Any ideas for a fun way to teach the binomial theorem?

Question:I hope my class enjoyed me teaching them about combinations and permutations today. I got them to guess certain things about me by first asking them how many possibilities are there and giving them hints to narrow down the possibilities. When they understood permutations, I got them to guess how many possible
combinations of winners I had for 3 prizes for the class.
Please feel free to criticise. I cannot think of a fun way to teach the binomial theorem. Any ideas?

Kyle suggested Wiki's article on Binomial Theory, that's pretty good. Mathworld has several dedicated to the subject:

Both of them I looked at and went, "Huh? Oh, right, yeah, okay I guess that makes sense with what I know." At first glance they both look like wingdings and nonsense - I think the first problem to overcome with students is pulling the teeth a little, making the theory look less intimidating.

I'm not saying 'no theory’; I'm saying at first glance some students might feel overwhelmed. High school is all about gentle introduction to concepts and easing into the bigger picture.

So how does that apply to a fun way to do things? Dunno. You know your class, and presumably understand the wingdings version of the theory - so ask for real life examples of permutations or complex distribution, then demonstrate how this applies.

If your students are older, this is a good segue into game theory, and possible distributions of a deck of cards - or the odds of getting a royal flush and how the odds can be predicted with binomial equations.

It's great you want to find ways to relate, the hardest part is getting teachers motivated to teach the students as opposed to teaching the material. My limited experience says the less time a teacher is out of college, the more likely they are to teach like a professor, and that's not really conducive to young minds.

Even if you can't find a way to make BT interesting, seeing the kids interested in math is an excellent second prize. If all else fails, keeping the individual students talking (call on them, make them answer, encourage wise acres to respond to anything *with* anything) so they are part of the experience, instead of just being the target of a lecture.

Looking back, the teachers (high school and college) who considered themselves 50% teacher 25% performer 12.5% Carnival MC 12.5% animal tamer really had a better success rate. The material may be dry and boring, but there's no reason *you* should be.

Wow, that was a lot of words. Sorry about that. Hope some of it's useful.
In the Sherlock Holmes books, the villain Professor Moriarty is the author of A Treatise on the Binomial Theorem.
The binomial theorem is mentioned in the Gilbert and Sullivan song "I am the Very Model of a Modern Major General".
The binomial theorem appears in at least three different works by Monty Python - Coal Mine in Llandarogh Carmarthen, The Tale of Happy Valley, and the film Monty Python's The Meaning of Life.
The binomial theorem is mentioned in the TV series NUMB3RS in episode #217 ("Mind Games") in Season 2.
The generalized binomial theorem is engraved on Isaac Newton's tomb in Westminster Abbey.
In chapter 18 of Mikhail Bulgakov's "The Master and Margarita," the black magic practitioner Woland says, "But by Newton's binomial theorem, I predict that he will die in nine month's time..." From this, "it's hardly Newton's binomial theorem" became a popular Russian expression.
These are all wonderful ideas - it pops up everywhere. I also agree that Pascals triangle is a great place to start, since it is so easy to construct and graph. I enjoy pointing out that "Pascals" triangle was known to the Chinese 6 centuries before Pascal was born!

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