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We are a group of people trying to motivate children, especially living in the countryside, to science and math. We have different activities with children such as doing scientific experiments and exploring robots. And I am responsible for the math activity and I am going to spend 40 minutes with children of age 11 to 15. I will make the same activity maybe for 10 times in 2 days. I look for good motivating materials to show that math is fun.

My friends who did the same activity before used some nice topics such as Fibonacci numbers and fractals in nature but the supporting materials were weak and it didn't take the attention of students. For example, this video is great but I don't have the projector so I need to show them printed materials and use the blackboard.

To sum up, I look for math games, historical examples and some visual materials to take the attention of kids to math. During the activity, I plan to play games, tell stories and show printed math materials to children.

By the way, there seems to be related questions such as this one, but the target age is smaller in my case. And this one has general answers but not specific examples.

Community
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petrichor
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    I think that at that age Nim will challenge (some of)them to think. You were planning on doing games anyway, so this might be an interesting addition (if you didn't have it included already). You can start to recursively build up the set of winning position as a group effort (a chalkboard will do nicely for that end), and have the most interested kids go on by themselves. – Jyrki Lahtonen Nov 14 '11 at 11:48
  • +1 I didn't know about it. I liked the game and the strategy. Here are some interactive versions: http://www.gamedesign.jp/flash/nim/nim.html and http://education.jlab.org/nim/index.html – petrichor Nov 14 '11 at 13:33
  • Since Nim was mentioned, I'll add that almost anything from the first half of the first book of "winning ways from your mathematical plays" would be good. – Carl Nov 18 '11 at 01:37

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Rational tangles, see image on page 11 to see it. You can take a tangle, show how a rational number is associated to it, how to untangle, about GCD and perhaps Euclidean algorithm.

sdcvvc
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  • That is super cool! More upvotes for @sdcvvc, please... – Dan Drake Nov 18 '11 at 07:21
  • This is Amazing :) – picakhu Nov 18 '11 at 22:43
  • I gave +1 for all answers, which are very good recommendations. But I gave the bounty for this answer since it had the most upvotes and was very amazing. As a note, I didn't accept any answer to welcome further contributions since any upcoming answer may help to instructors who want to have a similar lecture with the kids. – petrichor Nov 20 '11 at 13:05
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Maybe your students are too old for that, but I find the History of the Wheat and chessboard problem very interesting. It teaches young students to imagine huge numbers and at the same time the essentials about exponential functions.

lumbric
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    I was planning to use it actually because it is a good demonstration of showing what overestimation of math can lead to. – petrichor Nov 14 '11 at 13:35
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Have you thought about doing something on probability? I like talking about the martingale (doubling) strategy in roulette (or other games, or the stock market, etc.) and the story of Charles Wells. The St. Petersburg paradox is also very interesting. Both of these can be understood with no prior maths, and people usually find them interesting and counter-intuitive.

Flounderer
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As it happens, I'm reading Marcus du Sautoy, The Number Mysteries: A Mathematical Odyssey through Everyday Life. It's a nice reference (his Music of the Primes was, as I recall, excellent), and there's a website with a few activities. Half of the material, perhaps, would be suitable for kids.

An excellent reference, as far as I remember (I don't have it here, where is it?), was Keith Devlin, The Language of Mathematics: Making the Invisible Visible. I think you'll find plenty in it.

Perhaps you know these already. As I look up amazon, I see this book has excellent reviews, I'll buy it, if only for the title, Alex Bellos, Here's Looking at Euclid: From Counting Ants to Games of Chance - An Awe-Inspiring Journey Through the World of Numbers.

PatrickT
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Sam Loyd's 16 puzzle is a good intro to the concept of parity, you can follow it up with the Rubik's cube. The 16 puzzle also has an interesting history. Another good parity problem is the chessboard tiling with dominoes problem, but I'm not sure how much you want to talk about parity.

Any game of chance is a good start to probability theory -- dice games, card games, anything like that.

Craig
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    While the underlying grid is 4x4, this is generally known as the 15 Puzzle and you'll probably have more luck hunting for it by that name. – Steven Stadnicki Nov 18 '11 at 16:09
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There are an amazing set of videos by ViHart about doodling with maths, I'm not sure if the age range will grasp the underlying mathematics or not as its such an immense topic you could learn about geometry for a very long time. Whilst you won't be able to show the videos I'm sure you could teach the techniques she uses to doodle.

Snakes: http://www.youtube.com/watch?v=heKK95DAKms

Luke
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