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It’s a Slippery Slope! Using Similarity to Make Coherence March 20, 2012

This article explores the concept of coherence in the Common Core State Standards for Mathematics and how it can be applied through recognizing and applying connections across different domains. It provides specific examples of how similarity can be used to explain concepts such as the slope of the Leaning Tower of Pisa and the relationship between parallel lines and congruent angles.

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It’s a Slippery Slope! Using Similarity to Make Coherence March 20, 2012

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  1. It’s a Slippery Slope!Using Similarity to Make CoherenceMarch 20, 2012 Connie Laughlin Hank Kepner Rosann Hollinger Cynthia Schoonover Kevin McLeod Mary Mooney

  2. We are learning to … recognize and apply connections across domains in the CCSSM.

  3. We will know we are successful when we can… explain a specific example of coherence across domains.

  4. How can you describe the “lean” of the Leaning Tower of Pisa?

  5. With a partner… • Draw three new right triangles on the line. Each should be a different size. Label each triangle with as much information as you can. • What do these triangles have in common? • What are some relationships among these triangles?

  6. Poster Presentations What did we find?

  7. The Teacher Perspective What are the big ideas you would like students to understand?

  8. Apply • What if I draw a right triangle for this line with a horizontal change of 40? How big will the vertical change be? • What if I draw several right triangles on a different line? Can I still use the same ratio to find a missing vertical or horizontal change?

  9. With your partner… • Scan the Grade 8 Standards. • Identify standards that appear to relate to the lesson. • Link two of the standards you chose to highlight the connections between them.

  10. Grade 8 Equations and Expressions Understand the connections between proportional relationships, lines, and linear equations. 6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane… Geometry Understand congruence and similarity using physical models, transparencies, or geometry software. 5. Use informal arguments to establish…about the angles created when parallel lines are cut by a transversal.

  11. The Logical Argument • Parallel sides of the right triangles are parallel lines crossing a transversal. • Therefore, the parallel lines make congruent angles with the traversals. • Therefore, any two triangles are similar (AA~). • Therefore, the ratios of corresponding sides are equal. • This explains why the slope is the same between any two distinct points on a non-vertical line in a coordinate plane.

  12. We are learning to recognize and apply connections across domains in the CCSSM. We will be successful when we can explain a specific example of coherence across domains.

  13. Making Connections • What have I learned in this session? • What will I share at my schools? With whom/why? How?

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