Kids have strong feelings, and some kids have extra-big feelings. Expressing feelings, naming them, and noticing how people react to them are all ways children figure things out about themselves and others.
One way we explore feelings during dance/theatre classes for the K-3 age groups, is a game called "On Monday..." where something different happens each day of the week. It can take on different themes. Sometimes we do a weather theme and sometimes we do elaborate action words, such as, On Tuesday, sticky noodles swam crazily."
When we do the theme of feelings, I'll say something like, "On Monday, it was a sunshiny day and everyone in the town was happy." The class piano accompanist plays improvisational music, and the children express happiness through movement. Each day of the week introduces a new feeling - sad, tired, angry, excited, etc. The children make a choice on how they react and move.
Most kids jump right into this activity. Often there are one or two who are hesitant to give it a try. For those kids, I invite them to move with me - we do it together. This helps them become more at ease.
As a class, we discuss feelings before and after the game. Kids listen carefully when their peers talk about their experiences.