 Santa Monica High
 Geometry
Geometry P

The fundamental purpose of the Geometry course is to introduce students to formal geometric proof and the study of plane figures, culminating in the study of right triangle trigonometry and circles. The course formalizes and extends students' geometric experiences from the middle grades. Students begin to prove results about the geometry of the plane by using previously defined terms and notions. Similarity is explored in greater detail, with an emphasis on discovering trigonometric relationships and solving problems with right triangles. This course uses the Big Ideas Math Geometry textbook. Each lesson begins with an Essential Question and is followed by Explorations. Students will investigate, conjecture, validate, generalize, extend, connect, communicate and reflect upon mathematical ideas. A key difference in this course and the historical approach to teaching geometry is the emphasis on transformations. The Standards for Mathematical Practice complement the content standards so that students increasingly engage with the subject matter as they grow in mathematical maturity and expertise throughout their years at the secondary level.
In Geometry, instructional time should focus on six critical 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 circumference, area, and volume formulas; (4) apply the Pythagorean Theorem to the coordinate plane; (5) prove basic geometric theorems; and (6) extend work with probability.
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.Units of Study
Semester 1:
Unit 1: Reasoning and Foundations
Unit 2: Lines and Angles
Unit 3: Transformations and Congruent Triangles
Unit 4: Properties of Triangles and ParallelogramsSemester 2:
Unit 5: Similarity and Special Right Triangles
Unit 6: Trigonometry
Unit 7: Circles
Unit 8: Area and Volume
Unit 9: ProbabilityGeometry HP
Most topics of study in Honors Geometry are the same as described in Geometry P. The Honors Geometry course assumes a higher level of understanding of mathematical concepts (emphasis on applying algebraic expressions) and incorporates nonroutine problems.