also the concept of a penny on day 1, 2 cents day 2, doubled each day for a month
how many people in a room for a 50% chance two have the same birthday
i like the first one, though i found their math frustrating at times
Well, just learning the odds.
Add:
Monty Hall Problem
Take three cards, one of which is the Ace of Spades.
Have a kid choose a card.
You, the MC, look at the other cards, show them a card that is not the Ace of Spades, and ask if they want to switch to the unseen third card.
Applied probablity is an important topic!
Thanks for the ideas everyone!
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Now, I’m invested, so let us know how it goes.
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Gambling probability 
Once upon a time, I attempted the Cantor diagonal argument w/ a bunch of gifted middle school students, but it was waaaaay too abstract.
So for the next session, I went straight for gambling, probability – and the Monty Hall problem. That was a big hit.
I also did the birthday problem. I had a large enough class (you want at least 23 kids… and make sure there aren’t any twins…)
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I was doing some marking at a local university couple years ago. They have math moments, basically make math fun for 20 minutes for all the math nerds.
The prof at one did one of these questions where you take a number, do a bunch of operations and the results is known. Then he proceeded to almost prove it…got it down to two big equations. Asked if anyone saw the results by looking at the equations. Nobody did. Then he declared, if you divide the first equation by the second, you get the golden ratio. Everyone except me: oooooooooh!!!
Me: what’s the golden ratio?
So that day math was fun for everybody but me.
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@BruteForce what did you end up doing?
I’ll let you know when it’s done!
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Unfortunately the whole group didn’t show (due to a basketball game going late), but the boys who came seemed to have fun. While we waited for everyone to show up we watched a longer video to entertain them
We ended up pausing that one more than I expected to answer questions about the equations. Some of that video is over my head, but we talked about e and i and such. It was a little much for them, since I also had to explain what square root means (they’re in 6th grade), but I tried to keep my explanations simple.
Then we played Monty Hall. I bought some king size Twix bars, and we played the game with brown paper bags. It worked out perfectly that kids won exactly 2/3 of the time (don’t worry, everyone got a Twix)! Turns out they remembered me talking to them about it last September-ish, so that went pretty fast.
After that, we did the calculate horse power activity. Results were all between 0.4 and 0.8, but we only had a set of 6 steps to climb, so who knows how accurate our timing was 
Then the boys just started asking me random math questions like what happens when you divide by 0, and we somehow got onto the topic of Fibonacci sequence. I showed them a video about how it shows up in nature. Afterwards one of the boys was trying to explain it to his mom and he had to come back and ask me what it was called again, but he seemed excited to tell his mom about it, so that was fun to see.
I ended the night with a short spiel about why I love math and how it’s all around us. All told, we got out right at 1 hour, so I count it as a success!
They seemed to really like random math facts I threw at them, so I told them if we wanted to do a cool math facts night we could. I also told them about a few mathy YouTube channels I like (Veritasium, 3Blue1Brown, Numberphile). I know at least one adult went and subscribed to them right there
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Thanks for the help everyone! I appreciate the suggestions.
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