The National Council of Supervisors of Mathematics. The Common Core State Standards Illustrating the Standards for Mathematical Practice: Congruence & Similarity Through Transformations www.mathedleadership.org. Defining Congruence & Similarity through Transformations.
The Common Core State Standards
Illustrating the Standards for Mathematical Practice:
Congruence & Similarity Through Transformations
How would you define congruence?
How would you define similarity?
Used in the CCSS
Corresponding side lengths of similar figures are in proportion (height1sttriangle:height2nd triangle is equal to base 1sttriangle:base 2nd triangle)
Ratios of lengths within a figure are equal to ratios of corresponding lengths in a similar figure (height :base1sttriangle is equal to height :base2nd triangle)
What do you notice about the geometric
structure of the triangles?
Verify experimentally the properties of rotations, reflections, and translations:
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.Standards for Mathematical Content
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.Standards for Mathematical Practice
Which rectangles are similar to rectangle a?
Video clips are examples, not exemplars.
To spur discussion not criticism
Video clips are for investigation of teaching and learning, not evaluation of the teacher.
To spur inquiry not judgment
Video clips are snapshots of teaching, not an entire lesson.
To focus attention on a particular moment not what came before or after
Video clips are for examination of a particular interaction.
Cite specific examples (evidence) from the video clip, transcript and/or lesson graph.
One page overview of each lesson
Provides a sense of what came before and after the video clip
Take a few minutes to examine where the video clip is situated in the entire lesson
View Video Clip
Use the transcript as a reference when discussing the clip
What did Randy do? (What was his method?)
Why might we argue that Randy’s conception of similarity is more transformation-based than static?
What mathematical practices does he employ?
What mathematical argument is he using?
What tools does he use? How does he use them strategically?
How precise is he in communicating his reasoning?
2. Are there any aspects of your students’ mathematical learning that our work today has caused you to consider or reconsider? Explain.
Video Clips from Learning and Teaching Geometry Foundation Module
Laminated Field Guides Available in class sets