It is absolutely true that the best way to change how you feel is to change how you breathe. When you feel out of control, the breath is the one thing that you can control. This is not only true for children but also for adults. Everyone can benefit from using this natural control mechanism. However, it is best to teach and lead by example.
Instead of saying, "Take a deep breath", HELP THE CHILD BREATHE.
Hold the child's hands and look into their eyes or hold them close or just mindfully stand nearby and validate their feelings and begin to breathe in deeply through the nose and exhale out the mouth or nose. Do this until the child begins to emanate the breath. As you begin to breathe slowly and deeply, you will begin to calm and bring calm to the one who is experiencing feelings that are moving toward a lack of control (or is already there). Stay close and breathe together.