11+Geometry

= On this page you will find resources relating to the teaching and learning of geometries, including Euclidean geometry, coordinate geometry, and transformation geometry. =

1. Development of Geometric Thought: Van Hiele Levels (Visualization, Analysis, Informal Deduction, Deduction, Rigor)
For detailed explanations: (PDF)

2. Classifying quadrilaterals: Go Fly a Kite!
We classify quadrilaterals by reasoning with their diagonals: (PDF) Geogebra files: //CCSS controversy: Inclusive versus exclusive definition of a trapezoid//

3. Pythagoras: Reasoning about the relationship of areas of squares on sides of triangles.
Tile Activity: (DOCX) Tile Squares for Tile Activity: (DOCX) Geogebra File: Geogebra File: Geogebra File: Liquid "Proof" (YouTube): LINK Visual Proof (NCTM Illuminations): LINK Animated proof (YouTube): LINK Historical approach: Download (PDF) Inquiry Lesson Video focused on AREAS: @https://www.teachingchannel.org/videos/pythagorean-theorem-lesson Inquiry Lesson Video focused on SIDES: @https://www.teachingchannel.org/videos/teaching-pythagorean-theorem

**4. Tangrams are not Toys!** Reasoning with Tangrams by finding the underlying structure through a folding activity: (PDF)

5. Proving
a. The November 2009 issue of the NCTM journal The Mathematics Teacher is entirely devoted to proving: LINK b. An article I wrote regarding informal deductive reasoning in sixth graders: (PDF) c. The Travel Metaphor: (PDF) d. Three columns instead of two, a strategy to help students with proving: (PDF)

e. Proving and reasoning logically is not exclusive to Geometry. One example, Logic in the coordinate plane: (PDF)
 * Teacher examples: Example 1 Example 2 (DOC) Using Educreations to study facial symmetry LINK
 * GIP Template: Download (DOCX)
 * Example assignment: Download (DOCX)

Geogebra files:
 * 6. Proving Congruence and Similarity in the CCSS[[image:bad-poster.JPG align="right"]]**

7. Common Core development of Geometry grades 6-12: Download **(DOCX)**

 * PARCC sample Geometry Questions: LINK**

8. Transformation Geometry
Rotation Lesson Study PLAN: Rotation Lesson Study WORKSHEET:

Composition of reflections:

**9. Longsword dancing and stable geometrical shapes (Video):**
@http://simonsfoundation.s3.amazonaws.com/jwplayer/longsword/Longsword-dancing-2b_compressed2.mp4