Programming :: How To Find Files With Partial Name

I am fairly new to linux but I want to write a function to find any file with only a partial name. I can only use sh shell and busybox applets for this.I could do something like the sad code below...

Code:

TEST_ONE=$(find /path/to/directory -name *$1*)
TEST_TWO=$(find /path/to/directory -name $1*)
TEST_THREE=$(find /path/to/directory -name *$1)

[code]....

fi I just made that up but obviously it is pretty bad I'm sure there is a much better way to do it but I just can't think of a way. I also would like to have the file found even if capital letters are used and the file is all lower case.