Geometry Course Outline

This is my plan for Common Core Geometry so far. If you've taught this course in New York State, and have any insight, please comment!

CC Geometry Course Outline

1. First Day Business: Class Policies/Norms, Edmodo, Class Jobs, Getting to Know You
2. Set up INB: Pocket, TOC, Class Policies, Math Toolbox & Reference Sheet, Grade Record
3. What is Geometry? How is it different from Algebra and other math classes?
4. Undefined Terms: Point, Line, Plane & Definitions: Segment, Angle, Side, Collinear, Right/Acute/Obtuse Angles
5. Notation and Labeling Figures

Unit 1: Transformations

1. Transformations as Functions (+vocab: image, pre-image)
2. Symmetries
3. Rigid Transformations (Isometries) & Preserved Properties
4. Compositions of Transformations
5. Practice with Translations (with and without coordinates)
6. Practice with Reflections: reflect & find line of reflection
7. Reflections with Coordinates
8. Practice with Rotations: rotate & find center/angle of rotation
9. Rotations with Coordinates

Unit 2: Triangles

1. Segments in Triangles: medians, altitudes, angle bisectors, perpendicular bisectors
2. Linear Pairs, Vertical & Adjacent Angles
3. Complementary & Supplementary Angles
4. Sum of Interior Angles of a Triangle
5. Classifying Triangles by Side (Equilateral, Isosceles, Scalene) and by Angle (Acute, Right, Obtuse)
6. Exterior Angles of a Triangle
7. Isosceles Triangles
8. Triangle Inequalities
9. Pre-Proof Reasoning

Unit 3: Congruence

1. Congruent Figures
2. Rigid Motion and Congruence
3. Methods of Proving Triangles Congruent (SSS, SAS, ASA, AAS, HL)
4. Algebra Proofs (not in curric) as intro to Geometry Proofs
5. Proving Triangles Congruent (Mini Triangle Congruence Proofs)  ← Use Proof Blocks
6. Proving Triangles Congruent (Midpoints and Bisectors)
7. Proving Triangles Congruent (Linear Pair Supplementary Vertical Angles Medians Altitudes)
8. Proving Triangles Congruent (Substitution Transitive Addition Subtraction)
9. Angles and Parallel Lines: corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles
10. Algebraic Problems involving Angles and Parallel Lines + Proving Lines Parallel
11. Perpendicular Lines
12. Perpendicular Bisectors
13. Proving Triangles Congruent (Overlapping Triangles)
14. Corresponding Parts of Congruent Triangles (CPCTC)

Unit 4: Quadrilaterals

1. The Quadrilateral Family - properties of all quadrilaterals (4 sides, sum int angles 360)
2. Properties of Parallelograms
3. Parallelogram Proofs
4. Properties of Rectangles, Rhombuses, and Squares
5. Rectangle, Rhombus, and Square Proofs
6. Properties of Trapezoids and Kites
7. Midsegment of a Trapezoid
8. Mixed Practice Problems

Unit 5: Constructions & Concurrencies

1. Using a Compass and Straightedge: Copy a line segment, copy an angle
2. Bisect a Segment / Perpendicular Bisector, Bisect an Angle
3. Parallel through a Point
4. Perpendicular through a Point not/on a line
5. Construction: Regular Hexagon
6. Construction: Equilateral Triangle
7. Construction: Square
8. Construction: Reflections
9. Construction: Angles 90, 60, 45, 30
10. Construction: Altitude, Median, Angle Bisector in a Triangle
11. Construction: Congruent Triangles - SSS, SAS, ASA
12. Construction: Partition a Line Segment
13. Points of Concurrency
14. Centroid: Concurrent Medians
15. Orthocenter: Concurrent Altitudes
16. Circumcenter: Concurrent Perpendicular Bisectors
17. Incenter: Concurrent Angle Bisectors

Unit 6: Dilations & Similarity

1. Dilations
2. *Horizontal and Vertical Stretches
3. Dilations and Lines
4. Similarity
5. Midsegment of a Triangle
6. Side-splitter Theorem
7. Measurements in Similar Figures (perimeters, areas, volume)
8. Proving Similar Triangles
9. Radicals Review
10. Mean Proportional (Geometric Mean)
11. Mean Proportional in Right Triangles (HLLS & SAAS)
12. Pythagorean Theorem & Triples (Pythag Spiral for fun)
13. Special Right Triangle: 45-45-90
14. Special Right Triangle: 30-60-90
15. Trigonometric Ratios
16. Sine and Cosine of Complementary Angles
17. Trigonometry: Solving for a Side
18. Trigonometry: Solve for an Angle
19. Trigonometry: Word Problems (angle of elevation/depression)

Unit 7: Circles

1. Circle Basics
2. Circumference and Area (or save for unit 9??)
3. Arcs and Chords
4. Inscribed Angles
5. Radius and Tangents
6. Secants and Tangents
7. Angles, Chords, and Secants
8. Review Angle Rules
9. BIG Circles
10. Circle Proofs
11. Segment Rules: Secants and Tangents
12. Segment Rules: Intersecting Chords
13. Arc Length & Radian Measure
14. Area of Sectors
15. Inscribed and Circumscribed Polygons - angles, segments, constructions

Unit 8: Coordinate Geometry & Equations

1. Midpoint
2. Length/Distance
3. Slope
4. Partition a Directed Line Segment
5. Area and Perimeter on the Coordinate Plane
6. Coordinate Geometry Proofs: Triangles
7. Equations of Parallel Lines
8. Equations of Perpendicular Lines
9. Equations of Parabolas (?) as Conics
10. Review Completing the Square
11. Equations of Circles

Unit 9: Extending to 3 Dimensions

1. Types of Polygons (n-sides, regular)
2. Interior Angles of Polygons
3. Exterior Angles of Polygons
4. Area and Perimeter of Polygons
5. Area and Circumference of Circles
6. Right Prisms: Volume
7. Cavalieri’s Principle
8. Pyramids
9. Cylinders
10. Cones
11. Spheres and Hemispheres
12. Solids of Revolution
13. Modeling
14. Density

August Planning

There are only a few weeks until school starts again, so it's that bittersweet part of the summer where I'm savoring the last bits of vacation and also getting serious about my back to school planning.

I think (you never know) that I'll be teaching Algebra 1 and Geometry this year. My biggest change over the last year, which I plan to really flesh out this year, is the use of Interactive Notebooks. (I call them INBs, though I know that a lot of teachers call them ISNs.)

I teach in a school where getting students to consistently do homework is very difficult. It's just not part of the norm. I've gone from assigning homework every day, to most days, to twice a week, and now this year I have a new plan. I'm going to make small problem sets with spiraled work which are only given once a week. (Homework is always graded on effort/completion, not accuracy. I firmly believe that homework should be a no-risk opportunity to try and sometimes fail. Tests and quizzes are a higher risk time to try and possibly fail. We have enough of that.) It might sound crazy to only give homework once a week, but I'm hoping to create a mindset shift. I want students to view this problem set as something more like a project - something that they have more time to work on and is therefore worthy of its point value.

Because I want students to learn the value of their INBs, I'm going to make my weekly graded assessment open-notebook. That should motivate every student to do a good job with the notebook. This past year I didn't give tests (to me that means larger, longer, more structured in-class assessments). That did not work out so well. By the time we got to Regents review, students did not seem to be as comfortable handling the practice tests. I think it was because they were overwhelmed by the structure. To combat that this year, I'm going to give a "Marking Period Exam" (oooh, doesn't that sound big and important?). That means there will be a graded test roughly every 6 weeks, and I'll give a practice test about a week in advance so the students can freak out about the practice test instead of the real test. Hopefully this will also minimize the lost instructional time for tests.

I'm putting the finishing touches on my curriculum plans. I'm happy with my Algebra 1 outline, but only time will tell if my Geometry plan is ideal.

I'm still thinking through how I want to organize the classroom, group students, keep track of student work. Maybe seat students in pairs that can quickly turn to become groups of 4? With different classroom jobs for each person in the group? Folders for each student organized by group?

Aside from considering the teaching for the year, I'm anxious about my LIFE this school year. How am I going to maintain my work-life balance? I can't be the workaholic perfectionist I've been in the past. How am I going to figure out how to create/re-work lessons more efficiently and still have them meet my personal standards?

What new ideas are you trying out this year? How do you keep the work-life balance from sliding too far to one side?