NUMBER STRAND Geometry

2006 TEAM-Math Curriculum Guide (July 15) p. 17-1

Chapter 17. Curriculum for Geometry

Two versions of the Curriculum for Geometry are presented. The first, the “Cohort Version,” is intended for teachers who have completed the TEAM-Math Summer Institute and have been introduced to the Interactive Mathematics Program. An alternative version is intended for those who have not yet attended the Summer Institute. The Appendix provides the correlation of objectives, which should be useful for both groups of teachers.

Curriculum for Geometry (Cohort Version)

The geometry curriculum has been organized into four units. While the pacing of the units is left up to individual schools and teachers, the curriculum writers’ intent is for each unit to represent one-fourth of the total course content.

Unit titles reflect the “big ideas” of geometry. The main topics listed in each unit summarize the Alabama Course of Study and TEAM-Math objectives.

The texts referenced in the geometry curriculum are Glencoe Geometry, Interactive Mathematics Program, and Discovering Geometry. These resources guide teachers in using inquiry-based methods and are endorsed by the TEAM-Math Partnership. Teachers are encouraged to research, develop, and implement additional inquiry activities to meet their students’ learning needs.

Suggested Pacing Guide (Cohort Version)

Unit Semester Block Full Year Fundamentals of Geometry – Lines, Angles, and 4 ½ weeks 9 weeks Logic Triangles – Classification, Congruency, Similarity, 4 ½ weeks 9 weeks and Trigonometry Geometric Figures – Quadrilaterals, 4 ½ weeks 9 weeks Transformations, and Circles Area and Volume – Area of Polygons and Circles, 4 ½ weeks 9 weeks Surface Area and Volume 2006 TEAM-Math Curriculum Guide (July 15) p. 17-2 Chapter 17 – Curriculum for Geometry (Cohort Version)

Suggested Sequence of Instructions (Cohort Version)

UNIT: 1 Shadows: Fundamentals of Geometry – Lines, Angles and Logic

Topics AL COS TEAM- AHSGE Glencoe DG IMP Documentation Math Investigations Understand undefined terms of geometry 1-1 p 6-12 p 29 Analyze information in geometric contexts to 9 D4 Throughout Chapter P 106, p 112, p Shadows determine what relationships exist 2 118, p 136 [Throughout]

Demonstrate competency with measurement tools 17 M1 1-2 p 13-20 P 41, p 143, p Shadows 144, p 168 [Throughout] Determine equations of parallel and perpendicular 1,2,12 G5, G3 III-1, 2 3-3 p 139-144 P 165, p 210 Shadows [Days Must supplement lines IV-2 3-4 p 145-150 2-5] Shadows with V-1,2,4 3-5 p 151-157 Glencoe here Revisit Pythagorean theorem and apply distance, 12 G3 IV-2, 1-3 p 21-28 P 36, p 133, P Optional here, may midpoint, and slope formulas VII-2 2-7 p. 101-106 462, P 468, P be introduced in Bees 3-3 p. 139-144 486 Determine the equation of a circle 5a 10-8 p 575-580 P 488 Introduction to coordinate geometry through 11 M3 IV-1 1-6 p 45-52 perimeter of polygons VII-3 Use inductive and deductive reasoning 9, 17 D2, G5 2-1 p 62-66 P 96, p 102, P Shadows 2-3 p 75-80 551, P 611, [Days 9-12] 2-4 p 82-88 Using methods of proof to justify theorems 9 G5 II-1 2-5 p 89-93 P 692, P 696, Shadows II-2 P 708, [Throughout] Apply properties of similar triangles including use of 3a, 5 G2 VII-3 6-1 p 282-288 Shadows scale factors and proportions VII-4 6-2 p 289-297 [Days 7-13] VII-7 Application of inequalities to geometric problems 9a, 8 G6 5-2 p 247-254 P 214, p 215, p Shadows (triangle inequalities) 5-4 p 261-266 215, [Days 11-12] 5-5 p 267-273 Identify angle relationships and justify theorems 2 G4, G5, VII-1 1-4 p 29-36 P 49, p 120, Shadows related to pairs of angles D4 1-5 p 37-44 p 121, p 126, [Days 14-16] 2-8 p. 107-114 p 128 3-2 p. 133-138 3-3 p. 139-144 Application of equations to geometric problems 12 A1a II-1 Throughout Chapter Shadows 3 [Throughout] 2006 TEAM-Math Curriculum Guide (July 15) p. 17-3 Chapter 17 – Curriculum for Geometry (Cohort Version)

UNIT: 2 Triangles – Classification, Congruency, Similarity and Trigonometry

Topics AL COS TEAM- AHSGE Glencoe DG IMP Documentation Math Investigations Classify types of triangles 8 G2 4-1 p 178-183 P 60 Apply angle properties of triangles 8 G6 VII-1 4-2 p 184-191 P 199 Prove triangles are congruent and use properties of 5, 8 G2 4-3 p 192-198 P 220, p 221, p Shadows [Day 10] congruent triangles of find missing 4-4 p 200-206 225, p 230 Appendix A measures(CPCTC) 4-5 p 207-215 Triangular Data Utilize the properties of isosceles and equilateral 5, 8 G6 II-1 4-6 p 216-221 P 205, p 206, p triangles to determine missing measures VII-1 242 Identify special segments of triangles, their 8 G6 5-1 p 236-245 P 147, p 148, p intersections and their measurement properties 157, p 158, p 176, p 177, p 183, p 184, p 189, p 190, P 329, P 401 Apply properties of parallel lines, similar polygons 3a, 5 G2 VII-3 6-3 p 298-306 P 564, P 581, P Shadows and similar triangles including use of scale factors VII-4 6-4 p 307-315 586, P 588, P [Days 17-19] and proportions VII-7 6-5 p 316-323 604, P 606 Determine geometric mean to find missing lengths 5, 8a N4, G5 VII-3 7-1 p 342-348 in right triangles Apply Pythagorean theorem, special right triangle 6, 7 N4, G4, IV-2 7-2 p 349-356 P 475, P 476, P Bees [Days 11-16] rules, and other operations involving radicals to find G6 VII-2 7-3 p 357-363 634, P 635, P missing lengths of sides 641 Apply right triangle definitions of sine, cosine and 10 G6 II-1 7-4 p 364-370 P 622 Shadows tangent to find missing measures 7-5 p 371-376 [Days 22-25]

Apply factoring and use of polynomials in problem A3 I-3, I-4 Throughout text solving applications(covered throughout) II-2

UNIT: 3 Geometric Figures- Quadrilaterals, Transformations and Circles

Topics AL COS TEAM- AHSGE Glencoe DG IMP Documentation Math Determine the measures of interior and exterior 4, 4a M2, M2a VII-4 8-1 p 404-410 P 256, p 260 angles associated with polygons and verify the formulas Identify quadrilaterals from verbal descriptions of 3, 12 G1, A1a VII-4 8-2 p 411-416 P 62, p 268, p properties and apply the properties 8-3 p 417-423 273, p 274, p 8-4 p 424-430 279, p 287, p 8-5 p 431-438 288, p 289 2006 TEAM-Math Curriculum Guide (July 15) p. 17-4 Chapter 17 – Curriculum for Geometry (Cohort Version)

8-6 p 439-445 Understand and analyze properties of 13 G2 9-1 p 462-469 P 360, P transformations 9-2 p 470-475 367,P 374, P 9-3 p 476-482 375 9-5 p 490-497 Coordinate geometry applications of 13 M6 8-7 p 447-451 P 367, P 566, transformations 9-1 p 462-469 P 572, P 573, 9-2 p 470-475 P 574 9-3 p 476-482 9-5 p 490-497 Introduce operations with vectors N4 9-6 p 498-505 Understand and apply properties of circles 15 M4 VII-1 Chapter 10 10-1 to P 69, P 319, P including arcs, chords, secants, tangents, and VII-2 10-7 p 522-574 320, P 321, P angles related to circles VII-3 321, P 342 Real life applications related to circles, 5 A3 VII-3 Throughout Unit 3 P 86, p 307, p quadrilaterals and other geometric shapes VII-4 Chapters 8, 9 & 10 307, p 309, p 309, p 313, p 314 Construct with precision a circle graph 18 D3 10-2 p 529-535 representing data

UNIT: 4 Do Bees Build It Best? Area and Volume- Area of Polygons and Circles, Surface Area and Volume

Topics AL COS TEAM- AHSGE Glencoe DG IMP Documentation Math Apply geometric properties and relationships in G4 II-1 Throughout Text Bees - throughout solving multi-step problems in two and three unit dimensions (also throughout Units 2 and 3) Area of rectangles, triangles, parallelograms, and 11 G4, M3 VII-3 11-1 p 595-600 P 412, P 417, Bees [Days 2-8], trapezoids VII-4 11-2 p 601-609 P 417, P 418, [Day 11], [Day 17] P 426, P 433, Revisit similarity and right triangle definitions of 10 G6 II-1 7-4 p 364-370 P 622 Bees [Days 9-10] sine, cosine and tangent to find missing measures 7-5 p 371-376 [Day 18] [Day 21] Revisit Pythagorean theorem 12 G3 IV-2, VII- 1-3 p 21-28 P 462, P 468, Bees [Days 11-15] Optional here, 2 7-2 p 350-356 P 486 may be introduced in Bees Calculate measures of sectors of a circle 15 M4 11-5 p.622-627 Calculate probabilities arising in geometric contexts 17b D5 VII-6 11-5 p 622-627 P 442 Bees [Day 11] Application of equations to geometric problems 12 A1-a II-1 Throughout Bees [Days 15-16] Determine relationships between perimeter, surface 16c M5c 13-4 p 707-713 P 592, P 594, Bees [Day 18], area and volume of similar figures P 599 [Day 28] 2006 TEAM-Math Curriculum Guide (July 15) p. 17-5 Chapter 17 – Curriculum for Geometry (Cohort Version)

Area of polygons, circles, and irregular figures 11 G4, M3 VII-3 11-1 p 595-600 P 412, P 417, Bees [Days 18-20] Must VII-4 11-2 p 601-609 P 417, P 418, supplement bees 11-3 p 610-616 P 426, P 433 for irregular 11-4 p 617-621 figures Classify polyhedra according to their properties 14 G1 12-1 p 636-642 Bees [Days 25-26] Must supplement Bees for spheres, cones, pyramids and Platonic Solids Develop formulas for & calculate surface area; find 16, M5, VII-4 12-3 p 649-654 P 448, P 449, Bees [Days 22-29] Must missing dimensions of solid figures including 16a M5a 12-4 p 655-659 P 546 supplement bees cylinders, prisms, spheres, cones, and pyramids 16b M5b 12-5 p 660-665 for spheres, from surface area 12-6 p 666-670 cones, and 12-7 p 671-677 pyramids Develop formulas for & calculate volume; find 16 M5 VII-4 13-1 p 688-695 P 515, P 522, Bees [Days 23-29] Must missing dimensions of solid figures including 16a M5a 13-2 p 696-701 P 542 supplement bees cylinders, prisms, spheres, cones, and pyramids 16b M5b 13-3 p 702-706 for spheres, from volume cones and pyramids 2006 TEAM-Math Curriculum Guide (July 15) p. 17-6 Chapter 17. Curriculum for Geometry (Non-cohort Version)

Curriculum for Geometry (Non-Cohort Version)

The geometry curriculum for non-cohort teachers has been organized into four units. While the pacing of the units is left up to individual schools and teachers, the curriculum writers’ intent is for each unit to represent one-fourth of the total course content.

Unit titles reflect the “big ideas” of geometry. The main topics listed in each unit summarize the Alabama Course of Study and TEAM-Math objectives.

Suggested Pacing Guide

Unit Semester Block Full Year Fundamentals of Geometry – Lines, Angles, and 4 ½ weeks 9 weeks Logic Triangles – Classification, Congruency, Similarity, 4 ½ weeks 9 weeks and Trigonometry Geometric Figures – Quadrilaterals, 4 ½ weeks 9 weeks Transformations, and Circles Area and Volume – Area of Polygons and Circles, 4 ½ weeks 9 weeks Surface Area and Volume 2006 TEAM-Math Curriculum Guide (July 15) p. 17-7 Chapter 17. Curriculum for Geometry (Non-cohort Version) Part A. Suggested Sequence of Instruction (Non-Cohort Version) This curricular sequence is aligned with the chapters of the Glencoe textbook and should only be used by teachers who have not yet attended summer institute. Each unit is considered to be ¼ of the course.

UNIT: 1 Fundamentals of Geometry – Lines, Angles and Logic

Topics AL COS TEAM-Math Glencoe IMP Understand undefined terms of geometry (point, line, plane) 1-1 p 6-12 Demonstrate competency with measurement tools (ruler, protractor, compass) 17 M1 1-2 p 13-20 Revisit Pythagorean theorem and apply distance, midpoint, and slope formulas 12 G3 1-3 p 21-28 Identify angle relationships and justify theorems related to pairs of angles 2 G4, G5, 1-4 p 29-36 (1) Shadows D4 1-5 p 37-44 [Days 14-16] Introduction to coordinate geometry through perimeter of polygons (introduced 11 M3 1-6 p 45-52 here but covered throughout) Use inductive and deductive reasoning 9, 17 D2, G5 2-1 p 62-66 (1) Shadows 2-2 p 67-74 throughout unit 2-3 p 75-80 2-4 p 82-88 Using methods of proof to justify theorems 9 G5 2-5 p 89-93 2-6 p 99-100 2-7 p 101-106 2-8 p107-114 Analyze information (introduced here but covered throughout ) 9 D4 Throughout Chapter 2 (1) Shadows throughout unit Determine equations of parallel and perpendicular lines 1,2,12 G5 3-1 p 126-131 3-2 p 133-138 3-3 p 139-144 3-4 p 145-150 3-5 p 151-157 Application of equations to geometric problems(covered throughout) 12 A1a Throughout Chapter 3 (1) Shadows throughout unit

UNIT: 2 Triangles – Classification, Congruency, Similarity and Trigonometry

Topics AL COS TEAM-Math Glencoe IMP Classify types of triangles 8 G2 4-1 p 178-183 Apply angle properties of triangles 8 G6 4-2 p 184-191 Prove triangles are congruent and use properties of congruent triangles of find 5, 8 G2 4-3 p 192-198 missing measures(CPCTC) 4-4 p 200-206 4-5 p 207-215 Utilize the properties of isosceles and equilateral triangles to determine missing 5, 8 G6 4-6 p 216-221 measures 2006 TEAM-Math Curriculum Guide (July 15) p. 17-8 Chapter 17. Curriculum for Geometry (Non-cohort Version) Identify special segments of triangles, their intersections and their 8 G6 5-1 p 236-245 measurement properties Application of inequalities to geometric problems (triangle inequalities) 9a, 8 G6 5-2 p 247-254 (1) Shadows 5-4 p 261-266 [Days 11-12] 5-5 p 267-273 Apply properties of similar triangles including use of scale factors and 3a, 5 G2 6-1 p 282-288 (1) Shadows proportions 6-2 p 289-297 [Days 7-13 6-3 p 298-306 Days 17-19] 6-4 p 307-315 6-5 p 316-323 Determine geometric mean to find missing lengths in right triangles 5, 8a N4, G5 7-1 p 342-348 Apply Pythagorean theorem, special right triangle rules, and other operations 6, 7 N4, G4, 7-2 p 349-356 (1) Shadows involving radicals to find missing lengths of sides G6 7-3 p 357-363 [Days 7-13] (2) Bees [Days 11- 16] Apply right triangle definitions of sine, cosine and tangent to find missing 10 G6 7-4 p 364-370 (1) Shadows measures 7-5 p 371-376 [Days 22-25] (2) Bees [Days 9-10] Apply factoring and use of polynomials in problem solving A3 Throughout text applications(covered throughout)

UNIT: 3 Geometric Figures- Quadrilaterals, Transformations and Circles

Topics AL COS TEAM-Math Glencoe IMP Determine the measures of interior and exterior angles associated with 4, 4a M2, M2a 8-1 p 404-410 polygons and verify the formulas Identify quadrilaterals from verbal descriptions of properties and apply the 3 G1, A1a 8-2 p 411-416 properties (parallelogram, rhombus, square, and trapezoid.) 8-3 p 417-423 8-4 p 424-430 8-5 p 431-438 8-6 p 439-445 Understand and analyze properties of transformations G2 9-1 p 462-469 9-2 p 470-475 9-3 p 476-482 Coordinate geometry applications of transformations 13 M6 8-7 p 447-451 9-1 p 462-469 9-2 p 470-475 9-3 p 476-482 Introduce operations with vectors N4 9-6 p 498-505 Understand and apply properties of circles including arcs, chords, secants, 15 M4 Chapter 10 10-1 to 10-7 p 522-574 tangents, and angles related to circles Real life applications related to circles, quadrilaterals and other geometric 5 A3 Throughout Unit 3 shapes Chapters 8, 9 & 10 2006 TEAM-Math Curriculum Guide (July 15) p. 17-9 Chapter 17. Curriculum for Geometry (Non-cohort Version) Construct with precision a circle graph representing data 18 D3 10-2 p 529-535 Determine the equation of a circle 5a 10-8 p 575-580

UNIT: 4 Area and Volume- Area of Polygons and Circles, Surface Area and Volume

Topics AL COS TEAM- Glencoe IMP Math Area of polygons, circles, and irregular figures 11 G4, M3 11-1 p 595-600 (2) Bees [Days 3-8] 11-2 p 601-609 11-3 p 610-616 11-4 p 617-621 Calculate measures of sectors of a circle 15 M4 11-5 p 622-627 Calculate probabilities arising in geometric contexts 17b D5 11-5 p 622-627 Classify polyhedra according to their properties 14 G1 12-1 p 636-642

Develop formulas for & calculate surface area; find missing dimensions of 16, M5, 12-3 p 649-654 (2) Bees [Days 22-27] solid figures including cylinders, prisms, spheres, cones, and pyramids from 16a M5a 12-4 p 655-659 surface area 16b M5b 12-5 p 660-665 12-6 p 666-670 12-7 p 671-677 Develop formulas for & calculate volume; find missing dimensions of solid 16 M5 13-1 p 688-695 (2) Bees [Days 22-27] figures including cylinders, prisms, spheres, cones, and pyramids from volume 16a M5a 13-2 p 696-701 16b M5b 13-3 p 702-706 Determine relationships between surface area and volume of similar figures 16c M5c 13-4 p 707-713 Apply geometric properties and relationships in solving multi-step problems in G4 Throughout Text (2) Bees - throughout two and three dimensions (also throughout Units 2 and 3) unit 2006 TEAM-Math Curriculum Guide (July 15) p. 17-10 Chapter 17. Curriculum for Geometry (Appendix) Appendix: Correlation of Objectives with Recommended Textbooks

NUMBER STRAND – Geometry

Alabama Course of Study TEAM-Math AHSGE Glencoe IMP Unit Core Plus G4. Apply operations involving IV-2,VII-2 7-2 p 349-356 (3) Meadows or Malls [ Days 27-35 ] IV-A Unit 2 Lesson 1 radicals and introduce IV-2,VII- 9-6 p 498-505 Navigation operations with vectors. 1,VII-2 p 744-745 ALL:VII-4 II-A Unite 2 Lesson 1 Modeling p102

ALGEBRA STRAND – Geometry

Alabama Course of Study TEAM-Math AHSGE Glencoe IMP Unit Core Plus A1a. Extend solving equations ALL:VII-4 Scattered (3) Fireworks [ Day 2] III-A Unit 3 Lesson 5 and inequalities to throughout text Investigation 2 Algebraic applications. (Reasoning in Geo and b. Reinforce and apply Stat) operations on polynomials A3. Applying factoring when (3) Fireworks [ Day 4 ] IV-B Lesson 1 problem solving. Investigation 1 1. Determine the equation of a IV-2,VI-1 3-4 p 146-147 II-A Unit 2 Lesson 1 line parallel or perpendicular to a II-1,II-3,IV-2, 5-1 p 241-242 Modeling p 90 second line through a given point. VII-1

ALL:VII-4 2006 TEAM-Math Curriculum Guide (July 15) p. 17-11 Chapter 17. Curriculum for Geometry (Appendix) GEOMETRY STRAND – Geometry

Alabama Course of Study TEAM-Math AHSGE Glencoe IMP Unit Core Plus 3. Verify the relationships G1. Identify geometric II-1,VI-1,VII-1, 6-2 p 289-296 (1) Patterns [ p 115, 119] II-B Unit 6 Investigation 1 among different classes of figures from a verbal VII-3 6-3 p 300-301 (1) Shadows [ Day 11] Lesson 1 (Using Quadrilaterals polygons by using their description of its properties. II-1,IV-2, VI-1, 6-4 p 308-309 (3) Orchard Hideout [Day 1] In linkages) properties. (Course of Study #3 & #14) VII-1, VII-3 6-5 p 316-318 a. Determining the missing II-1,IV-2,VI-1, VII- I-B unit 5 Lesson 3 Investigation 1 lengths of sides or measures 3 (Polygons and Their Properties) of angles in similar II-1, IV-1 polygons 12-1 p 636-642 14. Classify polyhedrons according to their properties, including the number of faces. ALL:VII-4 b. Identifying Euclidean solids 8. Deduce relationships between G2. Understand and analyze (1) Shadows[ Days 6-16] II-A Unit 2 Investigation 1 two triangles, including properties of IV-2,VII-1 4-3 p 192-194 (2) Do Bees Build [ entire Modeling Rigid Transformations proving congruence or transformations, similarity, IV-2,VII-1 4-4 p 200-203 unit] similarity of the triangles from and congruence. (Course of VII-1 4-5 p 207- 210 (3) Orchard Hideout [Day 1] II-B Unit 2 Investigation 2 Lesson 1 given information, using the Study #8 & #13) VII-1 4-5 Follow Up p Linkages and Similarity relationships to solve 214- 215 problems and to establish 6-3 p 298-301 other relationships. II-1,IV-2, VI-1, 6-5 p 316-319 a. Determining the geometric VII-1, VII-3 7-1 p 342- 344 mean to find missing II-1, IV-1 lengths in right triangles II-2, VII-3 13. Identify the coordinates of the vertices of the image of a given polygon that is ALL:VII-4 translated, rotated, reflected, or dilated. 12. Apply distance, midpoint, G3. Apply distance, midpoint, I-2, II-1,IV-1,IV-2, 1-6 p 48-49 II-A Lesson 1 Unit 2 Investigation 1 and slope formulas to solve and slope formulas to solve VI-1,VII-1 6-2 p 295 Plotting Polygons and problems and to confirm problems and to confirm II-1,VI-1,VII-1, VII- 6-5 p 315 Computing distances properties of polygons. properties of polygons. 3 8-2 p 415 (Course of Study #12) II-1, IV-1 8-3 p 420-422 II-1,IV-2,VII-1 8-6 p 442-448 I-2,II-1,IV-1,IV-2, 9-2 p 472 VII-1 9-4 p 488 I-2,II-1,IV-2,VII-1 9-5 p 495 II-1,IV-1,VI-1 11-1 p 597-599 II-1,VII-1 11-2 p 603 2006 TEAM-Math Curriculum Guide (July 15) p. 17-12 Chapter 17. Curriculum for Geometry (Appendix) IV-1, IV-2,VII-3 11-2 p 605-606 IV-1, IV-2, 11-4 p 618-621 II-1, IV-1, IV-2

IV-1, IV-2, VI-1

ALL: VII-4

5. Solve real-life and G4. Apply geometric I-2,II-1,IV-1,IV-2, 1-6 P 47 (1) Shadows [ Days 10, 20] II-B Unit 6 Lesson 2 Investication 1 mathematical problems using properties and relationships VII-1,VI-1 4-1 P 178 (2) Do Bees Build [Days 12- (Triangles with a Variable – properties and theorems in solving multi-step IV-2 4-2 P 188 16] Length side) related to circles, problems in 2 & 3 II-1,VII-1 4-3 P 193 (3) Orchard Hideout Day [ 5- I-B Unit 5 Investigation 2 Lesson 2 quadrilaterals, and other dimensions. (Course of IV-2,VII-1 4-5 P 209-210 14,19] (Television screen and Pythagoras) geometric shapes. Study #5 & #6) VII-1 5-2 P 250 a. Determining the equation 5-5 P 270 of a circle given its center VII-1 6-2 P 290-292 and radius VI-1,VII-1,VII-3, 6-3 P 300-301 6. Apply the Pythagorean IV-2,VI-1,VII- 6-4 P 310 Theorem to solve application 1,VII-3 6-5 P 318 problems, expressing answers VII-3 7-1 P 344 in simplified radical form or VII-2,VII-3 7-2 P 350-356 as decimal approximations, IV-2,VII-2 7-3 P 358 using Pythagorean triples IV-2,VII-1,VII-2 7-5 P 371-372 when applicable. VI-1,VII-2 7-6 P 379-380 VI-1 7-7 P 387 VI-1,VII-2 8-1 p 405 VII-1 8-3 p 418 IV-2,VII-1 8-5 p 433 IV-2,VII-1 10-3 p 537 II-1,IV-1,VII-1 10-6 p 563 IV-1,VI-1 10-7 p 570 II-1,II-2,IV-1,VI-1 10-8 p 575-577 II-3,IV-2 11-1 p 596-597 IV-2 11-3 p 612 IV-2 11-4 p 618 IV-2,VI-1

ALL: VII-4

2. Justify theorems related to G5. Emphasize proof by I-2,II01,VI-1,VII-1 1-5 p 37- 40 (1) Patterns[ Day 20] II-B Unit 6 Lesson 1 Investigation 1 2006 TEAM-Math Curriculum Guide (July 15) p. 17-13 Chapter 17. Curriculum for Geometry (Appendix) pairs of angles, including having students communicate VII-1 2-8 p 107-114 (1) Shadows [ Days 9-16] (Using Quadrilateral in angles formed by parallel and with each other and justify 3-1 p 126-130 (2) Do Bees Build [Day 9] Linkages) perpendicular lines, vertical theorems and methods of ALL: VII-4 (3) Orchard Hideout [Days III-A Unit 4 Lesson 1 Investigation angles, adjacent angles, solving problems. (Course of 3,10] 4 (parallel Lines, Transversals, complementary angles, and Study #2 & #8) and Angles) supplementary angles. IV-A Unit 4 Lesson 3 Investigation 8. Deduce relationships between 1 (Infinity, recursion, and two triangles, including Mathematical Induction) proving congruence or I-A Unit 2 Investigation 1 Modeling similarity of the triangles from a Bungee Apparatus given information, using the relationships to solve problems and to establish other relationships. a. Determining the geometric mean to find missing 2-1 p 62-64 lengths in right triangles 2-2 p 68-69 9. Use inductive reasoning to 2-3 p 76-77 make conjectures and 2-4 p 82-87 deductive reasoning to justify p 88 conclusions. Study Guide p a. Recognizing the limitations ALL: VII-4 115-117 of justifying a conclusion 5-3 p 255-257 through inductive Spreadsheet Inv reasoning p 410 7. Use the ratios of the sides of G6. Determine lengths of I-2,II-1,IV-1,VII-1 8-1 p 404-410 (1) Patterns [ Days 15-20] II-B Unit 6 Lesson 2 Investigation 2 special right triangles to find sides and angle measures of (1) Shadows [ Days 13, 16, (What’s the Angle?) lengths of missing sides. triangles (including the use of 20, 22-25] III-A Unit 4 Lesson 1 Investigation a. Deriving the ratios of the trigonometry) (Course of (2) Do Bees Build [Days 8- 4 (Parallel Lines Transversals and sides of 30-60-90 and 45- Study #4 bullet & Course of 10,21] Angles) 45-90 triangles Study #7 & Course of Study IV-2,VII-1,VII-2 (3) Orchard Hideout [Day 1] 10. Find the missing measures of #10) II –B Unit 6 Lesson 2 Investigation sides and angles in right IV-2,VII-1,VII-2, 7-3 p 357-363 3 (Measuring without measuring) triangles by applying the right VII-3 triangle definitions of sine, IV-1,VI-1,VII-2, 7-4 p 364-370 cosine, and tangent. VII-4 7-5 p 371- 373

2006 TEAM-Math Curriculum Guide (July 15) p. 17-14 Chapter 17. Curriculum for Geometry (Appendix) MEASUREMENT STRAND – Geometry

Alabama Course of Study TEAM-Math AHSGE Glencoe IMP Unit Core Plus M1. Analyze various Scattered (1) Shadows [ Days 6-12 ] IV-A Unit 5 Lesson 4 problems to determine ALL: VII-4 throughout text (2) Do Bees Build [ Days 2-8 ] Investigation 1 which measurement and (3) Orchard Hideout [ Days 5-7 ] (Characteristics of tools are appropriate in (3) Meadows or Malls [Days 8-14 ] Experiments) relation to Geometry topics, (4) As The Cube Turns [ Days 20-30] including analyzing (4) Know How [ Days 3-4 } accuracy and approximate error. 4. Determine the measure of M2. Determine the measure I-2,II-1,IV-1, VII-1, 8-1 p 404-410 (1) Shadows [ Days 12, 14-15] III-A Unit 4 Lesson 1 interior and exterior angles of interior and exterior VII-4 Extending p295 associated with polygons. angles associated with III-A Capstone a. Verifying the formulas for polygons. Investigation 1 (Do Bees the measures of interior and a. Verifying the formulas Build it Best) exterior angles of polygons for the measures of inductively and deductively interior and exterior ALL: VII-4 angles of polygons inductively and deductively (Course of Study #4) 11. Determine the areas and M3. Determine the areas and I-2,II-1,IV-1,IV-2, 1-6 p 47-49 (2) Do Bees Build It [entire unit]] III-A Capstone perimeters of regular polygons, perimeters of regular VII-1,VI-1 4-1 p 180 (3) Orchard Hideout [Days 5-14] Investigation (Do Bees including inscribed or polygons, including IV-2 5-1 p 241-244 Build it Best?) circumscribed polygons, given inscribed or circumscribed IV-2,VII-1 6-3 p 302 I-A Unit 2 Lesson 4 P151 the coordinates of vertices or polygons, given the IV-2,VI-1,VII-1 6-3 p 305-306 #5 other characteristics. coordinates of vertices or 7-7 p 390 I-B Unit 5 Lesson 1 15. Calculate measures of arcs other characteristics. IV-1,VI-1,VII-2 8-5 p 432 Investigation 2 and sectors of a circle from ( Course of Study #11) IV-1,IV-2,VII-1 8-6 p 442-445 (Recognizing and given information. M4. Calculate measures of VII-1,IV-2 10-1 p 528 Constructing Space- Examples: finding the area of a arcs and sectors of a circle IV-1 11-1 p 595-598 Shapes) sector given its arc length and from given information. IV-1,IV-2 11-2 p 601-603 I-B Unit 5 Lesson 2 radius, finding the arc length of a Examples: finding the area of IV-1,IV-2 11-3 p 610-616 Investigation 1 sector given its area and radius, a sector given its arc length IV-1,IV-2 11-4 p 617-618 (Describing size) finding the area or arc length and radius, finding the arc IV-1,IV-2 12-1 p 642 I-B Unit 5 Lesson 2 given the measure of the central length of a sector given its Skills p 732-733 Investigation 3 (Size angle and the radius area and radius, finding the Measures for Space- 16. Calculate surface areas and area or arc length given the 10-2 p 529-535 Shapes) volumes of solid figures, measure of the central angle I-2,II-1,IV-1,VII-1 10-3 p 536- 543 including spheres, cones, and and the radius (Course of I-2,II-1,IV-1,VII-1, 11-5 p 623- 626 pyramids. Study #15) VII-2 a. Developing formulas for M5. Calculate surface areas VII-6 surface area and volume of and volumes of solid 12-5 p 660 –665 2006 TEAM-Math Curriculum Guide (July 15) p. 17-15 Chapter 17. Curriculum for Geometry (Appendix) Alabama Course of Study TEAM-Math AHSGE Glencoe IMP Unit Core Plus spheres, cones, and pyramids figures, including spheres, 12-6 p 666- 669 b. Calculating specific missing cones, and pyramids. IV-1,VII-2 12-7 p 671- 676 dimensions of solid figures a. Developing formulas for IV-1,VII-2 13-2 p 696- 700 from surface area or volume surface area and volume IV-1,VII-2 13-3 p 702 – c. Determining the relationship of spheres, cones, and IV-1 706 between the surface areas of pyramids IV-1 similar figures and volumes b. Calculating specific of similar figures missing dimensions of 12-4 p 656 solid figures from surface I-3,I-4,IV-1 13-4 p 707 – area or volume IV-1,VII-3 713 c. Determining the relationship between the All: VII-4 surface areas of similar figures and volumes of similar figures (Course of Study #16) 13. Identify the coordinates of M6. Identify the coordinates II-1,IV-1,VI-1 9-1 p 465-468 (1) Shadows [ p 43 ] I-B Unit 5 the vertices of the image of a of the vertices of the image IV-1,VII-1 9-2 p 470-474 (4) As The Cube Turns [ Days 8- Tessellations/Symmetry given polygon that is of a given polygon that is IV-1,IV-2,VII-3 9-3 p 479-481 20,31-33] I-B Unit 5 Lesson 3 translated, rotated, reflected, or translated, rotated, IV-1,IV-2 9-5 p 492- 495 (4) World Of Functions [Days 27-28] Investigation 3 dilated. reflected, or dilated. 11-1 p 600 (Symmetry, Patterns In Example: using a translation Strips) vector, rotating a triangle a given number of degrees around a specific point (Course of Study #13) All: VII-4 2006 TEAM-Math Curriculum Guide (July 15) p. 17-16 Chapter 17. Curriculum for Geometry (Appendix) DATA ANALYSIS & PROBABILITY STRAND – Geometry

Alabama Course of Study TEAM-Math AHSGE Glencoe IMP Unit Core Plus 4. Analyze sets of data from D2. Distinguishing between All: VII-4 2-1 p 62-64 I-B Unit 6 Lesson 2 geometric contexts, to conclusions drawn when using 2-2 p 68-69 Investigation 2 (Sierpinski determine what, if any, deductive and statistical 2-3 p 76-77 Carpets) relationships exist reasoning (Course of Study 2-4 p 82-87; a. Distinguishing between #17a) p 88 conclusions drawn when Study Guide p 115-117 using deductive and 5-3 p 255-257 statistical reasoning Spreadsheet Inv p 410 18. Construct with precision a D3. Construct with precision a I-2,II-1,IV-1,VII- 10-2 p 534 circle graph to represent data circle graph to represent data 1,VII-4 from given tables or from given tables or classroom classroom experiments. experiments. (Course of Study #18) 17. Analyze sets of data from D4. Analyze sets of data from IV-1, VII-4,VII-6 I-B Unit 6 Lesson 2 geometric contexts to geometric contexts to Investigation 2 (Sierpinski determine what, if any, determine what, if any, Carpets) relationships exist. relationships exist. (Course of a. Distinguishing between Study #17a) conclusions drawn when using deductive and statistical reasoning b. Calculating probabilities D5. Calculating probabilities Geometry Activity p 20 I-B Unit 7 Lesson 1 p494 arising in geometric arising in geometric contexts 11-5 p 622- 627 #5 contexts (Course of Study #17b) II-B Unit 7 Lesson 2 Investigation 1 (Multiplying Probabilities) 2006 TEAM-Math Curriculum Guide (July 15) p. 17-17 Chapter 17. Curriculum for Geometry (Appendix)

TEAM-Math Curriculum Guide References

GEOMETRY

Textbooks

Boyd, C., Cummins, J., Malloy, C., Carter, J., & Flores, A. (2005). Geometry (Alabama teacher wraparound edition). New York: Glencoe McGraw Hill. (ISBN 0-07-860381-1)

Online resources: http://www.al.geometryonline.com/

Serra, M. (2003). Discovering Geometry: An investigative approach (Teacher’s edition). Emeryville, CA: Key Curriculum Press. (ISBN 1-55953-460-5)

Online resources: http://www.keypress.com/

Interactive Mathematics Program

Fendel, D., Resek, D., Alper, L., & Fraser, S. (1997). Interactive mathematics program. Emeryville, CA: Key Curriculum Press.

Teacher’s Guides Title ISBN Year 1 Patterns 1-55953-251-3 The Game of Pig 1-55953-252-1 The Overland Trail 1-55953-253-X The Pit and the Pendulum 1-55953-254-8 Shadows 1-55953-255-6 Year 2 Solve It! 1-55953-258-0 Is There Really A Difference? 1-55953-259-9 Do Bees Build It Best? 1-55953-260-2 Cookies 1-55953-261-0 All About Alice 1-55953-264-5 Year 3 Fireworks 1-55953-262-9 Orchard Hideout 1-55953-294-7 Meadows or Malls? 1-55953-295-5 Small World, Isn’t It? 1-55953-296-3 Pennant Fever 1-55953-297-1 Year 4 High Dive 1-55953-345-5 As the Cube Turns 1-55953-346-3 Know How 1-55953-347-1 The World of Functions 1-55953-348-X The Pollster’s Dilemma 1-55953-349-8 Other Baker’s Choice 1-55953-145-2 2006 TEAM-Math Curriculum Guide (July 15) p. 17-18 Chapter 17. Curriculum for Geometry (Appendix)

Online resources: http://www.keypress.com/