 # Mathematics Content Expectations

 Form A: Math Alignment Table Alignment to Math High School Content Expectations Math High School Content Expectations Prealgebra Math 050 to Summer 2006 Prealgebra Math 050 to Fall 2006 Introductory Algebra Math 107 Summer and Fall 2006 Math 112 ACCUPLACER Tests STRAND 3: GEOMETRY AND TRIGONOMETRY (G) In Grades K–5, students study figures such as triangles, rectangles, circles, rectangular solids, cylinders, and spheres. They examine similarities and differences between geometric shapes. They learn to quantify geometric figures by measuring and calculating lengths , angles, areas and volumes. In Grades 6-8, students broaden their understanding of area and volume and develop the basic concepts of congruence, similarity, symmetry and the Pythagorean Theorem. They apply these ideas to solve geometric problems, including ones related to the real world. In Grades 9–12, students see geometry developed as a coherent, structured subject. They use the geometric skills and ideas introduced earlier, such as congruence and similarity, to solve a wide variety of problems. There is an emphasis on the importance of clear language (e.g. for postulates, definitions and theorems) and on learning to construct geometric proofs. In this process, students build geometric intuition and facility at deductive reasoning. They use elements of logic and reasoning as described in the Quantitative Literacy and Logic strand, including both direct and indirect proof presented in narrative form. They begin to use new techniques, including transformations and trigonometry. They apply these ideas to solve complex problems about two- and three-dimensional figures, again including ones related to the real world. Their spatial visualization skills will be developed through the study of the relationships between two- and three-dimensional shapes. STANDARD G1: FIGURES AND THEIR PROPERTIES Students represent basic geometric figures, polygons, and conic sections and apply their definitions and properties in solving problems and justifying arguments, including constructions and representations in the coordinate plane. Students represent three-dimensional figures, understand the concepts of volume and surface area, and use them to solve problems. They know and apply properties of common three-dimensional figures.   G1.1 Lines and Angles ; Basic Euclidean and Coordinate Geometry G1.1.1 Solve multi- step problems and construct proofs involving vertical angles, linear pairs of angles supplementary angles, complementary angles, and right angles. G1.1.2 Solve multi-step problems and construct proofs involving corresponding angles, alternate interior angles, alternate exterior angles, and sameside (consecutive) interior angles. G1.1.3 Perform and justify constructions, including midpoint of a line segment and bisector of an angle, using straightedge and compass. G1.1.4 Given a line and a point, construct a line through the point that is parallel to the original line using straightedge and compass; given a line and a point, construct a line through the point that is perpendicular to the original line; justify the steps of the constructions. G1.1.5 Given a line segment in terms of its endpoints in the coordinate plane, determine its length and midpoint. G1.1.6 Recognize Euclidean Geometry as an axiom system ; know the key axioms and understand the meaning of and distinguish between undefined terms (e.g., point, line, plane), axioms, definitions, and theorems. G1.2 Triangles and Their Properties G1.2.1 Prove that the angle sum of a triangle is 180° and that an exterior angle of a triangle is the sum of the two remote interior angles. G1.2.2 Construct and justify arguments and solve multi-step problems involving angle measure, side length, perimeter, and area of all types of triangles. G1.2.3 Know a proof of the Pythagorean Theorem and use the Pythagorean Theorem and its converse to solve multi-step problems    ELAGLG.pro CLM.pro G1.2.4 Prove and use the relationships among the side lengths and the angles of 30º- 60º- 90º triangles and 45º- 45º- 90º triangles. G1.2.5 Solve multi-step problems and construct proofs about the properties of medians, altitudes, and perpendicular bisectors to the sides of a triangle, and the angle bisectors of a triangle; using a straightedge and compass, construct these lines. G1.3 Triangles and Trigonometry G1.3.1 Define the sine, cosine, and tangent of acute angles in a right triangle as ratios of sides ; solve problems about angles, side lengths, or areas using trigonometric ratios in right triangles. CLM.pro G1.3.2 Know and use the Law of Sines and the Law of Cosines and use them to solve problems; find the area of a triangle with sides a and b and included angle using the formula Area = (1÷ 2) a b sin. CLM.pro G1.3.3 Determine the exact values of sine , cosine, and tangent for 0°, 30°, 45°, 60°, and their integer multiples , and apply in various contexts. G1.4 Quadrilaterals and Their Properties G1.4.1 Solve multi-step problems and construct proofs involving angle measure, side length, diagonal length, perimeter, and area of squares, rectangles, parallelograms, kites, and trapezoids. G1.4.2 Solve multi-step problems and construct proofs involving quadrilaterals (e.g., prove that the diagonals of a rhombus are perpendicular) using Euclidean methods or coordinate geometry. G1.4.3 Describe and justify hierarchical relationships among quadrilaterals, (e.g. every rectangle is a parallelogram). G1.4.4 Prove theorems about the interior and exterior angle sums of a quadrilateral. G1.5 Other Polygons and Their Properties G1.5.1 Know and use subdivision or circumscription methods to find areas of polygons (e.g., regular octagon, non-regular pentagon). G1.5.2 Know, justify, and use formulas for the perimeter and area of a regular n -gon and formulas to find interior and exterior angles of a regular n -gon and their sums. G1.6 Circles and Their Properties G1.6.1 Solve multi-step problems involving circumference and area of circles.  G1.6.2 Solve problems and justify arguments about chords (e.g., if a line through the center of a circle is perpendicular to a chord, it bisects the chord) and lines tangent to circles (e.g., a line tangent to a circle is perpendicular to the radius drawn to the point of tangency). G1.6.3 Solve problems and justify arguments about central angles, inscribed angles and triangles in circles. G1.6.4 Know and use properties of arcs and sectors, and find lengths of arcs and areas of sectors. G1.7 Conic Sections and Their Properties G.1.7.1 Find an equation of a circle given its center and radius; given the equation of a circle, find its center and radius. CLM.pro G1.7.2 Identify and distinguish among geometric representations of parabolas , circles, ellipses, and hyperbolas; describe their symmetries, and explain how they are related to cones. G1.7.3 Graph ellipses and hyperbolas with axes parallel to the x- and y-axes, given equations. G1.8 Three- Dimensional Figures G1.8.1 Solve multi-step problems involving surface area and volume of pyramids, prisms, cones, cylinders, hemispheres, and spheres.   ELAGLG.pro G1.8.2 Identify symmetries of pyramids, prisms, cones, cylinders, hemispheres, and spheres. 11/15/2006 bls BUSINESS and ED
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