The Homestead Act was signed into law 1862 and the first claims were made under it shortly after. Your challenge is to find out when the last claim was granted under the Homestead Act. Who was granted the last claim?
Depending on where you live, you might want to modify the challenge to finding out when the last claim was made in your state or county.
DocsTeach also has some activities built around Homestead Act. You might use those activities as is or modify them to meet your needs. Here's my overview of how to use DocsTeach.