Quadrilaterals are two-dimensional geometric shapes containing four sides. They take a number of shapes and dimensions, depending on the length of the sides and the angle at which they're joined. Most fourth-graders can name squares and rectangles, but they'll probably be stumped at first if you ask them to identify a rhombus, a trapezoid or a parallelogram. Identifying the points of similarity between quadrilaterals and the differences between them lays a foundation for the later understanding of more advanced geometry.
All quadrilaterals share in a limited number of characteristics. They are identified by the relative lengths of their sides, the angles formed where the sides connect and whether one or both pairs of sides are parallel. A rectangle has two pairs of parallel sides forming four right angles. So does a square. A parallelogram also has two pairs of parallel sides, but no right angles. A rhombus is a parallelogram with four equal sides, while a trapezoid is a quadrilateral with only one pair of parallel sides.
Show your class a picture of a rhombus and a square. Ask what makes them the same and what makes them different. The two are identical in most respects but can be differentiated by the lack or presence of right angles. The same holds true for a conventional parallelogram and a rectangle. Introduce the kids to the concept that not every characteristic is reciprocal. Every parallelogram is a quadrilateral, but not every quadrilateral is a parallelogram.
Show your students how to measure the angles at each corner of the quadrilaterals. Have them add up the totals and ask if there is a relationship. Most of the students should notice that the angles add up to a total of 360 degrees. For a practical exercise, ask the kids to make lists of objects they see that are quadrilaterals. List them and ask how many terms such as quadrilateral, rectangle or parallelogram apply to each one. Invite them to discuss their own and other students' reasoning.