Place three or four object on a table. Ask questions such as, "Which one is in first place?" or "The ball is in which place?" Shuffle the items so they are in different positions and ask the same questions again. Increase the number of objects from four to five. Add more as the task becomes easy.
Have students line up by counting off using numerical digits. When all are standing, explain that you are going to call out an ordinal number and the student who is in the corresponding place in line should raise a hand. When you say "fifth," the child occupying that spot should respond. This exercise can be repeated when lining up for lunch or recess.
Give half the class cards with numerical digits 1 through 10 written on them and half with cardinal numbers first through 10th. Allow the students to move around the room until they find the person who holds the card corresponding to their own. Once partners are found, everyone moves to the back of the class to form a line in order from first to 10th.
Read a book such as, "Where The Wild Things Are," by Maurice Sendak. Discuss the story with emphasis on the order in which events take place. Students should be able to tell you what happened first, second, third and so on. Turn it into an art lesson by letting the children create their own storyboards illustrating story sequence.
If your kindergartners are ready, teach them the commonly used ordinal abbreviations. Give one group cards with ordinal words written on them (first), a second group numerical digits (1), and a third group, ordinal abbreviations (1st). Place a row of chairs in front of the classroom. Ask the children to tape their cards to the correct chair. Make it a group effort by allowing them to help each other.