One 'fourth grade' way of doing this would be to actually be playing with something like straws, or connectrix sicks and joints.
I imagine the answer they are looking for is the 'kite'. This type of lateral thinking is appropriate at many levels. Sometimes it is easier for younger children, who are not as 'routinized'.
Interestingly, at the other end of experience, the first example I thought of was the 'butterfly' - which is self-interesecting, and probably further from what fourth grade students would image. This I would find by making something like a parallelogram from straws and strings, then playing with it into 3-space and back into the plane. In that kind of kinematic play, you realize the opposite sides are still equal in length, and only have to puzzle over whether it ceased to 'be a quadrilateral' when it dropped back into the plane with a crossing.
> Draw a quadrangle that has 2 pairs of equal sides but is NOT a > parallelogram. > Does this seem like 4th grade to anyone? I finally got the answer but > we have no book to use as a reference.