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Common Curriculum Map Discipline: Math Course: Geometry August/September: Standards: 9.B.4-Recognize and apply relationships within and among geometric figures. 9.B.2-Compare geometric figures and determine their properties including parallel, perpendicular, similar, congruent and line symmetry. Essential Questions: How do you name a point, line, plane, segment, and angle? How do I determine if points are collinear? What does it mean for two things to be congruent? Content: Chp. 1 Points Lines Planes Segments Angles Skills: 1. Identify the Coordinate Plane and its parts 2. Define basic terms of Geometry (point, line, plane, space) 3. Explore relationships between the points, lines, and planes 4. Measure Segments 5. Examine relationships among segments 6. Apply the Distance Formula 7. Apply the Midpoint Formula 8. Explore Angles 9. Explore Angle Relationships Assessment: Homework Quizzes covering from 1 to 3 sections of a Chapter Chapter Tests Formal and informal discussions with class Final Cumulative Semester Exam Think, Pair, Share October: Standards: 9.C.1-Draw logical conclusions and communicate reasoning about simple geometric figures and patterns using concrete materials, diagrams and contemporary technology 9.C.2-Formulate logical arguments about geometric figures and patterns and communicate reasoning 9.C.3a-Construct, develop and communicate logical arguments (informal proofs) about geometric figures and patterns Essential Questions: What is a conjecture, and how do I go about making one? How do I apply the Law of Detachment? What is a proof? Content: Chp. 2 Basic Logic Proof Skills: 1. Write Conditional Statements and their Variants 2. Apply the Basis Properties of Equality for Real Numbers 3. Basic Proofs Assessment: Homework Quizzes covering from 1 to 3 sections of a Chapter Chapter Tests Formal and informal discussions with class Final Cumulative Semester Exam Think, Pair, Share November: Standards: 9.B.4-Recognize and apply relationships within and among geometric figures. 9.B.2-Compare geometric figures and determine their properties including parallel, perpendicular, similar, congruent and line symmetry. Essential Questions: What does it mean for two lines to be Parallel? Skew? Perpendicular? What are the special angle relationships formed when two lines are cut by a transversal? What do I know about those angles when the lines happen to be parallel? Content: Chp. 3 Parallel Lines Angles and relationships created by transversal cutting lines Slopes of lines Distance between a point and a line Skills: 1. Identify examples of different sets of lines 2. Identify special angle names for pairs of angles formed by transversal cutting lines (interior, exterior, alternate interior, alternate exterior, consecutive interior) 3. Learn and apply theorems focusing on the special relationship between angles when the transversal cuts parallel lines 4. Determine slope of a line 5. Find the distance from a point to a line Assessment: Homework Quizzes covering from 1 to 3 sections of a Chapter Chapter Tests Formal and informal discussions with class Final Cumulative Semester Exam Think, Pair, Share December: Standards: 9.B.4-Recognize and apply relationships within and among geometric figures. 9.C.4a-Construct and test logical arguments for geometric situations using technology where appropriate. Essential Questions: How do I classify a triangle by its sides and by its angles? What makes triangles congruent? What is the minimum amount of information I need in order to show two triangles are congruent? Content: Chp. 4 Triangles Skills: 1. Classify triangles by angles 2. Classify triangles by sides 3. Apply the Angle Sum Theorem 4. Apply the Exterior Angle Theorem 5. Identify Congruent Triangles 6. Prove triangles congruent 7. Identify specific pieces of an isosceles triangle 8. Compare pieces of an isosceles triangle 9. Identify congruent parts of an isosceles triangle 10. Solve problems dealing with isosceles triangles Assessment: Homework Quizzes covering from 1 to 3 sections of a Chapter Chapter Tests Formal and informal discussions with class Final Cumulative Semester Exam Think, Pair, Share January: Standards: 9.B.4-Recognize and apply relationships within and among geometric figures. 9.C.4a-Construct and test logical arguments for geometric situations using technology where appropriate. Essential Questions: What are the special segments in triangles? What is the minimum amount of information that I need in order to show that two right triangles are congruent? What is the relationship among the sides of a triangle? Content: Chp. 5 Triangles Skills: 1. Identify and define special segments of a triangle (median, angle bisector, perpendicular bisector, altitude) 2. Use Geometer's Sketchpad to examine and investigate the special segments in a triangle 3. Identify theorems of congruence for right triangles 2. Solve problems involving right triangles and their congruence 3. Use indirect reasoning 4. Perform proof by contradiction 5. Define inequality 6. Use relationships of inequality for triangles 7. Identify relationships between sides and angles of a triangle (inequality) 8. Identify inequality relationship for the sides of a triangle (Triangle Inequality Theorem) 9. Calculate the possible values of a side or a variable representing the side of a triangle 10. Indentify inequalities involving two triangles 11. Solve problems dealing with inequalities between two triangles Assessment: Homework Quizzes covering from 1 to 3 sections of a Chapter Chapter Tests Formal and informal discussions with class Final Cumulative Semester Exam Think, Pair, Share February: Standards: 9.A.3a- Draw or construct two- and three- dimensional geometric figures including prisms, pyramids, cylinders and cones. 9.B.4-Recognize and apply relationships within and among geometric figures. 9.C.3a-Construct, develop and communicate logical arguments (informal proofs) about geometric figures and patterns Essential Questions: What are quadrilaterals? What are the properties of the named quadrilaterals (i.e. square, rectangle, rhombus, trapezoid)? Content: Chp. 6 Quadrilaterals Skills: 1. Define a parallelogram and define its properties 2. Establish tests for determining if a quadrilateral is a parallelogram 3. Solve systems of equations 4. Define a rectangle and define its properties 5. Define a rhombus and define its properties 6. Define a square and define its properties 7. Define a trapezoid and define its properties Assessment: Homework Quizzes Test over 1-7 Think, Pair, Share Classroom observations March: Standards: 9.A.3c-Use concepts of symmetry, congruency, similarity, scale, perspective, and angles to describe and analyze two- and three-dimensional shapes found in practical applications (e.g., geodesic domes, Aframe houses, basketball courts, inclined planes, art forms, blueprints). 9.B.4-Recognize and apply relationships within and among geometric figures. 9.C.4b-Construct and communicate convincing arguments for geometric situations. Essential Questions: What is a proportion? How do proportions relate to similar polygons? Content: Chp. 7 Similarity Skills: 1. Define a ratio and a proportion 2. Solve proportions by cross multiplication 3. Define similar polygons 4. Solve problems involving similar polygons 5. Identify similar triangles 6. Define postulates and theorems for similar triangles (AA, SSS, SAS) 7. Parallel lines and proportional parts of those lines 8. Define parts of similar triangles Assessment: Homework Quizzes Test over 1-8 Think, Pair, Share Classroom observations April: Standards: 9.D.3-Compute distances, lengths and measures of angles using proportions, the Pythagorean Theorem and its converse. 9.D.4-Analyze and solve problems involving triangles (e.g., distances which cannot be measured directly) using trigonometric ratios. 9.C.4b-Construct and communicate convincing arguments for geometric situations. Essential Questions: What is trigonometry, and what are the trigonometric ratios? How do you use trigonometric ratios to solve problems involving right triangles? Content: Chp. 8 Applying Right Triangles and Trigonometry Skills: 1. Define geometric mean. 2. Determine and discuss the use of geometric mean in relation to right triangles with altitudes drawn to the hypotenuse. 3. Define special right triangles (45-45-90) (30-60-90) 4. Define special side ratios for the special right triangles 5. Trigonometric ratios for right triangles 6. Define angles of elevation and depression and their relationship Assessment: Homework Quizzes Test over 1-6 Think, Pair, Share Classroom observations May/June: Standards: 9.D.3-Compute distances, lengths and measures of angles using proportions, the Pythagorean Theorem and its converse. 9.C.4a-Construct and test logical arguments for geometric situations using technology where appropriate. 9.C.4b-Construct and communicate convincing arguments for geometric situations. 9.B.4-Recognize and apply relationships within and among geometric figures. Essential Questions: What is a circle and what are its properties? What is a tangent? What is a secant? What is an arc? Content: Chp. 9 Circles Skills: 1. Define the parts of circles 2. Find Circumference given radius or diameter 3. Define central angles and their relationship to arcs 4. Solve problems dealing with central angles and arcs 5. Calculate arc measure and arc length 6. Discuss arcs and chords and their relationship 7. Solve problems using relationships of arcs and chords 8. Define inscribed angles and how to find their measure 9. Solve problems involving inscribed angles 10. Define and examine tangents and their properties 11. Define and examine secants and their properties 12. Examine the relationship between tangents, secants, and the angles formed by them (interior and exterior) 13. Solve problems using information about tangents, secants, and the angles formed by them 14. Determine the relationship between special segments in a circle (secants in the interior, secants intersecting in the exterior, secant and tangent in the exterior) 15. Discuss the quadratic formula and apply it to problems 16. Discuss the standard equation of a circle Assessment: Homework Tests Quizzes Formal and Informal Discussions with Class Think, Pair, Share May/June: Standards: 9.B.4-Recognize and apply relationships within and among geometric figures. 9.C.4b-Construct and communicate convincing arguments for geometric situations. 9.D.4-Analyze and solve problems involving triangles (e.g., distances which cannot be measured directly) using trigonometric ratios. Essential Questions: What are the properties of a polygon? How do you find the area of any given polygon? Content: Chp. 10 Polygons Area of Polygons Skills: 1. Define a polygon 2. Name common polygons up to 12 sides 3. Define convex, concave, and regular as they apply to polygons 4. Explore the interior and exterior angle measures of regular polygons, and solve problems involving those 5. Determine the formula for area for parallelograms, triangles, rhombi, and trapezoids; solve problems involving all of these 6. Define apothem, and determine formula for area of a regular polygon 7. Discuss formula for area of a circle 8. Apply knowledge of area to solve problems looking for area of shaded regions (partial areas) Assessment: Homework Quizzes Tests Formal and Informal Discussions with Class Think, Pair, Share