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Geometry/Geometry Pre-AP Currriculum Map 2008-2009 Troup High School 10th Grade NOTE: The Geometry class and the Geometry Pre-AP class are distinguished by the inclusion of special projects for the latter. These include group projects and individual research projects, which may be completed on or off campus as appropriate. (See below.) GT modifications: Special projects: Student-produced podcast(s), Research projects (e.g. Create most efficient sprinkler design plan, Determine most efficient bus route based on pick-up distribution, Campus Improvement Project (research a construction plan and optimize for geometrical efficiency), Who Uses Geometry guest speaker program, Shadow Day career project, etc. SE modifications: (one or more of the following) Reduced assignment length, extended or indefinite time to do assignments, use some or all student-created notes on tests, provide notes to students, allow students to use teacher notes on test, alternate (to proofs) extra credit opportunities. TA TEKS: Teacher: Elmo Projecting System, Promethean Board, Podcast creation, Geometer’s Sketchpad software, Promethean screencapture software, TI Smartview calculator simulation software, Apple moviemaking software, video camera and sound equipment (for podcast production). Student: Apple laptop computer used for notetaking, project creation (Pre-AP), Geometer’s Sketchpad, video camera and sound equipment (Pre-AP) Nine Weeks Content Skills Assessment TEKS -1- 1st • A REVIEW OF ALGEBRA • • • • • • Solve single variable equations. Solve single variable inequalities and graph the solution set. Solve systems of equations. Solve quadratic equations. Solve quadratic equations in application situations. Write equations of lines given different information. • • • Daily Assignments TEST TAKS Review A.6.D, A.7.B, A.8.B, A.10.A G.4, G.7.A, G. 7.C • GEOMETRY BASICS • • • • • ANGLE BASICS • • • • • • Model basic terms of geometry. Identify/define points, lines, planes, and their intersections. Find the distance between two points on a number line and two points on a coordinate plane. Find the midpoint of a segment on a number line and on a coordinate plane. Identify and classify angles. Use the Angle Addition Postulate to find the measures of angles. Identify and use congruent angles and the bisector of an angle. Identify and use adjacent, vertical, complementary, supplementary and liner pairs of angles. Apply properties of complementary and supplementary angles to word problems. Construct angles and their bisectors. -2- • • • • • • Daily Assignments Cumulative TEST TAKS Review Daily Assignments Cumulative TEST TAKS Review G.2.A, G.2.B, G.4, G.5.A • PARALLEL LINES & ANGLES • • • • • ANGLES OF POLYGONS • • • • • • • • • QUADRILATERALS • • • Identify parallel lines and planes and skew lines. Identify angles formed by two lines cut by a transversal. Determine if angles formed by two lines cut by a transversal are congruent or supplementary. Apply algebra to parallel lines and angles. • • Classify triangles both by length of sides and measure of angles. Use the sum of the angles of a triangle to determine measures. Recognize and apply relationships between sides and angles in a triangle. Apply the Triangle Inequality Theorem. Identify and name polygons. Find the sum of the measures of interior angles of polygons. Find the sum of the measures of the exterior angles of polygons and the measure of one exterior angle of a polygon. • • • • • • Recognize and apply the properties of a • parallelogram. • Recognize and apply the properties of a rectangle. • Recognize and apply the properties of squares and rhombi. Recognize and apply properties of a trapezoid. -3- Daily Assignments Activity-Parallel Lines Investigation Cumulative TEST TAKS Review G.2.B, G.4, G. 5.A, G.7.B, G. 9.A Daily Assignments Activity-Triangle Inequality with Straws Cumulative TEST TAKS Review G.2.B, G.4, G. 5.A, G.5.B, G. 9.B Daily Assignments Cumulative TEST TAKS Review G.4, G.5.A, G. 5.B, G.7.B, G. 9.B -4- Nine Weeks Content Skills Assessment -5- TEKS 2nd • SPECIAL TRIANGLES • • Use properties of isosceles triangles. Use properties of medians, altitudes, and angle bisectors. Use the Pythagorean Theorem and its Converse. Apply the Pythagorean Theorem to word problems. Use the properties of 45°-45°-90° Triangles. Use the properties of 30°-60°-90° Triangles. • • • • • • Recognize and use ratios and proportions. Find trigonometric ratios using right triangles. Use proportional parts of parallel lines to solve problems. • • • • • • Identify similar figures Solve problems involving similar figures Use similar triangles to find information about segments and angles Use proportional parts of triangles to solve problems. • • • • • • • • • RATIO AND PROPORTIONS SIMILARITY • • AREA & PERIMETER OF POLYGONS • • • • • • Understand and apply the meaning of area and • perimeter of a polygon. • Know and use the formulas for the area and perimeter of a rectangle. Know and use formulas for the areas and perimeters of parallelograms. Know and use the formulas for the areas and perimeters of triangles. Know and use formulas for the area and perimeter of rhombi and trapezoids -6- Daily Assignments Cumulative TEST TAKS Review Daily Assignments Cumulative TEST TAKS Review Daily Assignments Cumulative TEST TAKS Review G.4, G.5.A, G. 5.D, G.7.B, G. 8.C, G.11.C G.4, G.5.A, G. 9.A, G.9.B, G. 11.C G.4, G.5.A, G. 5.B, G.11.A, G.11.B, G. 11.C G.2.B, G.4, G. 8.A Daily Assignments Cumulative TEST TAKS Review • MORE AREA OF POLYGONS • • • • • • • PRISMS • • • • • PYRAMIDS • • • Define and identify center, radius, and apothem of • a regular polygon. • Calculate the area of regular triangles using radii • and apothems. • Calculate the area of regular quadrilaterals using radii and apothems. Calculate the area of regular hexagons using radii and apothems. Determine the effect that changing dimensions has on the area of two-dimensional figures. Find the area of polygons in which dimensions have been changed. Daily Assignments Quizzes Cumulative TEST TAKS Review Use top, front, side, and corner views of prisms to • create accurate representations. • Use and identify nets that representative of prisms • Calculate the Lateral Area, Total Area, and • Volume of right, regular prisms. • Determine the effects that changing dimensions will have on area and volume, and apply this pattern to problems. Daily Assignments Quizzes Activity-Net Building Cumulative TEST TAKS Review Identify and draw nets of pyramids and their parts • Calculate the Lateral Area, Total Area, and volume • of a right pyramid. • Determine the effect that changing dimensions has • on area and volume of a pyramid, and apply this pattern to problems. Daily Assignments Quizzes Cumulative TEST TAKS Review -7- G.2.B, G.4, G. 5.B, G.8.A, G. 9.B, G.11.D G.2.B, G.4, G. 5.B, G.6.A, G. 6.B, G.6.C, G. 8.D, G.9.D, G. 11.D G.2.B, G.4, G. 5.B, G.5.D, G. 6.B, G.8.D, G. 9.D, G.11.C, G.11.D Nine Weeks Content Skills Assessment -8- TEKS 3rd • • CIRCLES • • • • • • CYLINDERS, CONES, • & SPHERES • • • • • • • COORDINATE PLANE • • • • • ARCS & SECTORS • • • Identify the basic parts of a circle. Calculate the area and circumference of a circle. Calculate the area of shaded regions. Recognize tangents. Use properties of tangents to solve problems. • • • • Daily Assignments Quizzes Cumulative TEST TAKS Review G.2.B, G.4, G. 5.A, G.8.A, G. 9.C Identify the parts of a cylinder. Calculate the Lateral Area, Total Area, & Volume of a cylinder. Identify the parts of a cone. Calculate the Lateral Area, Total Area, and Volume of a cone. Identify the parts of a sphere. Calculate the Lateral Area, Total Area, and Volume of a Sphere. • • • • Daily Assignments Quizzes Cumulative TEST TAKS Review G.2.B, G.4, G. 5.B, G.6.B, G. 8.D, G.9.D, G. 11.D Graph ordered pairs on a coordinate plane. Locate images of figures by reflection. Describe symmetry of figures. Locate images of figures by translations. Locate images of figures by dilation. Recognize major arcs, minor arcs, semicircles, and central angles. Find measures of arcs and central angles. Recognize and use relationships among arcs, chords, and diameters. Calculate the arc length and area of sectors. -9- • • • • Daily Assignments Quizzes Cumulative TEST TAKS Review G.4, G.5.C, G. 7.A, G.7.C, G. 10.A, G.11.A G.2.B, G.4, G. 5.A, G.8.B, G. 9.C • • • • Daily Assignments Quizzes Cumulative TEST TAKS Review • CIRCLES & ANGLES • • • • DEDUCTIVE REASONING • • • • • CONGRUENT TRIANGLES • • • Understand and apply theorems involving properties of inscribed angles. Understand and apply theorems involving properties of angles formed by secants and tangents. Understand and apply theorems involving properties of segments in circles. • • • • Daily Assignments Quizzes Cumulative TEST TAKS Review G.2.B, G.4, G. 5.A, G.5.B, G. 9.C Write Conditional statements. Write the converse, inverse, and contrapositive of conditional statements. Use properties of equality in algebraic and geometric proofs. • • • • Daily Assignments Quizzes If-Then Story Board TEST G.1.A, G.3.A, G.3.C, G.3.D, G.3.E, G.4 Name and label corresponding parts of congruent • triangles. • Construct triangles using SSS, SAS, and ASA. • Prove two triangles congruent using SSS, SAS, and ASA. Prove that corresponding parts are congruent using CPCTC. - 10 - Daily Assignments Quizzes Cumulative TEST G.1.A, G.3.B, G.3.C, G.3.D, G.3.E, G.4, G. 10.B 4th TAKS Review • • • • • • • • • • Describe functional relationships in a variety of StudyIsland.com self-paced All math ways. modules, Tests, practice TEKS Demonstrate an understanding of the properties TAKS tests and attributes of functions. Demonstrate an understanding of linear functions. Formulate and use linear equations and inequalities. Demonstrate an understanding of quadratic and other nonlinear functions. Demonstrate an understanding of geometric relationships and spatial reasoning. Demonstrate an understanding of two- and threedimensional representations of geometric relationships and shapes. Demonstrate an understanding of the concepts and uses of measurement and similarity. Demonstrate an understanding of percents, proportional relationships, probability, and statistics in application problems. Demonstrate an understanding of the mathematical processes and tools used in problem solving. - 11 -