Teach kids how to say "Hello" in many languages and have them use a new word to greet each other for a day, week, month or even the whole year. Make sure to use languages from all over the globe, including European, Asian, African, Native American and Pacific Islander languages. This will teach children the essential parity of all languages and, by extension, of the peoples who speak them.
In a racially diverse environment, have students face each other in two parallel lines. Call out different "Have you ever" questions, such as "Have you ever owned a pet?" "Have you ever lived in another country?" and "Have you ever fought with your sibling?" Have the kids who can answer the questions in the affirmative jump into the middle. This teaches children that while people may look different, their hopes, likes and life experiences are not determined by skin color.
Have students of different races scrape some cells off their cheeks and make them into microscope slides. Shuffle the slides around and have students try to identify whose cells are whose. They won't be able to tell the difference between cells. This activity provides a powerful visual lesson that we are all essentially the same.
In her book, Dr. Tatum emphasizes the importance of using daily experiences to teach children about race. She writes about a time her son noticed how some eggs on the kitchen counter were white and others brown. She turned this into a teaching moment by cracking open a brown egg and then a white one. "See, they are different on the outside, but the same on the inside. People are the same way." You can replicate this exercise in the classroom using anything that comes in different colors.