The one thing I have noticed with The Magic Tree House series, you do have to read them in order. As an adult, I can pick up something, but in Vacation Under the Volcano #13, Jack and Annie have had so many adventures you need to know some of the pieces of information given before to help explain a few things. However, it is a standalone title if you and your child talk about it.
The story is basic: Jack and Annie go to Ancient Rome to save a book. Easy, right? Well, no. You see they do not realize that this is Pompei and today happens to be a pretty special day. A little thing called Mt. Vesuvius is going to blow its top! Of course, you see the things that made Ancient Rome, well Ancient Rome: Gladiators, the Baths, myths and soothsayers and more. You learn how books looked a little different and a bit about lava and how that works as well.
I did not know that each of the series within the Magic Tree House series are on different levels. Your child can grow with Jack and Annie as their reading abilities grow. I also had not realized how long these books have been around. Dinosaurs Before Dark #01 was published in 1992.
I recommend buying several of them at once. Because it your child is like me, they will be a little disappointed that you could not immediately start reading Day of the Dragon King #14 after finishing your Roman holiday.