Arkansas Mathematics Curriculum Framework

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correlated to the Arkansas Mathematics Curriculum Framework Geometry

McDougal Littell Geometry correlated to the Arkansas Mathematics Curriculum Framework Geometry Strand: Language of Geometry Standard 1: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates. LG.1.G.1 Define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations venn diagrams matrix logic conditional statements (statement, inverse, converse, and contrapositive) Lesson 1.1: 3-9, Lesson 2.1: 78 (#57-60); Lesson 2.3: 87-95 Chapter 1 Review/Test: 60, 63 (#19-20), 65 (#17-18); Lesson 2.5 Mixed Review: 107 (#28-30) 1-3, 35-37 1-3, 28-30 1-2, 30-32 Lesson: 2.3 Ch.1: 11-21; Ch. 2: 40-52 Lessons: 1.1, 2.3 Lessons: 1.1, 2.3 1

Lesson 1.2: 10-16; Lesson 1.3: 17-23; Lesson 1.4: 26-31 4-6, 7-10, 11-14 4-6, 7-9, 10-12 3-4, 5-7, 8-9 LG.1.G.2 Represent points, lines, and planes pictorially with proper identification, as well as basic concepts derived from these undefined terms, such as segments, rays, and angles Lesson 1.3 Mixed Review: 24 (#62-71); Lesson 1.4 Mixed Review: 32 (#70-73); Lesson 1.5 Mixed Review: 42 (#69-72); Lesson 1.6 Mixed Review: 50 (#66-69); Lesson 1.7 Mixed Review: 58 (#51-52); Chapter 1 Review/Test: 60-61, 63, 64 (#2-3, 6), 65 (#11-14) Ch. 1: 24-33, 36-48, 51-60 TransparencyPackage: Lessons: 1.2, 1.3, 1.4 Lesson: 1.2 Lessons:1.2, 1.3, 1.4 2

LG.1.G.3 Describe relationships derived from geometric figures or figural patterns Lesson 9.4: 551-557; Extra Practice: 820 (#28-30) Lesson 9.5 Quiz: 566 (#1-3); Chapter 9 Review/Test: 583, 585 (#11) 196-198 169-171 202-203 Ch. 9: 55-65 Lesson: 9.4 Lesson: 9.4 LG.1.G.4 Apply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics as complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines Lesson 1.6: 44-50; Lesson 2.2: 79, 82 (#13-19), 83 (#22); Lesson 2.6: 109-116 Chapter 1 Review/Test: 62, 63 (#10-14), 64 (#5-6, 9), 65 (#12); Chapter 2 Review/Test: 120, 121 (#19), 122 (#8), 123 19-21, 44-46 16-18, 37-39 13-14, 37-39 Ch. 1: 80-91; Ch. 2: 84-97 Lessons: 1.6, 2.6 Lessons: 1.6, 2.6 Lessons: 1.6, 2.6 3

Lesson 3.3: 142, 143-149; Lesson 3.4: 150-156; Lesson 3.5: 160-164 55-57, 58-60, 61-63 46-48, 49-51, 52-54 53-55, 56-57, 58-60 LG.1.G.5 Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel Chapter 3 Review/Test: 181, 183 (#9-11, 15-16), 184 (#2-3), 185 (#10-11); Cumulative Practice: 187 (#36) Ch. 3: 36-48, 51-65, 68-79 Lessons: 3.3, 3.4, 3.5 Lesson: 3.3 Lessons: 3.3, 3.4, 3.5 4

Lesson 2.5: 102-107; Lesson 2.6: 109-115; Lesson 3.2: 136-141; Lesson 3.4: 150-156; Cumulative Practice: 187 (#30); Lesson 4.3: 212-219; Lesson 4.4: 220-226; Lesson 4.7: 245-246, 248-249; Lesson 6.3: 338-345; Extra Practice: 806 (#30), 807 (#13), 810 41-43, 44-46, 52-54, 58-60, 79-81, 82-84, 91-93, 124-126 34-36, 37-39, 43-45, 49-51, 67-69, 70-72, 79-81, 106-108 35-36, 37-39, 51-52, 56-57, 79-80, 81-83, 88-89, 126-128 Lessons: 3.2, 4.3 LG.1.G.6 Give justification for conclusions reached by deductive reasoning Lesson 2.6 Quiz 2: 116 (#7-8); Chapter 2 Review/Test: 120, 121 (#17), 123 (#12-13, 17); Chapter 3 Review/Test: 180-181, 183 (#16), 185 (#11); Lesson 4.4 Quiz 2: 227 (#7); Chapter 4 Review/Test: 253-254, 255 (#17-18); Chapter 6 Review/Test: 387 (#11, 13, 20) Ch. 2: 66-81, 82-97; Ch. 3: 21-33, 49-65; Ch. 4: 40-52, 53-67, 94-109; Ch. 6: 36-49 Lessons: 2.5, 2.6, 3.2, 3.4, 4.3, 4.4, 4.7, 6.3 Lessons: 2.6, 4.3 Lessons: 2.5, 2.6, 3.2, 3.4, 4.3, 4.4, 4.7, 6.3 5

Strand: Triangles Standard 2: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric rations to solve problems in real world situations. T.2.G.1 Apply congruence (SSS ) and similarity (AA...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification Lesson 4.3: 212-219; Lesson 4.4: 220-227; Lesson 4.5: 229-235; Lesson 8.3: 472, 473-479; Lesson 8.4: 480-487; Lesson 8.5: 488-496; Lesson 8.6: 498-505 Chapter 4 Review/Test: 253, 255, 256-257; Chapter 8 Review/Test: 517-518, 519, 520-521 79-81, 82-84, 85-87, 170-172, 173-175, 176-178, 179-182 67-69, 70-72, 73-75, 145-147, 148-150, 151-153, 154-156 79-80, 81-83, 84-85, 174-176, 177-178, 179-181, 182-183 Lessons: 4.3, 4.5, 8.4, 8.5 Ch. 4: 42-52, 55-67, 70-80; Ch. 8: 35-46, 49-62, 65-80, 83-94 Lessons: 4.3, 4.4, 4.5, 8.3, 8.4, 8.5, 8.6 Lessons: 4.3, 8.5 Lessons: 4.3, 4.4, 4.5, 8.3, 8.4, 8.5, 8.6 6

T.2.G.2 Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem) Lesson 5.5: 297-300; Lesson 9.3: 544 Chapter 5 Review/Test: 312, 313 (#13-15), 315 (#7); Cumulative Practice: 389 (#22); Lesson 7.2 Mixed Review: 410 (#63-68); Lesson 9.4 Mixed Review: 557 (#42); Lesson 10.1 Mixed Review: 602 (#58) 109-111 94-96 108-109 Ch. 5: 69-80 Lesson: 5.5 Lesson: 5.5 Lesson: 5.5 7

T.2.G.3 Identify and use the special segments of triangles (altitude, median, angle bisector, perpendicular bisector, and midsegment) to solve problems Lesson 5.2: 272-278; Lesson 5.3: 279-285; Lesson 5.4: 287-293; Extra Practice: 811, 812 (#16-22) Chapter 5 Review/Test: 310-311, 313, 314, 315 (#12-14) 99-101, 102-104, 105-108 85-87, 88-90, 91-93 101-102, 103-105, 106-107 Lessons: 5.3, 5.4 Ch. 5: 27-36, 39-52, 55-66 Lessons: 5.2, 5.3, 5.4 Lesson: 5.3 Lessons: 5.2, 5.3, 5.4 T.2.G.4 Apply the Pythagorean Theorem and its converse in solving practical problems Lesson 9.2: 537-541; Lesson 9.3: 543-548; Extra Practice: 819 (#7-15) Lesson 9.3 Quiz: 549 (#8) 190-192, 193-195 163-165, 166-168 197-198, 199-201 Lesson: 9.2 Ch. 9: 24-36, 39-52 Lessons: 9.2, 9.3 Lesson: 9.2 Lessons: 9.2, 9.3 8

T.2.G.5 Use the special right triangle relationships (30-60 -90 and 45-45 -90 ) to solve problems Lesson 9.4: 551-557; Extra Practice: 820 (#28-30) Lesson 9.5 Quiz: 566 (#1-3); Chapter 9 Review/Test: 583, 585 (#11) 196-198 169-171 202-203 Ch. 9: 55-65 Lesson: 9.4 Lesson: 9.4 T.2.G.6 Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles in right triangles including angles of elevation and angles of depression Lesson 9.5: 558-566; Lesson 9.6: 567-572 Chapter 9 Review/Test: 583-584, 585 (#15-16), 586 (#7-9), 587; Cumulative Practice: 589 (#29-30) 199-201, 202-204 172-174, 175-177 204-206, 207-208 Ch. 9: 68-81, 84-95 Lessons: 9.5, 9.6 Lesson: 9.5 Lessons: 9.5, 9.6 9

Strand: Measurement Standard 3: Students will measure and compare, while using appropiate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume. M.3.G.1 Calculate probabilities arising in geometric contexts (Ex. Find the probability of hitting a particular ring on a dartboard.) Lesson 11.6: 699-705, 706 Chapter 11 Review/Test: 710, 711 (#17-18), 713 (#10, 19-22) 248-250 217-219 256-258 Ch. 11: 85-97 Lesson: 11.6 Lesson: 11.6 Lesson: 11.6 10

M.3.G.2 Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms Lesson 11.2: 671, 672 (#7-8), 673 (#34), 674; Lesson 12.2: 733-734; Lesson 12.3: 735, 740; Lesson 12.4: 745, 746 (#7-9), 748, 749 (#50), 750; Lesson 12.5: 754, 756-757; Lesson 12.6: 760-765 Chapter 11 Review/Test: 708; Lesson 12.7 Quiz: 772 (#1-7); Chapter 12 Review/Test: 774-776, 777, 778-779 236-238, 255-257, 258-261, 262-264, 265-267, 268-270 205-207, 223-225, 226-228, 229-231, 232-234, 235-237 247-248, 270-271, 272-274, 275-276, 277-279, 280-281 Lessons: 12.4, 12.6 Ch. 11: 25-37; Ch. 12: 23-33, 36-50, 53-64, 67-77, 80-93 Lessons: 11.2, 12.2, 12.3, 12.4, 12.5, 12.6 Lesson: 12.4 Lessons: 11.2, 12.2, 12.3, 12.4, 12.5, 12.6 M.3.G.3 Relate changes in the measurement of one attribute of an object to changes in other attributes (Ex. How does changing the radius or height of a cylinder affect its surface area or volume?) Lesson 12.2: 734 (#45-47); Lesson 12.3: 741 (#49) Chapter 12 Review/Test: 779 (#10) 255-257, 258-261 223-225, 226-228 270-271, 272-274 Ch. 12: 23-33, 36-50 Lessons: 12.2, 12.3 Lessons: 12.2, 12.3 11

M.3.G.4 Use (given similar geometric objects) proportional reasoning to solve practical problems (including scale drawings) Lesson 8.3: 472, 474, 477 (#43-44), 478 (#50-52); Lesson 8.4: 481-482, 486-487; Lesson 8.5: 490-491, 494-495; Lesson 8.6: 501, 503 (#29-30), 504 (#36-37); Lesson 8.7: 508, 511-512; Lesson 11.3: 678, 680 Chapter 8 Review/Test: 516, 519 (#18), 520 (#7) 170-172, 173-175, 176-178, 179-182, 183-184, 239-241 145-147, 148-150, 151-153, 154-156, 157-159, 208-210 174-176, 177-178, 179-181, 182-183, 184-185, 249-251 Lessons: 8.4, 8.5, 11.3 Ch. 8: 35-46, 49-62, 65-80, 83-94, 97-108; Ch. 11: 40-52 Lessons: 8.3, 8.4, 8.5, 8.6, 8.7, 11.3 Lessons: 8.5, 8.7 Lessons: 8.3, 8.4, 8.5, 8.6, 8.7, 11.3 M.3.G.5 Use properties of parallel lines and proportional reasoning to find the lengths of segments Lesson 8.6: 498-505; Cumulative Practice: 589 (#22); Extra Practice: 818 (#44-45) Chapter 8 Review/Test: 518, 519 (#6-7), 520 (#9) 179-182 154-156 182-183 Ch. 8: 83-94 Lesson: 8.6 Lesson: 8.6 12

Strand: Relationships between two- and three- dimensions Standard 4: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. R.4.G.1 Explore and verify the properties of quadrilaterals Lesson 6.1: 324-325, 327, 328 (#53); Lesson 6.2: 329, 330-337; Lesson 6.3: 338-346; Lesson 6.4: 347-355; Lesson 6.5: 356-362; Lesson 6.6: 364-370 Chapter 6 Review/Test: 382-384, 385, 386-387; Cumulative Practice: 389 (#25-30) 117-120, 121-123, 124-126, 127-130, 131-134, 135-137 100-102, 103-105, 106-108, 109-111, 112-114, 115-117 122-123, 124-125, 126-128, 129-130, 131-133, 134-135 Lessons: 6.1, 6.6 Ch. 6: 11-21, 24-35, 38-49, 52-65, 68-79, 82-92 Lessons: 6.1, 6.2, 6.3, 6.4, 6.5, 6.6 Lesson: 6.4 Lessons: 6.1, 6.2, 6.3, 6.4, 6.5, 6.6 13

R.4.G.2 Solve problems using properties of polygons: sum of the measures of the interior angles of a polygon interior and exterior angle measure of a regular polygon or irregular polygon number of sides or angles of a polygon Lesson 6.1: 322-328; Lesson 6.2: 329, 330-337; Lesson 6.5: 356-362 Lesson 6.6 Mixed Review: 370 (#61-62); Chapter 6 Review/Test: 382-383, 385, 386 (#2-3); Cumulative Practice: 389 (#25-30) 117-120, 121-123, 131-134 100-102, 103-105, 112-114 122-123, 124-125, 131-133 Lesson: 6.1 Ch. 6: 11-21, 24-35, 68-79 Lessons: 6.1, 6.2, 6.5 Lessons: 6.1, 6.2, 6.5 R.4.G.3 Identify and explain why figures tessellate Project for Chapters 6 and 7: 452-453 Project: Tessellations 14

R.4.G.4 Identify the attributes of the five Platonic Solids R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles Lesson 12.1: 721 Lesson 12.3 Quiz: 742 (#1) Lesson 10.1: 595-602; Lesson 10.2: 603-611; Lesson 10.3: 612, 613-619; Lesson 10.4: 621-627 Chapter 10 Review/Test: 650-651, 653, 654-655; Lesson 11.3 Mixed Review: 681 252-254 220-222 268-269 210-212, 213-215, 216-218, 219-221 181-183, 184-186, 187-189, 190-192 220-221, 222-223, 224-226, 227-228 Lesson: 10.3 Ch. 12: 11-20 Lesson: 12.1 Lesson: 12.1 Ch. 10: 11-23, 26-36, 39-50, 53-63 Lessons: 10.1, 10.2, 10.3, 10.4 Lesson: 10.3 Lesson: 12.1 Lessons: 10.1, 10.2, 10.3, 10.4 15

R.4.G.6 Solve problems using inscribed and circumscribed figures Lesson 5.2: 274; Lesson 10.3: 615-619; Lesson 10.4: 626 (#40), 627 (#44-45); Lesson 11.5: 693, 696-697; Lesson 12.3: 741 Chapter 10 Review/Test: 651, 653, 654 (#3), 655; Lesson 11.3 Mixed Review: 681 (#38) 216-218 187-189 224-226 Lesson: 10.3 Ch. 10: 39-50 Lesson: 10.3 Lesson: 10.3 Lesson: 10.3 R.4.G.7 Use orthographic drawings (top, front, side) and isometric drawings (corner) to represent threedimensional objects Project for Chapters 2 and 3: 188-189 16

R.4.G.8 Draw, examine, and classify cross-sections of threedimensional objects Lesson 12.1: 720, 724; Lesson 12.4: 744; Lesson 12.6: 760, 762 (#14-16), 764 (#35-37); Extra Practice: 825 (#7-8) 252-254 220-222 268-269 Ch. 12: 11-20 Lesson: 12.1 Lesson: 12.1 Lesson: 12.1 17

Strand: Coordinate Geometry and Transformations Standard 5: Students will specify locations, apply transformations and describe relationships using coordinate geometry. CGT.5.G.1 Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines Lesson 1.3: 19-24; Lesson 1.5: 35, 38, 39 (#25-30); Lesson 3.6: 165-170; Lesson 3.7: 172-177 Lesson 1.5 Mixed Review: 42 (#63-68); Chapter 1 Review/Test: 61-62, 63 (#16), 64 (#7); Chapter 3 Review/Test: 182, 184 (#4, 8), 185 (#16-17); Skills Review Handbook: 794 Teacher s Edition Wrap: Lesson 6.5: 356; Lesson 8.7: 506 64-66, 67-69 55-57, 58-60 61-62, 63-64 Lessons: 3.6, 3.7 Ch. 3: 82-92, 95-108 Lessons: 3.6, 3.7 Lesson: 3.6 Lessons: 3.6, 3.7 18

CGT.5.G.2 Write equations of lines in slope-intercept form and use slope to determine parallel and perpendicular lines Lesson 3.6: 167-171; Lesson 3.7: 172-177 Chapter 3 Review/Test: 182, 183 (#12-13), 184 (#6-7), 185 (#12-13); Cumulative Practice: 187 (#33) 64-66, 67-69 55-57, 58-60 61-62, 63-64 Lessons: 3.6, 3.7 Ch. 3: 82-92, 95-108 Lessons: 3.6, 3.7 Lesson: 3.6 Lessons: 3.6, 3.7 CGT.5.G.3 Determine, given a set of points, the type of figure based on its properties (parallelogram, isosceles triangle, trapezoid) Lesson 6.4: 354 (#55-58); Lesson 6.5: 360 (#36-38); Lesson 6.6: 368 (#36-41) Lesson 6.5 Mixed Review: 363 (#63-64); Lesson 6.5 Quiz: 363 (#2-5); Chapter 6 Review/Test: 384, 386 (#7) 127-130, 131-134, 135-137 109-111, 112-114, 115-117 129-130, 131-133, 134-135 Lesson: 6.6 Ch. 6: 52-65, 68-79, 82-92 Lessons: 6.4, 6.5, 6.6 Lesson: 6.4 Lessons: 6.4, 6.5, 6.6 19

CGT.5.G.4 Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle Lesson 10.6: 636-640 Lesson 10.7 Quiz: 648 (#5); Chapter 10 Review/Test: 652, 653 (#18), 654 (#8), 655 (#15); Lesson 11.5 Mixed Review: 698 (#55-58) 225-227 196-198 232-233 Ch. 10: 81-94 Lesson: 10.6 Lesson: 10.6 Lesson: 10.6 20

Lesson 7.1: 395, 396-402; Lesson 7.2: 403, 404-410; Lesson 7.3: 411, 412-419; Lesson 7.4: 421-428; Lesson 7.5: 429, 430-436; Lesson 8.7: 506-512, 514 144-146, 147-149, 150-152, 153-155, 156-158, 183-184 121-123, 124-126, 127-129, 130-132, 133-135, 157-159 147-148, 149-150, 151-153, 154-155, 156-157, 184, 185 Lessons: 7.2, 7.4 CGT.5.G.5 Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane translations reflections rotations (90, 180, clockwise and counterclockwise about the origin) dilations (scale factor) Chapter 7 Review/Test: 446-448, 449, 450-451; Lesson 8.5 Mixed Review: 495 (#46-49); Chapter 8 Review/Test: 518, 519 (#16-18), 520 (#7), 521 (#11-12) Ch. 7: 11-20, 23-36, 39-52, 55-65, 68-81; Ch. 8: 97-108 Lessons: 7.1, 7.2, 7.3, 7.4, 7.5, 8.7 Lessons: 7.3, 7.4, 7.5, 8.7 Lessons: 7.1, 7.2, 7.3, 7.4, 7.5, 8.7 21

AR 80 4/2005 2004 CC2

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