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Progressive Mathematics Initiative www.njctl.org Mathematics Curriculum Unit Plan # 3 Title: Transformations Subject: Geometry Length of Time: 2 weeks Unit Summary: In this unit several different transformations will be explored and their properties will be compared. Function notation will be used to describe transformations and more rigorous definitions will be developed for these transformations. A variety of tools (tracing paper, Geometry software, etc.) will be used to show the effect of a transformation upon a figure. Students will learn to predict the effect of a transformation upon a given figure, find transformations or sequences of transformations that map one figure onto another. Learning Targets Domain: Congruence Cluster: Experiment with transformations in the plane Standard#: G-CO.2 G-CO.3 G-CO.4 Standard: Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G-CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Cluster: Understand congruence in terms of rigid motions G-CO.6 G-CO.7 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G-CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Domain: Similarity, Right Triangles, & Trigonometry Cluster: Understand similarity in terms of similarity transformations Standard#: Standard: Verify experimentally the properties of dilations given by a center and a G-SRT.1 scale factor: Given two figures, use the definition of similarity in terms of similarity G-SRT.2 transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. G-SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Unit Essential Questions: Unit Enduring Understandings: What types of transformations Rigid motions: translation, reflection, rotation and are rigid motions? glide reflection Dilations How can you represent a Reflectional and rotational symmetry transformation in the coordinate Compositions of Transformations plane? Congruence and Similarity Transformations How do recognize symmetry in a figure? What does it mean for two figures to be congruent? To be similar? Which sequence of transformations can map one figure onto the other? Unit Objectives: Students will be able to identify rigid motions and images Students will be able to describe transformations in the coordinate plane using function notation. Students will be able to translate, reflect, rotate and dilate a figure using a variety of tools Students will be able to identify reflectional or rotational symmetry of a figure if it exists. Given congruent figures or similar figures, students will be able to find a sequence of transformations that moves one figure onto the other Evidence of Learning Formative Assessments: SMART Response questions at the end of each section throughout the unit. 2 Labs 2 Quizzes Summative Assessment: Performance Task Unit Test Lesson Plan Topics Topic #1: Transformations Topic #2: Translations Lab: Reflections Activity Topic #3: Reflections Lab: Rotations Activity Topic #4: Rotations Quiz 1: Reflections and Translations Topic #5: Composition of Transformations Topic #6: Congruence Transformations Topic #7: Dilations Topic #8: Similarity Transformations Quiz 2: Rotations and Glide Reflections Unit Review Performance Task / Unit Test Curriculum Resources https://njctl.org/courses/math/geometry/ Video: Drawing Reflections Demo Video: Drawing Rotations Demo Class Periods 0.5 0.5 0.5 0.5 0.5 0.5 1 1 1 1 1 1 1