Arkansas was a state that our library didn't have much on so in our personal studies we weren't able to do as much, but I have some fun ideas to tell you about afterwards.
Rosie's Fiddle- the state instrument of Arkansas is the fiddle, and I found this wonderful book about a fiddle. Rosie challenges a visitor to a fiddling contest only to discover it's the Devil. After reading the story we wrote down how we would win in a challenge against the Devil.
Arkansas Flag- Most state flags have specific reasons behind their creation, but I'm not always able to find the reason behind them. In the case of Arkansas I was able to find some great resources on their state flag, and so we learned all about it and then made a flag to represent ourselves.
Diamond production- Arkansas is the only state in the contiguous United States that has a diamond mine, it's actually one of the big tourist draws for that state. So we did a lot of talking about what you can make with diamonds, and then made our own "jewelry."
Hot Springs- there are natural hot springs that are a big draw.
Bill Clinton- honestly I didn't have a good book about him at our library, which was rather shocking to me
Clever Beatrice- a set of tall tales from Michigan, if your library has a copy I highly recommend getting these tall tales. They're clever, well written, and highly entertaining. After reading them we worked on puzzles and brain games.
Log Cabin Quilt- We don't tend to think of Michigan as a frontier state, but once upon a time it was, and this book is set during that time. Most of the plot of this book revolves around chinking a cabin, filling in the empty space between logs. For our activity we drew what our cabin would look like if properly chinked.
And that was the TWO books I could find, as I said my library had practically nothing for these two states, so we had 2 activities for each of them. So, here's my other suggestions:
Make a car, Detroit is the car capital of the world
Kellogg's is based there. You could poll your students for favorite cereals. My kids don't like cereals which is why I didn't do this activity.
Ginger Ale was invented there. You could make a homemade soda using water, dry ice and lots of flavoring of your choice, then compare it to the traditional sodas you buy.
What would you do to study Arkansas or Michigan? These studies need some serious boning up, but my resources weren't able to do it, at least not without breaking my budget.