A few months ago I was a Windows user, although I finally got myself a MacBook Pro and one of the things which "worried" me the most was that I couldn't get The Sims 3 installed on it, I had some of the CDs so I could install them but I had bought many EPs online and Origin, which is a Windows app, doesn't work on Mac.
After lots of research I found out how to install The Sims 3 on a Mac without CDs. Go to GameTreeMac and download the app: there's no link for an actual download, the app will download itself and intall itself as well on your Mac on the first game you purchase from the site.
If you used to be a Windows user and are a proud Simmer like myself, you probably purchased some of the games using Origin, if you did I have some bad news. Unfortunately you can't use the games you bought o Origin on GameTreeMac, this means you have to buy them again. I did try to find a way to move the games I already had purchased from Origin so that I could install them on my MacBook Pro using GameTreeMac, but there is no way possible. I contacted both Origin and GameTreeMac and they told there's no way possible to transfer purchased games on Origin to GameTreeMac, meaning you have to buy your games all over again.
Apart from the issue that old Windows users have to purchase their games again, I hope you now have a happy simming on your Mac.