Hi Linda,
If I'm not mistaken, the one of which you have a plate-block, albeit damaged, was the fourth half-cent in American philately, and was issued in 1938. The first, of 1925, is the original flat-plate half-cent, and depicting Nathan Hale; the second, the rotary-press variant of the original, and issued during the Great Depression(1929); and the third, issued in 1932, for the Washington Bi-Centennial. These are my mint copies of the first, third and fourth, and a used copy of the second, and from my mint and used sets, respectively, which I hope to share, if I don't expire first, in all their apple-pie glory after I hit the mandatory 50-post count...

The half-cent value would appear again, during the release of the "Liberty" issue beginning in 1954, and in 1955. Said issue also saw the first and perhaps the only one-and-a-fourth cent...

I got that one out of a Mystic "trish-trash" packet from the 1990s, and the only thing I've ever gotten and will get from them.
There were also four-and-a-half cent stamps during those later times, too. The half-cent was for some need, and of which I'm unaware; additional weight, I suppose, or for something other, something special. The rate was before my time when I first began using stamps for mailings.
In so far as your plate-block, if it were mine I'd toss the two on the right, and take one or both copies on the left and begin a Presidential collection of 1938, which runs all the way up to the $5 Calvin Coolidge.
Cheers,
Alan