It

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Its a Slippery Slope!Using Similarity to Make
CoherenceMarch 20, 2012

• Connie Laughlin
• Hank Kepner
• Rosann Hollinger Cynthia Schoonover
  Kevin McLeod
• Mary Mooney

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We are learning to

• recognize and apply connections across domains in
  the CCSSM.

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We will know we are successful when we can

• explain a specific example of coherence across
  domains.

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How can you describe the lean of the Leaning
Tower of Pisa?
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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?

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Poster Presentations

• What did we find?

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The Teacher Perspective

• What are the big ideas you would like students to
  understand?

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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?

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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.

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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 establishabout the
• angles created when parallel
• lines are cut by a transversal.

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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.

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• 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.

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Making Connections

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