Curriculum Management System
Total Page:16
File Type:pdf, Size:1020Kb
Curriculum Management System MONROE TOWNSHIP SCHOOLS Course Name: Dynamics of Geometry Grade: High School Grades 10-12 For adoption by all regular education programs Board Approved: November 2014 as specified and for adoption or adaptation by all Special Education Programs in accordance with Board of Education Policy # 2220. Table of Contents Monroe Township Schools Administration and Board of Education Members Page 3 Mission, Vision, Beliefs, and Goals Page 4 Core Curriculum Content Standards Page 5 Scope and Sequence Pages 6-9 Goals/Essential Questions/Objectives/Instructional Tools/Activities Pages 10-102 Quarterly Benchmark Assessment Pages 103-106 Monroe Township Schools Administration and Board of Education Members ADMINISTRATION Mr. Dennis Ventrillo, Interim Superintendent Ms. Dori Alvich, Assistant Superintendent BOARD OF EDUCATION Ms. Kathy Kolupanowich, Board President Mr. Doug Poye, Board Vice President Ms. Amy Antelis Ms. Michele Arminio Mr. Marvin I. Braverman Mr. Ken Chiarella Mr. Lew Kaufman Mr. Tom Nothstein Mr. Anthony Prezioso Jamesburg Representative Mr. Robert Czarneski WRITERS NAME Ms. Samantha Grimaldi CURRICULUM SUPERVISOR Ms. Susan Gasko Mission, Vision, Beliefs, and Goals Mission Statement The Monroe Public Schools in collaboration with the members of the community shall ensure that all children receive an exemplary education by well-trained committed staff in a safe and orderly environment. Vision Statement The Monroe Township Board of Education commits itself to all children by preparing them to reach their full potential and to function in a global society through a preeminent education. Beliefs 1. All decisions are made on the premise that children must come first. 2. All district decisions are made to ensure that practices and policies are developed to be inclusive, sensitive and meaningful to our diverse population. 3. We believe there is a sense of urgency about improving rigor and student achievement. 4. All members of our community are responsible for building capacity to reach excellence. 5. We are committed to a process for continuous improvement based on collecting, analyzing, and reflecting on data to guide our decisions. 6. We believe that collaboration maximizes the potential for improved outcomes. 7. We act with integrity, respect, and honesty with recognition that the schools serve as the social core of the community. 8. We believe that resources must be committed to address the population expansion in the community. 9. We believe that there are no disposable students in our community and every child means every child. Board of Education Goals 1. Raise achievement for all students paying particular attention to disparities between subgroups. 2. Systematically collect, analyze, and evaluate available data to inform all decisions. 3. Improve business efficiencies where possible to reduce overall operating costs. 4. Provide support programs for students across the continuum of academic achievement with an emphasis on those who are in the middle. 5. Provide early interventions for all students who are at risk of not reaching their full potential. 6. To Create a 21st Century Environment of Learning that Promotes Inspiration, Motivation, Exploration, and Innovation. Common Core State Standards (CSSS) The Common Core State Standards provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy. Links: 1. CCSS Home Page: http://www.corestandards.org 2. CCSS FAQ: http://www.corestandards.org/frequently-asked-questions 3. CCSS The Standards: http://www.corestandards.org/the-standards 4. NJDOE Link to CCSS: http://www.state.nj.us/education/sca 5. Partnership for Assessment of Readiness for College and Careers (PARCC): http://parcconline.org Quarter 1 Unit Topics(s) I. Points, Lines, Planes h. Distance Between Two Parallel Lines a. Collinear and Coplanar b. Lines, Segments, and Rays c. Space d. Distance Formula e. Midpoint Formula f. Segment Addition g. Angles and Bisectors h. Types of Angles i. Angle and Segment Bisectors j. Angle Pair Relationships k. Polygons l. Convex vs. Concave m. Regular vs. Irregular II. Proof and Reasoning a. Conjectures based on Patterns b. Hypothesis and Conclusion c. If-Then form, Converse, Inverse, Contrapositive d. Postulates vs. Theorems e. Algebraic Proofs f. Two Column Proofs III. Parallel and Perpendicular Lines a. Transversals b. Identifying Angles c. Parallel Lines and Transversals d. Angle Relationships e. Algebraic Reasoning f. Proof of Parallel Lines g. Slope of a Line Quarter 2 Unit Topic(s) I. Triangle Congruence a. Classifying Triangles b. Isosceles vs. Equilateral c. Angle Sum Theorem d. Exterior Angle Theorem e. Congruency Theorems: SSS, SAS, ASA, AAS f. Right Triangle Congruency: LL, HA,LA, HL g. Proofs using above Theorems II. Relationships in Triangles a. Perpendicular Bisectors b. Angle Bisectors c. Medians d. Altitudes (inside and outside the triangle) e. Inequalities f. Angle Measure vs. Side Measure g. Greatest Side or Angle of a Triangle h. Acute, Right or Obtuse by Side Measures III. Similarity a. Proportions b. Application and Reasoning c. Scale Factor d. Similar Polygons and Similar Figures e. Similarity Postulates for Triangles: AA, SSS, SAS Quarter 3 Unit Topic(s) I. Right Triangles and Trigonometry b. Proving Quadrilaterals to be Parallelograms a. Perfect Squares c. Rectangles, Rhombi, and Squares b. Radical Simplification d. Trapezoids c. Geometric Mean e. Properties of Trapezoids d. Pythagorean Theorem and its Converse f. Medians of Trapezoids (Midsegments) e. Proof of Pythagorean Theorem g. Coordinate Geometry f. Special Right Triangles h. Other Quadrilaterals (Kites) g. Trigonometric Ratios h. Angles of Elevation and Depression i. Law of Sine’s II. Circles Parts and Properties a. Area and Circumference b. Arcs c. Properties d. Arc Measure vs. Arc Length e. Arcs and Chords f. Inscribed Angles g. Concentric Circles h. Tangents and Secants i. Equations III. Transformations and Symmetry a. Translations b. Reflections c. Rotations d. Congruence Transformations e. Dilations f. Similarity Transformations IV. Quadrilaterals a. Properties of Parallelograms Quarter 4 Unit Topic(s) I. Area of Polygons a. Regular vs. Irregular b. Sum of the Interior Angles of a Polygon c. Finding each Interior Angle in a Regular Polygon d. Sum of the Exterior Angles of a Regular Polygon e. Triangles f. Quadrilaterals g. Irregular Figures h. Regular Polygons i. Coordinate Geometry j. Perimeter vs. Area on a Coordinate Plane II. Surface Area and Volume a. Nets b. Prisms c. Cylinders d. Pyramids e. Cones f. Spheres III. Probability and Measurement a. Permutations and Combinations b. Fundamental Counting Principal c. Experimental Probability d. Theoretical Probability e. Geometric Probability Unit 1: Points, Lines, and Planes Stage 1 Desired Results ESTABLISHED GOALS Transfer Students will be able to independently use their learning to… CC9-12.G.CO.1 Know precise definitions of -Understand Geometry is a mathematical system built on accepted facts, basic terms, and angle, circle, perpendicular lines, parallel definitions. line, and line segment, based on the undefined notions of point, line, distance -Show segments, rays, and lines are very similar but each have their own properties and along a line, and distance around a circular can be combined to form larger figures in the geometric world. arc. - Use formulas to find the midpoint and length of any segment on a coordinate plane. CC9-12.G.CO.4 Develop definitions of -Apply special angle pairs to identify geometric relationships and to find angle measures. rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. CC9-12.G.CO.12 Make formal geometric Meaning constructions with a variety of tools and UNDERSTANDINGS ESSENTIAL QUESTIONS methods (compass and straightedge, string, Students will understand that… -What are the building blocks of geometry? reflective devices, paper folding, dynamic -A line is made up of an infinite amount of geometric software, etc.). points. Two lines can intersect a point, two -How can you describe the attributes of a planes can intersect to form a line, and three segment or angle? CC9-12.G.GPE.7 Use coordinates to compute planes intersect at a point in space. perimeters of polygons and areas of -Why are units of measure important? triangles and rectangles, e.g., using the - Linear measure is the distance between distance formula. two points. The formal definition of between is used often in geometry and applies to segments directly. Segment addition is the idea of adding two connected segments together to get the length of the larger segment formed. Measurements should be as precise as possible to ensure the most accurate dimensions. - The distance and midpoint formula can be applied to points on a coordinate plane. - A ray is a part of a line. Two opposite rays form a line, which is 180 degrees. Two rays with the same endpoint form and angle. Angles can be measured using a protractor. An angle can be named three different ways (vertex, three points, or a number). An angle bisector cuts the angle into two perfectly congruent angles. Angles can be congruent or can be added together to find the measure of the larger angle formed. - A perpendicular can be a line, segment, or ray that intersects another line, segment, or ray to form a 90-degree angle. Tick marks and arc marcs are a vital part of geometry and must be identified in order to solve problems effectively. - The definition of a polygon is a closed figure whose sides are all segments whose endpoints only intersect two other segments at their endpoints. A polygon can be concave, convex, regular, and irregular. Certain polygons have special names where others are referred to as n-gons.