I have (with some help via IRC) figured out that I was doing this ineffectively and needed to use the ip2long function.
I tested this, and it performed what I wanted it to. Here is my completed code, hopefully someone will find it useful.
// Function to take greater than a /24 CIDR block and make it into a /24
Function BreakTo24($CIDR)
{
$CIDR = explode("/", $CIDR); // this breaks the CIDR block into octlets and /notation
$octet = ip2long($CIDR[0]); //turn the first 3 octets into a long for calculating later
$NumberOf24s = pow(2,(24-$CIDR[1]))-1; //calculate the number of /24s in the CIDR block
$OutputArray = array();
for ($i=-256; $i<256 * $NumberOf24s; $OutputArray[] = (long2ip($octet + ($i += 256)))); //fancy math to output each /24
return $OutputArray; //returns an array of ranges
}