logging in or signing up Chapter 2 notes MS3 Geometry mwarner1968 Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 677 Category: Others/ Misc License: All Rights Reserved Like it (1) Dislike it (0) Added: July 24, 2008 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Chapter 2 Geometry“Location” : Chapter 2 Geometry“Location” July 23, 2008 Inductive vs. Deductive Reasoning : Inductive vs. Deductive Reasoning Inductive reasoning –making conjectures on the basis of data Deductive reasoning—begins with a statement that is accepted as true and demonstrates that other statements follow the original assumption. True or False? : True or False? If it is a square, then it is a rectangle. If it is a rectangle, then it is a square. If it is a square, then it is a rhombus. If it is a right triangle, then it is an equilateral triangle. All parallelograms have congruent diagonals. True or False? : True or False? If two rectangles have the same area, they are congruent. If two squares have the same perimeter, then they are congruent. Agenda : Agenda Shape Summary / Questions PS: Reasoning and Proof Pythagorean Theorem Discussion: Location Constructing Geometric Figures… Centers Process Centers & Wrap-up Reasoning & Proof : Reasoning & Proof Recognize R&P as fundamental aspects of mathematics Make and investigate mathematical conjectures Develop and evaluate mathematical arguments Select and use various types of reasoning and methods of proof. Reasoning and Proof : Reasoning and Proof Discourse Representations Writing Benefits: Extend thinking, solidify understandings, learn how classmates think Creating a Learning Environment that Promotes R&P : Creating a Learning Environment that Promotes R&P Our attitude towards mathematics A safe, supportive, and respectful classroom Engaging and challenging mathematics Questioning Reasoning about the Pythagorean Theorem : Reasoning about the Pythagorean Theorem Area Models—Grids/Cuisenaire Rods Language Pythagorean Triples HOT questions Euler’s formula BIG Idea: Location : BIG Idea: Location What do students learn about this idea in elementary? Selected Instructional Activities Turning the Grid System on the Calculator Pg. 34 Same area vs. congruent BIG Idea: LocationGrades 6-8 : BIG Idea: LocationGrades 6-8 Use coordinate geometry to represent and examine the properties of geometric shape Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular lines. Constructing Geometric Figures in Coordinate Space : Constructing Geometric Figures in Coordinate Space Goals: Reinforce or develop graphing skills Explore properties of shapes in a coordinate system Directions / Variations Math Centers : Math Centers Exploring Lines, Midpoints, & Triangles Similarity and the Coordinate Plane— Vocabulary: Dilation Exploring Slopes of Parallel & Perpendicular Lines 30 minutes for each center Discussion of Center Activities : Discussion of Center Activities Exploring Lines,…. Similarity … Exploring Slopes,… Conclusions : Conclusions Foundational ideas of algebra were connected to geometry. Coordinate geometry serves as a context for describing shapes, sizes, positions, and orientation of shapes and for extending ideas about congruence and similarity. For tomorrow… : For tomorrow… Read Chapter 3 pgs. 43-44. Create a kid-friendly definition for dilation with an action. Reminders: Skim Ball article for Friday. Begin thinking about final product. 3-2-1 : 3-2-1 3 things I’m feeling good about 2 things I will take away from today 1 thing I’m still wondering about You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
Chapter 2 notes MS3 Geometry mwarner1968 Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 677 Category: Others/ Misc License: All Rights Reserved Like it (1) Dislike it (0) Added: July 24, 2008 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Chapter 2 Geometry“Location” : Chapter 2 Geometry“Location” July 23, 2008 Inductive vs. Deductive Reasoning : Inductive vs. Deductive Reasoning Inductive reasoning –making conjectures on the basis of data Deductive reasoning—begins with a statement that is accepted as true and demonstrates that other statements follow the original assumption. True or False? : True or False? If it is a square, then it is a rectangle. If it is a rectangle, then it is a square. If it is a square, then it is a rhombus. If it is a right triangle, then it is an equilateral triangle. All parallelograms have congruent diagonals. True or False? : True or False? If two rectangles have the same area, they are congruent. If two squares have the same perimeter, then they are congruent. Agenda : Agenda Shape Summary / Questions PS: Reasoning and Proof Pythagorean Theorem Discussion: Location Constructing Geometric Figures… Centers Process Centers & Wrap-up Reasoning & Proof : Reasoning & Proof Recognize R&P as fundamental aspects of mathematics Make and investigate mathematical conjectures Develop and evaluate mathematical arguments Select and use various types of reasoning and methods of proof. Reasoning and Proof : Reasoning and Proof Discourse Representations Writing Benefits: Extend thinking, solidify understandings, learn how classmates think Creating a Learning Environment that Promotes R&P : Creating a Learning Environment that Promotes R&P Our attitude towards mathematics A safe, supportive, and respectful classroom Engaging and challenging mathematics Questioning Reasoning about the Pythagorean Theorem : Reasoning about the Pythagorean Theorem Area Models—Grids/Cuisenaire Rods Language Pythagorean Triples HOT questions Euler’s formula BIG Idea: Location : BIG Idea: Location What do students learn about this idea in elementary? Selected Instructional Activities Turning the Grid System on the Calculator Pg. 34 Same area vs. congruent BIG Idea: LocationGrades 6-8 : BIG Idea: LocationGrades 6-8 Use coordinate geometry to represent and examine the properties of geometric shape Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular lines. Constructing Geometric Figures in Coordinate Space : Constructing Geometric Figures in Coordinate Space Goals: Reinforce or develop graphing skills Explore properties of shapes in a coordinate system Directions / Variations Math Centers : Math Centers Exploring Lines, Midpoints, & Triangles Similarity and the Coordinate Plane— Vocabulary: Dilation Exploring Slopes of Parallel & Perpendicular Lines 30 minutes for each center Discussion of Center Activities : Discussion of Center Activities Exploring Lines,…. Similarity … Exploring Slopes,… Conclusions : Conclusions Foundational ideas of algebra were connected to geometry. Coordinate geometry serves as a context for describing shapes, sizes, positions, and orientation of shapes and for extending ideas about congruence and similarity. For tomorrow… : For tomorrow… Read Chapter 3 pgs. 43-44. Create a kid-friendly definition for dilation with an action. Reminders: Skim Ball article for Friday. Begin thinking about final product. 3-2-1 : 3-2-1 3 things I’m feeling good about 2 things I will take away from today 1 thing I’m still wondering about