This course covers Common Core Geometry standards and serves as an introduction to Common Core Geometry for students who need it. The following topics will be covered: congruence, similarity, right triangles, trigonometry, circles, geometric properties with equations, measurement and dimensions and modeling (engageny.org)
- Loose-leaf paper
- Graphing calculator suggested for homework (a classroom set is available in school)
Course Format and Procedures
The course structure includes lectures, inquiry-based learning (i.e., flipped classroom), project-based learning, collaborative activities and weekly quizzes (5-40 minutes in duration). Students are expected to take notes daily; complete homework when assigned; make up missed work in a timely manner; refrain from using electronic devices (such as cell phones, mp3 players, laptops, tablets, etc.), in class; direct questions at the instructor, not other students.
- Quizzes (weekly): 100%
- Midterm and final exams: 10%
Student and Parent Resources
- Students who are struggling during the semester should seek immediate help from the instructor during math lab or after school.
- Parent Resources:
- Parent Portal
- Google Classroom
- Regents Prep Online Database
- Khan Academy
- Email the instructor or schedule a meeting through the guidance department
Essential Skills: Name segments, points, rays, planes, angles, etc.; classify angles (acute, obtuse, right, straight); define bisect, midpoint, etc.; classify triangles by angles and sides.
Equilateral Triangles: Construct equilateral and isosceles triangles, inscribed square and hexagon; copy segments.
Bisectors: Copy and bisect an angle; construct perpendicular bisector.
Concurrences: Construct circumcenter, incenter and inscribe and circumscribe a circle about a triangle; concurrences theorems.
Concurrences: Construct centroid, orthocenter concurrences theorems.
Parallel Lines and Apps: Construct parallel lines.
Essential Skills: Identify reflections, translations, rotations, dilations, line of symmetry, point symmetry, rotational symmetry, angles of rotation, degree and order of rotation.
Rigid Motion Exploration: Learn ABCD preservation method for rigid motion; orientation.
Coordinate Plane: Explore transformation rules in the coordinate plane.
Sequences: Explore compositions and identifying sequences of rigid motion.
Finding Angles: Learn about small algebraic proofs with angles; sum of angles on a straight line is 180; the sum of adjacent angles around a point is 360; vertical angles are congruent.
Transversal Angles: Explore parallel lines angles and auxiliary lines.
Triangle Angles: Learn sum of interior angles of a triangle theorem; exterior angle of a triangle theorem.
Isosceles Triangle Theorems: Explore parts of an isosceles triangle; isosceles triangle theorems.
Inequalities: Explore triangle inequality theorem; largest angle across from the longest side; exterior angle inequality theorem.
Concurrence on Coordinate Plane: Determine the equation of a perpendicular line; centroid formula; find the circumcenter algebraically.
Concurrence off Coordinate Plane: Revisit constructing concurrences; divide a segment into congruent pieces.
Essential skills: Derive distance formula and investigate (graphically). Use distance formula to find area and perimeter of figures.
Real life Apps: Explore ratios, proportions and scale factors; find the point on a directed line segment between two given points that partitions the segment in a given ratio (e.g., board is cut…); 2-1 (e.g., designing an object or structure to satisfy physical constraints or minimize cost; work with typographic grid systems based on ratios)
Introduce Similarity and Dilations
- Show how to find the center of dilation.
- Proofs with dilation.
Triangle proportionality and mid-segment theorem
Essential skills: Learn vocabulary of a right triangle (OHA) and Pythagorean theorem.
Basic trig ratios: Set up trig ratios.
- Real life apps
Solving trig ratios, real life apps
- Explain and use the relationship between the sine and cosine of complementary angles.
Apps: Practice trig and Pythagorean theorem modeling problems.
Find lines of symmetry for each quadrilateral
Essential Skills 2-Dimensional: Perform multi-step problems; hand out formula sheet; learn unit conversions (hand out NYS reference sheet).
Volume: Explore prisms (rectangular, triangular, etc.); use reference sheets, applications; work backwards and derive formulas.
Volume: Explore pyramids.
Volume: Learn about non polyhedrons (spheres, cylinders, cones); reference sheet, applications; derive formulas.
Cross-section of prisms, pyramids, cylinders, cones, spheres (include Cavalieri’s principle)
Essential Skills: Solve equation of circle, graph circle on coordinate plane; derive the equation of a circle in center-radius form by completing the square.
Angles of a circle
Segments in a circle: Learn about chords equidistant and parallel chords, tangents, secants and chord lengths.
Arc length and area of sector: Derive the formula for the area of sectors, radian measure, S=OR