Download Common Curriculum Map Discipline: Math Course: Geometry

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