Perfect squares

Does anyone out here have ideas about how to set up a nice visual activity to teach middle school kids square numbers (perfect squares)?

Also, any challenging problems are welcome, e-mail me your instructions! I am very fond of logical thinking that doesn't involve much calculations. The kids are always delighted to find the answer by looking at the problem from a different angle, drawing a picture or just arranging the data in a way that makes the questions simple.

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In unrelated news, several students told me that I had lost weight. I wonder how it's even possible, given the quantities I've been eating over the past two weeks. Well, miracles are at your doorstep, as it were.