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Students will create, classify and sort quadrilaterals.
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.
1. Demonstrate a positive learning attitude toward mathematics.
3. Reason mathematically.
4. Communicate mathematically.
5. Make mathematical connections.
Invitation to Learn
Provide each student with a geoboard and geoband. Ask them to create several four-sided polygons, then choose their most unique quadrilateral to share with their group.
Ring 1 (Left side): At least one pair of parallel sides
Ring 2 (Right side) No sides parallel
Ask students to justify their placement of different pieces. What do all the shapes in one ring have in common? How might the shapes in one ring be different? (Some shapes in Ring 1 are trapezoids, and some are parallelograms.) What different label would eliminate one or more of the shapes from a ring? (Only one pair of parallel sides.) If we drew a giant circle around everything, including any shapes that are outside the rings, what might the label for this new ring be? (Quadrilaterals) Try further explorations using the following labels:
Ring 1 (Inner ring): All sides of equal length
Ring 2 (Outer ring): At least one pair of parallel sides
Ring 1 (Left side): At least one right angle
Ring 2 (Right side): No right angles
Ring 1 (Left side): All sides the same length
Ring 2 (Right side): At least one acute angle
Ring 1 (Left side): At least one set of parallel sides
Ring 2 (Right side): At least one obtuse angle
Have students take home the quadrilateral pieces to share with their family. Show them how to sort the pieces in each ring according to the labels given. They may need to overlap some rings to form intersections. Make “mystery rings” for family members to solve.