Wheat (Triticum aestivum) is in the grass family (Poaceae = Gramineae) and so does not constitute a family itself. The Poaceae includes almost all the plants we call grasses as well as bamboos and reeds. Many of the most important food-plants are in the family, including barley, maize/corn, oats, rice, rye and wheat.

Graminaceae, the grass family.

Wheat is a cereal grain which is one of the common grasses. It is a member of the family Poaceae (formerly Gramineae) of the genus Triticum.

Maize (corn) belongs to the family Poaceae.