9/14/2023 0 Comments Rigid motionThese transformations can be performed using constructions, patty paper, and on a coordinate plane using properties of perpendicular and parallel lines.The word "rigid" has two different meaning when applied to a graph. Rigid motions can be performed to map one figure to another in single or a composition of transformations.Constructions are a precise way to create geometric figures with the simple tools of a compass and a straightedge. Geometric constructions show properties of a figure through the construction of that figure.Through this process, we can establish new facts. Geometric facts are established through proof by determining a sequence of logical statements and reasons that drive toward a conclusion that is the theorem proved.Every geometric definition, property, theorem, or conjecture exists because there was a question about whether a relationship exists and then a subsequent chain of reasoning based on previously known facts, or through geometric constructions, to convince us that this relationship exists.This document has quite a few helpful strategies to develop a logical explanation. While this unit references two column proofs, it is more important that students understand the thinking that is necessary to develop a logical explanation of why a relationship exists. Proofs can be a real challenge for teachers and students.Dan Meyer's If Proof Is Aspirin, Then How Do You Create the Headache?.Notice the progression of concepts through the unit using “Unit at a Glance”.Lesson(s) to which the assessment points.Relationship to Essential Understandings of unit.Strategies and representations used in daily lessons.Purpose of each question: spiral, foundational, mastery, developing.Standards to which each question aligns.Internalization of Standards via the Unit Assessment Pacing: 21 instructional days (19 lessons, 1 flex day, 1 assessment day) Through the establishment of a solid foundation of precise vocabulary and developing arguments in Unit 1, students are able to use these strategies and theorems to identify and describe geometric relationships throughout the rest of the year. In the next unit, students use the concepts of constructions, proof, and rigid motions to establish congruence with two dimensional figures. Students focus on rigid motions with points, line segments and angles in this unit through transformation both on and off the coordinate plane. Students learn that rigid motions can be used as a tool to show congruence. Topic C merges the concepts of specificity of definitions, constructions, and proof to formalize rigid motions studied in 8th Grade Math. In Topic B, students formalize understanding developed in middle school geometry of angles around a point, vertical angles, complementary angles, and supplementary angles through organizing statements and reasons for why relationships to construct a viable argument. Students are introduced to the concept of a construction, and use the properties of circles to construct basic geometric figures. Unit 1 begins with students identifying important components to define- emphasizing precision of language and notation as well as appropriate use of tools to represent geometric figures. This unit lays the groundwork for constructing mathematical arguments through proof and use of precise mathematical vocabulary to express relationships. These rigid motion transformations are introduced through points and line segments in this unit, and provide the foundation for rigid motion and congruence of two-dimensional figures in Unit 2. Transformations that preserve angle measure and distance are verified through constructions and practiced on and off the coordinate plane. In Unit 1, students are introduced to the concept that figures can be created by just using a compass and straightedge using the properties of circles, and by doing so, properties of these figures are revealed.
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