Various Transformations Affect Distances and Angles of Figures Differently. These Effects

MS 104

Unit Plan4

Unit Name:
Butterflies, Pinwheels & Wallpaper / Grade: 8 / Month(s): January-February / Duration: 3 weeks
Essential Question:
How do transformations affect congruence and similarity? / Big Ideas/Enduring Understandings:

• Various transformations affect distances and angles of figures differently. These effects help you compare figures and determine the similarity or congruence between figures.
• Two shapes are congruent if a specific sequence of rigid transformations will transform one shape to the other. Two figures are similar if a specific sequence of rigid transformations and dilation will transform one shape to the other.
• Properties of transformations, congruence, and similarity can be used to solve problems about shapes and measurements.

Common Core Learning Standards:
8.G.A.1:Verifyexperimentallytheproperties ofrotations,reflections, andtranslations.
8.G.A.2:Understandthat atwo-dimensionalfigureiscongruenttoanother ifthesecondcanbeobtainedfromthefirstbyasequenceofrotations, reflections,andtranslations;giventwocongruentfigures,describea sequencethat exhibits thecongruencebetweenthem.
8.G.A.3:Describetheeffectofdilations, translations,rotations,and reflectionsontwo-dimensionalfiguresusingcoordinates.
8.G.A.4:Understandthat atwo-dimensionalfigureissimilartoanotherifthe secondcanbeobtainedfromthefirstbyasequenceofrotations,reflections,translations,anddilations; giventwosimilartwo-dimensionalfigures, describeasequencethat exhibits thesimilaritybetweenthem
8.G.A.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.
Student Objectives:
Transformations
Describe types of transformations that relate points by the motions of reflections, rotations, and translations, and describe methods for identifying and creating symmetric plane figures
Recognize properties of reflection, rotation, and translation transformations
Explore techniques for using rigid motion transformations to create symmetric designs
Use coordinate rules for basic rigid motion transformations
Congruence and Similarity
Understand congruence and similarity and explore necessary and sufficient conditions for establishing congruent and similar shapes
Recognize that two figures are congruent if one is derived from the other by a sequence of reflection, rotation, and/or translation transformations
Recognize that two figures are similar if one can be obtained from the other by a sequence of reflections, rotations, translations, and/or dilations
Use transformations to describe a sequence that exhibits the congruence between figures
Use transformations to explore minimum measurement conditions for establishing congruence of triangles
Use transformations to explore minimum measurement conditions for establishing similarity of triangles
Relate properties of angles formed by parallel lines and transversals, and the angle sum in any triangle, to properties of transformations
Use properties of congruent and similar triangles to solve problems about shapes and measurements
Activities/Tasks
Investigation 1: Symmetry and Transformations
Line reflections
Rotations
Translations
Properties of transformations
Investigation 2: Transformations and Congruence
Congruent triangles
Investigation 3: Transforming Coordinates
Coordinate rules for reflection
Coordinate rules for translations
Coordinate rules for rotations
Parallel lines, transversals and angle sums
Investigation 4: Dilations and Similar Figures
Similarity transformations
Assessments:
Transformation Performance task
Key Terms/Vocabulary: angle of rotation, center of rotation, congruent figures, dilation, line of symmetry, line reflection, reflectional symmetry, rotation, rotational symmetry, similar figures, similarity, transformationsymmetry, transformation, translation, translational symmetry
Resources:
CMP3: Butterflies, Pinwheels & Wallpaper
Glencoe