Arkansas Mathematics Curriculum Framework

Transcription

1 correlated to the Arkansas Mathematics Curriculum Framework Geometry

2 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: Chapter 1 Review/Test: 60, 63 (#19-20), 65 (#17-18); Lesson 2.5 Mixed Review: 107 (#28-30) 1-3, , , Lesson: 2.3 Ch.1: 11-21; Ch. 2: Lessons: 1.1, 2.3 Lessons: 1.1, 2.3 1

3 Lesson 1.2: 10-16; Lesson 1.3: 17-23; Lesson 1.4: , 7-10, , 7-9, , 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, TransparencyPackage: Lessons: 1.2, 1.3, 1.4 Lesson: 1.2 Lessons:1.2, 1.3, 1.4 2

4 LG.1.G.3 Describe relationships derived from geometric figures or figural patterns Lesson 9.4: ; Extra Practice: 820 (#28-30) Lesson 9.5 Quiz: 566 (#1-3); Chapter 9 Review/Test: 583, 585 (#11) Ch. 9: 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: Chapter 1 Review/Test: 62, 63 (#10-14), 64 (#5-6, 9), 65 (#12); Chapter 2 Review/Test: 120, 121 (#19), 122 (#8), , , , Ch. 1: 80-91; Ch. 2: Lessons: 1.6, 2.6 Lessons: 1.6, 2.6 Lessons: 1.6, 2.6 3

5 Lesson 3.3: 142, ; Lesson 3.4: ; Lesson 3.5: , 58-60, , 49-51, , 56-57, 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, Lessons: 3.3, 3.4, 3.5 Lesson: 3.3 Lessons: 3.3, 3.4, 3.5 4

6 Lesson 2.5: ; Lesson 2.6: ; Lesson 3.2: ; Lesson 3.4: ; Cumulative Practice: 187 (#30); Lesson 4.3: ; Lesson 4.4: ; Lesson 4.7: , ; Lesson 6.3: ; Extra Practice: 806 (#30), 807 (#13), , 44-46, 52-54, 58-60, 79-81, 82-84, 91-93, , 37-39, 43-45, 49-51, 67-69, 70-72, 79-81, , 37-39, 51-52, 56-57, 79-80, 81-83, 88-89, 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: , 183 (#16), 185 (#11); Lesson 4.4 Quiz 2: 227 (#7); Chapter 4 Review/Test: , 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, ; Ch. 6: 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

7 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: ; Lesson 4.4: ; Lesson 4.5: ; Lesson 8.3: 472, ; Lesson 8.4: ; Lesson 8.5: ; Lesson 8.6: Chapter 4 Review/Test: 253, 255, ; Chapter 8 Review/Test: , 519, , 82-84, 85-87, , , , , 70-72, 73-75, , , , , 81-83, 84-85, , , , 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, 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

8 T.2.G.2 Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem) Lesson 5.5: ; 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) Ch. 5: Lesson: 5.5 Lesson: 5.5 Lesson: 5.5 7

9 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: ; Lesson 5.3: ; Lesson 5.4: ; Extra Practice: 811, 812 (#16-22) Chapter 5 Review/Test: , 313, 314, 315 (#12-14) , , , 88-90, , , Lessons: 5.3, 5.4 Ch. 5: 27-36, 39-52, 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: ; Lesson 9.3: ; Extra Practice: 819 (#7-15) Lesson 9.3 Quiz: 549 (#8) , , , Lesson: 9.2 Ch. 9: 24-36, Lessons: 9.2, 9.3 Lesson: 9.2 Lessons: 9.2, 9.3 8

10 T.2.G.5 Use the special right triangle relationships ( and ) to solve problems Lesson 9.4: ; Extra Practice: 820 (#28-30) Lesson 9.5 Quiz: 566 (#1-3); Chapter 9 Review/Test: 583, 585 (#11) Ch. 9: 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: ; Lesson 9.6: Chapter 9 Review/Test: , 585 (#15-16), 586 (#7-9), 587; Cumulative Practice: 589 (#29-30) , , , Ch. 9: 68-81, Lessons: 9.5, 9.6 Lesson: 9.5 Lessons: 9.5, 9.6 9

11 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: , 706 Chapter 11 Review/Test: 710, 711 (#17-18), 713 (#10, 19-22) Ch. 11: Lesson: 11.6 Lesson: 11.6 Lesson:

12 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: ; Lesson 12.3: 735, 740; Lesson 12.4: 745, 746 (#7-9), 748, 749 (#50), 750; Lesson 12.5: 754, ; Lesson 12.6: Chapter 11 Review/Test: 708; Lesson 12.7 Quiz: 772 (#1-7); Chapter 12 Review/Test: , 777, , , , , , , , , , , , , , , , Lessons: 12.4, 12.6 Ch. 11: 25-37; Ch. 12: 23-33, 36-50, 53-64, 67-77, 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) , , , Ch. 12: 23-33, Lessons: 12.2, 12.3 Lessons: 12.2,

13 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: , ; Lesson 8.5: , ; Lesson 8.6: 501, 503 (#29-30), 504 (#36-37); Lesson 8.7: 508, ; Lesson 11.3: 678, 680 Chapter 8 Review/Test: 516, 519 (#18), 520 (#7) , , , , , , , , , , , , , , , Lessons: 8.4, 8.5, 11.3 Ch. 8: 35-46, 49-62, 65-80, 83-94, ; Ch. 11: 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: ; Cumulative Practice: 589 (#22); Extra Practice: 818 (#44-45) Chapter 8 Review/Test: 518, 519 (#6-7), 520 (#9) Ch. 8: Lesson: 8.6 Lesson:

14 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: , 327, 328 (#53); Lesson 6.2: 329, ; Lesson 6.3: ; Lesson 6.4: ; Lesson 6.5: ; Lesson 6.6: Chapter 6 Review/Test: , 385, ; Cumulative Practice: 389 (#25-30) , , , , , , , , , , , , , , , Lessons: 6.1, 6.6 Ch. 6: 11-21, 24-35, 38-49, 52-65, 68-79, 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,

15 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: ; Lesson 6.2: 329, ; Lesson 6.5: Lesson 6.6 Mixed Review: 370 (#61-62); Chapter 6 Review/Test: , 385, 386 (#2-3); Cumulative Practice: 389 (#25-30) , , , , , , Lesson: 6.1 Ch. 6: 11-21, 24-35, 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: Project: Tessellations 14

16 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: ; Lesson 10.2: ; Lesson 10.3: 612, ; Lesson 10.4: Chapter 10 Review/Test: , 653, ; Lesson 11.3 Mixed Review: , , , , , , , , , Lesson: 10.3 Ch. 12: Lesson: 12.1 Lesson: 12.1 Ch. 10: 11-23, 26-36, 39-50, Lessons: 10.1, 10.2, 10.3, 10.4 Lesson: 10.3 Lesson: 12.1 Lessons: 10.1, 10.2, 10.3,

17 R.4.G.6 Solve problems using inscribed and circumscribed figures Lesson 5.2: 274; Lesson 10.3: ; Lesson 10.4: 626 (#40), 627 (#44-45); Lesson 11.5: 693, ; Lesson 12.3: 741 Chapter 10 Review/Test: 651, 653, 654 (#3), 655; Lesson 11.3 Mixed Review: 681 (#38) Lesson: 10.3 Ch. 10: 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:

18 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) Ch. 12: Lesson: 12.1 Lesson: 12.1 Lesson:

19 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: ; Lesson 3.7: 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: , , , Lessons: 3.6, 3.7 Ch. 3: 82-92, Lessons: 3.6, 3.7 Lesson: 3.6 Lessons: 3.6,

20 CGT.5.G.2 Write equations of lines in slope-intercept form and use slope to determine parallel and perpendicular lines Lesson 3.6: ; Lesson 3.7: Chapter 3 Review/Test: 182, 183 (#12-13), 184 (#6-7), 185 (#12-13); Cumulative Practice: 187 (#33) 64-66, , , Lessons: 3.6, 3.7 Ch. 3: 82-92, 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) , , , , , , Lesson: 6.6 Ch. 6: 52-65, 68-79, Lessons: 6.4, 6.5, 6.6 Lesson: 6.4 Lessons: 6.4, 6.5,

21 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: 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) Ch. 10: Lesson: 10.6 Lesson: 10.6 Lesson:

22 Lesson 7.1: 395, ; Lesson 7.2: 403, ; Lesson 7.3: 411, ; Lesson 7.4: ; Lesson 7.5: 429, ; Lesson 8.7: , , , , , , , , , , , , , , , , 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: , 449, ; 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: 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,

23 AR 80 4/ CC2