Geometry Honors P - MA5008

 

The fundamental purpose of the Honors Geometry course is to formalize and extend students’ geometric experiences from earlier courses. This course includes standards from the conceptual categories of Geometry and Statistics and Probability. In this course, students explore more complex geometric situations and deepen their explanations of geometric relationships, presenting and hearing formal mathematical arguments. Transformations and congruence are emphasized in this course. The critical areas of instruction focus on the following key areas: (1) establish criteria for congruence of triangles based on rigid motions; (2) establish criteria for similarity of triangles based on dilations and proportional reasoning; (3) informally develop explanations of perimeter and circumference, area, and volume formulas; (4) apply the Pythagorean Theorem to the coordinate plane; (5) prove basic geometric theorems; and (6) extend work with combinatorics and probability.

 

Some of the overarching ideas in the Honors Geometry course include: (1) the idea of an axiomatic system (e.g., that accepted truths are used to prove other truths), (2) the idea of a viable argument, (3) the idea of definitional thinking, (4) the complementary roles played by synthetic and analytic geometry, and by inductive and deductive reasoning, and (5) the usefulness of Geometry for analyzing the world around us. The Standards for Mathematical Practice will play a prominent role in the course, with students continually developing their ability to reason and argue. Students will solve complex problems, and use tools such as compasses, protractors, and dynamic software as appropriate.