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Main Curriculum Tie:
Background For Teachers:
A common activity involving geometry is for students to recognize and name various polygons. Their experiences with four-sided polygons may lack depth or may have some misconceptions. For example, students are often taught to categorize rectangles and squares separately. Typically, a polygon with four equal sides and four equal angles is referred to as a square; whereas, a polygon with four equal angles but one pair of long sides and one pair of short sides is referred to as a rectangle. We hear students refer to rectangles as being “long” or “tall.” Their system for differentiating between squares and rectangles is based on narrow experiences with a few specific examples.
These constructions may cause confusion later as students learn that squares also fit the description of rectangles. This new information does not fit logically to what they have already learned, and it does not allow for growth in understanding that a square is a more specific classification of a rectangle; just as a rectangle is a more specific classification of a parallelogram; and that a parallelogram is a specific classification of a quadrilateral. These shapes all fit in the quadrilateral “family.”
To aid understanding, teach quadrilaterals as a whole. Define quadrilaterals as a four-sided figure and give students the opportunity to create a variety of quadrilaterals. They look for similarities and differences and sort them into several different categories according to their attributes. The sorting activity offers insight into the mathematical hierarchy used in classifying quadrilaterals. It will become clear that every quadrilateral falls into three categories:
This activity will set the stage for students to understand that many types of quadrilaterals exist and that these shapes have some elements in common.
Intended Learning Outcomes:
Invitation to Learn
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