Modern Geometry Honors Williamsport Area School District Mathematics Grade: 10 Course Title: Modern Geometry Honors Unit Unit Title Page Geometric Definitions Duration (Days) 12 1 2 Angles and Parallel Lines 14 7 3 12 13 4 Equations of Parallel and Perpendicular Lines Triangles 14 17 5 Logic and Reasoning 16 22 6 19 26 7 Right Triangles and Similarity Circles 19 32 8 Quadrilaterals 14 39 9 Measuring in Space 12 45 10 Geometric Probability 12 50 1 Page 1 Modern Geometry Honors Williamsport Area School District Unit 1: Geometric Definitions Big Idea: Days: 12 Plane Geometry can be derived from three undefined terms. Unit Essential Question: How are the three undefined terms used to establish definitions in geometry? Concept Concept Title 1.1 Points, Lines, and Planes Duration (Days) 1 1.2 Segments, Rays, and Parallel Lines 3 1.3 Measuring Segments 2 1.4 Simplifying Radical Expressions 2 1.5 Coordinate Plane (Distance and Midpoint) 4 Page 2 Modern Geometry Honors Concept 1.1 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Points, Lines, and Planes 2.5.11.A, 2.5.11.B What are the basic building blocks of geometry? Geometry, point, space, line, collinear, plane, coplanar, theorem, postulate Learning Goals: Descriptor 1.1.A Identify and model points, lines, and planes. 1.1.B Identify collinear and coplanar points and intersecting lines and planes in space. Resources: Glencoe Geometry: 1-1 Assessment Sources: Daily Assignments Eligible Content NA Days NA 0.5 0.5 Notes: Page 3 Modern Geometry Honors Williamsport Area School District Concept 1.2 Segments, Rays, and Parallel Lines Lesson Essential Question(s): 2.3.11.A, 2.5.11.B, 2.9.11.A, M11.B.2.11 What is the difference between a line, a ray and a line segment? What is the difference between parallel, intersecting, and skew lines (and planes)? Vocabulary: Segment, ray, opposite rays, parallel lines, skew lines, parallel planes Learning Goals: Descriptor Eligible Content NA Days 1.2.A Identify the relationships between two lines and two planes. 1.2.B Identify and name segments, rays, lines, and planes. NA 0.5 1.2.C Formulate statements about segments, lines, and planes. NA 0.5 Resources: Glencoe Geometry: 3-1 Assessment Sources: Daily Assignments Notes: Additional Day for Quiz 1 Page 4 Modern Geometry Honors Williamsport Area School District Concept 1.3 Measuring Segments Lesson Essential Question(s): 2.3.11.A, 2.5.11.B, 2.5.11.C, 2.8.11.D, 2.8.11. J, 2.9.11.A, 2.9.11.G, M11.C.3.1.1 How is the length of segments used to determine congruency? What is segment addition and how is it used? Vocabulary: Line segment, ray, congruent, segment, addition postulate, midpoint, segment bisector Learning Goals: Descriptor 1.3.A Define segments using two points. 1.3.B Use segment postulates and the midpoint to solve problems. Resources: Glencoe Geometry: 1-3, 2-7 Assessment Sources: Daily Assignments Eligible Content NA Days NA 1 1 Notes: Page 5 Modern Geometry Honors Concept 1.4 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Simplifying Radical Expressions 2.1.11.A, 2.2.11.A, 2.5.11.B, M11.A.1.1.1, M11.A.1.1.3, M11.A.2.2.1, 2.1.A1.A How can we simplify a radical expression? Radical, perfect square, square root, factor Learning Goals: Descriptor 1.4.A Identify perfect squares and perfect square factors. 1.4.B Simplify radical expressions. Eligible Content A1.1.1.1.2 Days 0.5 0.5 Resources: Glencoe Geometry: pages 744-745 Assessment Sources: Daily Assignments A1.1.1.1.2 Notes: Page 6 Modern Geometry Honors Concept 1.5 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Coordinate Plane (Distance and Midpoint) 2.5.11.B, 2.5.11.C, 2.8.11.D, 2.8.11.J, 2.9.11.B, 2.9.11.G, M11.C.3.1.1, 2.9.G.C What is coordinate geometry? How can the midpoint of a segment be determined on the coordinate plane? How can the distance formula be used to solve problems and prove conjectures? Radical, perfect square, square root, factor Learning Goals: Descriptor 1.5.A Find the distance between two points. Eligible Content G.2.1.2.1 1.5.B Find the midpoint of a segment. G.2.1.2.1 Resources: Glencoe Geometry: 1-3 Assessment Sources: Daily Assignments Notes: Additional 2 Days for Unit Review and Test Days 1 1 Page 7 Modern Geometry Honors Williamsport Area School District Unit 2: Angles and Parallel Lines Days: 16 Big Idea: Find the measure of angles to determine congruency. Unit Essential Question: What are angles and how are they measured, paired and classified? Concept Concept Title 2.1 Measuring Angles Duration (Days) 2 2.2 Special Angle Pairs 3 2.3 Transversals and Angle Pairs 2 2.4 Special Angles and Parallel Lines 4 2.5 Justifying Parallel and Perpendicular Lines 5 Page 8 Modern Geometry Honors Williamsport Area School District Concept 2.1 Measuring Angles Lesson Essential Question(s): 2.3.11.A, 2.3.11.B, 2.5.11.A, 2.5.11.B, M11.B.2.11, 2.3.G.C What are angles, how are they measured, and how are the measures used to determine their congruency? What is angle addition and how is it used? Vocabulary: Angle, vertex, acute, right, obtuse, straight angle, congruent angles, protractor, angle addition postulate Learning Goals: Descriptor 2.1.A Measure and classify angles. 2.1.B Identify and use congruent angles and bisector of an angle. Resources: Glencoe Geometry: 1-4 Assessment Sources: Daily Assignments Eligible Content G.2.2.1.1 Days G.2.2.1.1 1 1 Notes: Page 9 Modern Geometry Honors Concept 2.2 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Special Angle Pairs 2.3.11.A, 2.3.11.B, 2.5.11.B, 2.9.11.A, M11.B.2.1.1, 2.3.G.C How are pairs of angles classified? Adjacent angles, vertical angle theorem, complementary angle theorem, supplementary angle theorem, linear pair, angle bisector Learning Goals: Descriptor 2.2.A Identify and use special angle pairs. Eligible Content G.2.2.1.1 2.2.B Use the properties of an angle bisector. G.2.2.1.1 Resources: Glencoe Geometry: 1-5 Assessment Sources: Daily Assignments, Quiz Notes: Add 1 Day for Quiz Days 1 1 Page 10 Modern Geometry Honors Concept 2.3 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Transversals and Angle Pairs 2.5.11.B, 2.3.G.C How do we classify pairs of angles formed by two lines and a transversal? Corresponding angle, alternate-interior angles, alternate-exterior angles, consecutive interior angles, transversal Learning Goals: Descriptor 2.3.A Name angles formed by a pair of lines and a transversal. Resources: Glencoe Geometry: 3-1 Assessment Sources: Daily Assignments Eligible Content G.2.2.1.2 Days 2 Notes: Page 11 Modern Geometry Honors Williamsport Area School District Concept 2.4 Angles and Parallel Lines Lesson Essential Question(s): 2.3.11.A, 2.3.11.B, 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, M11.B.2.1.1, 2.3.G.C When a transversal intersects parallel lines, how do the angles' measures compare? Vocabulary: Corresponding angles postulate, alternate interior angles theorem, consecutive interior angles theorem, alternate exterior angles theorem, perpendicular transversal theorem Learning Goals: Descriptor 2.4.A Use the properties of parallel lines to find congruent sides. 2.4.B Determine angle measures using angle relationships. Resources: Glencoe Geometry: 3-2 Assessment Sources: Daily Assignments, Activity, Quiz Eligible Content G.2.2.1.2 Days G.2.2.1.2 3 1 Notes: Page 12 Modern Geometry Honors Concept 2.5 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Proving Lines Parallel 2.3.11.A, 2.3.11.B, 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, M11.B.2.1.1, 2.4.G.A How can lines be proven parallel? Converse of corresponding angles postulate, converse of alternate exterior angles theorem, converse of consecutive interior angles theorem, converse of alternate interior angle theorem, converse of perpendicular transversal theorem Learning Goals: Descriptor 2.5.A Recognize angle conditions that occur with parallel lines. 2.5.B Prove that two lines are parallel based on given angle relationships. Resources: Glencoe Geometry: 3-5 Assessment Sources: Daily Assignments, Activity Notes: Add 1 day for unit test Eligible Content G.1.3.2.1 Days G.1.3.2.1 2 2 Page 13 Modern Geometry Honors Williamsport Area School District Unit 3: Parallel and Perpendicular Lines Big Idea: Days: 12 Special relationships apply to angles formed by parallel and intersecting lines and planes. Unit Essential Question: How are angles formed by transversals related? Concept Concept Title 3.1 Slopes of Parallel and Perpendicular Lines Duration (Days) 2 3.2 Equations of Parallel and Perpendicular 4 3.3 Systems of Equations and Inequalities 6 Page 14 Modern Geometry Honors Concept 3.1 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Slopes of Parallel and Perpendicular Lines 2.5.11.A, 2.8.11.D, 2.8.11.J, 2.8.11.K, M11.C.3.1.2, M11.D.3.2.1, 2.9.G.C How can slope determine if lines are parallel, perpendicular or neither? Perpendicular, parallel, slope formula, slope-intercept form Learning Goals: Descriptor 3.1.A Find slopes of lines. 3.1.B Use slope to identify parallel and perpendicular lines. Resources: Glencoe Geometry: 3-3 Assessment Sources: Daily Assignments Eligible Content G.2.1.3.1 Days G.2.1.2.2 1 1 Notes: Page 15 Modern Geometry Honors Concept 3.2 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Equations of Parallel and Perpendicular Lines 2.3.11.A, 2.3.11.B, 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, M11.B.2.1.1 2.5.11.A, 2.8.11.D, 2.8.11.J, 2.8.11.K, M11.C.3.1.2, M11.D.3.2.1, 2.9.G.C, 2.1.A1.F, 2.8.A1.E, 2.8.A1.F What is the difference between equations of parallel and perpendicular lines? Point-slope form Learning Goals: Descriptor 3.2.A Write an equation of a line given information about its graph. 3.2.B Find the equation of a line that is parallel or perpendicular to a given line that passes through a given point. Resources: Glencoe Geometry: 3-4 Assessment Sources: Daily Assignments, Quiz Eligible Content A1.1.2.1.1 Days G.2.1.2.2 2 2 Notes: Page 16 Modern Geometry Honors Concept 3.3 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Systems of Equations and Inequalities 2.2.11.F, 2.4.11.E, 2.5.11.A, 2.5.11.B, 2.5.11.C, 2.5.11.D, 2.8.11.D, 2.8.11.F, 2.8.11.G, 2.8.11.H, 2.8.11.J, 2.8.11.K, 2.8.11.L, 2.8.11.N, 2.9.11.I, M11.C.3.1.1, M11.C.3.1.2, M11.D.4.1.1, M11.D.2.1.1, M11.D.2.1.2, M11.D.2.1.3, M11.D.2.1.4, 2.8.G.B, 2.8.A1.E, 2.8.A1.F How can systems of linear equations and inequalities be solved? How do systems of equations and inequalities model real life situations? How can systems of equations and inequalities help solve geometry problems? Point of intersection, consistent, inconsistent, dependent, independent, parallel, perpendicular, coinciding lines, substitution, elimination, linear combination, feasible region Learning Goals: Descriptor Eligible Content A1.1.3.2.1 Days 3.3.A Graph systems of equations and inequalities. 3.3.B Solve systems of equations. A1.1.2.2.1 1 3.3.C Use systems of equations and inequalities to solve coordinate geometry problems. G.2.1.4.1 2 Resources: Glencoe Geometry: p. 742-743 Assessment Sources: Daily Assignments, Activity Notes: Additional 2 Days for Unit Review and Test 1 Page 17 Modern Geometry Honors Williamsport Area School District Unit 4: Triangles Days: 14 The classification and properties of triangles can be determined by their distinct characteristics. Big Idea: Unit Essential Question: What special properties exist for each type of triangle? How can congruency be determined? Concept Concept Title 4.1 Classify Triangles Duration (Days) 2 4.2 Angles of Triangles 5 4.3 Isosceles and Equilateral Triangles 3 4.4 Congruent Triangles 4 Page 18 Modern Geometry Honors Williamsport Area School District Concept 4.1 Classify Triangles Lesson Essential Question(s): 2.5.11.B, M11.B.2.1.1, M11.C.1.2.3, 2.9.G.A What are the different types of triangles based on side and angle measure? How can the existence of a triangle be determined? What is the correlation between the longest side and the largest angle? Vocabulary: Acute, right, obtuse, straight, scalene, isosceles, equilateral, equiangular, regular, triangle inequality Learning Goals: Descriptor 4.1.A Identify and classify triangles by angles. Eligible Content G.1.2.1.1 4.1.B Identify and classify triangles by sides. G.1.2.1.1 Resources: Glencoe Geometry: 4-1 Assessment Sources: Daily Assignments Days 1 1 Notes: Page 19 Modern Geometry Honors Williamsport Area School District Concept 4.2 Angles of Triangles Lesson Essential Question(s): 2.4.11.A, 2.4.11.B, 2.5.11.B, M11.B.2.1.1, 2.9.G.A What are the interior and exterior angle sums of a triangle? What is the relationship between an exterior angle of a triangle and its remote interior angles? Vocabulary: Interior angle sum, remote interior angles, exterior angle, exterior angle sum Learning Goals: Descriptor 4.2.A Apply the angle sum theorem. Eligible Content G.1.2.1.1 4.2.B Apply the exterior angle theorem. G.1.2.1.1 Resources: Glencoe Geometry: 4-2 Assessment Sources: Daily Assignments Notes: Additional Day for Quiz Days 2 2 Page 20 Modern Geometry Honors Concept 4.3 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Isosceles and Equilateral Triangles M11.C.1.2.3, 2.9.G.A What properties are unique to isosceles and equilateral triangles? Isosceles, isosceles triangle theorem, converse of isosceles triangle theorem, equilangular Learning Goals: Descriptor 4.3.A Use properties of isosceles triangles. Eligible Content G.1.2.1.3 4.3.B Use properties of equilateral triangles. G.1.2.1.3 Resources: Glencoe Geometry: 4-6 Assessment Sources: Daily Assignments Days 2 1 Notes: Page 21 Modern Geometry Honors Williamsport Area School District Concept 4.4 Congruent Triangles Lesson Essential Question(s): 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, 2.9.11.B, 2.9.11.D, M11.C.1.2.1, M11.C.1.3.1, 2.9.G.A, 2.9.G.B How can we identify corresponding parts of congruent triangles? What relationships exist between corresponding parts of congruent triangles? Vocabulary: Congruent triangles, corresponding angles, corresponding sides, corresponding parts of congruent triangles are congruent (CPCTC) Learning Goals: Descriptor 4.4.A Name and label corresponding parts of congruent triangles. Resources: Glencoe Geometry: 4-3 Assessment Sources: Daily Assignments, Quiz Notes: Additional 2 days for Review and Test Eligible Content G.1.3.1.1 Days 2 Page 22 Modern Geometry Honors Williamsport Area School District Unit 5: Logic and Reasoning Big Idea: Days: 16 Spatial reasoning and visualization are ways to orient thinking about the physical world. Unit Essential Question: What strategies can we use to draw conclusions in geometry? Concept Concept Title 5.1 Reasoning Duration (Days) 3 5.2 Introduction to Proofs 5 5.3 Proving Triangles Congruent 8 Page 23 Modern Geometry Honors Concept 5.1 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Reasoning 2.3.11.A, 2.3.11.B, 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.4.11.D, 2.5.11.B, M11.B.2.1.1 How do conditional statements support geometric reasoning? What is the difference between inductive and deductive reasoning? What strategies can we use to draw conclusions in geometry? Conjecture, inductive reasoning, counterexample, deductive reasoning, conditional/if-then statement, hypothesis, conclusion, converse, inverse, contra-positive, bi-conditional Learning Goals: Descriptor Eligible Content NA Days 5.1.A Make conjectures based on inductive reasoning. 5.1.B Find counterexamples of conjectures. 2.4.G.A 1 5.1.C Analyze if-then statements and write the converse, inverse, and contra-positive. 2.4.G.B 1 Resources: Glencoe Geometry: 2-1, 2-3, 2-4 Assessment Sources: Daily Assignments Notes: Optional Activities Available 1 Page 24 Modern Geometry Honors Concept 5.2 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Introduction to Proofs 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, 2.5.11.C, 2.5.11.D, M11.B.2.1.1, 2.4.G.A What are proofs? How do you construct a proof? Conjecture, inductive reasoning, counterexample, deductive reasoning, conditional/if-then statement, hypothesis, conclusion, converse, inverse, contra-positive, bi-conditional Learning Goals: Descriptor 5.2.A Write two-column algebraic and geometric proofs. 5.2.B Use properties of equality in geometry proofs. Resources: Glencoe Geometry: 2-5, 2-6 Assessment Sources: Daily Assignments Notes: Quiz Eligible Content G.1.3.2.1 Days G.1.3.2.1 2 2 Page 25 Modern Geometry Honors Concept 5.3 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Proving Triangles Congruent 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, 2.9.11.B, 2.9.11.D, M11.C.1.2.1, M11.C.1.3.1, 2.9.G.B, 2.4.G.A What are the ways to prove triangles congruent? SSS, SAS, ASA AAS, & HL Learning Goals: Descriptor Eligible Content G.1.3.1.1 Days 5.3.A Use the SSS and SAS Postulates to test for triangle congruence. 5.3.B Use the ASA Postulate and AAS Theorem to test for triangle congruence. G.1.3.2.1 2 5.3.C Use the HL Postulate to test for triangle congruence. G.1.3.2.1 2 Resources: Glencoe Geometry: 4-4 and 4-5 Assessment Sources: Daily Assignments, Quiz Notes: Additional 2 Days for Unit Review and Test 2 Page 26 Modern Geometry Honors Williamsport Area School District Unit 6: Right Triangles and Similarity Big Idea: Days: 19 Right triangles and similar figures have a broad range of relationships that lead to many applications and uses. Unit Essential Questions: What are the different methods that can be used to solve right triangles? How can similar figures be used to find missing lengths and angle measures? Concept Concept Title 6.1 Pythagorean Theorem Duration (Days) 3 6.2 Triangles 45, 45, 90 1 6.3 Triangles 30, 60, 90 3 6.4 Similar Figures 4 6.5 Right Triangle Trigonometry 6 6.6 Law of Sines 1 6.7 Law of Cosines 1 Page 27 Modern Geometry Honors Williamsport Area School District Concept 6.1 Pythagorean Theorem Lesson Essential Question(s): 2.2.11.A, 2.5.11.B, M11.A.1.1.3, M11.A.2.2.1, 2.1.11.A, 2.4.11.B, 2.4.11.C, 2.10.11.B, M11.A.1.1.1, M11.C.1.2.1, M11.C.1.4.1, 2.10.G.A How would we simplify a radical expression? How and when can the Pythagorean Theorem be used to find a missing side length? How can the converse of the Pythagorean Theorem be used to determine the type of triangle? Vocabulary: Radical, perfect square, square root, legs, hypotenuse, Pythagorean triple Learning Goals: Descriptor Eligible Content G.2.1.1.1 Days 6.1.A Simplify radical expressions. 6.1.B Find the missing side of a right triangle using the Pythagorean Theorem. G.2.1.1.1 0.5 6.1.C Determine whether a triangle is a right triangle. G.2.1.1.1 1 Resources: Glencoe Geometry: 7-2 Assessment Sources: Daily Assignments, Quiz Notes: Additional Day for Quiz 0.5 Page 28 Modern Geometry Honors Williamsport Area School District Concept 6.2 Triangles 45, 45, 90 Lesson Essential Question(s): 2.1.11.A, 2.10.11.B, M11.A.1.1.3, M11.A.2.1.3, M11.A.2.2.1, M11.C.1.2.1, M11.C.1.2.3, 2.10.G.A How do we determine the ratios of the sides in a 45, 45, 90 special right triangle? Vocabulary: 45, 45, 90 triangle Learning Goals: Descriptor 6.2.A Use properties of a 45, 45, 90 triangle Resources: Glencoe Geometry: 7-3 Assessment Sources: Daily Assignments Notes: Interactive GSP File Available Eligible Content G.2.1.1.1 Days 1 Page 29 Modern Geometry Honors Williamsport Area School District Concept 6.3 Triangles 30, 60, 90 Lesson Essential Question(s): 2.1.11.A, 2.10.11.B, M11.A.1.1.3, M11.A.2.1.3, M11.A.2.2.1, M11.C.1.2.1, M11.C.1.2.3, 2.10.G.A How do we determine the ratios of the sides in a 30, 60, 90 special right triangle? Vocabulary: 30, 60, 90 triangle Learning Goals: Descriptor 6.3.A Use the properties of 30, 60, 90 triangles. Resources: Glencoe Geometry: 7-3 Assessment Sources: Daily Assignments, Quiz Notes: Interactive GSP File Available Additional Day for Quiz Eligible Content G.2.1.1.1 Days 2 Page 30 Modern Geometry Honors Concept 6.4 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Similar Figures 2.5.11.B, M11.A.2.1.3, M11.B.2.1.1, M11.C.1.3.1, 2.2.11.A, 2.5.11.A, M11.A.2.1.2, M11.A.2.1.3, M11.B.2.3.1, M11.C.1.3.1, 2.2.11.A, 2.4.11.E, 2.5.11.A, 2.8.11.D, 2.9.11.I, M11.A.2.1.2, M11.A.2.1.3, M11.C.1.3.1, 2.9.G.B How can figures be identified as similar? How can we find the relationship between similar figures? How do we create and solve proportions to find missing parts of similar figures? Similar, ratio, proportion, scale factor, cross products Learning Goals: Descriptor 6.4.A Identify similar triangles. Eligible Content G.1.3.1.2 6.4.B Solve problems using a scale factor. G.1.3.1.2 1 6.4.C Solve problems using proportions. G.1.3.1.2 2 Resources: Glencoe Geometry: 6-2 Assessment Sources: Daily Assignments Days 1 Notes: Page 31 Modern Geometry Honors Williamsport Area School District Concept 6.5 Right Triangle Trigonometry Lesson Essential Question(s): 2.1.11.A, 2.4.11.E, 2.5.11.A, 2.5.11.B, 2.8.11.D, 2.9.11.I, 2.10.11.B, M11.A.1.1.1, M11.A.1.1.3, M11.A.2.1.3, M11.C.1.2.1, 2.10.G.A What are the trigonometric ratios? How do we use them to solve triangles? How can trigonometric be used to solve real-world problems? Vocabulary: Sine, cosine, tangent, opposite, adjacent, hypotenuse, angle of elevation, angle of depression Learning Goals: Descriptor 6.5.A Find trigonometric ratios using right triangles. 6.5.B Solve problems using trigonometric ratios. Resources: Glencoe Geometry: 7-4 Assessment Sources: Daily Assignments Eligible Content G.2.1.1.2 Days G.2.1.1.2 2 2 Notes: Page 32 Modern Geometry Honors Concept 6.6 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Law of Sines 2.1.11.A, 2.4.11.E, 2.5.11.A, 2.5.11.B, 2.8.11.D, 2.9.11.I, 2.10.11.B, M11.A.1.1.1, M11.A.1.1.3, M11.A.2.1.3, M11.C.1.2.1, 2.10.G.A What is Law of Sines? When is it used? How do we use it to solve triangles? How can trigonometry be used to solve real-world problems? Law of Sines Learning Goals: Descriptor 6.5.A Solve triangles using Law of Sines. Eligible Content G.2.1.1.2 6.5.B Solve problems using Law of Sines. G.2.1.1.2 Resources: Glencoe Geometry: 7-6 Assessment Sources: Daily Assignments Days 1 1 Notes: Page 33 Modern Geometry Honors Williamsport Area School District Concept 6.7 Law of Cosines Lesson Essential Question(s): 2.1.11.A, 2.4.11.E, 2.5.11.A, 2.5.11.B, 2.8.11.D, 2.9.11.I, 2.10.11.B, M11.A.1.1.1, M11.A.1.1.3, M11.A.2.1.3, M11.C.1.2.1, 2.10.G.A What is Law of Cosines? When is it used? How do we use it to solve triangles? How can trigonometry be used to solve real-world problems? Vocabulary: Law of Cosines Learning Goals: Descriptor 6.5.A Solve triangles using Law of Cosines. Eligible Content G.2.1.1.2 6.5.B Solve problems using Law of Cosines. G.2.1.1.2 Resources: Glencoe Geometry: 7-7 Assessment Sources: Daily Assignments Notes: Additional 2 Days for Unit Review and Test Days 1 1 Page 34 Modern Geometry Honors Williamsport Area School District Unit 7: Circles Days: 19 Big Idea: The properties of angles, arcs, chords, tangents and secants can be used to solve problems involving circles. Unit Essential Question: What are the relationships between a circle and its arcs, lines, segments and angles? Concept Concept Title 7.1 Introduction to Circles Duration (Days) 2 7.2 Arcs and Chords 4 7.3 Inscribed Angles 2 7.4 Areas of Circle and Sectors 3 7.5 Tangents of Circles 2 7.6 Secants, Tangents, and Angle Measures 6 Page 35 Modern Geometry Honors Concept 7.1 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Introduction to Circles 2.5.11.B, M11.C.1.1.1, M11.C.1.1.2, 2.9.G.A, 2.11.G.C, 2.3.G.C What are the basic components of a circle? Radius, diameter, chord, circle, circumference, secant Learning Goals: Descriptor 7.1.A Identify and use parts of circles. 7.1.B Solve problems involving circumference of a circle. Resources: Glencoe Geometry: 10-1 Assessment Sources: Daily Assignments Notes: Investigation Available for Discovering Pi Eligible Content G.1.1.1.1 Days G.2.2.2.1 1 1 Page 36 Modern Geometry Honors Williamsport Area School District Concept 7.2 Arcs and Chords Lesson Essential Question(s): 2.9.11.F, M11.C.1.1.2, 2.9.G.A, 2.1.G.C, 2.6.A1.E How do you determine the measure of an arc in a circle? How do you determine the circumference of a circle and/or an arc length? Vocabulary: Arc measure, minor arc, major arc, semicircle, arc, central angle, sum of central angles, arc length Learning Goals: Descriptor Eligible Content G.1.1.1.2 Days 7.2.A Recognize and use relationships between arcs and central angles. 7.2.B Recognize and use relationships between arcs, chords, and diameters. G.1.1.1.3 1 7.2.C Create and analyze pie charts. A1.2.3.2.1 1 Resources: Glencoe Geometry: 10-2, 10-3 Assessment Sources: Activity, Daily Assignments Notes: Add 1 day for quiz 1 Page 37 Modern Geometry Honors Williamsport Area School District Concept 7.3 Inscribed Angles Lesson Essential Question(s): 2.9.11.E, 2.9.11.F, M11.B.2.1.1, M11.C.1.1.2, 2.3.G.C How is the measure of a central angle or an inscribed angle related to the measure of the intercepted arc? Vocabulary: Inscribed angle, inscribed angle theorem, intercepted arc Learning Goals: Descriptor 7.3.A Find measures of inscribed angles. 7.3.B Find measures of angles of inscribed polygons. Resources: Glencoe Geometry: 10-4 Assessment Sources: Daily Assignments Eligible Content G.2.2.2.2 Days G.2.2.2.2 1 1 Notes: Page 38 Modern Geometry Honors Concept 7.4 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Areas of Circles and Sectors 2.2.11.A, 2.9.11.F, M11.C.1.1.1, M11.B.2.3.1, M11.B.2.2.4, M11.C.1.1.2, 2.11.G.C, 2.3.G.C How do you find the area of a circle or a sector? Area, sector Learning Goals: Descriptor 7.4.A Find the area of a circle. Eligible Content G.2.2.2.1 7.4.B Find the area of a sector in a circle. G.2.2.2.5 Resources: Glencoe Geometry: 11-5 Assessment Sources: Daily Assignments, Quiz Notes: Additional Day for Quiz Days 1 1 Page 39 Modern Geometry Honors Williamsport Area School District Concept 7.5 Tangents of Circles Lesson Essential Question(s): 2.9.11.F, M11.C.1.1.1, 2.9.G.A How is the tangent of a circle related to the circle's radius at the point of tangency? Vocabulary: Tangent, point of tangency, circumscribed Learning Goals: Descriptor 7.5.A Use properties of tangents. 7.5.B Solve problems involving circumscribed polygons. Resources: Glencoe Geometry: 10-5 Assessment Sources: Daily Assignments Eligible Content G.1.1.1.1 Days NA 1 1 Notes: Page 40 Modern Geometry Honors Williamsport Area School District Concept 7.6 Secants, Tangents, and Angle Measures Lesson Essential Question(s): 2.9.11.F, M11.C.1.1.1, 2.9.G.A How do you find the measure of angles or segments formed by secants and tangents? Vocabulary: Secant, secant-secant, secant-tangent, tangent-tangent Learning Goals: Descriptor 7.6.A Find measures of angles formed by lines intersecting on or inside the circle. 7.6.B Find measures of angles formed by lines intersecting outside the circle. Resources: Glencoe Geometry: 10-6 Assessment Sources: Daily Assignments Notes: Additional 2 Days for Unit Review and Test Eligible Content G.1.1.1.3 Days G.1.1.1.3 2 2 Page 41 Modern Geometry Honors Williamsport Area School District Unit 8: Quadrilaterals Big Idea: Days: 14 We classify polygons by examining their sides and angles. Unit Essential Question: How can we use the properties of polygons to describe their sides and angles? Concept Concept Title 8.1 Introduction to Quadrilaterals Duration (Days) 2 8.2 Parallelograms 2 8.3 Rectangles 2 8.4 Rhombi and Squares 3 8.5 Trapezoids 5 Page 42 Modern Geometry Honors Concept 8.1 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Introduction to Quadrilaterals 2.5.11.B, 2.5.11.C, M11.C.1.2.2, 2.9.G.A, 2.9.G.C What properties distinguish one quadrilateral from another? Quadrilateral, parallelogram, rectangle, rhombus, square, trapezoid, isosceles trapezoid, kite Learning Goals: Descriptor 8.1.A Classify quadrilaterals. Resources: Glencoe Geometry: 8-1 Assessment Sources: Daily Assignments Eligible Content G.1.2.1.1 G.2.1.2.1 G.2.1.2.2 G.2.1.2.3 Days 2 Notes: Page 43 Modern Geometry Honors Concept 8.2 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Parallelograms 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, 2.5.11.C, 2.9.11.C, M11.C.1.2.2, M11.C.1.3.1, 2.9.G.A, 2.9.G.C What are the properties of parallelograms? Opposite sides, opposite angles, consecutive sides, consecutive angles, diagonals Learning Goals: Descriptor 8.2.A Recognize and apply properties of the sides and angles of parallelograms. 8.2.B Recognize and apply properties of the diagonals of parallelograms. Resources: Glencoe Geometry: 8-2 Assessment Sources: Daily Assignments Eligible Content G.1.2.1.2 Days G.2.1.2.3 1 1 Notes: Page 44 Modern Geometry Honors Concept 8.3 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Rectangles 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, 2.5.11.C, 2.9.11.C, M11.C.1.2.2, 2.9.G.A, 2.9.G.C What are the properties of a rectangle? Rectangle Learning Goals: Descriptor 8.3.A Recognize and apply properties of rectangles. 8.3.B Determine whether parallelograms are rectangles. Resources: Glencoe Geometry: 8-4 Assessment Sources: Daily Assignments Eligible Content G.1.2.1.2 Days G.2.1.2.2 1 1 Notes: Page 45 Modern Geometry Honors Concept 8.4 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Rhombi and Squares 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, 2.5.11.C, 2.9.11.C, M11.C.1.2.2, 2.9.G.A, 2.9.G.C What are the properties of rhombi and squares? Rhombus, square Learning Goals: Descriptor Eligible Content G.1.2.1.2 Days 8.4.A Recognize and apply properties of a rhombus. 8.4.B Recognize and apply properties of a square. G.1.2.1.4 1 8.4.C Determine if a parallelogram is a rhombus or a square. G.1.2.1.4 1 Resources: Glencoe Geometry: 8-5 Assessment Sources: Daily Assignments, Quiz 1 Notes: Page 46 Modern Geometry Honors Williamsport Area School District Concept 8.5 Trapezoids Lesson Essential Question(s): 2.4.11.A, 2.4.11.B, 2.4.11.C, 2.5.11.B, 2.5.11.C, 2.9.11.C, M11.C.1.2.2 Why is a trapezoid not a parallelogram? What are the properties of the median of a trapezoid? Vocabulary: Trapezoid, base, median, base angles, legs, isosceles trapezoid Learning Goals: Descriptor 8.5.A Recognize and apply properties of trapezoids. 8.5.B Determine whether a parallelogram is a trapezoid or isosceles trapezoid. Resources: Glencoe Geometry: 8-6 Assessment Sources: Daily Assignments Notes: GSP Review Activity Available Additional 2 Days for Unit Review and Test Eligible Content G.1.2.1.2 Days G.2.1.2.1 2 1 Page 47 Modern Geometry Honors Williamsport Area School District Unit 9: Measuring in Space Big Idea: Days: 12 Polygons and geometric shapes can be described by the space they occupy. Unit Essential Question How are polygons and geometric shapes measured? What strategies and formulas can be used to find perimeter, area, surface area, lateral area, and volume? Concept Concept Title 9.1 Irregular Shapes Duration (Days) 2 9.2 Rectangular Prisms and Cylinders 3 9.3 Pyramids, Cones, and Spheres 3 9.4 Changing Linear Dimensions 4 Page 48 Modern Geometry Honors Concept 9.1 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Irregular Shapes 2.2.11.A, 2.2.11.B, 2.3.11.A, 2.4.11.E, 2.5.11.A, 2.5.11.B, 2.5.11.C, 2.8.11.D, 2.9.11.I, M11.B.2.2.3, 2.3.G.C, 2.11.G.C How do we find the perimeter and area of an irregular shape? Irregular shape Descriptor 9.1.A Find areas and perimeters of irregular shapes. Resources: Glencoe Geometry: 11-4 Assessment Sources: Daily Assignments Eligible Content G.2.2.2.1 G.2.2.2.2 G.2.2.2.4 Days 2 Notes: Page 49 Modern Geometry Honors Williamsport Area School District Concept 9.2 Rectangular Prisms and Cylinders Lesson Essential Question(s): 2.2.11.E, 2.4.11.E, 2.5.11.A, 2.5.11.B, 2.5.11.C, 2.8.11.D, 2.9.11.I, M11.B.2.2.1, M11.B.2.2.2, 2.3.G.C, 2.9.G.A How is the base of a prism or cylinder used to determine its surface area and volume? Vocabulary: Prism, rectangular prism, cylinder, lateral area, surface area, volume Learning Goals: Descriptor 9.2.A Find the surface area of rectangular prisms and cylinders. 9.2.B Find the volume of rectangular prisms and cylinders. Resources: Glencoe Geometry: 12-3, 13-1 Assessment Sources: Daily Assignments, Activity Eligible Content G.1.1.1.4 G.1.2.1.5 G.2.3.1.1 G.2.3.1.2 G.2.3.1.3 Days 1 2 Notes: Page 50 Modern Geometry Honors Concept 9.3 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Pyramids, Cones, and Spheres 2.2.11.E, 2.4.11.E, 2.5.11.A, 2.5.11.B, 2.5.11.C, 2.5.11.D, 2.8.11.D, 2.9.11.I, M11.B.2.2.1, M11.B.2.2.2, 2.3.G.C, 2.9.G.A How can we find the surface area and volume of pyramids and cones? How do we solve problems involving the surface area and volume of a sphere? Pyramids, slant height, cone, sphere Learning Goals: Descriptor 9.3.A Find the surface area of a pyramid, cone, and sphere. Eligible Content G.1.2.1.5 G.2.3.1.1 9.3.B Find the volume of a pyramid, cone, and sphere. G.2.3.1.2 G.2.3.1.3 Resources: Glencoe Geometry: 12-5, 12-6, 12-7, 13-2, 13-3 Assessment Sources: Daily Assignments Notes: Add 1 day for quiz Days 1 1 Page 51 Modern Geometry Honors Concept 9.4 Lesson Essential Question(s): Vocabulary: Williamsport Area School District Changing Linear Dimensions 2.5.11.A, 2.5.11.C, 2.5.11.D, 2.8.11.D, 2.9.11.I, M11.A.2.1.3, M11.B.2.2.1, M11.B.2.2.2, M11.B.2.2.4, M11.D.3.1.2, 2.3.G.E, 2.1.G.C, 2.9.G.B How does a change in a linear dimension of a figure affect its volume? Linear dimensions, factor Learning Goals: Descriptor 9.4.A Describe how a change in the linear dimension of a figure affects its perimeter, circumference, area, or volume. Resources: PSSA Coach Book: Chapter 2 Assessment Sources: Daily Assignments Notes: Additional 2 Days for Unit Review and Test Eligible Content G.1.3.1.1 G.1.3.1.2 G.2.2.3.1 G.2.3.2.1 Days 2 Page 52 Modern Geometry Honors Williamsport Area School District Unit 10: Geometric Probability Days: 12 We can use of dimensions of geometric figures, combinations, and permutations to find probability and odds. Big Idea: Unit Essential Question: What is the difference between combinations and permutations and how to they relate to probability and odds? Concept Concept Title 10.1 Simple Probability and Odds Duration (Days) 2 10.2 Combinations 4 10.3 Permutations 6 Page 53 Modern Geometry Honors Williamsport Area School District Concept 10.1 Simple Probability and Odds Lesson Essential Question(s): 2.2.11.A, 2.2.11.F, 2.7.11.A, 2.7.11.B, 2.7.11.C, 2.7.11.D, 2.7.11.E, M11.E.3.1.1, M11.E.3.1.2, M11.E.3.2.1, M11.E.4.1.2, 2.7.G.A How do you use probability to predict outcomes? What is the difference between odds and probability? Vocabulary: Probability, odds, sample space, simple event Learning Goals: Descriptor 10.1.A Find the probability that a simple event will occur. 10.1.B Express probability as odds. Eligible Content G.2.2.4.1 Days G.2.2.4.1 1 Resources: Glencoe Geometry: 11-5, PSSA Coach Book: Chapter 5 Assessment Sources: Daily Assignments, Activity 1 Notes: Page 54 Modern Geometry Honors Concept 10.2 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Combinations 2.2.11.A, 2.2.11.F, 2.7.11.A, 2.7.11.B, 2.7.11.C, 2.7.11.D, 2.7.11.E, M11.E.3.1.1, M11.E.3.1.2, M11.E.3.2.1, M11.E.4.1.2, 2.7.G.A When is it relevant to use a combination? Combination, factorial Descriptor 10.2.A Solve counting problems using combinations. 10.2.B Solve probability problems using combinations. Resources: PSSA Coach Book: Chapter 5 Assessment Sources: Daily Assignments, Activity Eligible Content G.2.2.4.1 Days G.2.2.4.1 2 2 Notes: Page 55 Modern Geometry Honors Concept 10.3 Lesson Essential Question(s): Vocabulary: Learning Goals: Williamsport Area School District Permutations 2.2.11.A, 2.2.11.F, 2.7.11.A, 2.7.11.B, 2.7.11.C, 2.7.11.D, 2.7.11.E, M11.E.3.1.1, M11.E.3.1.2, M11.E.3.2.1, M11.E.4.1.2, 2.7.G.A How do you decide when to use a permutation verses a combination? Permutation Descriptor Eligible Content G.2.2.4.1 Days 10.3.B Solve probability problems using permutations. G.2.2.4.1 1 10.3.C Determine whether to use a combination or a permutation. G.2.2.4.1 1 10.3.A Solve counting problems using permutations. Resources: PSSA Coach Book: Chapter 5 Assessment Sources: Daily Assignments, Quiz Notes: Additional 3 Days for Quiz, Unit Review, and Test 1 Page 56 Modern Geometry Honors Williamsport Area School District Additional Information: Use Glencoe Algebra I Test as a reference for algebra review. Attached Documents: Add Course Description: Add Page 57