| The primary purpose of this course is to empower the student with a strong
experience in mathematical thinking, as well as problem solving.
Students will sharpen their critical thinking skills, learn to justify
theorems using various formal and informal methods, make meaningful
conjectures, and improve their visualization and problem-solving abilities.
Throughout the year, we will incorporate the following things in every unit:
• Technology (TI-83/84 plus calculators)
• Algebra (through exploring the function families)
• TAKS practice & review items
Furthermore, we will introduce proofs as a means of explaining and
convincing. Much of what is in this course has been encountered in earlier
grades. What we do in geometry is attempt to explain where all that stuff
comes from. I will review basic Algebra concepts as we use them in
geometry, but I will not be re-teaching Algebra. The TI 83plus will be used
as an instructional tool; but I expect the students to know their basic math
facts and be able to do mathematics without calculators.
These are the topics we will study along with their tentative order and
approximate placement in the year. Of course, this outline is subject to
change.
Semester 1
Points, lines, planes, segments, rays
Coordinate Systems
Angles & their relationships
Inductive and Deductive Reasoning
Introduction to Proofs
Distance, Midpoint formula
Coordinate Proofs
Equations of Lines (Algebra review)
Triangles
Irrational numbers
Pythagorean Theorem & Geometric Mean
Triangle congruence properties (Triangle inequalities)
Special Triangles
Right Triangle Trigonometry
Trig Ratios
Similar Triangles
Quadrilaterals
Proving properties of parallelograms using triangle congruence
Proportions & Similar polygons
Areas
Similar Shapes
Algebra Review (Multiplying Binomials, Factoring Quadratic Equations)
Polygons
Angle sums and exterior angles
Diagonal properties
Angle properties and more angle chasing
Semester 2
Circles
Properties of chords, tangents
Arcs and Inscribed Angles
Circumference and arc length
Areas
Circles and Their Equations
Square root function families
The unit circle
Transformations and Tessellations
Transformations and isometries
Symmetry
Tessellations
Using coordinates to describe transformations
Compositions of transformations
Transformations of Functions
Three Dimensional Geometry
Volumes of prisms, pyramids, cylinders, cones
Surface area and volume of spheres
Cubic Function Families
Similarity for 2 and 3 dimensional shapes
Inverse and direct variations.
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