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Knott County Schools 2012-2013 Mathematics Curriculum Grade: Geometry Days Topic KCAS Student Friendly Learning Target(s) 2 Algebraic Properties Pre-requisite skills 2 Solving Equations Slope Pre-requisite skills Pre-requisite skills Pre-requisite skills I can use algebraic properties (commutative, associative, distributive, identity, inverse, substitution) I can solve single step and multistep equations I can calculate slope from two points, graph and equation I can write linear equations given two points, a point and the slope, or the graph of the equation 2 4 Linear Equations G.GPE.5 5 Probability S.CP.1 I can graph linear equations using table of values, x- and yintercepts or slope-intercept form I can calculate the probability of a simple event S.CP.2 S.CP.3 S.CP.4 S.CP.5 S.CP.6 S.CP.7 I can use permutations and combinations to compute probabilities of compound events and solve problems Activities Assessments Bell Ringer on algebraic properties Individual Practice Knott County Schools 2012-2013 Mathematics Curriculum Grade: Geometry S.CP.8 S.CP.9 S.MD.6 S.MD.7 2 3 Quiz Definitions 3 Inductive and Deductive Reasoning 2 Conditional and Bi-conditional Statements 2 Parallel and Perpendicular Lines G.CO.1 I can use definitions, basic postulates and theorems about points, segments, lines, angles, and planes to write proofs and to solve problems Pre-requisite skills I can use inductive reasoning to make conjectures G.CO.9 I can use deductive reasoning to arrive at valid conclusion I can identify and write conditional and biconditional statements along with converse, inverse, and contrapositive of a conditional statement and use these statements to form conclusions I can use various methods to prove that two lines are parallel or perpendicular (using coordinates or angle measures) Graphic Organizer – WB p183 TB 1.3-1.4 WB p 189 Vocabulary Review Puzzle basic geometric graphic organizer Knott County Schools 2012-2013 Mathematics Curriculum Grade: Geometry 3 Proofs G.CO.9 G.C0.10 3 3 2 1 1 1 Congruent Triangles G.CO.11 G.CO.7 I can read and write different types and formulas of proofs including two-column, flowchart, paragraph, and indirect proofs I can prove triangles are congruent by SSS, SAS, ASA, AAS, and HL I can use the principle that corresponding parts of congruent triangles are congruent to solve problems Similar Triangles G.SRT.2 I can use several methods to G.SRT.3 prove similarity, including AA, G.SRT.5 SAS, SSS, corresponding sides are proportional, and corresponding angles are congruent Quiz on congruent and similar triangles – 10 MC Benchmark 1 Plane Figures G.CO.1 I can identify and model plane figures, including collinear and noncollinear points, lines, segments, rays and angles using appropriate mathematical symbols Angles G.CO.9 I can identify vertical, adjacent, complementary, and supplementary angles and use Congruent Triangles Graphic Organizer Knott County Schools 2012-2013 Mathematics Curriculum Grade: Geometry them to solve problems 3 Transversals G.CO.9 I can identify corresponding, same-side interior, same-side exterior, alternate interior, and alternate exterior angles formed by a pair of parallel lines and a transversal. Use these angles to solve problems I can apply properties and theorems of parallel and perpendicular lines to solve problems 2 Constructions G.CO.12 I can use construction techniques, including ruler and compass, to bisect and trisect segments and to create parallel and perpendicular lines, perpendicular bisectors, and angle bisectors 1 Locus 2 1 I can locate, describe and draw a locus in a plane or space Quiz on Transversals – 15 MC, 1 CR Triangles G.CO.10 G.CO.13 I can identify and classify triangles by their sides and angles Knott County Schools 2012-2013 Mathematics Curriculum Grade: Geometry 2 Triangles G.CO.10 I can identify medians, altitudes, perpendicular bisectors, and angles bisectors of triangles and use their properties to solve problems (find points of concurrency, segment length, or angle measure) 1 Triangles G.CO.10 I can apply Triangle Inequality Theorem to determine if a triangle exist and the order of sides and angles 1 Triangles G.CO.10 I can solve problems involving the relationships formed when the altitude to the hypotenuse of a right triangle is drawn 2 Pythagorean Theorem G.SRT.8 I can apply the Pythagorean Theorem and its converse to triangles to solve mathematical and real world problems I can identify and use Pythagorean triples in right triangles to find lengths of the unknown side 2 5 Quiz on Triangles and Pythagorean Theorem – 20 MC, 2 CR Quadrilaterals Identify and classify quadrilaterals, including Knott County Schools 2012-2013 Mathematics Curriculum Grade: Geometry parallelograms, rectangles, rhombi, squares, kites, trapezoids, and isosceles trapezoids and their properties 2 1 Quiz on Quadrilaterals – 15 MC, 1 CR Polygons I can identify and classify regular and non-regular polygons (pentagons, hexagons, heptagons, octagons, nonagons, decagons, dodecagons) based on the number of sides, the angle measures, and the side length 1 Angle Sum Theorem G.CO.10 I can apply the Angle Sum Theorem for triangles and polygons to find interior and exterior angles measures given the number of sides, to find the number of sides given angle measures and to solve real 1 Isosceles Triangle G.CO.13 I can apply the Isosceles Triangle Theorem and its converse to triangles to solve mathematical and real 2 5 Quiz on Polygons – 10 MC, 1CR Circles G.C.1 I can identify and define line segments associated with circles Knott County Schools 2012-2013 Mathematics Curriculum Grade: Geometry G.C.2 G.C.3 2 2 Quiz on Circles – 10 MC, 1 CR Prisms G.MG.1 G.MG.2 (radii, diameters, chords, secants, tangents) I can determine the measure of central and inscribed angles and their intercepted arcs I can find segment lengths, angle measures, and intercepted arc measures formed by chords, secants, and tangents intersecting inside and outside circles I can solve problems using inscribed and circumscribed polygons I can identify and classify prisms I can describe and draw cross sections of prisms G.MG.3 G.MG.4 1 1 Benchmark 2 Symmetry 1 Congruent Polygons G.CO.4 I can determine points or lines of symmetry and apply the properties of symmetry to figures G.SRT.5 I can identify congruent figures Knott County Schools 2012-2013 Mathematics Curriculum Grade: Geometry G.SRT.4 and their corresponding parts G.CO.8 5 Similar Polygons G.CO.11 G.SRT.2 G.SRT.3 G.SRT.6 2 2 I can identify similar figures and use ratios and proportions to solve mathematical and realworld problems I can use the definition of similarity to establish the congruence of angles, proportionality of sides, and scale factor of two similar polygons I can apply relationships between perimeters of similar figures, areas of similar figures, and volumes of similar figures, in terms of scale factor, to solve mathematical and real-world problems Quiz on Similar Figures – 15 MC, 1 CR Transformations G.CO.4 I can identify and draw images of transformations and use their G.CO5 properties to solve problems G.CO.3 G.CO.6 Knott County Schools 2012-2013 Mathematics Curriculum Grade: Geometry 1 Geometric Mean Pre-requisite skills I can determine the geometric mean between two numbers and use it to solve problems 2 Similar Solids G.SRT.5 I can identify and give properties of congruent or similar solids G.SRT.4 G.CO.8 2 1 5 2 G.CO.11 Quiz on Transformations – 15 MC, 2 CR Benchmark 3 Area and G.MG.1 I can find the perimeter and area Perimeter of common plane figures, including triangles, quadrilaterals, regular polygons, and irregular polygons I can manipulate perimeter and area formulas to solve problems (find missing length) I can use area to solve problems involving geometric probability I can find the area of a circle and the area of a sector of a circle Arc Length and Circumference G.C.1 G.C.2 I can find arc lengths and circumferences of circles from given information (radius, diameter, coordinates) Knott County Schools 2012-2013 Mathematics Curriculum Grade: Geometry 2 10 Quiz on Area and Perimeter – 15 MC, 2 CR Surface Area G.GMD.1 I can find the lateral area, and Volume surface area and volume of G.GMD.3 prisms, cylinders, cones and pyramids I can use cross sections of prisms, cylinders, pyramids, and cones to solve volume problems I can find the surface area and volume of a sphere in mathematical and real-world settings 2 10 Quiz on Surface Area and Volume – 20 MC, 2 CR Trigonometric G.SRT.7 I can apply properties of 45-45Ratios 90 and 30-60-90 triangles to G.SRT.8 determine lengths of sides of triangles G.SRT.11 I can find the sine, cosine, and tangent ratios of acute angles G.SRT.10 given the side lengths of right G.SRT.9 triangles I can use trigonometric ratios to find the sides or angles of right triangles and to solve real-world problems (angles of elevation and depression) 2 1 Quiz on Trigonometric Ratios – 15 MC, 2 CR Benchmark 4 Knott County Schools 2012-2013 Mathematics Curriculum Grade: Geometry 3 Slope G.GPE.5 I can use slope to distinguish between and write equations for parallel and perpendicular lines 2 Midpoint and Distance Formulas G.GPE.4 I can apply midpoint and distance formulas to points and segments to find midpoints, distances, and missing information G.GPE.7 G.GPE.6 2 Coordinate Geometry G.GPE.4 G.GPE.7 G.GPE.6 1 Circles G.C.1 G.C.2 G.GPE.1 4 Transformations G.CO4 G.CO.5 G.CO.3 2 1 I can use coordinate geometry to solve problems about geometric figures (segments, triangles, quadrilaterals) I can write equations for circles in standard form and solve problems using equations and graphs I can determine the effect of reflections, rotations, translations, and dilations and their compositions on the coordinate plane G.CO.6 Quiz on Coordinate Geometry – 10 MC, 1 CR Benchmark 5 Knott County Schools 2012-2013 Mathematics Curriculum Grade: Geometry