This odd and even game idea from E is for Explore was a huge hit in my classroom. It's played like rock, paper, scissor but they use their fingers instead and add them to get an odd or even number. Each partner chose odd or even and then they tallied to twenty to make a fun game of it.
I made a simple chart to introduce odd and even and then we used sticky notes to see the connection to bigger numbers. I had them give me a number between two numbers to practice that as well, such as...give me a number between 20 and 40.