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1 \ Plainfield Public Schools Mathematics Rigorous Curriculum Design Unit Planning Organizer Grade/Course Unit of Study Pacing Dates Grade 8 Unit 1 : Geometry 7 instructional weeks / 2 weeks for reteaching or enrichment September 3 – October 25, 2013 Standards for Mathematical Practice CCSSM Mathematical Practices Practices that apply to the unit: MP1. Make sense of problems and persevere in solving them. MP2. Reason abstractly and quantitatively. MP3. Construct viable arguments and critique the reasoning of others. MP4. Model with mathematics. MP5. MP6. MP7. MP8. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved. 2 UNIT STANDARDS 8.G.1 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. 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. 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two dimensional 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, and translations, and dilations; given two similar two-dimensional figures, describes 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 sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved. 3 “Unwrapped” Skills “Unwrapped” Concepts DOK Levels (students need to be able to do) (students need to know) FOCUS STANDARD: 8.G.1 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. Verify rotations, reflections, and 1 translations, lines, line segment “Unwrapped” Skills “Unwrapped” Concepts DOK Levels (students need to be able to do) (students need to know) FOCUS STANDARD: 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. Understand congruent , rotations, reflections, 1 and translations; “Unwrapped” Skills “Unwrapped” Concepts DOK Levels (students need to be able to do) (students need to know) FOCUS STANDARD: 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two dimensional figures using coordinates. Describe dilations, translations, rotations, 1 and reflection, coordinates “Unwrapped” Skills “Unwrapped” Concepts DOK Levels (students need to be able to do) (students need to know) FOCUS STANDARD: 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, and translations, and dilations; given two similar two-dimensional figures, describes a sequence that exhibits the similarity between them. Understand rotations, reflections, and 1 translations, and dilations; Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved. 4 “Unwrapped” Skills “Unwrapped” Concepts DOK Levels (students need to be able to do) (students need to know) FOCUS STANDARD: 8.G.5 Use 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 angleangle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Use the angle sum , exterior angle of triangles, parallel lines ,a 2 transversal, and the angle-angle criterion for similarity of triangles. Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved. 5 Unit Vocabulary Terms “Unwrapped” Focus Standards Supporting Standards Concepts and Concepts Other Unit-Specific Terms Exterior angle Parallel lines Triangle Rotation Reflection Isosceles Translation Dilation Equilateral Congruent Transversal Scalene Angle – angle criterion Coordinates Line segment Angle sum Perpendicular line Congruency Vertical angles Obtuse angle Triangle Sum Theorems Obtuse triangle Supplemental angle Essential Questions What effects does length and angle measurement have on triangles? . How do shapes change after each transformation? How are they the same? How do you manipulate a figure on the coordinate plane? What are some examples from the real world of transformational geometry? Given the pre-image, how can you determine what transformation has taken place? What kinds of patterns/designs can be created through multiple transformations? Corresponding Big Ideas The sum of the angle in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines equations of lines A translation is a transformation of an object that moves the object so that every point of the object moves in the same direction as well as the same distance. In a translation, the translated object is congruent to its pre-image A reflection is a transformation that flips an object across a line of reflection (in a coordinate grid the line of reflection may be the x or y axis). In a rotation, the rotated object is congruent to its preimage. A rotated figure is a figure that has been turned about a fixed point. This is called the center of rotation. A figure can be rotated up to 360˚. Rotated figures are congruent to their pre-image figures. Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved. 6 A dilation is a transformation that moves each point along a ray emanating from a fixed center, and multiplies distances from the center by a common scale factor. In dilated figures, the dilated figure is similar to its pre-image. Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved. 7 Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
