correlated to the connecticut mathematics curriculum framework · correlated to the connecticut...

correlated to the

ConnecticutMathematicsCurriculumFramework

PE = Pupil’s Edition 1

McDougal Littell Algebra 2 ©2008

correlated to the

Connecticut

Mathematics Curriculum Framework

ALGEBRAIC REASONING: PATTERNS AND FUNCTIONS - Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies.

1.1 Understand and describe patterns and functional relationships.

1.1.a Model real-world situations and make generalizations about mathematical relationships using a variety of patterns and functions.

1.1.a(1) Describe and compare properties and classes of functions, including exponential, polynomial, rational, logarithmic and trigonometric.

236-243, 337-345, 370-377, 379-386, 387-392, 428-434, 446-451, 478-485, 486-491, 492-498, 499-505, 558-563, 565-571, 852-858, 866-872, 908-914, 915-922

1.1.a(2) Analyze essential relations in a problem to determine possible functions that could model the situation.

19-20, 23-24, 29, 31-32, 34-39, 54, 57, 100, 103-104, 108, 110-111, 115, 119-120, 125, 128-129, 134, 137-138, 155, 157-158, 162, 165-166, 170, 172-173, 181, 189, 192, 198, 200-201, 204, 208-209, 213, 215-216, 239, 242-243, 246-247, 250-251, 254, 257-258, 261, 262, 264-265, 268-271, 287, 290-291, 295, 298-299, 311, 314, 331, 340, 343-344, 348, 351-352, 356, 358-361, 365, 367-368, 373, 376-377, 389, 391-392, 394-399, 421, 426-427, 447, 450-451, 480, 488, 494, 500, 528, 529-536, 552-553, 556-557, 560, 562-563, 567, 569-571, 589, 592, 594-595, 774-781, 910, 913-914, 918, 921-922, 927, 929-930, 941-947

1.1.a(3) Explore conic sections and their applications graphically and symbolically.

620-625, 626-632, 634-639, 640, 641, 642-648, 650-657, 658-664, 665-666, 667, 668, 669-672, 673, 674-675, 676-677

McDougal Littell Algebra 2 ©2008 correlated to the Connecticut Mathematics Curriculum Framework, 9-12 Extended


1.1.a(4) Solve problems involving financial applications including compound interest, amortization of loans, and investments.

19, 23, 155, 170, 362-369, 431, 481, 483, 484, 485, 488, 494-495, 497, 525, 526-527, 543, 679

1.1.a(5) Solve problems involving direct and inverse variation.

107-111, 120 (Quiz #7-14), 140, 143, 145 (#14-17, 25-26), 550-557, 571 (Quiz #1-4), 603, 607 (#1-6, 28), 876

1.1.a(6) Understand and use optimization strategies, including linear programming.

174-175, 239 (Example 5), 242-243, 389, 391-392

1.1.a(7) Apply the concepts of limits to sequences and asymptotic behavior of functions.

Opportunities to address this standard can be found on the following pages: 478-479, 486-487, 502, 558, 565, 642, 794, 918

1.2 Represent and analyze quantitative relationships in a variety of ways.

1.2.a Relate the behavior of functions and relations to specific parameters and determine functions to model real-world situations.

1.2.a(1) Relate the graphical representation of a function to its function family and find equations, intercepts, maximum or minimum values, asymptotes and line of symmetry for that function.

73-79, 80-81, 82-88, 89-96, 98-104, 107-111, 121, 123-129, 236-243, 245-251, 308-315, 337-344, 370-377, 379-385, 387-392, 393-399, 446-451, 478-485, 486-491, 492-498, 499-505, 558-563, 565-571, 620-625, 775-781, 908-914, 915-922, 941-947

1.2.a(2) Recognize the effect of changes in parameters on the graphs of functions or relations.

123-129, 236-243, 245-251, 337-345, 478-485, 486-491, 499-505, 558-563, 565-571, 915-922

1.2.a(3) Recognize that the slope of the tangent line to a curve represents the rate of change.

A6-A7

1.2.a(4) Represent functions and relations with polar coordinates and in the complex plane.

Opportunities to address this standard can be found on the following pages: 278-282, 860-865, 866-872, 873, 875-880, 898-900, 901, 905, A2-A3, A4-A5



1.3 Use operations, properties and algebraic symbols to determine equivalence and solve problems.

1.3.a Use and extend algebraic concepts to include real and complex numbers, vectors and matrices.

1.3.a(1) Determine equivalent representations of an algebraic equation or inequality to simplify and solve problems.

18-24, 26-32, 41-47, 50-58, 245-250, 252-258, 259-265, 266-271, 284-291, 300-307, 353-359, 393-399, 452-459, 515-521, 589-595, 598-600, 924-930, 931-937

1.3.a(2) Combine, compose and invert functions.

428-435, 437-445, 464 (#1b, 4a, 7a), 467 (Example 6.3, #20-23, Example 6.4, #24-26), 469 (#17-30, 37a, 38), 470-471, 472 (#1b), 473 (#7, 9, 13, 16, 18-19), 499-505, 830, 874, 875-880

1.3.a(3) Use logarithms, vectors and matrices to solve problems.

187-193, 195-202, 203-209, 210-217, 218-219, 221, 224-226, 227, 228-229, 230-231, 232 (#34-41), 499-505, 507-513, 515-521, 529-537, 538, 541, 1012, 1034



NUMERICAL AND PROPORTIONAL REASONING: Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.

2.1 Understand that a variety of numerical representations can be used to describe quantitative relationships.

2.1.a Extend the understanding of number to include the set of complex numbers.

2.1.a(1) Compare and contrast the properties of numbers and number systems, including rational, real and complex numbers.

1-9, 40 (#36-38), 16 (#68-69, Quiz: #1-3, 4-6), 24 (#83-86), 61, 88 (#50-55), 275-282, 281 (#69), 414-419, 420-421, 975, 976, 978, 1010

2.1.a(2) Select and use an appropriate form of number (integer, fraction, decimal, ratio, percent, exponential, scientific notation, irrational, complex) to solve practical problems involving order, magnitude, measures, labels, locations and scales.

3-6, 10-17, 330-335, 334 (#49-50), 352 (#1-4), 402, 415-419, 420-427, 465-467, 480-481, 483-485, 584, 594, 822, 852-858, 976-977, 979, 980, 982-983, 989, 1025

2.1.a(3) Justify mathematical procedures and determine how they apply to invented operations using field properties (closure, associative, commutative, distributive, identity and inverse).

4 (#7-8), 6 (#17-22), 7 (#55), 68, 188, 196-200, 271 (#42), 281 (#70-73), 391 (#32), 398 (#23), 418 (#59), 490 (#29), 512 (#71, 73), 550 (#1), 556 (#36), 748 (#24), 819 (#2), A18-A19

2.1.a(4) Judge the effects of computations with powers and roots on the magnitude of results.

10-17, 266, 275, 414-419, 421-427, 465, 466-468, 469 (#9-16), 507, 693-695, 1034

2.2 Use numbers and their properties to compute flexibly and fluently, and to reasonably estimate measures and quantities.

2.2.a Investigate mathematical properties and operations related to objects that are not numbers.

2.2.a(1) Recognize vectors and matrices as systems that have some, but not all, of the properties of real numbers.

187-193, 195-202, A10-A11, A12-A13

2.2.a(2) Perform operations with complex numbers, matrices, determinants and logarithms.

187-193, 194, 195-202, 203-209, 217 (Quiz #1-4), 224 (Example 3.5), 225, 227 (#15-22), 275-282, 291 (Quiz #1-12), 320 (Example 4.6), 321 (#29-34), 323 (#16-18), 499-505, 507-513, 541 (Example 7.5, #25-31), 543 (#10-12, 16-18)



GEOMETRY AND MEASUREMENT: Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies.

3.1 Use properties and characteristics of two- and three-dimensional shapes and geometric theorems to describe relationships, communicate ideas and solve problems.

3.1.a Use methods of deductive and inductive reasoning to make, test and validate geometric conjectures.

3.1.a(1) Recognize the relationships between a conditional statement and its converse, inverse and contrapositive.

1002-1003

3.1.a(2) Test the validity of logical arguments.

836-837, 1000-1001, 1002-1003

3.1.a(3) Use deductive arguments, including direct and indirect proofs, to develop an understanding of an axiomatic approach to geometry.

836-837, 1000-1001

3.1.b Explore non-Euclidean geometries.

3.1.b(1) Recognize that the familiar geometry of Euclid is based on a particular set of axioms and that a different set of axioms would lead to a different geometry.

A22-A23

3.2 Use spatial reasoning, location and geometric relationships to solve problems.

3.2.a Use a variety of coordinate systems and transformations to solve geometric problems in two- and three-dimensions using appropriate tools and technologies.

3.2.a.(1) Visualize three-dimensional objects from different perspectives and analyze cross-sections, surface area and volume.

63 (#31), 68 (#10), 334 (#40-42), 350 (#48-51), 567, 572 (#2), 580 (#51-53), 649, 993

3.2.a(2) Use Cartesian, navigational, polar and spherical systems to represent, analyze and solve geometric and measurement problems.

204 (Example 2, Guided Practice 4), 208 (#40-41), 209 (#45-46), 614-619, 620-625, 626-632, 634-639, 640, 641 (#1, 4-6), 642-648, 650-657, 658-664, 667 (#1-2, 4-6), 669-672, 673, 674-675

3.2.a(3) Represent translations, reflections, rotations and dilations of plane figures using sketches, coordinates, vectors, function notation and matrices to examine the effects of transformations and their composites and to solve related geometric problems.

202 (#45), 216 (#49), 988-989



3.3 Develop and apply units, systems, formulas and appropriate tools to estimate and measure.

3.3.a Approximate measurements that cannot be directly determined with some degree of precision using appropriate tools, techniques and strategies.

3.3.a(1) Use successive approximation, upper and lower bounds, and limits to solve measurement problems.

A8-A9

3.3.a(2) Use properties of similarity and techniques of trigonometry to make indirect measurements of lengths and angles to solve a variety of problems.

852-853, 866-872, 941-947, 875-880, 881, 882-888, 889-894



WORKING WITH DATA: PROBABILITY AND STATISTICS - Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies.

4.1 Collect, organize and display data using appropriate statistical and graphical methods.

4.1.a Model real data graphically using appropriate tools, technology and strategies.

4.1.a(1) Investigate and solve relevant problems by designing statistical experiments and collecting, organizing, displaying and analyzing data in tabular, graphical and symbolic forms.

112, 113-120, 139 (#3, 6), 143 (Example 2.6, #23), 145 (#18-19, 27), 146-147, 148 (#1, 4), 149 (#16), 308, 311-315, 323 (#32), 327 (#21), 528, 530-536, 537 (#1, 4), 744, 744-749, 774, 775-760, 781, 782 (#1, 5), 819, 1006-1009, A20-A21

4.1.a(2) Apply and defend regression models for bivariate data and use them to formulate predictions.

115-116, 117 (Guided Practice 4), 118 (#10-15, 19-20), 119, 120 (Quiz #15), 139 (#6), 143 (Example 2.6, #23), 145 (#18-19, 27), 308, 311, 314 (#48-50), 323 (#32), 528, 530, 531 (Guided Practice 4), 532, 533 (Example 6, Guided Practice 9, #11-14), 534 (#23-26, 31), 535, 536 (#36), 537 (#1, 4), 542 (#38), 543 (#29), 547 (#21), 775-780, 781, 782 (#1, 5), 786 (Example 11.5, #23), 787 (#14), 791 (#17)

4.1.a(3) Recognize the limitations of mathematical models based on sample data as representations of real-world situations.

314 (#50c), 779 (#13d), 782 (#5a)

4.2 Analyze data sets to form hypotheses and make predictions.

4.2.a Describe and analyze sets of data using statistical models.

4.2.a(1) Determine statistical measures to describe univariate data.

744-749, 750, 751-755, 756 (#1-2, 4-6), 784 (Example 11.1, #4-8), 785 (Example 11.2, #9-11), 787 (#1-3, 11), 790 (#1-2, 5-6, 9), 791 (#11-12, 16)

4.2.a(2) Describe characteristics of sampling methods and analyze the effects of random versus biased sampling.

766-771, 772-773, 782 (#9), 783, 791 (#15)



4.3 Understand and apply basic concepts of probability.

4.3.a Solve problems using the methods of discrete mathematics.

4.3.a(1) Understand and use permutations, combinations, recursion and mathematical induction to solve problems.

682-689, 690-697, 704 (#58-61), 705 (#1, 6, 8), 734 (Example 10.1), 735 (#5-9, 14), 737 (#1-8, 27), 740 (#1a), 741 (#8, 14), 826, 827-833, 836-837, 842 (Example 12.5, #32-38), 843 (#25-28), 846 (#2), 847 (#13, 20)

4.3.a(2) Solve problems using finite graphs.

Not addressed in this text.

4.3.b Make statistical inferences through the use of probability.

4.3.b(1) Explore the characteristics and applications of the normal distribution and standardized scores.

757-762, 780 (Quiz #1-3), 782 (#6-7), 783, 785 (Example 11.3, #12-17), 787 (#4-6), 790 (#3-4), 791 (#10, 13)

4.3.b(2) Construct and interpret confidence intervals.

A14-A15

4.3.b(3) Explore a variety of statistical tests such as chi-squares and t-tests and understand the meaning of hypothesis testing.

Opportunities to address this standard can be found on the following pages: 763-765

4.3.b(4) Use relative frequency and expected values to represent and solve problems involving uncertainty

A16-A17

CT 625/2007

2008 CC2

correlated to the connecticut mathematics curriculum framework · correlated to the connecticut...

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