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Livingston County Schools Eighth Math Unit 4 Translations Unit Overview Students use ideas about distance and angles, how they behave under translation, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze 2D figures and to solve problems. Length of unit: days KY Core Academic Standard 8.G.1abc Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. Learning Target K 71. I can define & identify rotations, reflections, and translations. X 72. I can identify corresponding sides & corresponding angles. X 73. I can understand prime notation to describe an image after a translation, reflection, or rotation. X 74. I can identify center of rotation. X 75. I can identify direction and degree of rotation. X 76. I can identify line of reflection. X Reasoning Targets 77. I can use physical models, transparencies, or geometry software to verify the properties of rotations, reflections, and translations (ie. Lines are taken to lines and line segments to line segments of the same length, angles are taken to angles of the R X S P Critical Vocabulary Texts/Resources/Activities rotations, reflection rigid transformation, translations, image, Crosswalk Lesson 24 Lesson 7-7 p. 358 Transformations 8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. same measure, & parallel lines are taken to parallel lines.) 78. I can define congruency. 79. I can identify symbols for congruency. X Reasoning Targets 80. I can apply the concept of congruency to write congruent statements. Reasoning Targets 85. I can describe the effects of dilations, translations, rotations, & reflections on 2-D figures using coordinates 86. I can define similar figures as corresponding angles are rotations, reflection, translations, image, rigid transformation Crosswalk Lesson 24 Lesson 7-6 p. 354 Congruence Translation, rotation, dilation, enlargement, image, reduction, rigid transformation, scale factor Crosswalk Lesson 24-25 Lesson 5-6 p. 244 Dilations AA Angle-angle similarity, SAS side Crosswalk Lesson 25-26 Lesson 5-5 p. 238 X 81. I can reason that a 2-D figure is congruent to another if the second can be obtained by a sequence of rotations, reflections, translation. 82. I can describe the sequence of rotations, reflections, translations that exhibits the congruence between 2-D figures using words. 8.G.3 Describe the effect 83. I can define dilations as a of dilations, translations, reduction or enlargement of a rotations, and figure. reflections on twodimensional figures 84. I can identify scale factor of using coordinates. the dilation. 8.G.4 Understand that a two-dimensional figure X X X X X X X is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. 8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the three angles appear to form a line, and give an congruent and corresponding sides are proportional. 87. I can recognize symbol for similar. X Reasoning Targets 88. I can apply the concept of similarity to write similarity statements. Similar Triangles Angle-angle similarity, alternate interior, alternate exterior, corresponding angles, exterior angles, interior angle, similar triangles, straight angle, supplementary, transversal, Crosswalk Lesson 26-28 Lesson 7-2 p. 330 Parallel and Perpendicular Lines X 89. I can reason that a 2-D figure is similar to another if the second can be obtained by a sequence of rotations, reflections, translation, or dilation. X 90. I can describe the sequence of rotations, reflections, translations, or dilations that exhibits the similarity between 2-D figures using words and/or symbols. 91. I can define similar triangles. X X 92. I can define and identify transversals. X 93. identify angles created when parallel line is cut by transversal. (alternate interior, alternate exterior, corresponding, vertical, adjacent, etc.) X Reasoning Targets 94. I can justify that the sum of angle side similarity, dilation, enlargement, reduction, scale factor, similar triangles X argument in terms of transversals why this is so. interior angles equals 180. (For example, arrange three copies of the same triangle so that the three angles appear to form a line.) 95. I can justify that the exterior angle of a triangle is equal to the sum of the two remote interior angles. 96. I can use Angle-Angle Criterion to prove similarity among triangles. (Give an argument in terms of transversals why this is so.) Common Assessments Developed (Proposed Assessment Dates): X X HOT Questions: