Thursday, September 25, 2014

Middle School Geometry Under Common Core Standards

The Common Core State Standards adopted by Oregon and most other states in the US describe what math students should understand and be able to do at various grades and in various "domains," or topics, such as Expressions and Equations (basically Algebra) or Statistics & Probability. The standards at each grade level are meant to build on the standards of the year before.

Here is my summary of what all middle school students are expected to learn about Geometry by the end of eighth grade, based on the Common Core state standards in math for sixth, seventh, and eighth grades. (Note: "e.g." means "for example".)

I. Area, perimeter, circumference, surface area, and volume

  1. Know and use formulas for area of triangles, rectangles, parallelograms, and two-dimensional shapes made from these (6.G.1), and circle area and circumference (7.G.4).
  2. Know and use formulas for the volumes of right rectangular prisms (boxes) with fractional edge lengths (6.G.2), three-dimensional objects composed of cubes and right prisms (7.G.6), and cones, cylinders, and spheres (8.G.9).
  3. Find the surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (7.G.6)
  4. Represent 3-D figures with nets, and use nets to find surface area. (6.G.4)
  5. Describe what 2-D shapes you would get by slicing 3-D objects like boxes, cylinders or pyramids. (7.G.3)

II. Scale and Similarity

  1. Interpret scale drawings, and reproduce scale drawings with a different scale. (7.G.1)
  2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions (e.g. triangles with certain angle measures and side lengths). (7.G.2)
  3. Recognize what conditions (e.g. combinations of side lengths or angles) determine a unique triangle, more than one triangle, or no triangle. (7.G.2)
  4. Use informal arguments to establish facts about the angle-angle criterion for similarity of triangles. (8.G.5)

III. Angles

  1. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. (7.G.5)
  2. Use informal arguments to establish facts about the angle sum and exterior angle of triangles. (8.G.5)
  3. Use informal arguments to establish facts about the angles created when parallel lines are cut by a transversal. (8.G.5)

IV. Transformations

  1. Rotations, reflections, and translations: know side lengths & angle measures are preserved, and parallel lines are still parallel. (8.G.1)
  2. Describe how to get one congruent or similar figure from another with transformation(s). (8.G.2 and 8.G.4)
  3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. (8.G.3) 

V. The Pythagorean Theorem

  1. Explain a proof of the Pythagorean Theorem and its converse. (8.G.6)
  2. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in two and three dimensions. (8.G.7)
  3. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. (8.G.8)

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