I've always wondered how the magic square got its name and how it applies to math, especially with the changing demands for teaching mathematics. I actually found a good reason to have students learn about magic squares.
A magic square is simply a larger square that is subdivided into smaller squares such as the one to the left where the big square was subdivided into 16 smaller squares. In addition, the rows, columns, and diagonals all add up to the same value. It sounds simple but it really isn't.
One of the biggest things it teaches is perseverance which is one of the big things in math right now. Students have to develop the ability to continue working on a problem until they reach a solution. They also provide a link between math and history and encourages problem solving.
Although this activity from the University of Cambridge, requires specific software for part of it but the introductory section is great because it offers a partially filled out square that students finish so it works. This provides a good guided practice before students are expected to put it together. The lesson plans are clear and it includes the necessary worksheets for the activity.
NCTM has a great activity in their Middle School Magazine from February 2015 on Magical Squares. It includes a good chunk of history and an activity that has students creating magic squares. It is well written and has the worksheets that are needed to complete the activity.
This article from Wolfram Math gives an in depth mathematical explanation of magic squares. It includes the formulas, the pattern for filling the squares out successfully. It gives multiple examples of both simple and the more complex squares so you can see how the pattern works for each one. This would work for either an AP class or a college prep math class because it does involve the higher level mathematics.
For students who are not as advanced, this PBS lesson provides some wonderful instructions and drawings so you know what to do. This lesson includes historical information plus all the worksheets needed and it has great step by step directions to fill out a simple 3 x 3 grid. I like the clarity the instructions have so I can see how to do it. The pattern decreases the chances of students becoming as frustrated.
I can see popping this in at the beginning of the day, on a shortened day due to weather issues, half days or any other time you need a quick something that will still meet standards and keep student interest.