3.G.A.1

Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.


 

Summary:

This standard deals with four-sided figures of all types. The focus is on the categorization of these with the outcome being that they are all part of a large group we classify as "quadrilaterals". Students should engage in activities that allow them to recognize the differences between rhombuses, rectangles, and squares, and students should be required to draw quadrilaterals that are not in any of these categories.

Understanding the Standard:

    • Students should draw quadrilaterals.
    • Students should investigate the unique nature of a square as the special case of a rhombus (i.e., a rhombus that has equal angle measurements) and a rectangle (i.e., a rectangle that has equal side lengths).
    • Students may discover that a trapezoid fits the "other" category.

      Questions to Focus Instruction:

        • Can students distinguish between a rhombus and a kite?
        • Can students draw a quadrilateral with given attributes? (e.g., draw a quadrilateral that has one right angle; two right angles; three right angles' four right angles' two equal sides; a pair of parallel sides: etc. 

          Skills


          Prior to: Students will know the names of shapes.  Go to 2.G.A.1. to see the previous skills in this progression.

          At Grade Level: Students will recognize parallel and perpendicular lines in quadrilaterals that have them (e.g., a rectangle).

          Beyond:  Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.