Summer Geometry

Geometry is a subject that is typically not very well taught.  Proofs especially, are almost universally confusing to students.  Many of my students in Tucson have started their tutoring with me when they were trying to get through a Geometry class.  Geometry requires a different approach than Algebra.  In order to be successful, you  have to learn to “see” certain relationships and connections.

Geometry 1 Geometry is different from any math that students have done up to that point.  And because it is so different, one really needs an excellent (or at least a good) teacher in order for students  to have a chance at mastering the basics of the subject.

This is especially true when it comes to proofs.  And  proofs are probably the most important part of geometry because learning to do proofs develops reasoning and thinking skills that are not taught in other high school math courses.

I credit the reasoning skills I gained in doing Geometry proofs with giving me a huge leg up when I was learning to program.  And I was lucky.   I had both an excellent Geometry teacher in school, and an older brother who enjoyed tutoring me.  As a result. even though I initially struggled, I ended up really enjoying Geometry proofs. I learned to like the  process of solving a mental puzzle.  And this is the real gift, the real potential of geometry.

In addition, the SATs, ACTs, and Arizona standardized tests all expect students to have a basic working knowledge of Geometry.  I have found myself torn between astonishment and tears  when trying to tutor students prepping for the Geometry portion of standardized tests.  Astonishment because there is so little that is really understood, and tears because there is so much material to cover.

Cathedral ChartresSummer is the perfect time to prep for Geometry in advance, or to go back and  fill in the Geometry gap.  Students can do summer Geometry tutoring any time after 7th grade and on up.  Geometry help can be formatted either as a small class, or as private tutoring.

I have created an 8 session geometry class that can give students a solid foundation in the basics of geometry.   Mastering this material will make it easy to do well in geometry in school,  (imagine knowing something before it is presented!),  and provide the geometry needed for the SAT and ACT tests.

The topics covered are grouped into two parts. Part A is all about proofs, and involves learning to think logically and to “see” relationships.   Part B involves using formulas to calculate areas, angles, and side lengths.  Part B involves more number crunching, and memorizing.

Parts  A and B can be covered over the course of 1 or 2 summers, and can be taken in either order.

Part A :  Proofs and a few Constructions

  • Parallel lines, corresponding angles, alternate interior angles, vertical angles, perpendicular lines, constructing the perpendicular bisector of a segment
  • Proving triangles congruent with SSS, SAS, ASA, HL, and AAS, constructing an equilateral triangle
  • Medians, altitudes, angle bisectors, more proofs, constructing an angle bisector
  • Similar triangles and proportions. more proofs, constructing a parallel line

Part B :  Area, Properties of Rectangles, Circles, Triangles, and Polygons

  • Areas of Circles, Triangles, Rectangles, Trapezoids, and Polygons
  • Calculating interior and exterior angles, properties of rectangles and other polygons
  • Circles, arcs, tangents, inscribed angles, chords
  • Special right triangles, the pythagorean theorem and more complex area problems

Rose window 3Each bulleted topic represents a 3 hour class session, so part A and part B are each 12 hours long, and  the entire course is  a total of 24 hours.

The classes can either be given in a small group format, or as individual tutorials of 1 hour and 30 minutes each.

Homework will be assigned.  😉

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