**Core Concept**
A supracondylar fracture of the humerus in children is a common injury that occurs when a child falls onto an outstretched hand, resulting in a fracture just above the elbow joint. The primary concern with this type of fracture is the potential for complications, such as nerve injury, compartment syndrome, or malunion, which can occur even after successful reduction.

**Why the Correct Answer is Right**
Admission to the hospital following reduction is essential in children with supracondylar fractures for close monitoring and potential management of these complications. This is particularly important in the first 24 hours after the injury, as the risk of compartment syndrome and nerve injury is highest during this period. The American Academy of Pediatrics recommends hospital admission for all children with supracondylar fractures, regardless of the stability of the fracture or the presence of neurovascular compromise.

**Why Each Wrong Option is Incorrect**
**Option B:** This statement is incorrect because the typical mechanism of injury for a supracondylar fracture is a fall onto an outstretched hand, not a direct blow to the point of the elbow.

**Option C:** This statement is incorrect because the majority of supracondylar fractures in children can be successfully treated with closed reduction and casting, without the need for open reduction.

**Option D:** This statement is incorrect because supracondylar fractures are typically non-displaced or minimally displaced, and are not usually compound (open) fractures, which involve a break in the skin.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that children with supracondylar fractures require careful monitoring for signs of compartment syndrome, such as pain, swelling, or decreased sensation in the hand or fingers, as this can occur even after successful reduction.

**✓ Correct Answer: A. Admission to hospital is essential following reduction**