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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

  • Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing. (7.G.1)

 

Concepts and Skills

* Power Standard Content

  • * Solve problems involving scale drawings
  • * Draw geometric shapes with given conditions
  • Use scale factors to compare similar figures
  • Use supplementary, complementary, vertical and adjacent angles to solve problems
  • Solve real-world problems involving area, volume, and surface area of compositions of triangles, quadrilaterals, polygons, cubes, and right prisms
  • Know and use formulas for finding area and circumference of a circle
  • Describe 2-dimensional cross sections of 3-dimensional figures

 

Critical Language

Language Usage

  • A student in seventh grade can demonstrate the ability to apply and comprehend critical language by explaining properties of similar figures and utilizing proportional reasoning when scaling is required in geometric situations.

 

Content-Specific Vocabulary

  • Scale
  • Scale factor
  • Similar
  • 2-Dimensional
  • 3-Dimensional
  • Supplementary
  • Complementary
  • Vertical
  • Adjacent
  • Angles
  • Circumference
  • Area
  • Volume
  • Surface area
  • Triangles
  • Quadrilaterals
  • Polygons
  • Cubes
  • Right prisms
  • Cross section

 

Process-Specific Vocabulary

  • Compare
  • Solve
  • Draw
  • Describe
  • Formula

 

Concept-Based Connections

Essential Understandings

  • Similarity is the geometric representation of proportion.
  • Understanding the unique measurable attributes of two-dimensional and three-dimensional shapes leads to the strategic use of space.

 

Factual Guiding Questions

  • How can angles be classified?
  • How do you find a scale factor?
  • How do you find the measurement of a circle (area and circumference)?
  • How do you find the area of triangles, quadrilaterals, and polygons?
  • How do you find the volume and surface area of cubes and right prisms?
  • What two-dimensional shapes create this three-dimensional figure?

 

Conceptual Guiding Questions

  • How do you use the measures of the angles given to find an unknown angle measure?
  • When two figures are similar, how can you describe the similarities/differences between the two figures?
  • How do you use similarity to find an unknown measurement?
  • How can you draw similar figures using a scale factor?
  • How do ratios relate to similarity?
  • How do you create a similar figure with a given volume?

 

Engaging/Debatable Guiding Questions

  • When is it necessary to find surface area in a real-world situation?
  • When is it necessary to find volume in a real-world situation?
  • What purpose does similarity have in real life?