I'm curious if anyone has used the materials from: https://www.exeter.edu/mathproblems I've seen several references elsewhere and after a brief glance (They are a complete math sequence from what I can tell and comprise a lot of pages) wanted some actual reviews. Thanks

I have a bunch of writeups of pre-algebra level group activities and how they went. If you're interested my year end summary is here: http://bit.ly/2sjuO2G and it has links to you can browse off of there. (I'm a bit free form in the summer so there are some more random recent posts.)

Thanks for the book recommendation. It just arrived yesterday and I was already inspired after my quick read of the preface and 1st chapter. I was motivated enough to put up a quick book review if anyone else is interested: http://bit.ly/2sZjH0x

Hi, After several years of doing an Elementary School Math Club, I'm switching to the Middle School level. I was curious if anyone else here is running one for 6th-8th graders? Right now, I'm trying to decide on the focus and structure going forward. The big existential question is whether to continue running like a math circle with occasional contests like AMC or MathCounts or to adopt a new format. There's the pre-canned MathCounts material but that doesn't thrill me much. Other questions I've been pondering: * Will the kids be more focused because they are a few years older, or less because they're teenagers? * Could I get them to research and present on a short topic or would that be too large of a commitment. * How long of a problem set will they typically sit for before losing focus? * I've used candy (rather shamelessly) to reward kids for bringing back completed problems of the week. Is that appropriate for older kids? * Generally what's the best approach if I get a large skill range: it could be as wide as Math 6 to Algebra II. Thanks

Did you try out the placement tests that AOPS offers? On https://artofproblemsolving.com/school/recommendations#state/4 There's the "Do you need this?" test for Algebra A: https://data.artofproblemsolving.com/course-docs/diagnostics/stretch-algebra-a-posttest.pdf

Its not a book or a whole curriculum but I really enjoy the numberphile videos and you can do alot of side explorations off the various topics discussed. What's nice about it as well is a chance to see various practicing mathematicians and get a sense of math as a living field of research.

That's funny watching the MathCounts finals always makes me think of this post: https://mathbabe.org/2011/07/17/math-contests-kind-of-suck/ . I actually showed parts of the final to 15 kids recently because I still think its fun to watch but ended up prefacing it with a long talk about speed being basically irrelevant in the longer term.

I just wanted to second the structure above. I've been doing MOEMS for 3 years and discussing the problems as soon as the test is over works out really well. The kids usually are never as excited to find out the answers and discuss their ideas than right in the moment. Also since I've tended to have 10-15 kids who never finish at the same time, its really useful to have a quiet light weight activity or game to give out to the early finishers to work on so they don't distract the others.

I had question for those who have already done both AOPS algebra books. It looks like after about chapter 15 in the intro book, all the topics are repeated in the intermediate book. Is it valuable to do them twice i.e. is the material very different or would it make sense to skip to the intermediate book once you finish the sections on quadratics.

Have you looked at the standard sequence on the AOPS site: https://artofproblemsolving.com/school/recommendations. The online versions are typically 1 week per chapter / lesson which gives a possible pace. But with the books, time seems to really vary kid to kid. I've seen threads here comparing the time to finish the algebra and pre-algebra books where it goes from 6 months to 2 years.

Natural Math (http://naturalmath.com/) has a lot of resources geared at math circles for younger ages.

Assuming I understand this correctly. Given two numbers x and y, there always is some gcf and you can rewrite both as a multiple of that gcf and the remaining parts k1 and k2 are relatively prime (you can think of them as a product of primes themselves if that makes it easier). i..e x = k1 * gcf and y = k2 * gcf Then when subtract the two the distributive law says the difference will still be a multiple of the gcf. i.e. assume x is greater than y x - y = k1 * gcf - k2 * gcf = (k1 - k2) * gcf So this difference definitely shares the original gcf as a common factor with both original numbers x and y. And the gcf must still be the greatest common factor for the inverse reason. If the other part of the product k1 - k2 contained another factor > 1 with either number then this factor would have to have been in both originals via the distributive law and we'd have a contradiction with the original gcf being the greatest factor. This looks a bit formal on rereading so I hope this helps.

Another thing to consider is trying to use questions rather than just hints when someone gets stuck. I always like asking what have you thought of so far, where are you stuck? What does this problem remind you of etc. What would make this easier? The process is very tactical and you kind of adjust as you go along.

MathCounts actually has a fairly precanned set of lesson plans to get started that you could go off of. PM me and I could put you in touch with a friend of mine who is fairly active within the group.

What age group is the circle going to be for?

I'd recommend reading Love and Math: The Heart of Hidden Reality by Edward Frenkel. The author describes being in very a similar position although I think he was about 15 in the narrative. What happened in his case was that he found an adult mentor (granted this was soviet russia)