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GEOMETRY 1-2 ENRICHED FIRST QUARTER Geometry: For Enjoyment and Challenge, McDougal Littell (1991) ISBN 0-86609-965-4 While students are in Geometry, there is a need to sustain their Algebra 1-2 knowledge through review. Specifically, the following topics were identified as topics for ongoing review: slope (parallel and perpendicular lines), linear equations, exponent rules, binomial expansion, graphing equations and inequalities, radicals, quadratic equations, factoring polynomials, multiplying polynomials, and solving systems of equations and inequalities, and coordinates. CCSS Specific Topic Algebra Review (1 week) Solving linear equations Graphing linear equations Equations of lines Systems of equations G.CO.1 G.CO.12 G.GPE.6 G.CO.2 G.CO.3 G.CO.4 G.CO.5 G.CO.6 G.CO.7 G.CO.8 G.CO.12 Introduction to Geometry Define basic geometric terms and symbols Apply deductive reasoning Define structure of postulates, theorems, and definitions Introduce format of 2-column and paragraph proofs Define complementary and supplementary angle relationships Congruence and Transformational Geometry Recognize, use, and compute transformations of rigid motion; including reflections, translations, and rotations. Recognize, use, and compute transformations of rigid motion Transformations (Reflections, Translations, Rotations) Input-output functions for translations, rotations, reflections Composite transformations to map figures onto other figures Use of translations, rotations, reflections to establish triangle congruency Apply definitions, postulates, and theorems to establish triangle congruence using side/angle criteria (SSS, SAS, ASA, AAS) Utilize congruent triangles to expand on theorems including CPCTC, overlapping triangles, medians and altitudes, etc. Teacher Resources Measurements & Constructions Algebra Review Chapter 13: 13.1-13.3 Chapter 1: 1.1 – 1.2 Chapter 2: All sections Segment lengths Angle measures Segment Bisectors Angle Bisectors Perpendicular Lines Solve linear equations Chapter 14: 14.4 Congruent segments Congruent Angles Chapter 14 Median Chapter 3: All sections Altitude Concurrence lines (14.3): Centroid (Medians) Orthocenter (Altitudes) Incenter (Angle Bisectors) Solving equations from CPCTC Coordinate plane Properties of Triangles Classify triangles based on side lengths and angle measures. G.CO.10 G.CO.13 Properties of Triangles Apply triangle theorems involving angles, exterior angles, and side lengths. o Triangle Sum Theorem o Isosceles Triangle Theorems Chapter 4: 4.2,4.3 Solve linear equations Chapter 3: 7.1 Chapter 3: 5.2,5.3 Common Core State Standards for Mathematics STANDARDS FOR MATHEMATICAL PRACTICE 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 express regularity in repeated reasoning. 8 Look for and make use of structure. Check the district website for additional math resources and information: www.psd150.org June 2013 GEOMETRY 1-2 ENRICHED SECOND QUARTER While students are in Geometry, there is a need to sustain their Algebra 1-2 knowledge through review. Specifically, the following topics were identified as topics for ongoing review: slope (parallel and perpendicular lines), linear equations, exponent rules, binomial expansion, graphing equations and inequalities, radicals, quadratic equations, factoring polynomials, multiplying polynomials, and solving systems of equations and inequalities. CCSS G.CO.10 G.CO.13 G.CO.1 G.CO.8 G.CO.9 G.CO.12 G.GPE.5 G.CO.3 G.CO.11 G.GPE.4 G.GPE.5 Specific Topic Properties of Triangles Apply triangle theorems involving angles, exterior angles, and side lengths. o Exterior Angle Theorem o Triangle Inequality a+b>c Construct and locate the perpendicular bisector of a segment Apply theorem stating points on the perpendicular bisector of a segment are equidistant from the endpoints Parallel and Perpendicular Line Relationships Define relationship between slopes and angle measures of parallel and perpendicular lines. Apply transversals and parallel lines to find associated angle pairs including AIA, AEA, Corresponding, SSI, & SSE. Properties of Polygons Classify quadrilaterals based on distinguishing characteristics. Prove theorems about sides, angles, and diagonals of quadrilaterals. Classify polygons by # of sides, regular/irregular, and concave / convex. Calculate interior and exterior angle measures. Teacher Resources Chapter 4: 4.2-4.4 Chapter 7: 7.1 Chapter 15: 15.2 Chapter 5: 5.2,5.3 Chapter 5: 5.4-5.7 Chapter 7: 7.3-7.4 Measurements & Constructions Algebra Review Perpendicular Bisector Concurrence lines (14.3): Circumcenter (Perp. Bisectors) Parallel Lines Solve linear equations Systems of equations Many algebra applications with equations established in these theorems Create equations for diagonals bisecting each other, diagonals that are congruent or perpendicular legs in isosceles trapezoid congruent Use formulas Linear equations Common Core State Standards for Mathematics STANDARDS FOR MATHEMATICAL PRACTICE 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 express regularity in repeated reasoning. 8 Look for and make use of structure. Check the district website for additional math resources and information: www.psd150.org June 2013 GEOMETRY 1-2 ENRICHED THIRD QUARTER While students are in Geometry, there is a need to sustain their Algebra 1-2 knowledge through review. Specifically, the following topics were identified as topics for ongoing review: slope (parallel and perpendicular lines), linear equations, exponent rules, binomial expansion, graphing equations and inequalities, radicals, quadratic equations, factoring polynomials, multiplying polynomials, and solving systems of equations and inequalities. CCSS G.CO.2 G.CO.10 G.SRT.1 G.SRT.2 G.SRT.3 G.SRT.4 G.SRT.5 G.SRT.5 G.SRT.6 G.SRT.7 G.SRT.8 G.SRT.10* G.SRT.11* G.GPE.7 G.CO.1 G.CO.13 G.C.1 G.C.2 G.C.3 G.C.4* G.C.5 G.GPE.1 G.GPE.4 Specific Topic Teacher Resources Measurements & Constructions Algebra Review Similarity Definitions Utilize dilations and reductions to establish similarity Solve problems involving similar shapes and proportions Apply similarity theorems including Midline Theorem, Side-splitter Theorem, 3+ parallel lines divided proportionally Chapter 8: All sections Properties of ratio and proportion Cross product property Proportions Right Triangles Apply similarity in right triangles to utilize the altitude on hypotenuse theorems. Use Pythagorean Theorem, special right triangles, and trigonometric ratios to solve right triangles. Apply the distance formula to find lengths of segments. *Calculate measures of missing sides and angles of non-right triangles using the Law of Sines and Law of Cosines Chapter 9: All sections Solving quadratic equations Simplify radicals Distance formula Geometric mean Circles Identify and calculate measures of parts of circles; including radii, diameters, circumference, arc length, area, and sector area. Define and solve problems involving inscribed and circumscribed polygons. Determine measures of angles and arcs; including minor arcs, major arcs, semicircles, central angles, inscribed angles, and angles related to tangents, chords, and secants. Determine lengths of segments related to tangents, chords, and secants. Chapter 10: All sections Chapter 13: 13.6 (Equations) *Construct a tangent to a circle from an exterior point. Equations of circle in coordinate plane Using Formulas Common Core State Standards for Mathematics STANDARDS FOR MATHEMATICAL PRACTICE 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 express regularity in repeated reasoning. 8 Look for and make use of structure. Check the district website for additional math resources and information: www.psd150.org June 2013 GEOMETRY 1-2 ENRICHED FOURTH QUARTER While students are in Geometry, there is a need to sustain their Algebra 1-2 knowledge through review. Specifically, the following topics were identified as topics for ongoing review: slope (parallel and perpendicular lines), linear equations, exponent rules, graphing linear equations and inequalities, radicals, quadratic equations, factoring polynomials, multiplying polynomials, binomial expansion, and solving systems of equations and inequalities. CCSS Specific Topic Teacher Resources Measurements & Constructions Algebra Review Circles Continued (Be more specific) G.GPE.7 G.SRT.9* G.GMD.3 2-D Figures Calculate areas of individual and composite 2-D figures including triangles, quadrilaterals, and regular polygons *Find area of non-right triangles using formula A=(1/2) ab sin (c) Determine ratios of perimeters and areas of similar figures. Chapter 11: All sections Formulas Solving Equations 3-D Figures Calculate surface area and volume of right prisms, regular pyramids, cylinders, cones, and spheres. Determine ratios of volumes of similar figures. Chapter 12: All sections Using formulas Common Core State Standards for Mathematics STANDARDS FOR MATHEMATICAL PRACTICE 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 express regularity in repeated reasoning. 8 Look for and make use of structure. Check the district website for additional math resources and information: www.psd150.org June 2013 GEOMETRY 1-2 ENRICHED Additional Content (Temp collection area) While students are in Geometry, there is a need to sustain their Algebra 1-2 knowledge through review. Specifically, the following topics were identified as topics for ongoing review: slope (parallel and perpendicular lines), linear equations, exponent rules, graphing linear equations and inequalities, radicals, quadratic equations, factoring polynomials, multiplying polynomials, binomial expansion, and solving systems of equations and inequalities. CCSS Specific Topic Teacher Resources Measurement s& Construction s Algebra Review Translate between the geometric description and the equation for a conic section G.GPE.2. Derive the equation of a parabola given a focus and directrix. G.GPE.3. (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. G.GPE.2* G.GPE.3* G.GMD.1* G.GMD.2* G.GMD.4* G.MG.1* G.MG.2* G.MG.3* Explain volume formulas and use them to solve problems G.GMD.1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. G.GMD.2. (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. G.GMD.4. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. Apply geometric concepts in modeling situations G.MG.1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). G.MG.2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). G.MG.3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Chapter 13 13.1-Graphing Equations 13.2-Equations of lines with parallel and perp 13.3-Systems of equations 13.4-Graphing linear inequalities 13.5-3D Graphing w/ distance formula & reflections 13.6-Equations of Circles 13.7-General Coordinate Geometry 14.3 – Orthocenter, incenter, orthocenter, centroid Chapter 14 14.1-Locus 14.2-Compound Locus 14.3-Concurrence Theorems 14.4-Basic Constructions 14.5-Applications of Constructions 14.6-Triangle Constructions 14.4 – Constructions 1. Segment Copy 2. Angle Copy 3. Angle Bisector 4. Perpendicular Bisector 5. Erecting Perp 6. Dropping a Perp 14.5 – Applications of Constructions 1. Parallels 2. Segment Divisions 3. Mean proportional 4. Fourth proportional Common Core State Standards for Mathematics STANDARDS FOR MATHEMATICAL PRACTICE 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 express regularity in repeated reasoning. 8 Look for and make use of structure. Check the district website for additional math resources and information: www.psd150.org June 2013