Sharing an idea from “How to Gamble if you Must” with my younger son

I was re-reading How to Gamble if you Must by Dubins and Savage and though it would be fun to talk through the gambling problem in the beginning of the book with my younger son.

The book isn’t exactly light reading, but definitely interesting if you want to understand a bit of the math behind gambling

The problem is fairly straightforward to understand -> you start with $1,000 and you need to get to $10,000 by making bets. How should you bet if the game is unfavorable, fair, and favorable?

I started the project today by explaining the game to my son and asking how he thought you should bet in the various games:

Next we wrote a short program in Mathematica (off camera) and then played the game. Here’s a discussion of the program and a few times through the unfavorable game:

Now we played the fair game and looked to see if the strategy was the same or different than the unfavorable game:

Finally, we played the favorable game – again we looked for what might be different in the betting strategy for this game:

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Playing Mapmaker -> the Gerrymandering Game

Saw a great tweet from Jordan Ellenberg over the weekend:

Though it would be fun to try . . . and the game arrived today!

Tonight I had the chance to play with my younger son – he didn’t know what gerrymandering was, but we talked a little bit about the idea as we opened the box:

Here’s a quick peek at the game set up:

Finally – here’s what the game looked like at the end and then a short discussion of some of the mathematical ideas for kids that come through in the game. What ideas can help you win? What can you do to cause your opponent some problems?

I really like this game a lot. It is easy to play right out of the box – the directions probably took under 5 min to read and understand. The game is a great way to teach important ideas about gerrymandering and also has great math ideas in it for kids. I highly recommend it – thanks to Jordan Ellenberg for the recommendation.

Playing with Colin Wright’s card puzzle

Aperiodical is hosting an “internet math off” right now and lots of interesting math ideas are being shared:

The Big Internet Math Off

The shared by Colin Wright caught my attention yesterday and I wanted to share it with the boys today:

The page for the Edmund Harriss v. Colin Wright Math Off

The idea is easy to play with on your own -> deal out a standard deck of cards (arranged in any order you like) into 13 piles of 4 cards. By picking any card you like (but exactly one card) from each of the 4 piles, can you get a complete 13-card sequence Ace, 2, 3, . . . , Queen, King?

Here’s how I introduced Wright’s puzzle. I started the way he started – when you deal the 13 piles, is it likely that the top card in each pile will form the Ace through King sequence:

Now we moved on to the main problem – can you choose 1 card from each of the 13 piles to get the Ace through King sequence?

As always, it is fascinating to hear how kids think through advanced mathematical ideas. By the end of the discussion here both kids thought that you’d always be able to rearrange the cards to get the right sequence.

Now I had the boys try to find the sequence. Their approach was essentially the so-called “greedy algorithm”. And it worked just fine.

To wrap up, we shuffled the cards again and tried the puzzle a second time. This time it was significantly more difficult to find the Ace through King sequences, but they got there eventually.

They had a few ideas about why their procedure worked, but they both thought that it would be pretty hard to prove that it worked all the time.

I’m always happy to learn about advanced math ideas that are relatively easy to share with kids. Wright’s card puzzle is one that I hope many people see and play around with – it is an amazing idea for kids (and everyone!) to see.

A simple test of our new skew dice

Last week we bought two packs of skew dice from the dice labs:

Today we decided to try a simple statistical test of the disc. Before we dove into that test, though, I asked the boys to tell me how they thought you might go about testing these dice to see how random they were.

We rolled the dice off camera. We rolled them in groups of 10 with each of us shaking up the dice in a container before each roll. After 12 rounds we had a total of 120 numbers -> here are the results:

Although we didn’t really have enough rolls to make a definitely statement about the dice, I think this was a nice way for the kids to see how a simple statistical test would work. I hope the kids are interested in playing around with these dice a bit more.

Using the Infinite Galaxy puzzle from Nervous System to talk topology with kids

The boys and I spent yesterday working on the new Infinite Galaxy Puzzle from Nervous System:

Having finished it, I thought a project talking about some of the math behind the puzzle would be really fun for the boys.

Since the front cover of the puzzle says that it was inspired by the Möbius strip, I started today’s project talking about that shape:

Next we talked about the puzzle and what geometric / topological properties it has. The interesting mathematical question here is whether or not the puzzle is a Möbius strip?

It turns out the puzzle is projective plane!!

We spent the last part of the project today talking about the projective plane and a few other similar shapes.

Even without any of the math, this new puzzle from Nervous System is a really fun challenge. The mathematical ideas behind the puzzle move it from the “fun puzzle” real to the “blow your mind” realm, though!

I’m so happy to have found one of these puzzles at the Nervous System open house last weekend. What an amazing way to share some introductory ideas from topology with kids!

The puzzles (and everything else!) from Nervous System will blow your mind

Yesterday Nervous System in Somerville, MA had an open house and I was lucky to have a few hours free while the boys were at their karate black belt tests. Visiting their shop was absolutely incredible:

Definitely check out their website and their twitter feeds. I follow Jessica Rosenkrantz – @nervous_jessica. Here’s the link to their website:

The Nervous System website

At the open house I bought two new puzzles. The boys had seen one previously at Christmas, too. For our project today I’d already wanted something on the easy to talk about / less heavy math side because of the black belt tests yesterday, so talking about the new puzzles was perfect.

We started with the geode puzzle – one of the fun things we talked about was how the boys thought the computer generated the geode shape:

After the introduction to the puzzles, we moved on to talking about the challenge of putting the puzzle together. Favorite line – “once you get started, it gets pretty hard.” Yep!

Next I showed them the latest creation from Nervous Systems – an “infinity puzzle” inspired by the Mobius strip!

I was incredibly lucky to be able to buy one of the infinity puzzles yesterday. So, for the last part of today’s project we did an unboxing:

If you know kids who like puzzles – or you like puzzles! – all I can say is the Nervous System puzzles are absolutely incredible.

3 hours after we finished the project this morning, my younger son had returned to the Geode puzzle:

Sharing a card shuffling idea from Jim Propp’s “Who knows two?” essay with kids

Jim Propp published a terrific essay last week:

Here’s a direct link in case the Twitter link has problems:

Who knows two? by Jim Propp

One of the topics covered in the essay is a special type of card shuffle called the Faro shuffle. We have done a few projects on card shuffling projects previously, so I thought the kids would be interested in learning about the Faro shuffle. Here are our prior card shuffling projects:

Card Shuffling and Shannon Entropy

Chard Shuffling and Shannon Entropy part 2

Revisiting card shuffling after seeing a talk by Persi Diaconis

I started the project by asking the kids what they knew about cards. They remembered some of the shuffling projects and then introducing the idea of the Faro shuffle.

My younger son thought he saw a connection with pi, which was a fun surprise.

We continued studying the Faro shuffle with 8 cards and looked for patterns in the card numbers and positions. The boys noticed some neat patterns and were able to predict when we’d return to the original order of cards!

Next we looked at the paths taken by individual cards. My older son thought that there might be a connection with modular arithmetic (!!!) and the boys were able to find the pattern. I’d hoped that finding the pattern here would be within their reach, so it was a really nice moment when he brought up modular arithmetic.

Finally, we wrapped up by talking about how to extend the ideas to a 52 card deck and calculated how many Faro shuffles we’d need to get back to where we started.

I think that kids will find the idea of the Faro shuffle to be fascinating. Simply exploring the number patterns is a really interesting project, and there’s lots of really interesting math connected to the idea. I’m really thankful that Jim Propp takes the time to produce these incredible essays each month. They are a fantastic (and accessible) way to explore lots of fun mathematical ideas.