Final answer:
The nurse should assess the infant with pertussis and receiving oxygen first, as they are at risk for severe respiratory distress and complications, followed by the child with diabetes, the adolescent ready for discharge, and the toddler needing assistance with feeding.
Step-by-step explanation:
When determining which patient a nurse should assess first, priority is typically given to those who are most unstable or whose condition may pose an immediate threat to their health or life. In this scenario, an infant who has pertussis and is receiving oxygen via nasal cannula should be assessed first. Pertussis, also known as whooping cough, can cause severe respiratory distress, and infants are particularly vulnerable to complications. The nurse should ensure that the infant is receiving adequate oxygenation and monitor for any signs of respiratory failure or distress.
The school-age child with diabetes mellitus would be the next priority for blood glucose monitoring, followed by the discharge instructions for the adolescent who is ready for discharge after a sickle cell crisis. The toddler with both arms in casts requires assistance with feeding but is likely to be stable and thus would be assessed after the more urgent cases.