Early Education

Wheeling, Illinois 60090

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# Mathematics

## Geometry

### 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

### 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

• Describe
• Analyze
• Prove
• Apply

### 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?