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.

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

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