Saturday, August 25, 2012

The (tentative) sequence

I think it goes without saying that when you create a new curriculum from scratch by yourself, it's probably going to be a rough draft through June.

The overarching theme: start with a the most specific idea and build upwards toward the general - kinda like how physics starts with constant velocity and builds towards acceleration. I feel that the traditional geometry curriculum does exactly the opposite; it starts with the very general (and simple) and eventually leads toward the specific. I don't know if there's evidence that one approach is better than the other, but I'm personally a bigger fan of specific -> general.

In any event, here goes - I'll try to update links to unit overviews as they're completed. I've also tried to prepare by writing necessary worksheets for the first few units and list the standards that will be covered in each unit.

1. Linear Equations
• Types of slope
• Slope-intercept form of a line
• Parallel, Perpendicular, & Oblique lines
• Solving equations algebraically & graphically
2. Segments & Angles (the basics)
• Definitions of measure (length & area)
• Ruler & Angle postulates
• Segment & Angle Addition postulates
• Angle classification
• Angle pairs
3. Squares
• Relationship between sides & diagonals/area/perimeter
• Midpoint
• Angle bisectors
4. Right Triangles
• Isosceles right triangles (from squares)
• Triangle Sum Theorem
• Area & perimeter
• Pythagorean Theorem / distance formula
• 30/60/90 right triangles
5. Ratios & Proportions
• Similar triangles
• Trigonometric ratios
6. Rectangles
• Area & perimeter
• Angles formed by parallel lines & transversal
• Triangle congruence & corresponding pieces
• Parallelograms
• Rhombus
• Trapezoid
• Kites
8. Polygons
• Interior & exterior angles
• Area & perimeter of regular polygons
9. Circles
10. Surface Area & Volume
11. Symmetry & Transformations
12. Special Segments in Triangles
With the traditional (lecture based) approach, I covered these same topics, just in a different order (based on the textbook). Based on past pacing, I've never been able to cover Symmetry & Transformations (so I wasn't terribly sure where it should fit), and I'm not a big fan of Special Segments in Triangles, which is why I threw it in at the bottom.

1 comment:

1. I looked at what you've done so far and think it will work well. Good progression to the content; although, maybe right triangles before squares. Of course, you can revisit squares when you do quadrilateral with the rhombus and rectangle.