I'm teaching my 8th graders the concept of relative primes. I've tried multiple different explanations, but there's a few of them that just don't get it. This is one of those topics that's so inuitively obvious to me, that I'm having trouble figuring out what's confounding them. How do the rest of you teach this?

I don't teach this, but I learned it from the concept of Families. 8 has a family that includes 2's and a 4. 6 has a family that includes a 2 and a 3. Since 2 is in the same family they're related and relative primes are never related to each other. 9 has a family that only includes 3 so it's related to the 6 but not the 8.

They can find it, there just appears to be a disconnect with finding the prime factorization and actually applying it in another problem. Can you see why I'm frustrated? We go through the motions...find the prime factorization of 27, now find the prime factorization of 14. Is there any number that appears on both lists? No, then they're relatively prime. They get totally hung up on the fact that neither 14 nor 27 is a prime number in and of themselves. That's the sticking point.

I do understand your frustration. you might try starting with two distinct primes and explaining why they are coprime (relatively prime) then take a prime and a composite number and show that they are RP (provided that they are). then go to two composite numbers. I have no idea if this will work. I can't remember if I have ever taught this before. I don't think I have.

I don't remember being taught it. I can't remember hearing it for the first time. It's just one of those terms that's always been there. I think I'll go through the sequence again. I've done it with prime/composite pair and a composite/composite pair, and done them several times each. I got frustrated today and said "if these two numbers were in the numerator and denominator of a fraction, could you reduce them?" UGH. Thanks for the thoughts. Why do I have to teach this anyway :lol:

You could use a Venn Diagram with factors for the numbers and tell them if the only factor in the middle is one they're relatively prime.

My main sticking point is they can't get past the fact that a composite number can be "prime" (relatively to another number, that is). That's what I'm trying to get them to see.

give it another name then.. give the rel prime property a name like the rep property or something... drop the word prime altogether

I never teach this concept (through 8th) and my kids do just fine with fractions. What is the real purpose of knowing the terms?

Ups...that's a question I can't answer. This is the Honors Algebra I class, and it's in the pacing guide. I didn't want to deal with it at all, but my P said it's there, so I have to teach it. It's really not a difficult concpet...just putting a technical term to something they already know, but it's presented a brick wall for some kids.

primes and their 'friends' are really cool. How are they going to study Euler's totient function if they don't know when two numbers are coprime.

lol, HMM. I think that's exactly the purpose. Since these are honors kids, I think we're just laying down the vocabulary for "real" math.