The piece is one of hundreds of different souvenir "woods" issued by towns/cities/counties in the US during (primarily) the 1930s, 40s, 50s and 60s. John B. Rogers was the largest manufacturer of the pieces and supplied them to organizations across the country.
Piqua, OH issued a number of woods over the years. Beginning with 14 different varieties in 1938, 3 varieties in 1946, 1 in 1972 and 2 in 1976.
In addition to the piece you've shown, Piqua also issued 1946 woods denominated in "10 Wooden Nickels" and "25 Wooden Nickels."
In terms of market value, they are not considered to be "rare" types (though you'll likely not see them with any frequency). I'd estimate that interested collectors would likely pay in the $6 to $12 range for an unbroken example.
Hope that helps!
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