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EMBRACING TRANSFORMATIONAL GEOMETRY IN CCSS- MATHEMATICS Presentation at Palm Springs 11/1/13 Jim Short [email protected]

Embracing transformational geometry in CCSS-Mathematics

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Embracing transformational geometry in CCSS-Mathematics. Jim [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 - PowerPoint PPT Presentation

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EMBRACING TRANSFORMATIONAL GEOMETRY IN CCSS-

MATHEMATICS

Presentation at Palm Springs 11/1/13

Jim [email protected]

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

Introductions

3

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

Workshop Goals

4

ATP Administrator Training - Module 1 – MS/HS Math

Workshop Norms

1. Bring and assume best intentions.

2. Step up, step back.

3. Be respectful, and solutions oriented.

4. Turn off (or mute) electronic devices.

Transformation Geometry 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

Flow of Transformational Geometry

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 Coordinate Plane

Develop Understanding of Effect of

Transformations on Figures

Develop Understanding of Functions

Develop Understanding of

Transformations as Functions on the

Plane/Space

Geometry Standards Progression

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

Golden Oldies: Constructions

“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?

More With Constructions Please read through “What Makes a

Triangle?” on p. 134-135 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?

Physical Movement in Geometry

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?

Transformations 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

Reflection

Is This A Reflection? Is This A Reflection?

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

Rotations 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

Translations 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

Dilations Do “Introduction to Dilations” Look at p. 189, “Dilation with Rubber Bands” Now do “Enlarging on a Copy Machine” (p.

191-192) “Dilation Investigations” – read over and

think about p. 193 ..\..\..\Desktop\Algebra in Motion\Geometric

Transformations (reflect, translate, rotate, dilate objects).gsp

Euclidean Transformations What changed and what remained the

same in the four Euclidean transformations?

Complete “Properties of Euclidean Transformations”

How do we now define congruent figures?

How do we now define similar figures?