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Transcript
Livingston County Schools Eighth Math Unit 5 Transformations 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: 30 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. 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 Learning Target K 71. Define & identify rotations, reflections, and translations. 72. Identify corresponding sides & corresponding angles. 73. Understand prime notation to describe an image after a translation, reflection, or rotation. 74. Identify center of rotation. 75. Identify direction and degree of rotation. 76. Identify line of reflection. Reasoning Targets 77. 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 same measure, & parallel lines are taken to parallel lines.) 78. Define congruency. 79. Identify symbols for congruency. Reasoning Targets 80. Apply the concept of congruency to write congruent X R X S P Critical Vocabulary Texts/Resources/Activities rotations, reflection rigid transformation, translations, image, Crosswalk Lesson 24 Lesson 7-7 p. 358 Transformations rotations, reflection, translations, image, rigid transformation Crosswalk Lesson 24 Lesson 7-6 p. 354 Congruence X X X X X X X X rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. 8.G.4 Understand that a two-dimensional figure 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. statements. 81. Reason that a 2-D figure is congruent to another if the second can be obtained by a sequence of rotations, reflections, translation. 82. Describe the sequence of rotations, reflections, translations that exhibits the congruence between 2-D figures using words. 83. Define dilations as a reduction or enlargement of a figure. 84. Identify scale factor of the dilation. Reasoning Targets 85. Describe the effects of dilations, translations, rotations, & reflections on 2-D figures using coordinates 86. Define similar figures as corresponding angles are congruent and corresponding sides are proportional. 87. Recognize symbol for similar. Reasoning Targets 88. Apply the concept of similarity to write similarity statements. 89. 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. 90. Describe the sequence of rotations, reflections, X X X X X X X X X 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 angle side similarity, dilation, enlargement, reduction, scale factor, similar triangles Crosswalk Lesson 25-26 Lesson 5-5 p. 238 Similar Triangles translations, or dilations that exhibits the similarity between 2-D figures using words and/or symbols. 8.G.5 Use informal 91. Define similar triangles arguments to establish 92. Define and identify facts about the angle transversals sum and exterior angle 93. Identify angles created of triangles, about the when parallel line is cut by angles created when transversal (alternate interior, parallel lines are cut by a alternate exterior, transversal, and the corresponding, vertical, angle-angle criterion for adjacent, etc.) similarity of triangles. Reasoning Targets For example, arrange 94. Justify that the sum of three copies of the same interior angles equals 180. (For triangle so that the example, arrange three copies three angles appear to of the same triangle so that the form a line, and give an three angles appear to form a argument in terms of line.) transversals why this is 95. Justify that the exterior so. angle of a triangle is equal to the sum of the two remote interior angles. 96. 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 X Angle-angle similarity, alternate interior, alternate exterior, corresponding angles, exterior angles, interior angle, similar triangles, straight angle, supplementary, transversal, X X X X HOT Questions: Crosswalk Lesson 26-28 Lesson 7-2 p. 330 Parallel and Perpendicular Lines