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Geometry
Description of Course
Geometry is a valuable course that includes many mathematical concepts. Geometry helps to build logical reasoning and problem solving skills. Algebra 1 is a pre-requisite to Geometry. This course is divided into two quarters and aligned to rigorous AZCCRS and national standards .This course incudes but not limited to mathematical concepts .The concepts learned in this course will deal with patterns, angles, logical reasoning, properties of lines, parallel and perpendicular lines, congruent triangles, triangles and their properties, quadrilaterals, proportions and similarity, transformations, similarity, circles, area, surface area, volume, and trigonometry.
Materials you need daily:
· 3-Ring Binder
· Spiral Notebook
· Lined Paper, Graph Paper
· Pencils, erasers or pens
· Calculator any one of these 83+, TI 84, TI-89, or TI-Nspire CAS
Grading:
Overall grading
Quarter 1 – ½ Credit
Quarter 2 – ½ Credit
Quarter Grade Breakdown
Assignments - 20%
Quizzes /Weekly Test - 30%
Test (mid-term and final) - 50%
Structure
The structure will include sketch pad, large lecture, power point presentation, explanations through videos, and practicing concept and student participation.
Objectives for Course.
Quarter 1
o Develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems.
o Use construction to explore attributes of geometric figures and to make conjectures about geometric relationships.
o Use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures.
o Find areas of regular polygons, circles, and composite figures.
o Use inductive reasoning to formulate a conjecture.
o Use logical reasoning to prove statements are true and find counterexamples to disprove statements that are false.
o Determine the validity of a conditional statement, its converse, inverse, and contrapositive.
o Use deductive reasoning to prove a statement.
o Make conjectures about lines and determine the validity of the conjectures.
o Make conjectures about angles and determine the validity of the conjectures.
o Use slopes of equations of lines to investigate geometric relationships, including parallel lines and perpendicular lines.
o Use one- and two-dimensional coordinate systems to represent lines.
o Make conjectures about polygons.
o Use numeric and geometric patterns to make generalizations about geometric properties.
o Use logical reasoning to prove statements are true.
o Use geometric concepts and properties to solve problems.
o Graph on a coordinate plane.
o Use slope and equations of lines to investigate geometric relationships, including special segments of triangles.
o Recognize and know historical development of geometric systems and know that mathematics was developed for a variety of purposes.
o Analyze geometric relationships in order to verify conjectures.
o Determine linear relationships.
o Graph on a coordinate plane.
o Represent relationships using tables and graphs.
o Solve linear equations.
Quarter 2
o Use geometric concepts and properties to solve problems in fields such as art and architecture.
o Identify and apply mathematics to everyday experience, to activities in and outside of school, with other disciplines, and with other mathematical topics.
o Communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.
o Use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons.
o Formulate and test conjectures about the properties and attributes of polygons.
o Derive and use formulas involving length, slope, and midpoint.
o Formulate and test conjectures about the properties and attributes of polygons
o Use ratios to solve problems involving similar figures.
o Formulate and test conjectures about the properties and attributes of polygons and their component parts based on explorations and concrete models.
o Solve real-life problems including those involving proportional relationships.
o Describe effects when dimensions change proportionally.
o Use and extend similarity properties to explore and justify conjectures about geometric figures.
o Derive, extend, and use the Pythagorean Theorem.
o Identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45°-45°-90° and 30°-60°-90°) and triangles with sides that are Pythagorean triples.
o Develop, apply, and justify triangle similarity relationships, such as trigonometric ratios using a variety of methods.
o Use congruence transformations to make conjectures and justify properties of geometric figures.
o Graph dilations, reflections, and translations on a coordinate plane.
o Represent relationships using tables and graphs.
o Solve linear equations.
o Find areas of sectors and arc lengths of circles using proportional reasoning.
o Use numeric and geometric patterns to make generalizations about geometric properties including properties of angle relationships in circles.
o Find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures.
o Describe the effect on area and volume when one or more dimensions of a figure are changed.
