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Academic Content Standards C P Geometry 9-12 Grade-Level Indicators M # Understanding # Indicator Assessment Unit 1 F G C Students must understand 1-dimension, 2-dimension, and 3-dimension, and be able to visualize and actually compute in these various dimensions NNSO 3 NNSO 4 MS 3 Explain the effects of operations Given the picture of some familiar such as multiplication or division, objects in various dimensions, and and of computing powers and roots labels showing the size of these.. on the magnitude of quantities. Students will compute the missing attribute of the object. Demonstrate fluency in computations using real numbers. Solve problems involving unit conversion for situations involving distances, areas, volumes and rates within the same measurement system. MS5 Solving problems involving unit conversion for situations involving distances, areas, volumes and rates within the same measurement system 3. U3. Use the ratio of lengths in similar two-dimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively. Unit 2 a Students must understand the difference between the understanding of the word and the actual definition of the word…also, they must know how to think inductively and deductively. Gsss2 2. Recognize and explain the necessity for certain terms to remain unidentified, such as point, line, and plane. Given a pattern, students will be able to continue the pattern and explain how they arrived at the solution. Given information about a drawing, the student will complete a formal proof pertaining to that drawing. Given a pattern, students will continue the pattern and explain how they arrived at that solution. Given some information about a drawing, students will complete a formal proof pertaining to that drawing. Pfas 13 e Model and solve problems involving direct and inverse variation using proportional reasoning. Unit 3 g Students must understand the difference between showing something is true and proving something is true C. Prove the theorems involving properties of lines, angles gsss b Gsss3 a Gsss1 a. Prove the Pythagorean theorem; 1. Formally define and explain key aspects of geometric figures, including: b. segments related to triangles (median, altitude, midsegment); c. Points of concurrency related to triangles (centroid, incenter, orthocenter, circumcenter) Students will explain what information is missing (or needed) while completing a formal proof. Unit 4 Gsss5 e Students must understand the difference between the mathematical perfection that is demonstrated by the construction/dynamic software and the actual construction that exists. Gsss4 Gsss3 5. Construct congruent figures and similar figures using tools, such as compass, straightedge, and protractor or dynamic geometry software. Given a shape, the student will copy that shape using the tools of construction. Given a shape on the co-ordinate plane, the student will explain any attribute of that shape by using the formulas of co-ordinate geometry (slope, midpoint, distance). 4. Construct right triangles, equilateral triangles, parallelograms, trapezoids, rectangles, rhombuses, squares and kites, using compass and straightedge or dynamic geometry software. Given a segment (or angle) students will construct a midpoint (or angle Analyze two-dimensional figures in a bisector). coordinate plane, e.g., use slope and distance formulas to show that a quadrilateral is a parallelogram. Unit 5 h Students must understand that congruent objects can be related through a simple motion or combination of motions. Gsss8 Gsss9 Derive coordinate rules for translations, reflections and rotations of geometric figures in the coordinate plane. 9. Show and describe the results of combinations of translations, reflections and rotations (compositions), e.g., perform compositions and specify the result of a composition as the outcome of a single motion, when applicable. Given an object and a transformation, students will give the resulting figure. Given the image of a figure, students will determine the original figure and/or the transformation. Gsss8 Derive coordinate rules for translations, reflections, and rotations of geometric figures in the coordinate plane. Gsss6 Identify the reflection and rotation symmetries of two- and threedimensional figures. Given points in the coordinate plane, and the transformation (in any form) the student will determine the resulting image. Unit 6 Ms5 g Students must understand that units may help in the problem-solving process. NNSO5 H 5. Solve problems involving unit conversion for situations involving distances, areas, volumes and rates within the same measurement system. Estimate the solutions for problem situations involving square roots and cube roots. Given a number, the student will give an estimate of its square root (or cube root). Given the instructions on how to convert in any measurement system, and a number in that system of units, students will compute an equivalent number with a different set of units in that system. Ms2 Ms 4, 5 Use unit analysis to check computations involving measurement. 4. Calculate distances, areas, surface areas and volumes of composite three-dimensional objects to a specified number of significant digits. Given a real-world problem involving measurements and a degree of precision, students will solve that problem. Unit 7 Use similar triangles to set-up trigonometry and then use the trigonometry to solve more complex problems that occur in other disciplines. Gsss2 Gsss1 i Gsss2 d Ms4 2. Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures. Define the basic trigonometric ratios in right triangles: sine, cosine, and tangent. Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures. 4. Use scale drawings and right triangle trigonometry to solve problems that include unknown distances and angle measures. Given a right triangle, a side and an acute angle, students will calculate all of the missing parts. Given the sides of a right triangle, students will calculate all of the angles. Given a real-world problem involving trigonometry (from another discipline), the student will solve that problem.