Very often, the younger child is shy when singing alone in front of their teacher. You'll get faster results if you use a hand puppet. A puppet is less threatening and creates a friendly atmosphere. Basically, the falling minor third is the best interval to begin with for a beginning singer. Then as the child begins to hear the matched pitches more easily, it is simpler to lead the child to sing higher and lower notes.
Teacher sings another melodic pattern and so on.
Now let's talk about involving body motions. Ask the child to show you how one would play a drum. The child responds with the appropriate motion. The child, most likely, won't know how to respond. I've got a game we can play that will help us to understand how our pitches move on the staff, when we sing.