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My 6-year old seems to be very interested in binary numbers and I'd like to explore the concept of base 2 (and possibly other bases) with him further. He loves anything that has to do with secret messages, codes, and "secret missions". What games/activities can I do with him to explore binary numbers in a playful way?

Comment

Maria Droujkova

**Answer** by Kirby
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Jun 20, 2013 at 04:46 PM

Yes, NetLogo is a wonderful resource and is used extensively at our Portland State University, in the Systems Science PhD program especially (I gave a guest lecture there once, and know some of the students). This March at Pycon (computer language conference) we had an eduSummit with Walter Bender a keynote speaker, another pioneer in the Logo tradition.

**Answer** by abrador
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Jun 20, 2013 at 02:41 PM

YouTube is a wonderful resource. My kids are learning tons from it. Still, NetLogo -- or any other modeling and simulation environment -- is just that one step closer to authentic inquiry. You can ask your own 'What if?..' question AND go about trying it out!

**Answer** by abrador
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Jun 18, 2013 at 02:06 AM

Similar to Kirby, I'd go for the probability direction. However, unlike Kirby, who happened to choose the classicist approach of combinatorial analysis (how many different ways etc.), I happend to choose the experimental (frequentist) direction. To wit, what objects in your house could serve as two-sided random generators? The obvious one is a coin, but you could find other things, such as tupperware lids... Anything that has only two presentations, such as when you toss/spin it. So say we're talking coins -- heads/tails. And say you toss a penny and leave it where it lands on the table. Then you toss another penny and place it to the right of the first coin (or to its left -- just be consistent). And then toss a third one and place it near the second one. Well now you have three coins in a row. And you'll have to decide that, say, Heads is 1 and Tails is 0 (zero). So now you need to read off that sequence. For example, Heads Tails Heads is 101 so that's, uhhm, 5, right? If you got it right, then you get all those coins. So I'm thinking there would be some "bank" where you get the pennies (prepare a stock of about 50 in a jar). But if you got it wrong the, uhhm, either the other player gets it or the bank gets it. Perhaps the other player. Yeah, that makes sense, because it's the other player that challenges your call. You can up the level by having four or five or even six coins in a string. Or you could put a time limit on the calculation by introducing a timer (such as in Boggle). [but some kids don't like time pressure, so use with care...] Another direction also uses random generators such as coins. Now I'm thinking of a bridge over the ocean. It needs to get from one island to the next. The bridge is made up of coins. (For better reading, I'd use squares that are black on one side and white on the other, or just habe a "1" on the one side and "0" on the other.) so you need to cross this bridge. And every time you step on a square, you flip it. Not sure where this is going, but perhaps it's a beginning of something. A last idea builds on the symmetry of "1" and "0". I'm thinking that if the two players sit opposite each other, then my right to left reading of a string of digits is your left to right. Not sure where this is going, but I find it interesting that we have different numbers (and zeros on the left can be ignored). I'm thinking it's interesting that my number is bigger than yours or vice versa. How do we know whose number is bigger. And what about adding two binary numbers. I'm thinking of a binary abacus. Ha, funny, no? you could enact it with coins, or beads, or.. what? Can you figure out a cool binary abacus? Trains on tracks? cups of water that you empty... if you that cup is full (1) and there's another cup to add, then you need to empty one of the cups into the next place value, and deal with that extra cup. Yeah, why not invent cool binary calculators?

One of my favorite pieces of apparatus, found in some science museums, is the one where balls fall from the top, Pachinko style, and rain down through rows of pins where at each pin the ball falls either left or right, giving a spanning binary tree. The chances of a ball always falling right, right, right... are small compared to a mixture of left and right, and at the bottom the balls pile up: a bell curve. Pascal's Triangle is a model of the same system. Many authors have elucidated these connections. My take:
http://www.4dsolutions.net/ocn/binomial.html

Ah, yes, I've seen this contraption at a kids museum once, but unfortunately, some pins were broken. I think it'd be fun to play it using a pen, paper and a coin.

I just checked Youtube and found quite a view video clips of these so-called 'Galton Boards'. Here's my favorite so far just because it's so quick:
http://www.youtube.com/watch?v=5_HVBhwhwV8

**Answer** by abrador
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Jun 20, 2013 at 02:23 PM

You can download the free NetLogo and run the simulation of Galton Box. Or just run it directly here
http://ccl.northwestern.edu/netlogo/models/GaltonBox

**Answer** by abrador
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Jun 18, 2013 at 02:25 PM

Interestingly, morality appears to be geography-bound... My Australian colleagues are perplexed by what they perceive as US puritanism around gambling. Apparently, in Australia gambling is a national family passtime of sorts, so much so that gambling contexts are completely mundane in mathematics classrooms.

**Answer** by ccross
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Jun 20, 2013 at 07:52 AM

I ran an activity last week on Binary Numbers at the Carolina House, an assisted living facility that we bring kids to for a monthly intergenerational activity. The Activity Director was delighted that the residents, some of whom were over 90, were actually doing something on the binary system! We did a craft activity I called Binary Weaving. I've been meaning to put it up on my blog, so I'll try to do that and add a link here once I post it.

**Answer** by Kirby
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Jun 18, 2013 at 01:23 PM

The usual way the AAB BAB "slots" game is presented, to adults, is in the form of "slot machines", which run at a higher base than 2, i.e. the imaginary wheels (all computer graphics these days) go through a larger range and not in the same order. It's when you get all Apples across, or all Jacks, that the pay off is big (rare permutations). Today's machines find the patterns for you and score accordingly. I'm not much of a player myself, but I do have a friend in IT who works for a casino and have enjoyed [touring the facilities][1]. Of course some families consider playing games of chance for money a vice and an addiction, so it's rare to have mass published curricula risk offense by delving into ['Casino Math'][2] or even to show playing cards. I've taken the opposite approach, in part because I'm more into andragogy (the teaching of adults) vs. pedagogy (of children) -- which isn't to say there's no overlap. My [Martian Math classes][3] have been mostly with middle school through high school aged through [Saturday Academy][4] in Oregon. [1]:
http://controlroom.blogspot.com/2008/07/touring-facilities.html (a new wing of Angel of the Winds going in, 2008, owned by the Stillaguamish Tribe north of Seattle) [2]:
http://wikieducator.org/Casino_Math [3]:
http://wikieducator.org/Martian_Math [4]:
http://www.saturdayacademy.org/

**Answer** by yelenam
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Jun 18, 2013 at 12:21 PM

Kirby and Abrador, thank you both for the great ideas! I tried Kirby's idea of exploring AB combinations. I found it really interesting myself which should'd given me a clue that my son wouldn't be as excited (we have very different styles). He did it, however, but it felt a bit like a chore to him. So then I showed him how to "convert" a base 10 number into base 2 using counting bears and grouping them on the "islands". This wasn't a big hit, but he seemed to understand the idea. So then I suggested a coin toss game based on Abrador's idea and that was a huge hit. We played 7 or 8 rounds, starting at 3 coins and going to 5. He did really well figuring things out and was so happy about his winnings :) So I think we'll play it a few more times and then I really want to move to Kirby's suggestion about Morse code and ASCII. I was also thinking about a game based on the Abrador's suggestion of the symmetry of "1" and "0". Maybe flipping coins and building numbers, then each player converts into base 10 (one going from left to right, the other - from right to left) and then the point goes to the one with a larger number. That's just for starters. We can make it more interesting as we start noticing things. BTW, the bridge idea for some reason reminded me of the Indiana Jones movie where Indy has to cross a paved path, but some stones are traps and he needs to figure out which ones. This can be a fun little path game.

**Answer** by Kirby
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Jun 17, 2013 at 11:16 PM

Just the idea of how many unique arrangements of two things, could be like letters, A B. If you have three "slots" __ __ __ how many distinct / unique / not-same patterns might you make. AAA AAB ABA ... that can be somewhat engaging preoccupation. Not forever of course. Right answer is 2 * 2 * 2... as many 2s as number of slots. So 8 (2 x 2 x 2) if 3 slots. As soon as you think ready, maybe go from Morse Code dots and dashes to ASCII bit-codes for all the letters and numbers on a US-English keyboard. Then talk about Unicode as a segue into studying other alphabets, in turn a segue to geography and Japan. In other words, let it fade / segue into other STEM topics that aren't necessarily purely mathematical, like you say: codes. 1-to-1 substitutions of letters for other letters to make secret messages... doable when you have a lot of letters to play with. No need to rush too fast. You, the adult, if you haven't read it: [Cryptonomicon][1] is fun, by Neal Stephenson:
cryptonomicon.com I've got some related crypto at my web site: [
4dsolutions.net/ocn/clubhouse.html][2] Kirby [1]:
http://cryptonomicon.com [2]:
http://www.4dsolutions.net/ocn/clubhouse.html

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