35
Revised 2006
COURSE: Honors Geometry
GRADE(S): 10h Grade
UNIT 2: Properties of Parallel Lines TIME FRAME: 9 days NATIONAL STANDARDS: 2. ALGEBRA
A. Understand patterns, relations, and functions. B. Represent and analyze mathematical situations and structures using algebraic symbols. C. Use mathematical models to represent and understand quantitative relationships. D. Analyze change in various contexts.
3. GEOMETRY
A. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships .
B. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
C. Apply transformations and use symmetry to analyze mathematical situations. D. Use visualization, spatial reasoning, and geometric modeling to solve problems.
4. MEASUREMENT
A. Understand measurable attributes of objects and the units, systems, and processes of measurement.
B. Apply appropriate techniques, tools, and formulas to determine measurements. 6. PROBLEM SOLVING
A. Build new mathematical knowledge through problem solving. B. Solve problems that arise in mathematics and in other contexts. C. Apply and adapt a variety of appropriate strategies to solve problems. D. Monitor and reflect on the process of mathematical problem solving.
7. REASONING AND PROOF
A. Recognize reasoning and proof as fundamental aspects of mathematics. B. Make and investigate mathematical conjectures. C. Develop and evaluate mathematical arguments and proofs. D. Select and use various types of reasoning and methods of proof.
8. COMMUNICATION
A. Organize and consolidate their mathematical thinking through communication. B. Communicate their mathematical thinking coherently and clearly to peers, teachers, and
others. C. Analyze and evaluate the mathematical thinking and strategies of others. D. Use the language of mathematics to express mathematical ideas precisely.
9. CONNECTIONS
A. Recognize and use connections among mathematical ideas. B. Understand how mathematical ideas interconnect and build on one another to produce a
coherent whole. C. Recognize and apply mathematics in contexts outside of mathematics.
10. REPRESENTATION
A. Create and use representations to organize, record, and communicate mathematical ideas. B. Select, apply, and translate among mathematical representations to solve problems. C. Use representations to model and interpret physical, social, and mathematical phenomena.
Revised 2006
STATE STANDARDS M11.D.2 Represent and/or analyze mathematical situations using numbers, symbols, words, tables and/or graphs M11.C.1.2 Recognize and/or apply properties of angles, triangles and quadrilaterals
UNIT OBJECTIVES:
• To recognize conditional statements and write their converses
• Write biconditional statements • Recognize good definitions • Connect reasoning in algebra and
geometry • Prove and apply theorems about angles
ACTIVITIES: Teacher directed differentiated instructional projects and activities are ongoing and based on student need. “Activity 4: If, then, goto…” “Activity 5: Reasoning From a Table” “Activity 6: Tangrams & Angles” ”Activity 39: Vertical Angles” “Chapter 2 Project: If You Advertise, They Will Buy” “Activity Lab: Mathematical Systems” (p. 101 in text) “Activity Lab: Paper-Folding Constructions” (p. 102 in text) “Activity Lab: The Delicious Side of Division” (pgs. 122-23 in text) Prentice Hall Geometry, 2007: All-in-One Student Workbook Skill and Concept Review Masters Grab & Go Chapter Support Files
ASSESSMENTS: Observation and questioning Presentation and discussions Projects and Investigations Homework Quizzes Tests REMEDIATION: Practice 2-1 and Reteaching 2-1 Conditional Statements Practice 2-2 and Reteaching 2-2 Biconditionals and Definitions Practice 2-3 and Reteaching 2-3 Deductive Reasoning Practice 2-4 and Reteaching 2-4 Reasoning in Algebra Practice 2-5 and Reteaching 2-5 Proving Angles Congruent Prentice Hall Geometry, 2007: Hands-On Activities Skill and Concept Review Masters Online Video Tutor Student EXPRESS MindPoint Quiz Show CD-ROM: End-of-Chapter reviews DIFFERENTIATION: Crytoquiz Kitchen Design Solving Syllogisms Right Angle Spiral Reflect on This Prentice Hall Geometry, 2007: Online Active Math: Built-in interactive explorations MindPoint Quiz Show CD-ROM Enrichment Masters PHSchool.com: Online support for Mathematics Web Codes within the textbook provide access to:
• Vocabulary Quizzes • Chapter Tests
Revised 2006
• Chapter Projects • Math at Work
RESOURCES: Prentice Hall Geometry, 2007: WEBSITES www.keypress.com/sketchpad/www.math.comwww.mathleague.com/help/geometry/geometry.htmwww.PHsuccess.net
Revised 2006
COURSE: Honors Geometry
GRADE(S): 10h Grade
UNIT 3: Parallel and Perpendicular Lines TIME FRAME: 9 days NATIONAL STANDARDS: 2. ALGEBRA
A. Understand patterns, relations, and functions. B. Represent and analyze mathematical situations and structures using algebraic symbols. C. Use mathematical models to represent and understand quantitative relationships. D. Analyze change in various contexts.
3. GEOMETRY
A. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
B. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
C. Apply transformations and use symmetry to analyze mathematical situations. D. Use visualization, spatial reasoning, and geometric modeling to solve problems.
4. MEASUREMENT
A. Understand measurable attributes of objects and the units, systems, and processes of measurement.
B. Apply appropriate techniques, tools, and formulas to determine measurements. 6. PROBLEM SOLVING
A. Build new mathematical knowledge through problem solving. B. Solve problems that arise in mathematics and in other contexts. C. Apply and adapt a variety of appropriate strategies to solve problems. D. Monitor and reflect on the process of mathematical problem solving.
8. COMMUNICATION
A. Organize and consolidate their mathematical thinking through communication. B. Communicate their mathematical thinking coherently and clearly to peers, teachers, and
others. C. Analyze and evaluate the mathematical thinking and strategies of others. D. Use the language of mathematics to express mathematical ideas precisely.
9. CONNECTIONS
A. Recognize and use connections among mathematical ideas. B. Understand how mathematical ideas interconnect and build on one another to produce a
coherent whole. C. Recognize and apply mathematics in contexts outside of mathematics.
10. REPRESENTATION
A. Create and use representations to organize, record, and communicate mathematical ideas. B. Select, apply, and translate among mathematical representations to solve problems. C. Use representations to model and interpret physical, social, and mathematical phenomena.
STATE STANDARDS M11.B.2.1 Use and/or compare measurements of angles M11.C.1.2 Recognize and/or apply properties of angles, triangles and quadrilaterals
UNIT OBJECTIVES:
• Identify angles formed by two lines and a transversal
• Recognize angle measures resulting from parallel lines and a transversal
• Relate parallel and perpendicular lines
Revised 2006
M11.D.2.1 Write, solve and/or graph linear equations and inequalities using various methods M11.C.3.1 Solve problems using analytic geometry
• Classify polygons • Find the sums of the interior and exterior
angles in a polygon • Graph lines given their equations • Write the equations of lines • Relate slopes of parallel and perpendicular
lines
ACTIVITIES: Teacher directed differentiated instructional projects and activities are ongoing and based on student need. “Activity 7: Playing Football” “Activity 8: Triangle Jigsaw” “Activity 40: Exterior Angles of Triangles” “Chapter 3 Project: Amazing Space” “Activity Lab: Angle Dynamics” (p. 146 in text) “Activity Lab: Exterior Angles of Polygons” (p. 156 in text) “Activity Lab: Solving Linear Equations with Graphs and Tables” (pgs. 172-73 in text) “Activity Lab: The Science of Reflection” (pgs. 194-95 in text) Prentice Hall Geometry, 2007: All-in-One Student Workbook Skill and Concept Review Masters Grab & Go Chapter Support Files
ASSESSMENTS: Observation and questioning Presentation and discussions Projects and Investigations Homework Quizzes Tests REMEDIATION: Practice 3-1 and Reteaching 3-1 Properties of Parallel Lines Practice 3-2 and Reteaching 3-2 Proving Lines Parallel Practice 3-3 and Reteaching 3-3 Parallel and Perpendicular Lines Practice 3-4 and Reteaching 3-4 Parallel Lines and The Triangle Angle-Sum Theorem Practice 3-5 and Reteaching 3-5 The Polygon Angle-Sum Theorems Practice 3-6 and Reteaching 3-6 Lines in the Coordinate Plane Practice 3-7 and Reteaching 3-7 Slopes of Parallel and Perpendicular Lines Practice 3-8 and Reteaching 3-8 Constructing Parallel and Perpendicular Lines Prentice Hall Geometry, 2007: Hands-On Activities Skill and Concept Review Masters Online Video Tutor Student EXPRESS MindPoint Quiz Show CD-ROM: End-of-Chapter reviews DIFFERENTIATION: It’s all Done with Mirrors Parallel Lines and Triangles Drafting Tools Applying the Triangle Angle-Sum Theorem Diagonals in Concave Polygons Coordinate Plane History Parallel and Perpendicular Lines Constructing Special Segments in Triangles
Revised 2006
Prentice Hall Geometry, 2007: Online Active Math: Built-in interactive explorations MindPoint Quiz Show CD-ROM Enrichment Masters PHSchool.com: Online support for Mathematics Web Codes within the textbook provide access to:
• Vocabulary Quizzes • Chapter Tests • Chapter Projects • Math at Work
RESOURCES: Prentice Hall Geometry, 2007: WEBSITES www.keypress.com/sketchpad/www.math.comwww.mathleague.com/help/geometry/geometry.htmwww.PHsuccess.net
Revised 2006
COURSE: Honors Geometry
GRADE(S): 10h Grade
UNIT 4: Congruent Triangles TIME FRAME: 9 days NATIONAL STANDARDS: 3. GEOMETRY
A. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
B. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
C. Apply transformations and use symmetry to analyze mathematical situations. D. Use visualization, spatial reasoning, and geometric modeling to solve problems.
4. MEASUREMENT
A. Understand measurable attributes of objects and the units, systems, and processes of measurement.
B. Apply appropriate techniques, tools, and formulas to determine measurements. 6. PROBLEM SOLVING
A. Build new mathematical knowledge through problem solving. B. Solve problems that arise in mathematics and in other contexts. C. Apply and adapt a variety of appropriate strategies to solve problems. D. Monitor and reflect on the process of mathematical problem solving.
7. REASONING AND PROOF
A. Recognize reasoning and proof as fundamental aspects of mathematics. B. Make and investigate mathematical conjectures. C. Develop and evaluate mathematical arguments and proofs. D. Select and use various types of reasoning and methods of proof.
8. COMMUNICATION
A. Organize and consolidate their mathematical thinking through communication. B. Communicate their mathematical thinking coherently and clearly to peers, teachers, and
others. C. Analyze and evaluate the mathematical thinking and strategies of others. D. Use the language of mathematics to express mathematical ideas precisely.
9. CONNECTIONS
A. Recognize and use connections among mathematical ideas. B. Understand how mathematical ideas interconnect and build on one another to produce a
coherent whole. C. Recognize and apply mathematics in contexts outside of mathematics.
10. REPRESENTATION
A. Create and use representations to organize, record, and communicate mathematical ideas. B. Select, apply, and translate among mathematical representations to solve problems. C. Use representations to model and interpret physical, social, and mathematical phenomena.
STATE STANDARDS M11.C.1.2 Recognize and/or apply properties of angles, triangles and quadrilaterals
UNIT OBJECTIVES:
• Recognize congruent figures and their corresponding parts
• Prove triangles congruent using SSS, SAS,
Revised 2006
M11.C.1.3 Use properties of congruence, correspondence and similarity in problem-solving settings involving two-and three- dimensional figures
ASA, AAS and HL • Use triangle congruence and CPCTC to
prove that parts of two triangles are congruent
• Identify overlapping triangles and prove them congruent
ACTIVITIES: Teacher directed differentiated instructional projects and activities are ongoing and based on student need. “Activity 10: Create your Own Logo” “Activity 11: Bowling Pins” “Activity 41: Relationships in Triangles” “Chapter 4 Project: Tri, Tri Again” “Activity Lab: Building Congruent Triangles” (p. 204 in text) “Activity Lab: Probability” Prentice Hall Geometry, 2007: All-in-One Student Workbook Skill and Concept Review Masters Grab & Go Chapter Support Files
ASSESSMENTS: Observation and questioning Presentation and discussions Projects and Investigations Homework Quizzes Tests REMEDIATION: Practice 4-1 and Reteaching 4-1 Congruent Figures Practice 4-2 and Reteaching 4-2 Triangle Congruence by SSS and SAS Practice 4-3 and Reteaching 4-3 Triangle Congruence by ASA and AAS Practice 4-4 and Reteaching 4-4 Using Congruent Triangles: CPCTC Practice 4-5 and Reteaching 4-5 Isosceles and Equilateral Triangles Practice 4-6 and Reteaching 4-6 Congruence in Right Triangles Practice 4-7 and Reteaching 4-7 Using Corresponding Parts of Congruent Triangles Prentice Hall Geometry, 2007: Hands-On Activities Skill and Concept Review Masters Online Video Tutor Student EXPRESS MindPoint Quiz Show CD-ROM: End-of-Chapter reviews DIFFERENTIATION: Quilting Patterns Overlapping Congruent Triangles Paper Airplanes Airplane Routes Triangular Swan Congruent Triangle Crossword Puzzle How Many Triangles? Prentice Hall Geometry, 2007: Online Active Math: Built-in interactive explorations MindPoint Quiz Show CD-ROM Enrichment Masters PHSchool.com: Online support for Mathematics
Revised 2006
Web Codes within the textbook provide access to: • Vocabulary Quizzes • Chapter Tests • Chapter Projects • Math at Work
RESOURCES: Prentice Hall Geometry, 2007: WEBSITES www.keypress.com/sketchpad/www.math.comwww.mathleague.com/help/geometry/geometry.htmwww.PHsuccess.net
Revised 2006
COURSE: Honors Geometry
GRADE(S): 10h Grade
UNIT 5: Relationships within Triangles TIME FRAME: 5 days NATIONAL STANDARDS: 2. ALGEBRA
A. Understand patterns, relations, and functions. B. Represent and analyze mathematical situations and structures using algebraic symbols. C. Use mathematical models to represent and understand quantitative relationships. D. Analyze change in various contexts.
3. GEOMETRY
A. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
B. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
C. Apply transformations and use symmetry to analyze mathematical situations. D. Use visualization, spatial reasoning, and geometric modeling to solve problems.
4. MEASUREMENT
A. Understand measurable attributes of objects and the units, systems, and processes of measurement.
B. Apply appropriate techniques, tools, and formulas to determine measurements. 6. PROBLEM SOLVING
A. Build new mathematical knowledge through problem solving. B. Solve problems that arise in mathematics and in other contexts. C. Apply and adapt a variety of appropriate strategies to solve problems. D. Monitor and reflect on the process of mathematical problem solving.
8. COMMUNICATION
A. Organize and consolidate their mathematical thinking through communication. B. Communicate their mathematical thinking coherently and clearly to peers, teachers, and
others. C. Analyze and evaluate the mathematical thinking and strategies of others. D. Use the language of mathematics to express mathematical ideas precisely.
9. CONNECTIONS
A. Recognize and use connections among mathematical ideas. B. Understand how mathematical ideas interconnect and build on one another to produce a
coherent whole. C. Recognize and apply mathematics in contexts outside of mathematics.
10. REPRESENTATION
A. Create and use representations to organize, record, and communicate mathematical ideas. B. Select, apply, and translate among mathematical representations to solve problems.
Use representations to model and interpret physical, social, and mathematical phenomena. STATE STANDARDS M11.C.1.2 Recognize and/or apply properties of angles, triangles and quadrilaterals
UNIT OBJECTIVES:
• Use properties of perpendicular bisectors and angle bisectors
• Identify properties of medians and altitudes of a triangle
Revised 2006
M11.C.3.1 Solve problems using analytic geometry
• Use inequalities involving angles and sides of triangles
ACTIVITIES: Teacher directed differentiated instructional projects and activities are ongoing and based on student need. “Activity 15: Toothpicks and triangles” “Activity 42: Isosceles Triangle” “Activity 43: Orthocenters” “Chapter 5 Project: Moving Entertainment” “Activity Lab: Special Segments in Triangles” (p. 271 in text) Prentice Hall Geometry, 2007: All-in-One Student Workbook Skill and Concept Review Masters Grab & Go Chapter Support Files
ASSESSMENTS: Observation and questioning Presentation and discussions Projects and Investigations Homework Quizzes Tests REMEDIATION: Practice 5-1 and Reteaching 5-1 Midsegments of Triangles Practice 5-2 and Reteaching 5-2 Bisectors in Triangles Practice 5-3 and Reteaching 5-3 Concurrent Lines, Medians, and Altitudes Practice 5-4 and Reteaching 5-4 Inverses, Contrapositives, and Indirect Reasoning Practice 5-5 and Reteaching 5-5 Inequalities in Triangles Prentice Hall Geometry, 2007: Hands-On Activities Skill and Concept Review Masters Online Video Tutor Student EXPRESS MindPoint Quiz Show CD-ROM: End-of-Chapter reviews DIFFERENTIATION: Midsegments and Areas of Triangles Angle Bisectors and Daisy Designs Constructions-Centroid and Orthocenter Fishy Conclusions The First of the Greek Geometers Prentice Hall Geometry, 2007: Online Active Math: Built-in interactive explorations MindPoint Quiz Show CD-ROM Enrichment Masters PHSchool.com: Online support for Mathematics Web Codes within the textbook provide access to:
• Vocabulary Quizzes • Chapter Tests • Chapter Projects • Math at Work
Revised 2006
RESOURCES: Prentice Hall Geometry, 2007: WEBSITES www.keypress.com/sketchpad/www.math.comwww.mathleague.com/help/geometry/geometry.htmwww.PHsuccess.net
Revised 2006
COURSE: Honors Geometry
GRADE(S): 10h Grade
UNIT 6: Quadrilaterals TIME FRAME: 8 days NATIONAL STANDARDS: 2. ALGEBRA
A. Understand patterns, relations, and functions. B. Represent and analyze mathematical situations and structures using algebraic symbols. C. Use mathematical models to represent and understand quantitative relationships. D. Analyze change in various contexts.
3. GEOMETRY
A. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
B. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
C. Apply transformations and use symmetry to analyze mathematical situations. D. Use visualization, spatial reasoning, and geometric modeling to solve problems.
4. MEASUREMENT
A. Understand measurable attributes of objects and the units, systems, and processes of measurement.
B. Apply appropriate techniques, tools, and formulas to determine measurements. 6. PROBLEM SOLVING
A. Build new mathematical knowledge through problem solving. B. Solve problems that arise in mathematics and in other contexts. C. Apply and adapt a variety of appropriate strategies to solve problems. D. Monitor and reflect on the process of mathematical problem solving.
7. REASONING AND PROOF
A. Recognize reasoning and proof as fundamental aspects of mathematics. B. Make and investigate mathematical conjectures. C. Develop and evaluate mathematical arguments and proofs. D. Select and use various types of reasoning and methods of proof.
8. COMMUNICATION
A. Organize and consolidate their mathematical thinking through communication. B. Communicate their mathematical thinking coherently and clearly to peers, teachers, and
others. C. Analyze and evaluate the mathematical thinking and strategies of others. D. Use the language of mathematics to express mathematical ideas precisely.
9. CONNECTIONS
A. Recognize and use connections among mathematical ideas. B. Understand how mathematical ideas interconnect and build on one another to produce a
coherent whole. C. Recognize and apply mathematics in contexts outside of mathematics.
10. REPRESENTATION
A. Create and use representations to organize, record, and communicate mathematical ideas. B. Select, apply, and translate among mathematical representations to solve problems. C. Use representations to model and interpret physical, social, and mathematical phenomena.
Revised 2006
STATE STANDARDS M11.C.1.2 Recognize and/or apply properties of angles, triangles and quadrilaterals
UNIT OBJECTIVES:
• Define and classify special types of quadrilaterals
• Use relationships among sides, angles and diagonals of parallelograms
• Determine whether a quadrilateral is a parallelogram
• Use properties of diagonals of rhombuses and rectangles
• Determine if a parallelogram is a rhombus • Verify and use the properties of trapezoids
and kites
ACTIVITIES: Teacher directed differentiated instructional projects and activities are ongoing and based on student need. “Activity 9: The Tangram” “Activity 16: Combining, Congruent Triangles” “Activity 17: Making Squares from Toothpicks” “Activity 18: Variations on a Quadrilateral Tree” “Activity 19: Coordinate Geometry and Area” (HONORS ONLY) “Activity 44: Quadrilaterals” “Activity 45: Using Different Menus to Construct Special Quadrilaterals” “Activity 46: Parallelograms and Triangles” “Chapter 6 Project: Go Fly a Kite” “Activity Lab: Diagonals of Parallelograms” (p. 328 in text) “Activity Lab: Quadrilaterals in Quadrilaterals” (p. 342 in text) (HONORS ONLY) “Activity Lab: Interpreting Data” (pgs. 362-63 in text) Prentice Hall Geometry, 2007: All-in-One Student Workbook Skill and Concept Review Masters Grab & Go Chapter Support Files
ASSESSMENTS: Observation and questioning Presentation and discussions Projects and Investigations Homework Quizzes Tests REMEDIATION: Practice 6-1 and Reteaching 6-1 Classifying Quadrilaterals Practice 6-2 and Reteaching 6-2 Properties of Parallelograms Practice 6-3 and Reteaching 6-3 Proving that a Quadrilateral is a Parallelogram Practice 6-4 and Reteaching 6-4 Special Parallelograms Practice 6-5 and Reteaching 6-5 Trapezoids and Kites Practice 6-6 and Reteaching 6-6 Placing Figures in the Coordinate Plane Practice 6-7 and Reteaching 6-7 Proofs using Coordinate Geometry Prentice Hall Geometry, 2007: Hands-On Activities Skill and Concept Review Masters Online Video Tutor Student EXPRESS MindPoint Quiz Show CD-ROM: End-of-Chapter reviews DIFFERENTIATION: Relationships among Quadrilaterals Parallelogram Puzzles The Inside Secrets of a Polygon
Revised 2006
Special Parallelograms Making Something out of Nothing Another Type of Coordinate Plane Introduction to Slides Prentice Hall Geometry, 2007: Online Active Math: Built-in interactive explorations MindPoint Quiz Show CD-ROM Enrichment Masters PHSchool.com: Online support for Mathematics Web Codes within the textbook provide access to:
• Vocabulary Quizzes • Chapter Tests • Chapter Projects • Math at Work
RESOURCES: Prentice Hall Geometry, 2007: WEBSITES www.keypress.com/sketchpad/www.math.comwww.mathleague.com/help/geometry/geometry.htmwww.PHsuccess.net
Revised 2006
COURSE: Honors Geometry
GRADE(S): 10h Grade
UNIT 7: Similarity TIME FRAME: 7 days NATIONAL STANDARDS: 2. ALGEBRA
A. Understand patterns, relations, and functions. B. Represent and analyze mathematical situations and structures using algebraic symbols. C. Use mathematical models to represent and understand quantitative relationships. D. Analyze change in various contexts.
3. GEOMETRY
A. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
B. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
C. Apply transformations and use symmetry to analyze mathematical situations. D. Use visualization, spatial reasoning, and geometric modeling to solve problems.
4. MEASUREMENT
A. Understand measurable attributes of objects and the units, systems, and processes of measurement.
B. Apply appropriate techniques, tools, and formulas to determine measurements. 6. PROBLEM SOLVING
A. Build new mathematical knowledge through problem solving. B. Solve problems that arise in mathematics and in other contexts. C. Apply and adapt a variety of appropriate strategies to solve problems. D. Monitor and reflect on the process of mathematical problem solving.
7. REASONING AND PROOF
A. Recognize reasoning and proof as fundamental aspects of mathematics. B. Make and investigate mathematical conjectures. C. Develop and evaluate mathematical arguments and proofs. D. Select and use various types of reasoning and methods of proof.
8. COMMUNICATION
A. Organize and consolidate their mathematical thinking through communication. B. Communicate their mathematical thinking coherently and clearly to peers, teachers, and
others. C. Analyze and evaluate the mathematical thinking and strategies of others. D. Use the language of mathematics to express mathematical ideas precisely.
9. CONNECTIONS
A. Recognize and use connections among mathematical ideas. B. Understand how mathematical ideas interconnect and build on one another to produce a
coherent whole. C. Recognize and apply mathematics in contexts outside of mathematics.
10. REPRESENTATION
A. Create and use representations to organize, record, and communicate mathematical ideas. B. Select, apply, and translate among mathematical representations to solve problems. C. Use representations to model and interpret physical, social, and mathematical phenomena.
Revised 2006
STATE STANDARDS M11.A.2.1 Apply ratio and/or proportion in problem-solving situations M11.C.1.2 Recognize and/or apply properties of angles, triangles and quadrilaterals M11.C.1.3 Use properties of congruence, correspondence and similarity in problem-solving settings involving two-and three- dimensional figures
UNIT OBJECTIVES:
• Write ratios and solve proportions • Identify and apply similar polygons • Use AA, SAS and SSS similarity statements to
determine if triangles are similar • Find and use relationships in similar right
triangles • Use the side-splitter theorem • Use the Triangle-Angle Bisector Theorem
ACTIVITIES: Teacher directed differentiated instructional projects and activities are ongoing and based on student need. “Activity 24: Proportions in Overlapping Triangles” “Activity 22: Fractals” (HONORS ONLY) “Activity 50: Similarity” Prentice Hall Geometry, 2007: All-in-One Student Workbook Skill and Concept Review Masters Grab & Go Chapter Support Files
ASSESSMENTS: Observation and questioning Presentation and discussions Projects and Investigations Homework Quizzes Tests REMEDIATION: Practice 7-1 and Reteaching 7-1 Ratios and Proportions Practice 7-2 and Reteaching 7-2 Similar Polygons Practice 7-3 and Reteaching 7-3 Proving Triangles Similar Practice 7-4 and Reteaching 7-4 Similarity in Right Triangles Practice 7-5 and Reteaching 7-5 Proportions in triangles Prentice Hall Geometry, 2007: Hands-On Activities Skill and Concept Review Masters Online Video Tutor Student EXPRESS MindPoint Quiz Show CD-ROM: End-of-Chapter reviews DIFFERENTIATION: Applications The Golden Ratio Similarity Proofs Similarity of Right Triangles Great Geometers
Revised 2006
Prentice Hall Geometry, 2007: Online Active Math: Built-in interactive explorations MindPoint Quiz Show CD-ROM Enrichment Masters PHSchool.com: Online support for Mathematics Web Codes within the textbook provide access to:
• Vocabulary Quizzes • Chapter Tests • Chapter Projects • Math at Work
RESOURCES: Prentice Hall Geometry, 2007: WEBSITES www.keypress.com/sketchpad/www.math.comwww.mathleague.com/help/geometry/geometry.htmwww.PHsuccess.net
Revised 2006
COURSE: Honors Geometry
GRADE(S): 10h Grade
UNIT 8: Right Triangles and Trigonometry TIME FRAME: 5 days NATIONAL STANDARDS: 2. ALGEBRA
A. Understand patterns, relations, and functions. B. Represent and analyze mathematical situations and structures using algebraic symbols. C. Use mathematical models to represent and understand quantitative relationships. D. Analyze change in various contexts.
3. GEOMETRY
A. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
B. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
C. Apply transformations and use symmetry to analyze mathematical situations. D. Use visualization, spatial reasoning, and geometric modeling to solve problems.
4. MEASUREMENT
A. Understand measurable attributes of objects and the units, systems, and processes of measurement.
B. Apply appropriate techniques, tools, and formulas to determine measurements. 6. PROBLEM SOLVING
A. Build new mathematical knowledge through problem solving. B. Solve problems that arise in mathematics and in other contexts. C. Apply and adapt a variety of appropriate strategies to solve problems. D. Monitor and reflect on the process of mathematical problem solving.
8. COMMUNICATION
A. Organize and consolidate their mathematical thinking through communication. B. Communicate their mathematical thinking coherently and clearly to peers, teachers, and
others. C. Analyze and evaluate the mathematical thinking and strategies of others. D. Use the language of mathematics to express mathematical ideas precisely.
9. CONNECTIONS
A. Recognize and use connections among mathematical ideas. B. Understand how mathematical ideas interconnect and build on one another to produce a
coherent whole. C. Recognize and apply mathematics in contexts outside of mathematics.
10. REPRESENTATION
A. Create and use representations to organize, record, and communicate mathematical ideas. B. Select, apply, and translate among mathematical representations to solve problems. C. Use representations to model and interpret physical, social, and mathematical phenomena.
STATE STANDARDS M11.C.1.4 Solve problems involving right triangles using Pythagorean Theorem
UNIT OBJECTIVES:
• Use the Pythagorean theorem and the converse to find missing sides in a right triangle
Revised 2006
M11.A.2.1 Apply ratio and/or proportion in problem-solving situations M11.C.1.2 Recognize and/or apply properties of angles, triangles and quadrilaterals
• Find missing lengths in right triangles using the properties of 30-60-90 and 45-45-90 triangles
• Use tangent, cosine and sine ratios to determine lengths in right triangles
ACTIVITIES: Teacher directed differentiated instructional projects and activities are ongoing and based on student need. “Activity 21: Proving the Pythagorean Theorem” “Activity 49: Pythagorean Triples” “Activity 23: Exploring Pythagorean Triples” “Activity 25: Right Triangle Ratios” “Chapter 9 Project: Measure for Measure” “Activity Lab: The Pythagorean Theorem” (p. 416 in text) “Activity Lab: Exploring Trigonometric Ratios” (p. 438 in text) “Activity Lab: How Far can You See?” (pgs. 466-467 in text) Prentice Hall Geometry, 2007: All-in-One Student Workbook Skill and Concept Review Masters Grab & Go Chapter Support Files
ASSESSMENTS: Observation and questioning Presentation and discussions Projects and Investigations Homework Quizzes Tests REMEDIATION: Practice 8-1 and Reteaching 8-1 The Pythagorean Theorem and Its Converse Practice 8-2 and Reteaching 8-2 Special Right Triangles Practice 8-3 and Reteaching 8-3 The Tangent Ratio Practice 8-4 and Reteaching 8-4 Sine and Cosine Ratios Practice 8-5 and Reteaching 8-5 Angles of Elevation and Depression Practice 8-6 and Reteaching 8-6 Vectors Prentice Hall Geometry, 2007: Hands-On Activities Skill and Concept Review Masters Online Video Tutor Student EXPRESS MindPoint Quiz Show CD-ROM: End-of-Chapter reviews DIFFERENTIATION: Bull’s-Eye Wheel of Square Root Angles of Intersection Measure and Discover! A Towering Problem Treasure Hunt
Revised 2006
Prentice Hall Geometry, 2007: Online Active Math: Built-in interactive explorations MindPoint Quiz Show CD-ROM Enrichment Masters PHSchool.com: Online support for Mathematics Web Codes within the textbook provide access to:
• Vocabulary Quizzes • Chapter Tests • Chapter Projects • Math at Work
RESOURCES: Prentice Hall Geometry, 2007: WEBSITES www.keypress.com/sketchpad/www.math.comwww.mathleague.com/help/geometry/geometry.htmwww.PHsuccess.net
Revised 2006
COURSE: Honors Geometry
GRADE(S): 10h Grade
UNIT 9: Transformations TIME FRAME: 4 days NATIONAL STANDARDS: 2. ALGEBRA
A. Understand patterns, relations, and functions. B. Represent and analyze mathematical situations and structures using algebraic symbols. C. Use mathematical models to represent and understand quantitative relationships. D. Analyze change in various contexts.
3. GEOMETRY
A. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
B. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
C. Apply transformations and use symmetry to analyze mathematical situations. D. Use visualization, spatial reasoning, and geometric modeling to solve problems.
4. MEASUREMENT
A. Understand measurable attributes of objects and the units, systems, and processes of measurement.
B. Apply appropriate techniques, tools, and formulas to determine measurements. 8. COMMUNICATION
A. Organize and consolidate their mathematical thinking through communication. B. Communicate their mathematical thinking coherently and clearly to peers, teachers, and
others. C. Analyze and evaluate the mathematical thinking and strategies of others. D. Use the language of mathematics to express mathematical ideas precisely.
9. CONNECTIONS
A. Recognize and use connections among mathematical ideas. B. Understand how mathematical ideas interconnect and build on one another to produce a
coherent whole. C. Recognize and apply mathematics in contexts outside of mathematics.
10. REPRESENTATION
A. Create and use representations to organize, record, and communicate mathematical ideas. B. Select, apply, and translate among mathematical representations to solve problems. C. Use representations to model and interpret physical, social, and mathematical phenomena.
STATE STANDARDS M11.C.2 Identify and/or apply concepts of transformations or symmetry
UNIT OBJECTIVES:
• Identify an isometry • Find translations, reflection, rotation, glide
reflection and dilation images • Identify the type of symmetry in a figure • Identify a tessellation
Revised 2006
ACTIVITIES: Teacher directed differentiated instructional projects and activities are ongoing and based on student need. Geometer’s Sketchpad Packet “Activity 52: Rotations” “Chapter 12 Project: Frieze Frames” “Activity Lab: Tracing Paper Transformations” (pgs.490-91 in text) “Activity Lab: Kaleidoscopes” (p. 513 in text) “Activity Lab: How’d they Do That?” (pgs. 528-29 in text)
Prentice Hall Geometry, 2007: All-in-One Student Workbook Skill and Concept Review Masters Grab & Go Chapter Support Files
ASSESSMENTS: Observation and questioning Presentation and discussions Projects and Investigations Homework Quizzes Tests REMEDIATION: Practice 9-1 and Reteaching 9-1 Translations Practice 9-2 and Reteaching 9-2 Reflections Practice 9-3 and Reteaching 9-3 Rotations Practice 9-4 and Reteaching 9-4 Symmetry Practice 9-5 and Reteaching 9-5 Dilations Practice 9-6 and Reteaching 9-6 Compositions of Reflections Practice 9-7 and Reteaching 9-7 Tessellations Prentice Hall Geometry, 2007: Hands-On Activities Skill and Concept Review Masters Online Video Tutor Student EXPRESS MindPoint Quiz Show CD-ROM: End-of-Chapter reviews DIFFERENTIATION: Soccer Field Translations Lines of Reflection Three Dimensional Rotations Playing Card Symmetries Three-Dimensional Dilations Patty Paper Compositions Transformation Crossword Puzzle Prentice Hall Geometry, 2007: Online Active Math: Built-in interactive explorations MindPoint Quiz Show CD-ROM Enrichment Masters PHSchool.com: Online support for Mathematics Web Codes within the textbook provide access to:
• Vocabulary Quizzes • Chapter Tests • Chapter Projects • Math at Work
Revised 2006
RESOURCES: Prentice Hall Geometry, 2007: WEBSITES www.keypress.com/sketchpad/www.math.comwww.mathleague.com/help/geometry/geometry.htmwww.PHsuccess.net
Revised 2006
COURSE: Honors Geometry
GRADE(S): 10h Grade
UNIT 10: Area TIME FRAME: 8 days NATIONAL STANDARDS: 2. ALGEBRA
A. Understand patterns, relations, and functions. B. Represent and analyze mathematical situations and structures using algebraic symbols. C. Use mathematical models to represent and understand quantitative relationships. D. Analyze change in various contexts.
3. GEOMETRY
A. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
B. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
C. Apply transformations and use symmetry to analyze mathematical situations. D. Use visualization, spatial reasoning, and geometric modeling to solve problems.
4. MEASUREMENT
A. Understand measurable attributes of objects and the units, systems, and processes of measurement.
B. Apply appropriate techniques, tools, and formulas to determine measurements. 6. PROBLEM SOLVING
A. Build new mathematical knowledge through problem solving. B. Solve problems that arise in mathematics and in other contexts. C. Apply and adapt a variety of appropriate strategies to solve problems. D. Monitor and reflect on the process of mathematical problem solving.
8. COMMUNICATION
A. Organize and consolidate their mathematical thinking through communication. B. Communicate their mathematical thinking coherently and clearly to peers, teachers, and
others. C. Analyze and evaluate the mathematical thinking and strategies of others. D. Use the language of mathematics to express mathematical ideas precisely.
9. CONNECTIONS
A. Recognize and use connections among mathematical ideas. B. Understand how mathematical ideas interconnect and build on one another to produce a
coherent whole. C. Recognize and apply mathematics in contexts outside of mathematics.
10. REPRESENTATION
A. Create and use representations to organize, record, and communicate mathematical ideas. B. Select, apply, and translate among mathematical representations to solve problems. C. Use representations to model and interpret physical, social, and mathematical phenomena.
STATE STANDARDS M11.B.2.2 Use and/or develop procedures to determine or describe measures of perimeter, circumference, area, surface area and/or volume
UNIT OBJECTIVES:
• Find the area of a parallelogram • Find the area of a triangle • Find the area of a trapezoid • Find the area of a rhombus and kite
Revised 2006
M11.C.1.1 Identify and/or use parts of circles and segments associated with circles
• Find the area of a regular polygon • Identify the relationships between area
and perimeters with similar figures • Find the measures of central angles and
arcs • Find circumference and arc length • Find the area of a circle, a sector of a
circle and a segment of a circle
ACTIVITIES: Teacher directed differentiated instructional projects and activities are ongoing and based on student need. “Activity 20: Area of Quadrilaterals” “Activity 48: Area” “Chapter 7 Project: And Sew On” “Activity Lab: Transforming to Find Area” (pgs. 532-33 in text) “Activity Lab: Exploring Area and Circumference” (p. 581 in text) “Activity Lab: Misleading Graphs” (pgs. 594-95 in text) Prentice Hall Geometry, 2007: All-in-One Student Workbook Skill and Concept Review Masters Grab & Go Chapter Support Files
ASSESSMENTS: Observation and questioning Presentation and discussions Projects and Investigations Homework Quizzes Tests REMEDIATION: Practice 10-1 and Reteaching 10-1 Areas of Parallelograms and Triangles Practice 10-2 and Reteaching 10-2 Areas of Trapezoids, Rhombuses, and Kites Practice 10-3 and Reteaching 10-3 Areas of Regular Polygons Practice 10-4 and Reteaching 10-4 Perimeters and Areas of Similar Figures Practice 10-5 and Reteaching 10-5 Trigonometry and Area Practice 10-6 and Reteaching 10-6 Circles and Arcs Practice 10-7 and Reteaching 10-7 Areas of Circles and Sectors Practice 10-8 and Reteaching 10-8 Geometric Probability Prentice Hall Geometry, 2007: Hands-On Activities Skill and Concept Review Masters Online Video Tutor Student EXPRESS MindPoint Quiz Show CD-ROM: End-of-Chapter reviews DIFFERENTIATION: An Area Proof of the Pythagorean Theorem Building Blocks, Trapezoids, and Triangles Area Using a Coordinate Plane Midpoints, Area, and Similar Polygons Using the Area of a Triangles to Find Polygon Measurements Exploring Circumference and Diameter Still Life with Circles and Polygons Polygon Probability
Revised 2006
Prentice Hall Geometry, 2007: Online Active Math: Built-in interactive explorations MindPoint Quiz Show CD-ROM Enrichment Masters PHSchool.com: Online support for Mathematics Web Codes within the textbook provide access to:
• Vocabulary Quizzes • Chapter Tests • Chapter Projects • Math at Work
RESOURCES: Prentice Hall Geometry, 2007: WEBSITES www.keypress.com/sketchpad/www.math.comwww.mathleague.com/help/geometry/geometry.htmwww.PHsuccess.net
Revised 2006
COURSE: Honors Geometry
GRADE(S): 10h Grade
UNIT 11: Surface Area and Volume TIME FRAME: 6 days NATIONAL STANDARDS: 2. ALGEBRA
A. Understand patterns, relations, and functions. B. Represent and analyze mathematical situations and structures using algebraic symbols. C. Use mathematical models to represent and understand quantitative relationships. D. Analyze change in various contexts.
3. GEOMETRY
A. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
B. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
C. Apply transformations and use symmetry to analyze mathematical situations. D. Use visualization, spatial reasoning, and geometric modeling to solve problems.
4. MEASUREMENT
A. Understand measurable attributes of objects and the units, systems, and processes of measurement.
B. Apply appropriate techniques, tools, and formulas to determine measurements. 6. PROBLEM SOLVING
A. Build new mathematical knowledge through problem solving. B. Solve problems that arise in mathematics and in other contexts. C. Apply and adapt a variety of appropriate strategies to solve problems. D. Monitor and reflect on the process of mathematical problem solving.
8. COMMUNICATION
A. Organize and consolidate their mathematical thinking through communication. B. Communicate their mathematical thinking coherently and clearly to peers, teachers, and
others. C. Analyze and evaluate the mathematical thinking and strategies of others. D. Use the language of mathematics to express mathematical ideas precisely.
9. CONNECTIONS
A. Recognize and use connections among mathematical ideas. B. Understand how mathematical ideas interconnect and build on one another to produce a
coherent whole. C. Recognize and apply mathematics in contexts outside of mathematics.
10. REPRESENTATION
A. Create and use representations to organize, record, and communicate mathematical ideas. B. Select, apply, and translate among mathematical representations to solve problems. C. Use representations to model and interpret physical, social, and mathematical phenomena.
STATE STANDARDS M11.B.2.3 Describe how a change in one dimension of a figure (2 or 3 dimensional) affects other measurements of that figure
UNIT OBJECTIVES:
• Find the surface area of a prism, cylinder, pyramid and cone
• Find the volume of a prism, cylinder, pyramid and cone
Revised 2006
M11.B.2.2 Use and/or develop procedures to determine or describe measures of perimeter, circumference, area, surface area and/or volume
• Find the surface area and volume of a sphere
• Identify the relationship between similar figures and their surface area and volume
ACTIVITIES: Teacher directed differentiated instructional projects and activities are ongoing and based on student need. “Activity 29: Circles in Cones” “Activity 30: Lines on a Sphere” “Activity 51: Volume” “Chapter 10 Project: The Place is Packed” “Activity Lab: Exploring Surface Area” (p. 616 in text) “Activity Lab: Exploring Similar Solids” (p. 645 in text) “Activity Lab: A Colossal Task” (pgs. 658-59) Prentice Hall Geometry, 2007: All-in-One Student Workbook Skill and Concept Review Masters Grab & Go Chapter Support Files
ASSESSMENTS: Observation and questioning Presentation and discussions Projects and Investigations Homework Quizzes Tests REMEDIATION: Practice 11-1 and Reteaching 11-1 Space Figures and Cross Sections Practice 11-2 and Reteaching 11-2 Surface Area of Prisms and Cylinders Practice 11-3 and Reteaching 11-3 Surface Area of Pyramids and Cones Practice 11-4 and Reteaching 11-4 Volume of Prisms and Cylinders Practice 11-5 and Reteaching 11-5 Volume of Pyramids and Cones Practice 11-6 and Reteaching 11-6 Surface Areas and Volumes of Spheres Practice 11-7 and Reteaching 11-7 Areas and Volumes of Similar Solids Prentice Hall Geometry, 2007: Hands-On Activities Skill and Concept Review Masters Online Video Tutor Student EXPRESS MindPoint Quiz Show CD-ROM: End-of-Chapter reviews DIFFERENTIATION: Three Dimensional Puzzles Constructing Rectangle Boxes Frustum of a Solid Coordinate Geometry and Ordered Triples A Pyramid Potpourri Thin Spherical Shells Working for Scale RESOURCES: Prentice Hall Geometry, 2007: WEBSITES www.keypress.com/sketchpad/www.math.comwww.mathleague.com/help/geometry/geometry.htmwww.PHsuccess.net
Revised 2006
COURSE: Honors Geometry
GRADE(S): 10h Grade
UNIT 12: Circles TIME FRAME: 7 days NATIONAL STANDARDS: 2. ALGEBRA
A. Understand patterns, relations, and functions. B. Represent and analyze mathematical situations and structures using algebraic symbols. C. Use mathematical models to represent and understand quantitative relationships. D. Analyze change in various contexts.
3. GEOMETRY
A. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
B. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
C. Apply transformations and use symmetry to analyze mathematical situations. D. Use visualization, spatial reasoning, and geometric modeling to solve problems.
4. MEASUREMENT
A. Understand measurable attributes of objects and the units, systems, and processes of measurement.
B. Apply appropriate techniques, tools, and formulas to determine measurements. 6. PROBLEM SOLVING
A. Build new mathematical knowledge through problem solving. B. Solve problems that arise in mathematics and in other contexts. C. Apply and adapt a variety of appropriate strategies to solve problems. D. Monitor and reflect on the process of mathematical problem solving.
8. COMMUNICATION
A. Organize and consolidate their mathematical thinking through communication. B. Communicate their mathematical thinking coherently and clearly to peers, teachers, and
others. C. Analyze and evaluate the mathematical thinking and strategies of others. D. Use the language of mathematics to express mathematical ideas precisely.
9. CONNECTIONS
A. Recognize and use connections among mathematical ideas. B. Understand how mathematical ideas interconnect and build on one another to produce a
coherent whole. C. Recognize and apply mathematics in contexts outside of mathematics.
10. REPRESENTATION
A. Create and use representations to organize, record, and communicate mathematical ideas. B. Select, apply, and translate among mathematical representations to solve problems. C. Use representations to model and interpret physical, social, and mathematical phenomena.
STATE STANDARDS M11.C.1.1 Identify and/or use parts of circles and segments associated with circles
UNIT OBJECTIVES:
• Use the relationship between tangent lines and a radius
• Use the relationship between two tangents
Revised 2006
from the same point • Find the measure of an inscribed angle • Find the measure of an angle formed by
the tangent and a chord • Find the measures of angles formed by
tangents, secants and chords • Find associated lengths of segments
associated with circles • Write the equation of a circle • Find the center and the radius of a circle
ACTIVITIES: Teacher directed differentiated instructional projects and activities are ongoing and based on student need. “Activity 31: Tangent Segments and Angle Measure” “Activity 32: The Nine-Point Circle” “Activity 33: Finding the Center of a Circle” “Chapter 11 Project: Going in Circles” “Activity Lab: Paper Folding With Circles” (p. 669 in text) “Activity Lab: Exploring Chords and Secants” (p. 686 in text) “Activity Lab: Tangent Lines and Tangent Ratios” (p. 694 in text) Prentice Hall Geometry, 2007: All-in-One Student Workbook Skill and Concept Review Masters Grab & Go Chapter Support Files
ASSESSMENTS: Observation and questioning Presentation and discussions Projects and Investigations Homework Quizzes Tests REMEDIATION: Practice 12-1 and Reteaching 12-1 Tangent Lines Practice 12-2 and Reteaching 12-2 Chords and Arcs Practice 12-3 and Reteaching 12-3 Inscribed Angles Practice 12-4 and Reteaching 12-4 Angle Measures and Segment Lengths Practice 12-5 and Reteaching 12-5 Circles in the Coordinate Plane Practice 12-6 and Reteaching 12-6 Locus : A Set of Points Prentice Hall Geometry, 2007: Hands-On Activities Skill and Concept Review Masters Online Video Tutor Student EXPRESS MindPoint Quiz Show CD-ROM: End-of-Chapter reviews DIFFERENTIATION: A Remarkable Theorem N Chords and Triangular Numbers The Impossible Dream Ten Angles Circles Loci Prentice Hall Geometry, 2007: Online Active Math: Built-in interactive explorations MindPoint Quiz Show CD-ROM
Revised 2006
Enrichment Masters PHSchool.com: Online support for Mathematics Web Codes within the textbook provide access to:
• Vocabulary Quizzes • Chapter Tests • Chapter Projects • Math at Work
RESOURCES: Prentice Hall Geometry, 2007: WEBSITES www.keypress.com/sketchpad/www.math.comwww.mathleague.com/help/geometry/geometry.htmwww.PHsuccess.net
