Yesterday I was working with a sixth-grader who said to me, "I can never remember the difference between prime and composite."

So I started going through an explanation of what prime numbers and composite numbers are. She showed very good understanding of the concepts. Then she said, "No, I mean, I always forget which is which!"

Ah. I understand. So, I had to, on the fly, come up with a way of helping her remember which is which. Since I don't generally work with sixth graders, I didn't have any mnemonic devices in mind for this particular issue, so I had to come up with one off the top of my head. 

Knowing that this particular student plays the violin, and is part of an orchestra, I said to her, "Do you know what a composer is?"

She did know. In case you don't, a composer is someone who writes music. Beethoven, Bach, Mozart and Tchiakovsky are examples of well-known composers.

"When a composer is writing music for an orchestra, he's writing a violin part, a viola part, a cello part, a flute part, and so on. It's a lot of parts, right?"

She nods, because she knows this is true from her experiences in an orchestra.

So then I showed her the two words "compose" and "composite," and said, "Those words are very similar. They both start with "compos", and there's a reason they're similar; they both mean, 'made up of several parts.' The composer makes something made of several parts, and a composite number is made up of several factors."

I then showed her where, on the white board, she had written the factors of 17, and the factors of 30. "You see that 30 has several parts, or factors. 17, on the other hand, only has 2. If a number only has 2 factors, that's not 'several.' So that's one way of remembering which is which."

Of course, this mnemonic was only helpful to her because she is familiar with music, and plays in an orchestra. But for her, that idea made a lot of sense.