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Tallapoosa County Mathematics Guide Advanced Geometry The objectives to be covered are listed by 9-weeks and should be covered during the four grading periods. You are also provided with a suggested sequencing of the objectives per term but you may choose to reorder them as long as you cover the stated objectives during the indicated quarter. The benchmark tests that will be administered at the end of each 9-weeks grading period will reflect the objectives listed for each term. TEXTBOOK: Glencoe – Geometry incorporating the IMP units: “Shadows” and “Bees Do It Best” whenever possible. Refer to the TEAM-Math Curriculum Guide for the incorporation of the IMP units. 1st 9-Weeks 2nd 9-Weeks 3rd 9-Weeks 4th 9-weeks COS #1, #2, #9, #11, #12, #17 COS #3, #5, #6, #7, #8, #9, #10 COS #3, #4, #5, #13, #15, #18 COS #11, #14, #15, #16, #17 SUGGESTED PACING GUIDE Approximate time frame for instruction: Begin 1st 9-weeks grading period. Chapter 1: Sections 1-6 Chapter 2: Sections 1-8 Chapter 3: Sections 1-5 End 1st 9-weeks grading period. 2.5 weeks 3 weeks 2.5 weeks Begin 2nd 9-weeks grading period. Chapter 4: Sections 1-6 Chapter 5: Sections 1-2, 4-5 Chapter 6: Sections 1-5 Chapter 7: Sections 1-5 End 2nd 9-weeks grading period. 2.5 weeks 2.0 weeks 2.0 weeks 1.5 weeks Begin 3rd 9-weeks grading period. Chapter 8: Sections 1-7 Chapter 9: Sections 1- 3, & 6 Chapter 10: Sections 1-8 *Exit Exam review & testing End 3rd 9-weeks grading period. 2.5 weeks 1.5 weeks 2.5 weeks 1.5 weeks Begin 4th 9-weeks grading period Chapter 11: Sections 1-5 Chapter 12: Sections 1-7 Chapter 13: Sections 1-4 th End 4 9-weeks grading period 2 weeks 3 weeks 2.5 weeks Chapter(s) 1, 2 & 3 Chapter(s) 4, 5, 6, & 7 Chapter(s) 8, 9 & 10 Chapter(s) 11, 12, & 13 Tallapoosa County Sequencing Guide Advanced Geometry 1st 9-Weeks UNIT 1: Fundamentals of Geometry – Lines, Angle, and Logic - Chapters 1, 2 & 3 TOPIC: 1) Understand undefined terms of geometry – point, line, plane (Chapter 1: Section 1) 2) Demonstrate competency with measurement tools – ruler, protractor, compass (Chapter 1: Section 2) 3) Apply distance, midpoint, and slope formulas connecting to the Pythagorean Theorem (Chapter 1: Section 3) 4) Identify angle relationships and justify theorems related to pairs of angles (Chapter 1: Sections 4 & 5) 5) Introduction to coordinate geometry through perimeter of polygons (Chapter 1: Section 6) 6) Use inductive and deductive reasoning to analyze information (Chapter 2: Sections 1-4) 7) Using methods of proof to justify theorems and to analyze information(Chapter 2: Sections 5-8) 8) Determine equations of parallel and perpendicular lines (Chapter 3: Sections 1-5) 9) Apply equations to geometric problems (Chapter 3) COS #1: Determine the equation of a line parallel or perpendicular to a second line through a given point. COS #2: Justify theorems related to pairs of angles, including angles formed by parallel and perpendicular lines, vertical angles, adjacent angles, complementary angles, and supplementary angles. COS #9: Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions. Recognizing the limitations of justifying a conclusion through inductive reasoning COS # 11: Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. COS #12: Apply distance, midpoint, and slope formulas to solve problems and to confirm properties of polygons. Examples: finding the area of a rectangle given the coordinates of its vertices, showing that the median of a trapezoid is half the sum of the bases. COS #17: Analyze sets of data from geometric contexts to determine what, if any, relationships exist. Example: Collect data and create a scatterplot comparing the perimeter and area of various rectangles. Determine whether a line of best fit can be drawn. Distinguishing between conclusions drawn when using deductive and statistical reasoning Tallapoosa County Sequencing Guide Advanced Geometry Calculating probabilities arising in geometric contexts Example: finding the probability of hitting a particular ring on a dart board whose rings are formed by equally spaced concentric circles 2nd 9-Weeks UNIT 2: Triangles – Classification, Congruency, Similarity, and Trigonometry – Chapters 4, 5, 6, & 7 TOPIC: 1) Classify types of triangles (Chapter 4: Section 1) 2) Apply angle properties of triangles (Chapter 4: Section 2) 3) Prove triangles are congruent and us properties of congruency to find missing measures (CPCTC) (Chapter 4: Sections 3, 4, & 5) 4) Utilize the properties of isosceles and equilateral triangles to determine missing measures (Chapter 4: Section 6) 5) Identify special segments of triangles, their intersections and their measurement properties (Chapter 5: Section 1) 6) Apply triangle inequalities and other inequalities to geometric problems (Chapter 5: Sections 2, 4, & 5) 7) Apply properties of similar triangles including use of scale factors and proportions (Chapter 6: Sections 1-5) 8) Determine geometric mean to fins missing lengths in right triangles (Chapter 7: Section 1) 9) Apply Pythagorean theorem, special right triangle rules, and other operations involving radicals to find missing lengths of sides (Chapter 7: Sections 2 & 3) 10) Apply right triangle definitions of sine, cosine and tangent to find missing measures (Chapter 7: Sections 4 & 5) 11) Apply factoring and use of polynomials in problem solving applications (Chapters 4-7) COS #3: Verify the relationships among different classes of polygons by using their properties Example: showing that a square has all the properties of both a rectangle and a rhombus Determining the missing lengths of sides or measures of angles in similar polygons COS #5: Solve real-life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes. Example: finding the center of a solid wooden wheel using the perpendicular bisectors of two chords Determining the equation of a circle given its center and radius COS #6: Apply the Pythagorean Theorem to solve application problems, expressing answers in simplified radical form or as decimal approximations, using Pythagorean triples when applicable. Tallapoosa County Sequencing Guide Advanced Geometry COS #7: Use the ratios of the sides of special right triangles to find lengths of missing sides. Deriving the ratios of the sides of 30-60-90 and 45-45-90 triangles COS #8: Deduce relationships between two triangles, including proving congruence or similarity of the triangles from given information, using the relationships to solve problems and to establish other relationships. Determining the geometric mean to find missing lengths in right triangles COS #9: Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions. Recognizing the limitations of justifying a conclusion through inductive reasoning COS #10: Find the missing measures of sides and angles in right triangles by applying the right triangle definitions of sine, cosine, and tangent. 3rd 9-Weeks UNIT 3: Geometric Figures – Quadrilaterals, Transformations and Circles (Chapters 8 & 9) TOPIC: 1) Determine the measures of interior and exterior angles associated with polygons and verify the formulas (Chapter 8: Section 1) 2) Identify quadrilaterals from verbal descriptions of properties and apply the properties of these quadrilaterals (Chapter 8: Sections 2 – 6) 3) Understand and analyze properties of transformations and apply the coordinate geometry of transformations (Chapter 8: Section 7 and Chapter 9: Sections 1-3) 4) Introduce operations with vectors (Chapter 9: Section 6) 5) Understand and apply properties of circles including arcs, chords, secants, tangents, and angles related to circles (Chapter 10: Sections 1-7) 6) Real life applications related to circles, quadrilaterals and other geometric shapes (Chapters 8, 9 & 10) 7) Construct with precision a circle graph representing given data (Chapter 10: Section 2) 8) Determine the equation of a circle (Chapter 10: Section 8) COS #3: Verify the relationships among different classes of polygons by using their properties. Example: showing that a square has all the properties of both a rectangle and a rhombus Determining the missing lengths of sides or measures of angles in similar polygons COS #4: Determine the measure of interior and exterior angles associated with polygons. Tallapoosa County Sequencing Guide Advanced Geometry Verifying the formulas for the measures of interior and exterior angles of polygons inductively and deductively COS #5: Solve real-life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes. Example: finding the center of a solid wooden wheel using the perpendicular bisectors of two chords Determining the equation of a circle given its center and radius COS #13: Identify the coordinates of the vertices of the image of a given polygon that is translated, rotated, reflected, or dilated. Example: rotating a triangle a given number of degrees around a specific point, comparing the vertices of the image and preimage COS #15: Calculate measures of arcs and sectors of a circle from given information. Examples: finding the area of a sector given its arc length and radius, finding the arc length of a sector given its area and radius, finding the area or arc length given the measure of the central angle and the radius COS #18: Construct with precision a circle graph to represent data from given tables or classroom experiments. 4th 9-Weeks UNIT 4: Area and Volume – Area of Polygons and Circles, Surface Area and Volume of 3-D Figures (Chapters 11, 12, & 13) TOPIC: Area of polygons, circles and irregular figures (Chapter 11: Sections 1 – 4) Calculate measures of sectors of a circle (Chapter 11: Section 5) Calculate probabilities arising in geometric contexts (Chapter 11: Section 5) Classify polyhedra according to their properties (Chapter 12: Section 1) Surface Area of Solid Figures (Cylinders, Spheres, Cones, Pyramids): develop formulas, calculate values, find missing dimensions (Chapter 12: Section 3 – 7) 6) Volume of Solid Figures (Cylinders, Spheres, Cones, Pyramids): develop formulas, calculate values, find missing dimensions (Chapter 13: Section 1 – 3) 7) Determine relationships between surface area and volume of similar figures (Chapter 13: Section 4) 8) Apply geometric properties and relationships in solving multi-step problems in two and three dimensions (Chapters 11, 12, & 13) 1) 2) 3) 4) 5) COS #11: Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. COS #14: Classify polyhedrons according to their properties, including the number of faces. Example: identifying a polyhedron having 6 vertices and 12 edges Identifying Euclidean solids Tallapoosa County Sequencing Guide Advanced Geometry COS #15: Calculate measures of arcs and sectors of a circle from given information. Examples: finding the area of a sector given its arc length and radius, finding the arc length of a sector given its area and radius, finding the area or arc length given the measure of the central angle and the radius COS #16: Calculate surface areas and volumes of solid figures, including spheres, cones, and pyramids. Developing formulas for surface area and volume of spheres, cones, and pyramids Calculating specific missing dimensions of solid figures from surface area or volume Determining the relationship between the surface areas of similar figures and volumes of similar figures COS #17: Analyze sets of data from geometric contexts to determine what, if any, relationships exist. Example: Collect data and create a scatterplot comparing the perimeter and area of various rectangles. Determine whether a line of best fit can be drawn. Distinguishing between conclusions drawn when using deductive and statistical reasoning Calculating probabilities arising in geometric contexts Example: finding the probability of hitting a particular ring on a dart board whose rings are formed by equally spaced concentric circles Tallapoosa County Mathematics Guide Geometry Concepts & Applications The objectives to be covered are listed by 9-weeks and should be covered during the four grading periods. You are also provided with a suggested sequencing of the objectives per term but you may choose to reorder them as long as you cover the stated objectives during the indicated quarter. The benchmark tests that will be administered at the end of each 9-weeks grading period will reflect the objectives listed for each term. TEXTBOOK: Glencoe – Geometry (Incorporate the IMP units: “Shadows” and “Bees Do It Best” whenever possible. Refer to the TEAM-Math Curriculum Guide for the incorporation of the IMP units.) 1st 9-Weeks COS #1, #2, #9, #11, #12, #17 Chapter(s) 1, 2, 3, 4, 6 & 15 nd 2 9-Weeks COS #3, #5, #6, #7, #8, #9, #10 Chapter(s) 5, 6, 7, 9, 13 rd 3 9-Weeks COS #3, #4, #5, #13, #15, #18 Chapter(s) 8, 10, 11, 14, 16 th 4 9-weeks COS #11, #14, #15, #16, #17 Chapter(s) 11, 12, & 15 SUGGESTED PACING GUIDE Approximate time frame for instruction: Begin 1st 9-weeks grading period. Chapter 1: Sections 1-5 Chapter 2: Sections 1-5 Chapter 6: Sections 6-7 Chapter 3: Sections 1-7 Chapter 4: Sections 1-6 Chapter 15: Sections 1-5 st End 1 9-weeks grading period. Begin 2nd 9-weeks grading period. Chapter 5: Sections 1-6 Chapter 6: Sections 1-5 Chapter 7: Sections 1-4 Chapter 9: Sections 1-7 Chapter 13: Sections 1-5 nd End 2 9-weeks grading period. Begin 3rd 9-weeks grading period. Chapter 8: Sections 1-5 Chapter 16: Sections 3-6 Chapter 10: Sections 1-2 Chapter 11: Sections 1-3 Chapter 14: Sections 1-5 End 3rd 9-weeks grading period. Begin 4th 9-weeks grading period Chapter 11: Sections 4-6 Chapter 12: Sections 1-7 Chapter 15: Section 6 Chapter 16: Sections 1-2 th End 4 9-weeks grading period 1.5 weeks 1 week .5 week (in conjunction with chapter 2) 2 weeks 1.5 weeks 1.5 weeks 2 weeks 1.5 weeks 1 week 1.5 weeks 2 weeks 1.5 weeks 1 week (in conjunction with Chapter 8) .5 week (in conjunction with Chapter 8) 1.5 weeks 2 weeks 1 week 3 weeks 1 week 1 week Tallapoosa County Sequencing Guide Geometry: Concepts and Applications 1st 9-Weeks UNIT 1: Fundamentals of Geometry – Lines, Angle, and Logic - Chapters 1, 2, 3, 4, 6 & 15 TOPIC: 1) Use inductive and deductive reasoning to analyze information (Chapter 1: Sections 1, 4) 2) Understand undefined terms of geometry – point, line, plane (Chapter 1: Sections 2-3) 3) Demonstrate competency with measurement tools – ruler, protractor, compass (Chapter 1: Section 5) 4) Apply distance, midpoint, and slope formulas connecting to the Pythagorean Theorem (Chapter 2: Sections 1-5; Chapter 6: Sections 6-7 ) 5) Identify angle relationships and justify theorems related to pairs of angles (Chapter 3: Sections 1-6, Chapter 4: Sections 1-4) 6) Introduction to coordinate geometry through perimeter of polygons (Chapter 1: Section 6) 7) Using methods of proof to justify theorems and to analyze information (Chapter 1: Sections 1-6, Chapter 15: Sections 1-5) 8) Determine equations of parallel and perpendicular lines (Chapter 3: Section 7, Chapter 4: Sections 5 & 6) 9) Apply equations to geometric problems (Chapter 3) COS #1: Determine the equation of a line parallel or perpendicular to a second line through a given point. COS #2: Justify theorems related to pairs of angles, including angles formed by parallel and perpendicular lines, vertical angles, adjacent angles, complementary angles, and supplementary angles. COS #9: Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions. Recognizing the limitations of justifying a conclusion through inductive reasoning COS # 11: Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. COS #12: Apply distance, midpoint, and slope formulas to solve problems and to confirm properties of polygons. Examples: finding the area of a rectangle given the coordinates of its vertices, showing that the median of a trapezoid is half the sum of the bases. COS #17: Analyze sets of data from geometric contexts to determine what, if any, relationships exist. Tallapoosa County Sequencing Guide Geometry: Concepts and Applications Example: Collect data and create a scatterplot comparing the perimeter and area of various rectangles. Determine whether a line of best fit can be drawn. Distinguishing between conclusions drawn when using deductive and statistical reasoning Calculating probabilities arising in geometric contexts Example: finding the probability of hitting a particular ring on a dart board whose rings are formed by equally spaced concentric circles 2nd 9-Weeks UNIT 2: Triangles – Classification, Congruency, Similarity, and Trigonometry – Chapters 5, 6, 7, 9, & 13 TOPIC: 1) Classify types of triangles (Chapter 5: Section 1) 2) Apply angle properties of triangles (Chapter 5: Section 2) 3) Prove triangles are congruent and us properties of congruency to find missing measures (CPCTC) (Chapter 5: Sections 4, 5, & 6) 4) Utilize the properties of isosceles and equilateral triangles to determine missing measures (Chapter 6: Section 4) 5) Identify special segments of triangles, their intersections and their measurement properties (Chapter 6: Sections 1-3) 6) Apply triangle inequalities and other inequalities to geometric problems (Chapter 7: Sections 1-4) 7) Apply properties of similar triangles including use of scale factors and proportions (Chapter 9: Sections 1-7) 8) Determine geometric mean to find missing lengths in right triangles (Chapter 9: Section 2) 9) Apply Pythagorean theorem, special right triangle rules, and other operations involving radicals to find missing lengths of sides (Chapter 6: Sections 5 & 6; Chapter 13: Sections 2 & 3) 10) Apply right triangle definitions of sine, cosine and tangent to find missing measures (Chapter 13: Sections 4 & 5) 11) Apply factoring and use of polynomials in problem solving applications (Chapters 5-7 & 9) COS #3: Verify the relationships among different classes of polygons by using their properties Example: showing that a square has all the properties of both a rectangle and a rhombus Determining the missing lengths of sides or measures of angles in similar polygons COS #5: Solve real-life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes. Tallapoosa County Sequencing Guide Geometry: Concepts and Applications Example: finding the center of a solid wooden wheel using the perpendicular bisectors of two chords Determining the equation of a circle given its center and radius COS #6: Apply the Pythagorean Theorem to solve application problems, expressing answers in simplified radical form or as decimal approximations, using Pythagorean triples when applicable. COS #7: Use the ratios of the sides of special right triangles to find lengths of missing sides. Deriving the ratios of the sides of 30-60-90 and 45-45-90 triangles COS #8: Deduce relationships between two triangles, including proving congruence or similarity of the triangles from given information, using the relationships to solve problems and to establish other relationships. Determining the geometric mean to find missing lengths in right triangles COS #9: Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions. Recognizing the limitations of justifying a conclusion through inductive reasoning COS #10: Find the missing measures of sides and angles in right triangles by applying the right triangle definitions of sine, cosine, and tangent. 3rd 9-Weeks UNIT 3: Geometric Figures – Quadrilaterals, Transformations and Circles (Chapters 8, 10, 11, 14 & 16) TOPIC: 1) Determine the measures of interior and exterior angles associated with polygons and verify the formulas (Chapter 8: Section 1, Chapter 10: Sections 1-2) 2) Identify quadrilaterals from verbal descriptions of properties and apply the properties of these quadrilaterals (Chapter 8: Sections 2 – 5) 3) Understand and analyze properties of transformations and apply the coordinate geometry of transformations (Chapter 8, Chapter 16: Sections 3-6) 4) Understand and apply properties of circles including arcs, chords, secants, tangents, and angles related to circles (Chapter 11: Sections 1-3, Chapter 14: Sections 1-5) 5) Real life applications related to circles, quadrilaterals and other geometric shapes (Chapters 8, 10 & 14) Tallapoosa County Sequencing Guide Geometry: Concepts and Applications 6) Construct with precision a circle graph representing given data (Chapter 11 & Chapter 14) 7) Determine the equation of a circle (Chapter 14: Section 6) COS #3: Verify the relationships among different classes of polygons by using their properties. Example: showing that a square has all the properties of both a rectangle and a rhombus Determining the missing lengths of sides or measures of angles in similar polygons COS #4: Determine the measure of interior and exterior angles associated with polygons. Verifying the formulas for the measures of interior and exterior angles of polygons inductively and deductively COS #5: Solve real-life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes. Example: finding the center of a solid wooden wheel using the perpendicular bisectors of two chords Determining the equation of a circle given its center and radius COS #13: Identify the coordinates of the vertices of the image of a given polygon that is translated, rotated, reflected, or dilated. Example: rotating a triangle a given number of degrees around a specific point, comparing the vertices of the image and preimage COS #15: Calculate measures of arcs and sectors of a circle from given information. Examples: finding the area of a sector given its arc length and radius, finding the arc length of a sector given its area and radius, finding the area or arc length given the measure of the central angle and the radius COS #18: Construct with precision a circle graph to represent data from given tables or classroom experiments. 4th 9-Weeks UNIT 4: Area and Volume – Area of Polygons and Circles, Surface Area and Volume of 3-D Figures (Chapters 11, 12, & 15) TOPIC: 1) Area of polygons, circles and irregular figures (Chapter 11: Sections 5 & 6, Chapter 12: Section 1) 2) Calculate measures of sectors of a circle (Chapter 11: Section 6) 3) Calculate probabilities arising in geometric contexts (Chapter 15: Sections 1-2) Tallapoosa County Sequencing Guide Geometry: Concepts and Applications 4) Classify polyhedra according to their properties (Chapter 12: Section 1) 5) Surface Area of Solid Figures (Cylinders, Spheres, Cones, Pyramids): develop formulas, calculate values, find missing dimensions (Chapter 12: Section 2, 4, 6) 6) Volume of Solid Figures (Cylinders, Spheres, Cones, Pyramids): develop formulas, calculate values, find missing dimensions (Chapter 12: Section 3, 5, 6) 7) Determine relationships between surface area and volume of similar figures (Chapter 12: Section 7) 8) Apply geometric properties and relationships in solving multi-step problems in two and three dimensions (Chapters 11, 12, & 15) COS #11: Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. COS #14: Classify polyhedrons according to their properties, including the number of faces. Example: identifying a polyhedron having 6 vertices and 12 edges Identifying Euclidean solids COS #15: Calculate measures of arcs and sectors of a circle from given information. Examples: finding the area of a sector given its arc length and radius, finding the arc length of a sector given its area and radius, finding the area or arc length given the measure of the central angle and the radius COS #16: Calculate surface areas and volumes of solid figures, including spheres, cones, and pyramids. Developing formulas for surface area and volume of spheres, cones, and pyramids Calculating specific missing dimensions of solid figures from surface area or volume Determining the relationship between the surface areas of similar figures and volumes of similar figures COS #17: Analyze sets of data from geometric contexts to determine what, if any, relationships exist. Example: Collect data and create a scatterplot comparing the perimeter and area of various rectangles. Determine whether a line of best fit can be drawn. Distinguishing between conclusions drawn when using deductive and statistical reasoning Calculating probabilities arising in geometric contexts Example: finding the probability of hitting a particular ring on a dart board whose rings are formed by equally spaced concentric circles.