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Transcript
Elizabethtown Lewis Central School Geometry Common Core Syllabus 2015-16 Instructors: James E. Sheffer & Mindy Schaefer Re-align on June 25, 2015 Course Description While New York State Common Core Algebra I was to deepen and extend the understanding of linear and exponential relationships, the emphasis in Geometry Common Core is congruence, proof, constructions, similarity, and trigonometry. Students will learn to apply the laws of logic to traditional deductive proofs, both direct and indirect. Topics include triangles, transformations, trigonometric ratios, law of sines and cosines, trigonometry to determine area, inequalities, coordinate geometry proofs, ratio, circles, quadrilaterals, three dimensional shapes, and locus. Course Content and Schedule This is a tentative outline. Students will be informed of the necessary variations. 9/8 9/9 9/10 9/11 Introduction; Rules; Basic Geometry Review Pre-Test of Geometry Common Core Regents Properties of Real Number Systems; Definitions, Lines, Segments, Copy and Bisect an Angle Midpoint, Bisectors, Angles, Construct a Perpendicular Bisector 9/14 9/15 9/16 9/17 9/18 Classify Triangles; Construct an Equilateral Triangle; Review Assessment: Essentials of Geometry Pythagorean Theorem Tangent Ratio Applications of the Tangent Ratio 9/21 9/22 9/23 9/24 9/25 Sine and Cosine Ratios Applications of the Sine and Cosine Ratios Solving Problems using Trigonometric Ratios (AM Schedule) Review of Trigonometry of the Right Triangle Assessment: Trigonometry of the Right Triangle 9/28 9/29 9/30 10/1 10/2 10/5 Deductive Reasoning: Using Logic to Form a Geometry Proof Properties of Equality; Substitution; Addition and Subtraction Postulates Multiplication, Division, Powers, and Roots Postulates Solving for Unknown Angles (Angles and Lines at a Point) Solving for Unknown Angles (Transversals) 10/6 10/7 10/8 10/9 Solving for Unknown Angles (Triangles); Review of Proving Statements in Geometry Assessment: Proving Statements in Geometry & Angles Postulates of Lines, Line Segments, and Angles Using Postulates and Definitions in Proofs Proving Theorems about Angles 10/12 10/13 10/14 10/15 10/16 Columbus Day Congruent Polygons and Corresponding Parts Proving Triangles Congruent by SAS Proving Triangles Congruent by ASA Proving Triangles Congruent by SSS, SAA, and HL 10/19 10/21 10/22 10/23 Review of Congruence of Line Segments, Angles, and Triangles Assessment: Congruence of Line Segments, Angles, and Triangles Line Segments Associated with Triangles; CPCTC Isosceles and Equilateral Triangles More CPCTC 10/26 10/27 10/28 10/29 10/30 Proving Overlapping Triangles Congruent Basic Constructions; Points of Concurrencies Review of Congruence Based on Triangles Assessment: Congruence Based on Triangles Cumulative Review 11/2 11/3 11/4 Cumulative Review Ten Week Exam (1st Interim) Graphing Polygons; Finding Area; Using Trig to Determine Area Using Trigonometry to Find Side Lengths of an Acute Triangle 10/20 11/5 11/6 Applying the Laws of Sines and Cosines 11/9 11/10 11/11 11/12 11/13 Review of Trigonometry in Geometry Assessment: Trigonometry in Geometry Veteran’s Day Line Reflections (x-axis, y-axis, origin, y=x); (PM Schedule) Parent Conferences from 1:00 to 7:00 Translations and Rotations 11/16 11/17 11/18 11/19 11/20 Glide Reflections and Dilations Transformations as Functions Review of Transformations and the Coordinate Plane Assessment: Transformations and the Coordinate Plane Basic Inequality Postulates (Add, Sub, Mult, Div) 11/23 11/24 Inequality Involving the Lengths of a Triangle Inequality Involving Exterior Angles of a Triangle; (AM Schedule) November 25th through November 29th: Thanksgiving Recess 11/30 12/1 12/2 12/3 12/4 Review of Geometric Inequalities Assessment: Geometric Inequalities Slope of a Line Equation of a Line (PM Schedule) Review; Midpoint of a Line Segment 12/7 12/8 12/9 12/10 12/11 Slopes of Perpendicular Lines Coordinate Proof Using Slope Review of Slopes and Equations of Lines Review of Slopes and Equations of Lines Assessment: Slopes and Equations of Lines 12/14 12/15 12/16 12/17 12/18 Parallel Lines Parallel Lines in the Coordinate Plane Sum of the Measures of the Angles of a Triangle Interior and Exterior Angles of Polygons Review of Parallel Lines and More 12/21 Review of Parallel Lines and More 12/22 12/23 Assessment: Parallel Lines and Polygons Extra Day (Winter Solstice) December 24th through January 3rd: Winter Recess 2016 1/4 1/5 1/6 1/7 1/8 Cumulative Review Simplifying Radicals Multiplying and Dividing Expressions with Radicals Rationalizing a Denominator Adding and Subtracting with Expressions with Radicals 1/11 1/12 1/13 1/14 1/15 Mean Proportion; Review of Operations with Radicals Assessment: Operations with Radicals Cumulative Review Cumulative Review Mid-Term Assessment (2nd Interim) 1/18 1/19 1/20 1/21 1/22 Martin Luther King, Jr. Day Parallelogram: Proving and Word Problems Rectangle: Proving and Word Problems Rhombus: Proving and Word Problems Square: Proving and Word Problems Regents Week 1/25 Trapezoid and Isosceles Trapezoid 1/27 Review of Coordinate Geometry Proofs 1/28 Assessment: Coordinate Geometry Proofs 1/29 Review 1/30 Superintendent’s Day (Regional Scoring) 2/1 2/2 2/3 2/4 2/5 Area of Polygons Points, Lines, Planes, Perpendicular, and Parallel Surface Area of a Prism Volume of a Prism Surface Area and Volume of a Pyramid 2/8 2/9 2/10 Surface Area and Volume of a Cylinder Surface Area and Volume of a Cone Surface Area and Volume of a Sphere 2/11 2/12 Review of Three Dimensional Geometry Assessment: Three Dimensional Geometry February 13th to February 21st: Mid-Winter Recess 2/22 2/23 2/24 2/25 2/26 Ratio and Proportion Proportions Involving Line Segments Similar Polygons Proving Triangles Similar Dilations Relating to Similarity 2/29 3/1 3/2 3/3 3/4 Proportional Relations among Segments Related to Triangles Proportions in the Right Triangle Review of Ratio, Proportion, and Similarity Review of Ratio, Proportion, and Similarity Assessment: Ratio, Proportion, and Similarity 3/7 3/8 3/9 3/10 3/11 Pythagorean Theorem Special Triangles (30º-60º-90º and 45º-45º-90º) Distance Formula Proofs Involving the Distance Formula Proofs Involving the Distance Formula 3/14 3/15 3/16 3/17 3/18 Review of Coordinate Geometry Proofs Assessment: Coordinate Geometry Proofs Circles, Central Angles No Class: Superintendent’s Day (AM Schedule) Extra Day 3/21 3/22 3/23 3/24 3/25 Proofs Involving Circles and Polygons Inscribed Angles and Their Measures Tangents and Secants Angles Formed by Tangents, Chords, and Secants No School: Good Friday 3/28 3/29 3/30 3/31 4/1 Measures of Tangent Segments, Chords, and Secant Segments Review of Geometry of the Circle Assessment: Geometry of the Circle Cumulative Review for 30 Week Exam Thirty Week Assessment (3rd Interim) 4/4 4/5 4/6 4/7 4/8 Circles in the Coordinate Plane Tangents and Secants in the Coordinate Plane Tangents and Secants in the Coordinate Plane Review of Circles in the Coordinate Plane Assessment: Circles in the Coordinate Plane 4/11 Review of Trig Ratios 4/12 Complex Trig Problems 13-15 NYS 3-8 Math Exams 4/13 Cumulative Review 4/14 Cumulative Review 4/15 Cumulative Review 4/18 4/19 4/20 4/21 4/22 Complex Trig Problems Trig Word Problems Using Trig in Solving 3-Dimensional Volume and Surface Review of Complex Trig Problems Assessment: Complex Trig Problems April 23rd to May 1st: Spring Recess 5/2 5/3 5/4 5/5 5/6 Writing Equations of a Line given the Slope and a Point Parallel Lines: Writing Equations Perpendicular Lines: Writing Equations Review Assessment: Writing Equations of a Line 5/9 5/10 5/11 5/12 5-13 Review of 3-Dimensional Geometry Complex 3-Dimensional Geometry Complex 3-Dimensional Geometry Complex 3-Dimensional Geometry Assessment: Complex 3-Dimensional Geometry 5/16 through 6/13 Regents Review Students will have at least one cumulative assessment each week to prepare for the Geometry Common Core Regents in June. Extra Help If you are having difficulty, see me immediately or try working with other students in the class. I am available before or after school, my prep period, or my lunch study hall.