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2 Discovering Geometry Curiculum Map 2010-2011      
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4       
5 Chapter 0 Geometric Art     
6 Section Description PE # Performance Expectation Lesson Notes Time (Days) 
7 0.1 Geometry in Nature and Art G.5.DDescribe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.    
8 0.2 Line Designs G.5.D Describe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.    
9 0.3 Circle Designs G.3.I G.5.DExplain and perform constructions related to the circle. Describe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.   
10 0.4 Op Art G.5.D Describe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.    
11 0.5 Knot Designs G.5.D Describe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.    
12 0.6 Islamic Tile Designs     
13     Total days with assessments 0 
14 Essential Understandings:   All components of unit zero are   
15    covered in subsequent chapters. It is   
16    recommended to begin at unit 1 and return to    
17    unit zero later in the semester if time   
18    allows.   
19       
20 Chapter 1 Introducing Geometry     
21 Section Description PE # Performance Expectation Lesson Notes Time (Days) 
22 1.1 Building Blocks of Geometry G.7.E Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics.  2 
23  Algebra Skils 1: Midpoint G.4.B Determine the coordinates of a point that is described geometrically.  0.5 
24 1.2 Poolroom Math G.7.E Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics. Emphasize how to use a protractor 0.5 
25 1.3 What's a Widget? G.1.E G.7.C Identify errors or gaps in a mathematical argument and develop counterexamples to refute invalid statements about geometric relationships. Evaluate a solution for reasonableness, verify it's accuracy, and interpret the solution in the context of the original problem.   2 
26 1.4 Polygons    1 
27 1.5 Triangles and Special Quadrilaterals G.1.E Identify errors or gaps in a mathematical argument and develop counterexamples to refute invalid statements about geometric relationships. second day could include a quiz 2 
28 1.6 Circles    1 
29 1.7 A Picture is Worth a 1000 Words G.7.B Select and apply strategies to solve problems.  1 
30 1.8 Space Geometry G.2.D G.3.K Describe the intersections of lines in the plane and in space, of lines and planes, and of planes and planes. Analyze cross sections of cubes, prisms, pyramids, and spheres and identify the resulting shapes.   1 
31     Total instructional days 11 
32 Essential Understandings:   Vocabulary, symbols and notation Review and assess 3 
33     Total days 14 
34     Estimated finish date Sept. 30 
35       
36       
37 Chapter 2 Reasoning in Geometry     
38 Section Description PE # Performance Expectation Lesson Notes Time (Days) 
39 2.1 Inductive Reasoning G.1.B G.7.B G.7.D G.7.HUse inductive reasoning to make conjectures, to test the plausibility of a geometric statement, and to help find a counter example. Select and apply strategies to solve problems. Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems. Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.   1 
40 2.2 Deductive Reasoning G.1.A G.1 C Distinguish between deductive and inductive reasoning. Use deductive reasoning to prove that a valid geometric statement is true.  1 
41 2.3 Finding the nth term G.7.A G.7.B G.7.E Analyze a problem situation and represent it mathematically. Select and apply strategis to solve problems. Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics.  1 
42 2.4 Mathematical Modeling G.7.A G.7.B G.7.HAnalyze a problem situation and represent it mathematically. Select and apply strategis to solve problems. Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.   0 
43 2.5 Angle Relationships G.1.A G.1 C G.2.B G.7.HDistinguish between deductive and inductive reasoning. Use deductive reasoning to prove that a valid geometric statement is true. Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal. Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.   1 
44 2.6 Special Angles on Parallel Lines G.1.A G.1.B G.2.A G.2.B G.7 EDistinguish between deductive and inductive reasoning. Use inductive reasoning to make conjectures, to test the plausibility of a geometric statement, and to help find a counter example. Know, prove, and apply theorems about parallel and perpendicular lines. Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal. Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics.  2 
45  Using Algebra Skills: Slope    1 
46     Total instructional days 7 
47 Essential Understandings:   Distinguish between inductive and deductive Review and assess 3 
48    reasoning. Angle relationships and vocabulary Total days 10 
49     Estimated finish date Oct.15 
50       
51       
52 Chapter 3 Using Tools of Geometry     
53 Section Description PE # Performance Expectation Lesson Notes Time (Days) 
54 3.1 Duplicating Segments and angles   How can we utilize technology in this chapter? (Sketchpad) 1 
55 3.2 Constructing Perpendicular Bisectors G.2.CExplain and perform basic compass and straight edge constructions related to parallel and perpendicular lines.   1 
56 3.3 Constructing Perpendiculars to a Line G.2.CExplain and perform basic compass and straight edge constructions related to parallel and perpendicular lines.   2 
57 3.4 Constructing Angle Bisectors    1 
58 3.5 Constructing Parallel Lines G.2.CExplain and perform basic compass and straight edge constructions related to parallel and perpendicular lines.   1 
59  Algebra Skills 3: Slopes of Parallel and Perpendicular Lines G.4.CVerify and apply properties of triangles and quadrilaterals in the coordinate plane.  2 
60 3.6 Construction Problems    0 
61 3.7 Constructing Points of Concurrency G.3.A G.3.IKnow, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle. Explain and perform constructions related to the circle.   2 
62 3.8 The Centroid G.3.A Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle.   1 
63   Exploration: the Euler Line G.3.A Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle.   0 
64     Total instructional days 11 
65 Essential Understandings:   Students should be able to understand Review and assess 3 
66    and perform all basic constructions. Total days 14 
67    Understand slope of parallel and Estimated finish date Nov. 3 
68    perpendicular lines.   
69       
70       
71 Chapter 4 Discovering and Proving Triangle Properties     
72 Section Description PE # Performance Expectation Lesson Notes Time (Days) 
73 4.1 Triangle Sum Conjecture G.1.B G.3.A G.6.E G.7.CUse inductive reasoning to make conjectures, to test the plausibility of a geometric statement, and to help find a counter example. Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle. Use different degrees of precision in measurement, explain the reason for using a certain degree of precision, and apply estimation strategies to obtain reasonable measurements with appropriate precision for a given purpose. Evaluate a solution for reasonableness, verify it's accuracy, and interpret the solution in the context of the original problem.  1 
74 4.2 Properties of Special Triangles G.1.D G 2.B G.3.A G.7.DWrite the converse, inverse, and contrapositive of a valid proposition and determine their validity. Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal. Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle. Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems.  1 
75  Algebra Skills 4: Writing Linear Equations G.4.A Determine the equation of a line in the coordinate plane that is described geometrically, including a line through two given points, a line through a given point parallel to a given line, and a line through a given point perpendicular to a given line.  1 
76 4.3 Triangle Inequalities G.3.AKnow, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle.  1 
77 4.4 Congruence Shortcuts (SSS,SAS) G.3.B Determine and prove triangle congruence, triangle similarity, and other properties of triangles. See 13.1 Can we work formal proof in here? 1 
78 4.5 Other Congruence Shortcuts (ASA) G.3.B Determine and prove triangle congruence, triangle similarity, and other properties of triangles.  1 
79 4.6 Corresponding Parts of Congruent Triangles G.2.D G.3.B G.7.B Describe the intersections of lines in the plane and in space, of lines and planes, and of planes and planes. Determine and prove triangle congruence, triangle similarity, and other properties of triangles. Select and apply strategis to solve problems.  1 
80 4.7 Flowchart Thinking G.1.C G.7.G G.7.H Use deductive reasoning to prove that a valid geometric statement is true. Synthesize information to draw conclusions and evaluate the arguments and conclusions of others. Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures. See 13.2 1.5 
81 4.8 Proving Isosceles Triangle Conjectures G.1.C G.3.A G.7.HUse deductive reasoning to prove that a valid geometric statement is true. Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle. Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures. See 13.3 1.5 
82     Total instructional days 10 
83 Essential Understandings:   Understand basic properties of triangles. Review and assess 3 
84    Determine and prove trinagle congruence Total days 13 
85     Estimated finish date 24-Nov 
86       
87       
88       
89 Chapter 5 Discovering and Proving Polygon Properties     
90 Section Description PE # Performance Expectation Lesson Notes Time (Days) 
91 5.1 Polygon Sum Conjecture G.3.G G.7 HKnow, prove, and apply theorems about properties of quadrilaterals and other polygons. Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.   1 
92 5.2 Exterior Angles of a Polygon G.1.B G.2.B G.3.G G.7.DUse inductive reasoning to make conjectures, to test the plausibility of a geometric statement, and to help find a counter example. Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal. Know, prove, and apply theorems about properties of quadrilaterals and other polygons. Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems.  1 
93  Exploration: Star Polygons G.2.B Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal.  0 
94 5.3 Kite and Trapezoid Properties G.3.G Know, prove, and apply theorems about properties of quadrilaterals and other polygons.  2 
95 5.4 Properties of Midsegments G.3.A G.3.G G.4.B G.4.CKnow, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle. Know, prove, and apply theorems about properties of quadrilaterals and other polygons. Determine the coordinates of a point that is described geometrically. Verify and apply properties of triangles and quadrilaterals in the coordinate plane.   2 
96 5.5 Properties of Parallelograms G.2.A G.3.FKnow, prove, and apply theorems about parallel and perpendicular lines. Know, prove and apply basic theorems about parallelograms. Introduce Vectors 1 
97  Algebra Skills 5: Solving Systems of Linear Equations G.4.A G.4 B G.7.A G.7.E Determine the equation of a line in the coordinate plane that is described geometrically, including a line through two given points, a line through a given point parallel to a given line, and a line through a given point perpendicular to a given line. Determine the coordinates of a point that is described geometrically. Analyze a problem situation and represent it mathematically. Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics  2 
98 5.6 Properties of Special Parallelograms G.2.A G.3.F G.4.B Know, prove, and apply theorems about parallel and perpendicular lines. Know, prove and apply basic theorems about parallelograms. Determine the coordinates of a point that is described geometrically  1 
99 5.7 Proving Quadrilateral Properties G.1.C G.2.A G.3.F G.7.B Use deductive reasoning to prove that a valid geometric statement is true. Know, prove, and apply theorems about parallel and perpendicular lines. Know, prove and apply basic theorems about parallelograms. Select and apply strategies to solve problems. See 13.4 2 
100     Total instructional days 12 
101 Essential Understandings:   Understand basic properties of quadrilaterals Review and assess 3 
102    Proving properties of quadrilaterals Total days 15 
103     Estimated finish date 17-Dec 
104       
105       
106 Chapter 6 Discovering and Proving Circle Properties     
107 Section Description PE # Performance Expectation Lesson Notes Time (Days) 
108 6.1 Chord Properties G.3.H G.3.IKnow, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles. Explain and perform constructions related to the circle.  2 
109 6.2 Tangent Properties G.3.H G.3.IKnow, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles. Explain and perform constructions related to the circle.  1 
110 6.3 Arcs and Angles G.1.B G.3.H G.7.DUse inductive reasoning to make conjectures, to test the plausibility of a geometric statement, and to help find a counter example. Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles. Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems  2 
111 6.4 Proving Circle Conjectures G.1.C G.3.H G.7.HUse deductive reasoning to prove that a valid geometric statement is true. Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles. Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures. 2nd day can include a quiz 2 
112  Algebra Skills 6: Finding the Circumcenter G.4.A Determine the equation of a line in the coordinate plane that is described geometrically, including a line through two given points, a line through a given point parallel to a given line, and a line through a given point perpendicular to a given line.  0 
113 6.5 The Circumference/Diameter Ratio G.3.H G.6.E Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles. Use different degrees of precision in measurement, explain the reason for using a certain degree of precision, and apply estimation strategies to obtain reasonable measurements with appropriate precision for a given purpose. Make sure students know how to express answer in terms of pi 1 
114 6.6 Around the World    1 
115 6.7 Arc Length G.6.ADerive and apply formulas for arc length and area of a sector of a circle.  1 
116     Total instructional days 10 
117 Essential Understandings:   Understand basic properties of circles. Review and assess 3 
118    Vocabulary Total days 13 
119     Estimated finish date 20-Jan 
120    Unit 6 should conclude semester 1. You should have appox. 6 days for review and finals at this pace   
121       
122       
123 Chapter 7 Transformations and Tessellations     
124 Section Description PE # Performance Expectation Lesson Notes Time (Days) 
125 7.1 Transformations and Symmetry G.5.A G.5.B G.5.D Sketch results of transformations and compositions of transformations for a given two-dimensional figure on the coordinate plane, and describe the rule(s) for performing translations or for performing reflections about the coordinate axis or the line y=x. Determine and apply properties of transformations. Describe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.   1 
126 7.2 Properties of Isometries G.5.A G.5.B G.5.D Sketch results of transformations and compositions of transformations for a given two-dimensional figure on the coordinate plane, and describe the rule(s) for performing translations or for performing reflections about the coordinate axis or the line y=x. Determine and apply properties of transformations. Describe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.   1 
127 7.3 Compositions of Transformations G.5.A G.5.B G.5.C G.5.D Sketch results of transformations and compositions of transformations for a given two-dimensional figure on the coordinate plane, and describe the rule(s) for performing translations or for performing reflections about the coordinate axis or the line y=x. Determine and apply properties of transformations. Given two congruent or similar figures in a coordinate plane, describe a composition of translations, relections, rotations and dilations that superimpose one figure on the other. Describe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.   1 
128 7.4 Tessellations with Regular Polygons G.3.G G.5.B Know, prove, and apply theorems about properties of quadrilaterals and other polygons. Determine and apply properties of transformations.   0 
129 7.5 Tessellations With Non-Regular Polygons G.3.G G.5.B Know, prove, and apply theorems about properties of quadrilaterals and other polygons. Determine and apply properties of transformations.   0 
130 7.6 Tessellations Using Only Translations G.5.B Determine and apply properties of transformations.   0 
131 7.7 Tessellations That Use Rotations G.5.B Determine and apply properties of transformations.   0 
132 7.8 Tessellations That Use Glide-Reflections G.5.B Determine and apply properties of transformations.   0 
133  Algebra skills 7: Finding the Orthocenter and Centroid G.4.A G.4.B G.4.C Determine the equation of a line in the coordinate plane that is described geometrically, including a line through two given points, a line through a given point parallel to a given line, and a line through a given point perpendicular to a given line. Determine the coordinates of a point that is described geometrically. Verify and apply properties of triangles and quadrilaterals in the coordinate plane   
134     Total instructional days 3 
135 Essential Understandings:   Understand and apply the basic transformations Review and assess 3 
136    of translation, rotation and reflection Total days 6 
137    See section 11.1 for dilation Estimated finish date 9-Feb 
138       
139       
140       
141 Chapter 8 Area     
142 Section Description PE # Performance Expectation Lesson Notes Time (Days) 
143 8.1 Areas of Rectangles and Parallelograms    1 
144 8.2 Areas of Triangles, Trapezoids and Kites    1 
145 8.3 Area Problems    1 
146 8.4 Areas of Regular Polygons    1 
147  Exploration: Picks Formula G.7.D Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems.   0 
148 8.5 Areas of Circles    1 
149 8.6 Any Way You Slice It G.6.ADerive and apply formulas for arc length and area of a sector of a circle.  2 
150 8.7 Surface Area G.6.C Apply formulas for surface area and volume of three-dimensional figures to solve problems  2 
151     Total instructional days 9 
152 Essential Understandings:   Understand and apply formula's for area, Review and assess 3 
153    arc length, area of a sector of a circle, Total days 12 
154    surface area of three-dimensional figures Estimated finish date 3-Mar 
155       
156       
157       
158 Chapter 9 The Pythagorean Theorem     
159 Section Description PE # Performance Expectation Lesson Notes Time (Days) 
160  Using Your Algebra Skills 8: Radical Expressions Page 473   Spend two days on simplifying radical expressions prior to beginning unit 9. Show students what it meand to rationalize the denominator. 2 
161 9.1 The Theorem of Pythagoras G.1.C G.3.D G.7.FUse deductive reasoning to prove that a valid geometric statement is true. Know, prove, and apply the Pythagorean Theorem and its converse. Summarize mathematical ideas with precision and efficiency for a given audience and purpose. Apply beyond a basic right triangle. (How to find the diagonal in a box) 1 
162 9.2 The Converse of the Pythagorean Theorem G.1.B G.1.D G.3.DUse inductive reasoning to make conjectures, to test the plausibility of a geometric statement, and to help find a counter example. Write the converse, inverse, and contrapositive of a valid proposition and determine their validity. Know, prove, and apply the Pythagorean Theorem and its converse.  1 
163 9.3 Two Special Right Triangles G.1.B G.3.CUse inductive reasoning to make conjectures, to test the plausibility of a geometric statement, and to help find a counter example. Use properties of special right triangles (30-60-90 and 45-45-90) to solve problems  2 
164 9.4 Story Problems G.3.D Know, prove, and apply the Pythagorean Theorem and its converse.  1 
165 9.5 Distance in Coordinate Geometry G.3.D G.4.D G.7.DKnow, prove, and apply the Pythagorean Theorem and its converse. Determine the equation of a circle that is described geometrically in the coordinate plane and, given equations for a circle and a line, determine the coordinates of their intersection(s). Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems.   1 
166 9.6 Circles and the Pythagorean Theorem G.3.C G.3.DUse properties of special right triangles (30-60-90 and 45-45-90) to solve problems. Know, prove, and apply the Pythagorean Theorem and its converse  0 
167     Total instructional days 8 
168 Essential Understandings:   Know and apply the Pythagorean Thm and its Review and assess 3 
169    Converse. Understand and apply properties of Total days 11 
170    30-60 and 45-45 right triangles. Solve problems Estimated finish date 21-Mar 
171    using these properties.   
172       
173 Chapter 10 Volume     
174 Section Description PE # Performance Expectation Lesson Notes Time (Days) 
175 10.1 Geometry of Solids G.3.J G.7.E Describe prisms, pyramids, parallelepipeds, tetrahedra, and regular polyhedra in terms of their faces, edges, vertices, and properties. Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics.  1 
176  Exploration: Eulers Formulas for Polyhedrons G.3.J Describe prisms, pyramids, parallelepipeds, tetrahedra, and regular polyhedra in terms of their faces, edges, vertices, and properties.  0 
177 10.2 Volume of Prisms and Cylinders G.6.C Apply formulas for surface area and volume of three-dimensional figures to solve problems  1 
178 10.3 Volumes of Pyramids and Cones G.6.C Apply formulas for surface area and volume of three-dimensional figures to solve problems  1 
179  Exploration: 5 Platonic Solids G.3.J Describe prisms, pyramids, parallelepipeds, tetrahedra, and regular polyhedra in terms of their faces, edges, vertices, and properties. This section is optional. It can be done if time permits. 2-3 days may be needed. 0 
180 10.4 Volume Problems G.6.C Apply formulas for surface area and volume of three-dimensional figures to solve problems  1 
181 10.5 Displacement and Density G.6.C Apply formulas for surface area and volume of three-dimensional figures to solve problems  1 
182 10.6 Volume of a Sphere G.6.C Apply formulas for surface area and volume of three-dimensional figures to solve problems  1.5 
183 10.7 Surface Area of a Sphere G.6.C Apply formulas for surface area and volume of three-dimensional figures to solve problems  1.5 
184     Total instructional days 8 
185 Essential Understandings:   Understand and apply formulas Review and assess 3 
186    for surface area and volume of Total days 11 
187    three-dimensional figures Estimated finish date 18-Apr 
188       
189       
190       
191 Chapter 11 Similarity      
192 Section Description PE # Performance Expectation Lesson Notes Time (Days) 
193  Using Your Algebra Skills 9: Proportion and Reasoning    1 
194 11.1 Similar Polygons    1 
195 11.2 Similar Triangles G.3.B Determine and prove triangle congruence, triangle similarity, and other properties of triangles.  1 
196 11.3 Indirect Measurement with Similar Triangles    1 
197 11.4 Corresponding Parts of Similar Triangles G.3.B G.7.FDetermine and prove triangle congruence, triangle similarity, and other properties of triangles. Summarize mathematical ideas with precision and efficiency for a given audience and purpose. See section 13.7 1.5 
198 11.5 Proportions with Area and Volume G.6.DPredict and verify the effect that changing one, two or three linear dimensions has on perimeter, area, volume,or surface area of two-and three-dimensional figures.  1.5 
199 11.6 Proportional Segments Between Parallel Lines    0 
200  Exploration: Two More forms of Valid Reasoning G.1.D Write the converse, inverse, and contrapositive of a valid proposition and determine their validity.  0 
201     Total instructional days 7 
202 Essential Understandings:   Understand and apply properties of Review and assess 3 
203    similar triangles. Understand how the Total days 10 
204    proportion between area and volume Estimated finish date 3-May 
205    change as a linear measurement    
206    changes   
207       
208 Chapter 12 Trigonometry     
209 Section Description PE # Performance Expectation Lesson Notes Time (Days) 
210 12.1 Trigonometric Ratios G.3.E G.6.E Solve problems involving the basic trigonometric ratios of sine, cosine and tangent. Use different degrees of precision in measurement, explain the reason for using a certain degree of precision, and apply estimation strategies to obtain reasonable measurements with appropriate precision for a given purpose.  3 
211 12.2 Problem Solving with Right triangles G.3.E G.7.A Solve problems involving the basic trigonometric ratios of sine, cosine and tangent. Analyze a problem situation and represent it mathematically.   3 
212 12.3 The Law of Sines   Spend time a desired  
213 12.4 The Law of Cosines   Spend time a desired  
214 12.5 Problem Solving with Trigonometry   Spend time a desired  
215     Total instructional days 6 
216 Essential Understandings:   Understand basic definitions of sine, Review and assess 2 
217    cosine, tangent ratio's. Solve problems Total days 8 
218    involving basic sine, cosine, tangent Estimated finish date 16-May 
219    ratios.   
220       
221    Complete portions of unit 13 that were   
222    not incorporated along the way.    
223       
224    Options for use of any extra time:   
225    Prep for Geom EOC exam   
226    Prep for teacher generated final   
227    Review essential algebra skills to prep   
228    students for Algebra II (systems of eq,   
229    quadratics, radicals,….)   
230       
231 Chapter 13 Geometry as a Mathematical System     
232 Section Description PE # Performance Expectation Lesson Notes Time (Days) 
233 13.1 The Premises of Geometry G.1.C G.1.F G.7.EUse deductive reasoning to prove that a valid geometric statement is true. Distinguish between definitions and undefined geometric terms and explain the role of definitions, undefined terms, postulates (axioms), and theorems. Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics. As time permits  
234 13.2 Planning a Geometry Proof G.1.C G.1.F G.2.A G.2.B G.7.G G.7.HUse deductive reasoning to prove that a valid geometric statement is true. Distinguish between definitions and undefined geometric terms and explain the role of definitions, undefined terms, postulates (axioms), and theorems. Know, prove, and apply theorems about parallel and perpendicular lines. Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal. Synthesize information to draw conclusions and evaluate the arguments and conclusions of others. Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures. As time permits  
235 13.3 Triangle Proofs G.1.C G.1.F G.3.A G.3.B G.7.HUse deductive reasoning to prove that a valid geometric statement is true. Distinguish between definitions and undefined geometric terms and explain the role of definitions, undefined terms, postulates (axioms), and theorems. Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle. Determine and prove triangle congruence, triangle similarity, and other properties of triangles. Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures. As time permits  
236 13.4 Quadrilateral Proofs G.3.F G.3.G Know, prove and apply basic theorems about parallelograms. Know, prove, and apply theorems about properties of quadrilaterals and other polygons. As time permits  
237 13.5 Indirect Proof   As time permits  
238 13.6 Circle Proofs G.1.F G.3.HDistinguish between definitions and undefined geometric terms and explain the role of definitions, undefined terms, postulates (axioms), and theorems. Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles. As time permits  
239 13.7 Similarity Proofs G.1.F G.3.BDistinguish between definitions and undefined geometric terms and explain the role of definitions, undefined terms, postulates (axioms), and theorems. Determine and prove triangle congruence, triangle similarity, and other properties of triangles. As time permits  
240  Algebra skills 10: Coordinate Proof G.4.CVerify and apply properties of triangles and quadrilaterals in the coordinate plane. As time permits  
241  Exploration: Non-Eulcidean Geometries G.6.B Analyze distance and angle measures on a sphere and apply these measurements to the geometry of the earth.   
242     Total instructional days  
243 Essential Understandings:    Review and assess  
244     Total days  
245     Estimated finish date  

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