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Westmoreland County Public Schools
High School Curriculum
Geometry Units - Right Triangle Relationships

Geometry
Congruency/Similarity: Triangles/Proofs
The learner will be able to prove the congruence of triangles using different proof formats (G.5.b).
Bloom's Scope Activities
  Master Classroom
  Unit Instructional Resources
 
· Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
· Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]
  Unit Assessment Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
  
Logic: Deductive Arguments
The learner will be able to incorporate definitions, postulates, theorems, and logical reasoning techniques to develop deductive arguments in paragraph form, flow chart form, or formal proofs to solve real-world scenario problems and classroom problems. (G.1.d).
Bloom's Scope Activities
  Master Classroom
  Unit Instructional Resources
 
· Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
· Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]
  Unit Assessment Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
  
Triangles: Relationships
The learner will be able to solve real-world problems by applying the relationships found within 30-60-90 and 45-45-90 triangles (G.7).
Bloom's Scope Activities
Application Master Classroom
  Unit Instructional Resources
 
· Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
· Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]
  Unit Assessment Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
  
Pythagorean Theorem: Apply
The learner will be able to use the Pythagorean theorem, and the theorem's converse, to solve real-world scenario problems involving right triangles (G.7).
Bloom's Scope Activities
Application Master Classroom
  Unit Instructional Resources
 
· Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
· Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]
  Unit Assessment Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
  
Proofs: Angle Measures Theorem
The learner will be able to compose formal proofs where theorems related to angle measures of triangles are applied (G.5.b).
Bloom's Scope Activities
Synthesis Master Classroom
  Unit Instructional Resources
 
· Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
· Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]
  Unit Assessment Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
  
Congruency: SAS/ASA
The learner will be able to determine side - angle - side (SAS), angle - side - angle (ASA), hypotenuse-leg (HL), LL, HA, or LA congruence in triangles using the angle sum property for triangles and the Pythagorean theorem (G.5. a, b).
Bloom's Scope Activities
Comprehension Master Classroom
  Unit Instructional Resources
 
· Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
· Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]
  Unit Assessment Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
  
Right Triangles: Geometric Mean
The learner will be able to use the properties of right triangles to obtain problem solutions using geometric mean. (G.5; G.7).
Bloom's Scope Activities
Application Master Classroom
  Unit Instructional Resources
 
· Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
· Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]
  Unit Assessment Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
  
Right Triangles: Solve Using Trig
The learner will be able to use the properties of right triangles to obtain problem solutions using definitions of sine, cosine, and tangent. (G.5; G.7).
Bloom's Scope Activities
Application Master Classroom
  Unit Instructional Resources
 
· Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
· Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]
  Unit Assessment Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
  
Constructions and Proofs
The learner will be able to identify, construct, and incorporate in to proofs the four special constructions (angle bisectors, perpendicular bisectors, median, and altitude).
Bloom's Scope Activities
Knowledge, Comprehension, Application, Analysis Master Classroom
  Unit Instructional Resources
 
· Compasses/Protractors, N/A, N/A, Math Office [Manipulative]
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
· Sup. Star T. Geometry (1-4), The Teaching Company, 1994, Library Resource Room [Software]
  Unit Assessment Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· MIRA's, N/A, N/A, Math Office [Manipulative]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
· Overhead Manipulative Kit, N/A, N/A, Math Office [Manipulative]
  
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Technology
Calculator: Approximations
The learner will be able to apply approximations suitably in computations made with calculators and identify errors occurring as a result (G.7; G.13).
Bloom's Scope Activities
  Master Classroom
  Unit Instructional Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
  Unit Assessment Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
  
Geometry: Congruency/Similarity
The learner will be able to use computers to solve problems with congruent triangles (G.5.a).
Bloom's Scope Activities
Comprehension Master Classroom
  Unit Instructional Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
  Unit Assessment Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
  
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Trigonometry
Triangles: Solving Right
The learner will be able to find the measure of each unknown side (to the nearest tenth or hundredth) or angle (to the nearest degree), solve real-world trigonometry problems, and include the angle of depression or elevation in calculations (G.7).
Bloom's Scope Activities
Application Master Classroom
  Unit Instructional Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
  Unit Assessment Resources
 
· Glencoe Geometry: Integration, Applications, Connections, McGraw Hill, 1998, Classroom [Textbook]
· Math Dept. Resource Book - Geometry, N/A, N/A, Classroom [Resource Notebook]
· TI-83 Graphing Calculators, Texas Instrument, N/A, Classroom [Calculator]
· TI-92 Graphing Calculator, Texas Instrument, N/A, Math Office [Calculator]
· Skills Connection, EdVision, 2001, Classroom - Computer [Tests]
· Boxer Trigonometry, Boxer Learning, 1995, Math Office [Software]
· Intelligent Tutor: Geometry, Intelligent Software, Inc., Unknown, Math Office [Software]
  
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