Geometry Standard 5: The student makes hypotheses, models situations, draws conclusions, and supports claims using geometric concepts and procedures. Components Evidence of Learning 5.1 Make and test conjectures a. Use physical, symbolic, and technological models NOTE: This to explore conjectures. Standard assumes about 2-D figures (polygons the student is already and circles) and 3-D figures proficient with the (spheres, right prisms and concepts and pyramids, right circular procedures described cylinders and cones), or in Components 1.2 and 1.3 of the figures constructed Washington State from these shapes. Grade Level [see GLE 1.3.1] Expectations (GLEs) through grades 9/10. Of the components 5.2 Represent the relevant a. Use basic 2-D figures such as circles or polygons included here, standard features of a physical to represent objects essential to a situation. 5.4 represents the most significant extension situation using 2-D figures of geometric with and without a coordinate b. Include additional line segments to represent understanding beyond system. important known or unknown distances. the Grade 9/10 GLEs. [see GLE 1.3.3, Grades 9/10] c. Introduce a coordinate system when useful for describing the position of objects in a situation. 5.3 Use properties of and a. Inductively generate a conjecture and deductively relationships between 2-D or support it. 3-D figures to draw and justify conclusions b. Apply and justify the applicability of about a situation represented transformations, congruence, similarity, ratios, and proportions in problem-solving situations. with such figures with or without a coordinate c. Distinguish between area and perimeter of 2-D system. figures, surface area, and volume of 3-D figures. [see GLE 1.3.2, 1.3.3, 1.3.4 (grades 8, 9/10)] d. Calculate the area and perimeter of circles, triangles, quadrilaterals, and regular polygons. e. Use the Pythagorean Theorem (or distance formula) in 2-D and 3-D situations when appropriate to compute unknown distances. f. Calculate the volume and surface area of spheres, right rectangular prisms, and right circular cylinders, right prisms ,right pyramids, and right cones g. Graph ellipses and hyperbolas whose axes are parallel to the x and y axes, and demonstrate understanding of the relationship between their standard algebraic form and their graphical characteristics. Geometry (continued Components Evidence of Learning For more 5.4 Recognize and apply the a. Use sine, cosine or tangent to find unknown information basic right triangle distances and angles. on Washington trigonometric relationships State’s Grade b. Use the inverse of sine, cosine, or tangent to find (sine, cosine, and tangent) to Level Expectations the measure of a missing angle. (GLEs), visit the solve problems. OSPI website: www.k12.wa.us/ c. Understand the relationship of cotangent, secant, curriculumInstruct/ and cosecant to basic right-triangle ratios mathematics/pubdocs . /pdf/MathGLE.pdf d. Use Law of Cosines and Law of Sines to solve problems.
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