You have a student who is trying to solve a 3×3 magic square. She’s been trying for a week, and keeps getting it *almost* to work: usually she gets to 6 directions out of 8 that add to 15, the other two add to 12 and 18. She keeps wanting to give up and keeps asking for help. So far you’ve just told her to keep going, and she has, but her near-misses are starting to repeat themselves, and she’s getting bored.

What ~~should I~~ do you tell her to aid her investigation without taking it away from her? In other words, help her out, possibly making the problem simpler, without giving an answer or algorithm.

No deadline, but answers arriving before Monday will be more likely to have real-world impact.

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I’d suggest picking a number to put in the center, then looking at all pairs that add up to 15 minus that number. If the pairs can be arranged to work, great! If not, then think about choosing a different number in the center.

I’d suggest making an organized list of all the triples that sum to 15. How could you organize the list systematically? Could you put the triples into groups in some way?

Just google the solution! (Kidding, but I’m surprised more students don’t realize the vast resources of the web.)

Adding on to Joshua’s idea, after the student has made a list of all triples that sum to 15, ask her to see which number(s) show up the most / the least. Looking at the magic square, which cells are used the most / the least?

Just brainstorming, but how about: have her move on to something else and come back to it later?

Has she figured out that the sum should be 15? If not, I would ask her what she thinks the sum should be? Or, “what is the most important spot on the board? what do you think goes there?”

quoted from Alan Schoenfeld, who said the following to me when I was working on this exact same problem: “what piece of information is the most important?” me: “the middle.” Alan: “If you could ask me for only one piece of information, what would it be?” me: “I don’t want your stinking information!” Alan: “I wasn’t going to tell you anyways.”

Okay, okay. I *may* have been paraphrasing there at the end.

These are great! Huge thanks to everyone.

My first reaction was what Ben said. But you did say it’s been a week. How did the other students do or was this something she chose to work on by herself? I was thinking you could pose this same question to another class (one that she’s not in), “What do I tell her to aid her… ”

Yours is a great question that we as teachers should be asking of ourselves all the time. And it’d be nice to learn how students would respond.

Late to the game here, but this is a puzzle where e mathematical habit of mind “look at extreme cases” could be helpful. More specifically, where can the 9 and 8 go?