), 456 (#37-39, 40a, 41-42), 457 (#43-44, 53-58, Quiz #1-12), , 462 (#5-7), 463 (#8-31), 475 (Example 7.1, #5-7), 476 (Example 7.2, #8-11, Example 7.3), 477 (#12-17, Example 7.4, #18-24), 478 (Example 7.5, #25-27), 479 (#1-24, 28-29), 944 (#1-33) 10. Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology. 595, 596 (Example 5, Guided Practice 9), 597 (#23-51), 598 (#58, 59b, 61), 599 (#63b, Quiz #16-24, 25b), 602, 603 (#25-39), 604 (#46-47, 48b), 605 (#51b, 57-61), 613 (#13-14), 618 (Example 9.4, #28-33), 619, 621 (#23-31, 32b, 33b, 34), , 647 (#3-45), 649 (#10-18), 651 (Example 2, #7-14), , 674 (#3-27), 676 (#10-12), 683 (#63-65), 697 (Example 10.3, #11-13), 699 (Example 10.6, #24-30), 701 (#10-15), 946 (#31-36, 43-48), 947 (#15-20, 33-38) 11. Add, subtract, multiply and divide monomials and polynomials (division of polynomials by monomials only). 555 (Example 3, Guided Practice 3), 556, 557 (#17-29), 558 (#30-35, 36a, 37-38, 39a), 559 (#40, 41a), , 565 (Guided Practice 7, 8a, #3-16), 566, 567 (#49a, 50a, 51b, 52a), 569, 570 (Example 2), 572 (#3-18, 23-37, 39), 574 (Quiz #1-9), 580 (#60-71), 589 (#74-81), 599 (#73-81), 605 (#71-76), 616 (Example 9.1, #7-12), 617, 621 (#1-13, 35a), 784, 788 (#3-6), 809 (#47-52), 946 (#1-18), 949 (#19) 12. Simplify rational expressions by eliminating common factors and applying properties of integer exponents , 497 (Guided Practice 5-8, Example 4b), 498 (Example 5, #3-18), 499 (#19-37, 42-45), 500 (#49b, 50-53), 501 (#54a-54b, Quiz #15-18), 505 (Example 3b, Guided Practice 9), 506 (#36-44), 518 (Quiz #3-4), 544 (#16-21), 547 (#3, 5, 8, 10-11, 14, 16-18), , 797 (Example 5), 798 (#11-32, 36-38), 799, 800 (#45a, 46, Quiz #5-8), 801 (#4a), 833 (Example 12.4, #19-21), 835 (#11-13), 906 (#20), 949 (#25-32) 7
9 Analyze Change 13. Model and solve problems involving direct and inverse variation using proportional reasoning. 256 (Example 5), 260 (Method 2, #1-2, 4-6), 258 (#-44), 259 (#46a-46b), 770 (#48) 14. Describe the relationship between slope and the graph of a direct variation and inverse variation. 254 (Direct Variation Graphs), 255 (Key Concept), 274 (Example 4.6), 769 (#2) 15. Describe how a change in the value of a constant in a linear or quadratic equation affects the related graphs. 264, 265 (Example 5), 266 (#23-28, 36c, 37), 267 (#42), 268 (Quiz #9), 269 (#6), 274 (#31), 629 (Example 3, Guided Practice 3), 630 (Key Concept), 631 (Example 5, Guided Practice 7), 632 (#16-21, 23), 633 (#33-36), 634 (#42a, 44c), 691 (#35-36), 705 (#4), 941 (#56-57), 947 (#5-6) Data Analysis and Probability Standard Students pose questions and collect, organize, represent, interpret and analyze data to answer those questions. Students develop and evaluate inferences, predictions and arguments that are based on data. Data Collection 1. Classify data as univariate (single variable) or bivariate (two variables) and as quantitative (measurement) or qualitative (categorical) data. Opportunities to address this standard can be found on the following pages: 334, 342, , , , 886, , 933, 934, Create a scatterplot for a set of bivariate data, sketch the line of best fit, and interpret the slope of the line of best fit , 328 (#6-7), 329 (#8-10, 12-15), 330 (#16a, 17a, 17c, 18), 332, 333 (Example 2, #1, 3), 335 (Example 1a), 338 (#3-6), 339 (#18a), 340 (#19a, 22a), 341 (#23a), 342 (Example 1, #2), 343 (#1a, 1c, 4), 344 (Big Idea 3), 348 (Example 5.6, #21), 349 (#15-16, 18a, 18c), 352 (#5a), 353 (#17a, 18c), 942 (#28-31) 8
10 Statistical Methods 3. Analyze and interpret frequency distributions based on spread, symmetry, skewness, clusters and outliers , 877 (#3-16, 19), 878 (#20-22), , 881 (Guided Practice 2), 883 (#8-9), 885 (#20, 21b, 23-25), 888 (Example 2, Guided Practice 2), 889 (Example 3, Guided Practice 3), 890 (#8-13), 891 (#17b, 18b, 19), 892 (#20, Quiz #6), 894 (#3-4, 6, 7b), 899 (Example 13.6, #23), 901 (#14a-14b, 14d), 904 (#2b, 3, 5b), 905 (#14-15, 17a, 17c), 907 (#51a, 51d), 918, 950 (#21, 23) 4. Describe and compare various types of studies (survey, observation, experiment), and identify possible misuses of statistical data. 843, 849, 871, 896 (#2) 5. Describe characteristics and limitations of sampling methods, and analyze the effects of random versus biased sampling; e.g., determine and justify whether the sample is likely to be representative of the population , 873 (#1-5, 7-10), 874 (#13-18), 885 (#26-27), 892 (Quiz #1), 894 (#2), 899 (Example, #22), 901 (#13), 904 (#6), 950 (#18-20) 6. Make inferences about relationships in bivariant data, and recognize the difference between evidence of relationship (correlation) and causation. 325, 326 (Example 2b, Guided Practice #2), 328 (#3-5), 329 (#12-14), 330 (#16b), 333 (#1), 343 (#4), 348 (Example 5.6, #21), 353 (#18a) Probability 7. Use counting techniques and the Fundamental Counting principle to determine the total number of possible outcomes for mathematical situations. 843, 846 (#3-6), 847 (#17), 848 (#24-26), , 853 (#2-10), 854 (#20-34), 856, 857 (Example 2, Guided Practice 2), 858 (#3-20), 859 (#23, 25a, 33), 867 (#28-34, Quiz #2, 4-7), 870 (#2, 8), 874 (#24-27), 897 (#6-9, Example 13.3, #11-15), 901 (#5-10), 904 (#1a, 4a), 905 (#12-13), 906 (#38-41), , 950 (#1, 4-5, 7-14) 9
11 8. Describe, create and analyze a sample space and use it to calculate probability. 844, 845 (Example 3, Guided Practice 4), 846 (#7-10), 847 (#17), 853 (Example 3, Guided Practice 4), 854 (#34), 857 (Example 3, Guided Practice 3), 859 (#25), 897 (Example 13.2), 904 (#1), 950 (#1-2) 9. Identify situations involving independent and dependent events, and explain differences between and common misconceptions about probabilities associated with those events , 864 (#9-12), 865 (#20) 10. Use theoretical and experimental probability, including simulations or random numbers, to estimate probabilities and to solve problems dealing with uncertainty; e.g., compound events, independent events, simple dependent events. 844, 845 (Example 3, Guided Practice 4), 846 (#7-10), 847 (#17, 19-21), 848 (#22-23), , 853 (Example 3, Guided Practice 4), 854 (#34c), 855, 857 (Example 3, Guided Practice 3), 859 (#24, 25b, 26-27, 32), , 864 (#3-12), 865 (#13-20, 21a), 866 (#22-23, 24a-24b, 25c, 26), 867 (#27a-27b, Quiz #1a, 3, 8), , 870 (#1, 3a, 6a, 7a-7b), 896 (Example 13.1, #4-5), 897 (Example 13.2, #10), 898 (Example 13.4a, #16-19, Example 13.4b, #20-21), 901 (#1-4, 11-12), 907 (#42-46), 950 (#2, 15-17) 10
12 OH 270 4/ CC2
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