In our Sustainable Landscape Design course, we use a game to teach about composting. It is another great example of an edutainment game. It starts with explaining what composting is, and then, what items you can and cannot compost. Then, you must try and catch the items you can compost and avoid the items you cannot.
As you can see in the examples I have given so far, fluent gameplay is what makes games fun and addictive. So, while these games teach us something, so they do not randomly stop gameplay to force the learning on us. The teaching is built into menus or as part of the gameplay in a fluid way. Doing this will definitely ensure your game is engaging, yet still educational.