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# Embracing transformational geometry in CCSS-Mathematics - PowerPoint PPT Presentation

Embracing transformational geometry in CCSS-Mathematics. Jim Short [email protected] Presentation at Palm Springs 11/1/13. Introductions. Take a minute to think about, and then be ready to share: Name School District Something you are doing to implement CCSS-M

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### Embracing transformational geometry in CCSS-Mathematics

Jim Short [email protected]

Presentation at Palm Springs 11/1/13

Take a minute to think about, and then be ready to share:

• Name

• School

• District

• Something you are doing to implement CCSS-M

• One thing you hope to learn today

• Briefly explore the Geometry sequence in CCSS-M

• Deepen understanding of transformational geometry and its role in mathematics

• In the CCSS-M

• In mathematics in general

• Engage in hands-on classroom activities relating to transformational geometry

• Special thanks to Sherry Fraser and IMP

• Special thanks also to CMP and the CaCCSS-M Resources

2. Step up, step back.

3. Be respectful, and solutions oriented.

4. Turn off (or mute) electronic devices.

Workshop Norms

ATP Administrator Training - Module 1 – MS/HS Math

• What is a transformation?

• In Geometry: An action on a geometric figure that results in a change of position and/or size and or shape

• Two major types

• Affine – straight lines are preserved (e.g. Reflection)

• Projective – straight lines are not preserved (e.g. map of the world)

• School mathematics focuses on a sub-group of affine transformations: the Euclidean transformations

• Ideas of transformational geometry are developed over time, infused in multiple ways

• Transformations are a big mathematical idea, importance enhanced by technology

Develop Understanding of Attributes of Shapes

Develop Understanding of Effect of Transformations on Figures

Develop Understanding of Transformations as Functions on the Plane/Space

Develop Understanding of Coordinate Plane

Develop Understanding of Functions

• Share the standards with your group. Take turns reading the content standards given

• Analyze the depth and complexity of the standards

• Order the standards across the Progression from K – High School

Geometric Transformations In CCSS-Mathematics

• Begins with moving shapes around

• Builds on developing properties of shapes

• Develops an understanding of dynamic geometry

• Provides a connection between Geometry and Algebra through the co-ordinate plane

• Provides a more intuitive and mathematically precise definition of congruence and similarity

• Lays the foundation for projections and transformations in space – video animation

• Lays the foundation for Linear Algebra in college – a central topic in both pure and applied mathematics

• “Drawing Triangles with a Ruler and Protractor” (p. 125-126)

• Which of the math practice standards are being developed?

• How can this activity be used to prepare students for transformations?

• Please do p. 136, “Tricky Triangles”

• How can we use constructions to prepare students for a definition of congruence that uses transformations as the underlying notion?

• What, if any, is the benefit of using constructions to motivate the development of geometric reasoning?

• Each person needs to complete #1 on p. 148

• Each group will then complete #2 for one of the 5 parts of #1.

• What are the related constructions, and how do we ensure that students see the connections?

• In any transformation, some things change, some things stay constant

• What changes?

• What stays constant?

• What are the defining characteristics of each type of transformation?

• Reflection

• Rotation

• Translation

• Dilation

Is This A Reflection?

Is This A Reflection?

• Do “Reflection Challenges” on p. 168 either using paper and pencil, or using Geometer’s Sketchpad (or Geogebra or other dynamic geometry system)

• What is changed, what is left constant, by a reflection?

• What is gained by having students use technology? What is lost by having students use technology?

• ..\..\..\Desktop\Algebra in Motion\Geometric Transformations (reflect, translate, rotate, dilate objects).gsp

• Do activity “Rotations”

• Patty paper might be helpful for this activity

• Do “Rotation with Coordinates” p. 177

• What are students connecting in this activity?

• Look at “Sloping Sides” on p. 178.

• What are students investigating and discovering?

• ..\..\..\Desktop\Algebra in Motion\Geometric Transformations (reflect, translate, rotate, dilate objects).gsp

• Look at “Isometric Transformation 3: Translation” (p. 180)

• Do “Translation Investigations” p. 183

• ..\..\..\Desktop\Algebra in Motion\Geometric Transformations (reflect, translate, rotate, dilate objects).gsp

• Do “Introduction to Dilations”

• Look at p. 189, “Dilation with Rubber Bands”

• Now do “Enlarging on a Copy Machine” (p. 191-192)