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