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999 West Dundee Road
Wheeling, Illinois 60090

Phone: 847-537-8270

Superintendent: Dr. Michael Connolly

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Mathematics

Geometry

Critical Content

Power Standards

  • Use coordinates to describe the effect of transformations (dilations, translations, rotations, reflections). (8.G.3)
  • Apply the Pythagorean Theorem in mathematical problems, including those in real-world contexts. (8.G.7)

 

Concepts and Skills

* Power Standard Content

  • * Rotations, reflections, translations
  • * Prove congruency using transformations
  • * Prove similarity using dilations and transformations
  • * Apply the Pythagorean Theorem (e.g., missing triangle side lengths, distance between two points)
  • Describe and analyze symmetries of figures

 

Critical Language

Language Usage

  • A student in 8th grade will demonstrate the ability to apply and comprehend critical language by describing the effect of transformations, and by explaining the Pythagorean Theorem.

 

Content-Specific Vocabulary

  • Rotations
  • Reflections
  • Translations
  • Congruent
  • Transformations
  • Similar
  • Dilation
  • Pythagorean Theorem
  • Symmetries
  • Distance

 

Process-Specific Vocabulary

  • Describe
  • Analyze
  • Prove
  • Apply

 

Concept-Based Connections

Essential Understandings

  • Right triangles have a unique and important side-length relationship known as the Pythagorean Theorem.
  • Knowing and applying geometric properties and equations allows one to solve complex problems involving geometric figures.

 

Factual Guiding Questions

  • What is the difference between each type of transformation?
  • What is the Pythagorean Theorem?
  • How do you find the distance between two points?
  • How do you determine if two figures are similar?
  • How can you identify which transformations have been made to create a figure?

 

Conceptual Guiding Questions

  • What specific information about distances can we use when we transform a figure?
  • What properties can be used to determine if two figures are similar?
  • How can it be determined whether or not a triangle is a right triangle if only the side lengths are known?

 

Engaging/Debatable Guiding Questions

  • When is it appropriate and useful to use the Pythagorean Theorem?
  • What connections exist between geometry and algebra?