Geometry Pacing Guide Lynchburg City Schools

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1 Grading Period: 1 st Nine Weeks Total Days to Teach = 44 days SOL & Enabling Objectives: Description Text Recommended Activities Time Frame Begin the school year with relationship building activities continue integrating relationship building throughout the school year Activity Ideas PRE-TEST (for Teacher Evaluation & School Improvement: Interactive Achievement) will be released by the division to be administered at a time TBA Begin teaching the 3 rd day of school. DO NOT FEEL BOUND TO THE TEXT BOOK! PLEASE USE ONLINE RESOURCES, APPLETS, & HANDS-ON ACTIVITIES Basics of Geometry Prereq. Understand basic definitions, algebra review (p.24) G.4a Construct & justify the construction of: -a line segment congruent to a given line segment 1-2, 1-3, 1-4, p Video: Thinking About Geometry Part 1 Section A (2-53) Video: Points, Lines, Planes, and Space (Part 1 Section B) (6-38) ESS G.4a Constructions = 16 days 7 days

2 -perpendicular bisector of a line segment -bisector of a given angle -angle congruent to a given angle Constructions G.3f Apply the distance formula to find the length of a line segment when given the coordinates of the endpoints. (Show using the Pythagorean Theorem) 1-6, 7-2 ESS G.3af Distance & Midpoint Formulas Distance Formula Applet G.3a Find the coordinates of the midpoint of a segment, using the midpoint formula 1-6 Video Disc Math: Pt 01 Ex 1: The Cart Coord. Sys (2-23) Video Discovering Math: Pt. 1 Ex 3: Dist. And Mid DC (2-54) Reasoning and Proofs G.1a Identify the converse, inverse, & contrapositive of a condition statement. 2-1, 2-3, 5-4 ESS G.1ab Inductive & Deductive Reasoning Venn Diagram Worksheet = 16 days G.1g Interpret Venn diagrams. G.1c Determine the validity of a logical argument. G.1h Recognize & use the symbols of formal logic, which include 2-1, , 2-2, Supp. 5-4 ESS G.1a-h Logic & Conditional Statements Logic and Truth Value Intersection Union

3 G.1f Use Venn diagrams to represent relationships, such as intersection & union. G.1d Use valid forms of deductive reasoning, including the law of syllogism, the law of contrapositive, the law of detachment, & counterexamples. G.1e Select & use various types of reasoning & methods of proof as appropriate. 2-3, , 2-5 Sets and the Venn Diagram Reasoning Video: Many-sided World, Prog 1: Postulates & Theorems (6-37) Illuminations Lesson Pieces of Proof Illuminations Lesson Venn Diagrams & Logic 4 days Angle Relationships Prereq. Vertical, supplementary, complementary anlges. 2-5 Introduction to Angles Angle Classification Complementary Angles Supplementary Angles Vertical Angles Video: Many-Sided World of Geo: Prog 1: Pt 2 angles (5-20) = Parallel & Perpendicular Lines ESS G.2ab Lines & Angles

4 G.2abc Use algebraic & coordinate methods as well as deductive proofs to verify whether 2 lines are parallel. 3-1, 3-2 Interactive Lines and Angles Parallel Lines = 7 days 4 days Solve problems by using the relationships between pairs of angles formed by the intersection of 2 parallel lines & a transversal including corresponding angles, alternate interior angles, alternate exterior angles, & same-side (consecutive) interior angles. G.10a Solve real-world problems involving the measures of interior & exterior angles of polygons (specifically triangles). 3-3 Angle Sum: Theorem Exterior Angle Sum Theorem Interior Angle sum Theorem Interior angle Sum Proof ESS G.10bcd Angles in Polygons ESS G.3bc Slope Flex days/remediation Grading Period: 2 nd Nine Weeks Total Days to Teach = 45 days SOL & Enabling Objective: Description Text Recommended Activities Time Frame Parallel & Perpendicular Line (cont d)

5 G.10a Solve real-world problems involving the measures of interior and exterior angles of polygons (all other polygons) 3-4 Slope = 7 days G.10c Find the sum of the measures of the interior and exterior angles of a convex polygon. 3-4 Parallel & Perpendicular Line Applet G.10d Find the measure of each interior and exterior angle of a regular polygon. 3-4 G.10e Find the number of sides of a regular polygon, given the measures of interior or exterior angles of the polygon. p. 151 G.3b Use a formula to find the slope of a line. G.3c Compare the slopes to determine whether 2 lines are parallel, perpendicular, or neither. 3-6 Constructions G.4a Construct & justify the construction of: -perpendicular to a given line from a point not on 3-7 ESS G.4a Constructions =

6 the line. -perpendicular to a given line at a point on the line. -line parallel to a given line thru a point not on the given line. Constructions G.4b Construct an equilateral triangle, a square, & a regular hexagon inscribed in a circle. Supp. Constructions Congruent Triangles Prereq. Understand concepts of congruent figures. 4-1 Video Many-sided world, Prog 2: triangles (pt 3, sec A (9-35) = 6 days G.6a Use definitions, postulates, & theorems to prove triangles congruent. G.6c Use algebraic methods to prove 2 triangles are congruent. 4-2, 4-3, 4-5, ESS G.6a Congruent Triangles SSS Congruence ASA Congruence AAS Congruence SAS Congruence G.6b Use coordinate methods, such as distance formula & the slope formula to prove 2 triangles are congruent. 4-5 Puzzle Proofs CPCTC Triangle Inequalities Coordinate Proofs

7 G.5abcde Order the sides of a triangle by their lengths when given the measures of the angles. Order the angles of a triangle by their measures when given the lengths of the sides. 5-1 to ESS G.5abcd How many triangles Triangle Inequalities Inequalities in Triangles = 5 days 5 days Given the lengths of 3 segments, determine whether a triangle could be formed. Given the length of 2 sides of a triangle, determine the range in which the length of the 3 rd side must lie. Solve the real-world problems given information about the lengths of sides &/or measures of angles in triangles. Quadrilaterlas G.9a Solve problems, including real-world problems, using the properties specific to parallelograms, rectangles, rhombi, squares, isosceles trapezoids, & trapezoids. G.9b Prove that quadrilaterals have specific properties, using coordinate & algebraic Introduction to Quadrilaterals Parallelogram Properties Square Properties Rectangles Properties = 15 days 1s 4 days

8 methods, such as the distance formula, slope, & midpoint formula. Geometry Pacing Guide EXAM WEEK Exams Exam Review and Exams Powerpoint: Jeopardy Geometry 1 st Semester Exam Review = 5 days 5 days Flex days/remediation: 4 days Grading Period: 3 rd Nine Weeks Total Days to Teach = 48 days SOL & Enabling Objective: Description Text Recommended Activities Time Frame Quadrilaterals (continued) G.9c Prove the characteristics of quadrilaterals, using deductive reasoning, algebraic, & coordinate methods. 6-7 Rhombus Properties Trapezoid Properties = 4 days 4 days

9 Illuminations lesson Diagonals to Quadrilaterals Square Properties Lesson Diagonals of Quadrilaterals ESS G.9bc Properties of Quadrilaterals Coordinate Properties of Quadrilaterals Coordinate Properties of Quadrilaterals Similarity Prereq. Solve for variables within proportions. G.7a Use definitions, postulates, & theorems to prove triangles similar. G.7b Use algebraic methods to prove that triangles are similar. G.7c Use coordinate methods, such as distance formula, to prove 2 triangles are similar , , , 8-4 Video Project Mathematics: Similarity: Similar Triangles (4.48) ESS G.7abc Similar Triangles Similar Triangle Proofs = 1s

10 Pythagorean Theorem & Special Right Triangles G.8e Solve real-world problems, using right triangle trig & properties of right triangles. G.8a Determine whether a triangle formed w/3 given lengths is a right triangle. G.8b Solve for missing lengths in geometric figures, using properties of degree triangles. 7-2, Pythagorean Theorem Pythagorean Theorem Lesson Plans ESS G.8a Pythagorean Relationship Video Project: Mathematics: Pythagorean Theorem (2-35) Pythagorean Theorem Proof = 4 days G.8c Solve for missing lengths in geometric figures using properties of degree triangles. ESS G.8bcd Special Rt Triangles & right Triangle Trig Video Many Sided World of Geometry Program 5: The Pythagorean Thm. (pt 2 sec C) Right Triangle Trigonometry G.8d Solve problems involving right triangles, using sine, cosine, and tangent ratios. 9-1, 9-2, 9-3 ESS G.8bcd Special Rt. Triangles & right Triangle Trig. = 7 days 4 days

11 G.8f Explain & use the relationship between the sine & cosine of complementary angles. G.8e Solve real-world problems, using right triangle trig & properties of right triangles. Supp. 9-1, 9-2, 9-3 Trig. Ratio Applet. Right Triangle Solver Video: Discovering Math: Part 2, Right Triangle Trigonometry (10-07) Trig Real World Problems Trig Project Idea Video: Discovering Math: Part 2: Using Trig Ratio apps. (9-17) Trigonometry Lesson Circles Prereq. Determine area and circumference of a circle. 1-7 Video Project Mathematics: Pi Through the ages (4-14) = 19 days G.11a Find the lengths, angle measures, & arc measures associated with: central angles G.11b Calculate the area of a sector & length of an 7-6, 7-7 ESS G.11a Angles, Arcs & Segments in Circles 4 days

12 arc of a circle, using proportions. G.11c Solve real-world problems associated with circles, using properties of angles, lines, & arcs. G.11acd Find the lengths, angle measures, & arc measures associated with: -2 intersecting chords -2 intersecting secants 11-1, 11-2, 11-3, 11-4 Illuminations Lesson Pi Line Illuminations 3 Circles Lesson Central vs Inscribed Angles Inscribed Angles Applet Pi, Circumference, & Diameter 8 days -intersecting secant & tangent -2 intersecting tangents -inscribed angles -Solve real-world problems associated with circles, using properties of angles, lines, & arcs. -Verify properties of circles, using deductive reasoning algebraic, & coordinate methods. G.9d Prove properties of angles for a quadrilateral inscribed in a circle. G.12abcdef Identify the center, radius, & diameter of a circle from a given standard equation (7-2) Chord Perpendicular to Diameter Intersecting Chords Intersecting Secants Intersecting Tangents Intersecting Tangent & secant Intersecting secants Intersecting Tangents Intersecting Tangent & Secant Use the distance formula to find the radius Quadrilateral Proof 4 days

13 of a circle. Given the coordinates of the center & radius of the circle, identify a point on the circle. Given the equation of a circle in standard form, identify the coordinates of the center & find the radius of the circle. Given the coordinates of the endpoints of a diameter, find the equation of the circle. Given the coordinates of the center & a point on the circle, find the equation of the circle. Quadrilateral Inscribed Applet Circle Equation: Tutorial Circle Equation Applet Circle equation Applet 2 Recognize that the equation of a circle of given center & radius is derived using the Pythagorean Theorem. Flex days/remediation Grading Period: 4 th Nine Weeks Total Days to Teach = 4 SOL & Enabling Objective: Description Text Recommended Activities Time Frame Constructions

14 G.4c Construct the inscribed & circumscribed circles of a triangle. Supp. Constructions = G.4d Construct a tangent line from a point outside of a given circle to the circle. Surface Area, Lateral Area, Volume Prereq Find the area of triangles and parallelograms G.13a Find the total surface area of cylinders, prisms, pyramids, cones, & spheres, using the appropriate formulas. G.13b Calculate the volume of cylinders, prisms, pyramids, cones, & sphere using the appropriate formulas. G.13c Solve problems including real-world problems involving total surface area & volume of cylinders, prisms, pyramids, cones & spheres as well as combinations of 3D figures. 7.1, 7.2-4, 7.7, 10-3, 10-4, , 10-6, , 10-4, 10-5, 10-6, 10-7 Triangle Area Parallelogram Area ESS G.13abc Surface Area & Volume Surface Area and volume Introduction Surface Area & Volume Surface Area of Prisms Project Interactive SA Rectangular Prism Lesson Surface Area of Rectangular Prisms Investigating Volume = 10 days Surface Area & Volume

15 Project Interactive Activity Surface Area & Volume Volume of Rectangular Prisms Proportional Reasoning G.14abcd Compare the ratios between side lengths, perimeters, areas, & volumes, given 2 similar figures. Describe how changes in 1 or more dimensions affect other derived measures (perimeter, area, total surface area, & volume) of an object. Describe how changes in 1 or more measures (perimeter, area, total surface area, & volume) affect other measures of an object. Solve real-world problems involving measured attributes of similar objects. Surface Area & Volume of Combined solids 10-8, 8-6 ESS G.14ad Similar Solids & Proportional Reasoning Proportions of Area & Volume Applet Video Project Mathematics Similarity Perimeter, Areas, Volumes, & Recap (4:00) = Symmetry & Transformations ESS G.3d Symmetry

16 G.3d Determine whether a figure has point symmetry, line symmetry, both, or neither. G.3e Given an image & preimage, identify the transformation that has taken place as a reflection, rotation, dilation, or translation. Tessellations G.10b Identify tessellations in art, construction, & nature , 12-3, 12-7, Symmetry Activities ESS G.3e Transformations Transformation Applet Translations, Reflections, Rotations Rotations Reflections Translations Composition of Transformations Geometry in Tessellations ESS G.10cd Angles in Polygons Tessellations Applet Tessellations.org Visual Patterns in Tessellations = 4 days = POST-TEST (for Teacher Evaluation & School Improvement use same test as PRE-TEST) SOL Review (before ANY SOL testing begins): 14 days Expedited Retakes Exam Review Exams 8 days Recommended Websites for additional lesson plans, activities, virtual manipulatives, and applets:

17 Illuminations NCTM Suffolk Geometry Resources Jefferson Lab SOL Review Project Interactive Henrico Math resources National Library of Virtual Manipulatives NLVM Texas Instrument Activities Geometry: Math Crosswalk 2001 and 2009 SOLs The length of the test has increased from 45 items to 50 items. Changed to the reporting categories for the Geometry SOL test: Now there are 3 reporting categories instead of 5. Lines & angles, Logic, and Coordinate Relations & Transformations have been combined into one reporting category called: Reasoning, Lines & Transformations. Triangles & Logic has become Triangles. The 2001 Triangles & Logic reporting category as been split with the Logic content moving to the new Reasoning, Lines, & Transformations reporting category. As a result, the percentages shown in the table mask the fact that the Triangles standards are now more heavily-weighted, while the Reasoning, Lines, & Transformations standards are less heavily-weighted

18 o For example, suppose that of the 12 questions in the 2001 Triangles & Logic category, 3 of them typically addressed Logic standards and 9 of them addressed Triangles standards; that would mean that the Triangles standards comprised 9/45 = 20% on the 2001 SOL test, compared with 14/50 = 28% of the new 2009 SOL test Similarly, the relative weight of each standard in the new Reasoning, Lines, & Transformations reporting category has been diluted by the inclusion of the Logic standards in this category. Polygons & Circles and Three-Dimensional Figures have been combined into one reporting category/strand. The Geometry formula sheet has been revised. Reporting Category Reasoning, Lines, & Transformations Triangles Polygons, Circles, & Three- Dimensional Figures SOL # items % of test # items % of test G.1a-d, G.2 a-c, G.3a-d, G.4a-g G.5a-d, G.6, G.7, G.8 G.9, G.10, G.11a-c, G.12, G.13, G.14ad % 18 36% % 14 28% % 18 36

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