Hidden Math: Book Edition
My daughter and I have learned so much math by finding it wherever we are and in whatever we’re doing. For the last year we have been paying attention to the physical world around us and finding as many different examples of math in our lives as we can. It’s quite stunning how beautiful and full of math even a city sidewalk can be if you have your math glasses on.
Back in May, for example, I wanted to start looking for spirals but only found two examples, one in a garden and one in our local playground. Long story short, at some point my daughter picked up on the spiral thing and started pointing them out, only to have me say, “No, those are actually concentric circles,” which then lead to a few days of clarification about what a spiral is and isn’t. Now she sees them everywhere!
We’re a team, her and I. It’s really fun that things we have taken for granted all our lives suddenly have a new dimension. This is why, I think, that a recent return to reading familiar picture books from our home library made me notice math in books that are not obviously math readers.
My very favorite almost-hidden math story book is Five Creatures, by Emily Jenkins. It’s about the similarities and differences (attributes!) between the members of a lovely little family.
“Five creatures live in our house,” it begins, “Three humans and two cats. Three short, and two tall….Three with orange hair, and two with gray.” We read this book when my daughter was in preschool and it was fun for both of us to look at the pictures to see who matched each description. The categories of family attributes are not always straightforward, which makes this a wonderfully interactive read.
In Ezra Jack Keats’ The Snowy Day, cut paper illustrations show math from the very first pages. In addition to great spatial vocabulary (up and down the hills, tracks in the snow, on top of, snowballs flying over the boy’s head) patterns abound. Check out this wallpaper — I love how the pattern units are so different from each other, and yet the overall pattern is so regular:
Parallel lines made by sticks and feet and gates:
The foot prints alternate, making a kind of frieze pattern:
I love this grid pattern in the mother’s dress, and it’s not just a color pattern. If you look closely there’s another attribute of shading (solid and striped):
This background is a great example of ‘scattered’ like in a scatter plot. Which section has more dots, and which has less? How do you know?
In nature, every snowflake has the same structure yet each one is different from every other snowflake. That’s not exactly the case here. How many different kinds of snowflakes can you find? How are they different and how are they the same?
So, now I’m curious what other books are out there that have this kind of ‘hidden’ math? I just thought of one more book: My daughter listened to the novel Half Magic on CD back in the fall. In the story, the kids find a charm that gives them half their wish and they quickly learn to wish for twice as much as what they really want. It’s fabulous.
What other kinds of books have you found that have this kind of hidden math? I’d love to hear your ideas!
Posted in Grow
Learning Math with Board Games
What are you more willing to buy for your child, a toy or a board game? Personally, while I cringe and say “no” every time my son asks me for a toy, I would happily indulge him if he asked me to buy him Monopoly Jr or Life or Four in a Row. Well, he doesn’t ask, so I end up buying them anyway and now we have a growing collection of card and board games. My excuse, of course, is that playing games helps my son to learn math (here’s an article about using games for teaching math and here’s a great list of board games that build math skills). Which it does, at least until we lose game pieces or a few cards or go on a road trip. What if there were (or we could invent) board games that would be portable, DIY-able, cheap (better yet, free), and full of interesting math?
Once you start looking for something, you find it everywhere. Once I asked myself this “what if…” question, I started coming across just such games. And then I was lucky to meet Daniel Solis, who asked what if there were tabletop games that lasted thousands of years? What would those games be like? (I particularly appreciated the longevity angle since a few days before I met Daniel I bought UNO and some of the cards were already missing or bent).
Turns out, Daniel, who himself is a game designer, did more than just ask. Back in 2011 he actually created and ran The Thousand-Year Game Design Challenge. (You can also watch Daniel’s presentation about the project here). Participants were asked to
Create a game. The game can be of any theme or genre you desire, but there is one restriction: You’re creating a “new classic,” like Chess, Tag or card games. So, create a game to be enjoyed by generations of players for a thousand years.
The original Thousand-Year Game Design post has links to each month’s submissions. One of the games Daniel mentioned was Numeria. You can make it in less than 5 minutes if you have a chess board and a set of tiles numbered 1 through 36 (numbered pieces of paper will do). I haven’t played this game yet, but it sounds like a cross between a connect-four and a mathematical Scrabble.
For Daniel himself, Numeria was one of the few entries that actually made him want to create or buy a set for himself. At the same time, since the game is based on the ability to build and recognize number patterns, Daniel noted that “there are some problems if players have different levels of knowledge of mathematical tropes.”
I think Numeria is a rather tough game to play with the little ones. But you can try playing a Function Machine game. If you are interested in reading more about how playing board games helps children with math, check out this article. If you need some ideas on commercially available games, LivingMath.net has a nice list of board, dice and card games for learning math, strategy and logic.
Which table games do you play with your children? Do you invent your own games?
Image source: Nara J via Flickr!
Posted in Make
The Hundred Chart and Game Cards
It’s been a little while since I did the original post about the hundred chart I put together for my son and his reaction to it. Finally, I have a professionally done (thank you, Ever!) chart you can download, play with, explore and, if framed, admire (it has a certain beauty to it, don’t you think). The chart prints to 1 letter page. Additionally, you can print individual cards and play with those.
Download the low-res PDF hundred chart.
Download individual cards to print.
Download full size high resolution chart. It prints to a 30×60 poster.
As you might know, Maria collects Hundred Charts like the one she shared in our newsletter. So now I’m curious to see other charts in her collection. Have you come across different versions of the good ol’ Hundred Chart? Please let us know!
And if you are looking for games to play with the chart, check out Let’s Play Math post about 20+ things to do with a hundred chart.
Posted in Make
Newsletter January 15, 2013
Welcome to adventurous math for the playground crowd! I am Moby Snoodles, and I love to hear from you at moby@moebiusnoodles.com
Book news
The book cover is ready! This is the version we will be using in the first print and ebook run. Much appreciation to Ever Salazar for many little miracles that turn mere words into real kids playing with real math.
Volunteer reviewers are hard at work giving us comments and suggestions, as we prepare the book for copy editing. At all stages, this book is a community effort!
We are actively working on two super-secret projects to support every family or math club using the book. Both will also support young math projects of our colleagues – blogs, books, puzzles, videos… The first super-secret project is a powerful question and answer tool we call “Ask Moby.” Parents and educators will have a quick and easy way to get answers from like-minded adventurous people who appreciate advanced young math. The second super-secret project is also for grown-ups. I am only going to say, for now, that it goes by the code name “The Game.”
Blogs and networks
We reviewed three books on our blog, all of them about the topic of unitizing – that is, making one unit out of several individual entities.
“Unlikely additions” invites you to think what two units you can add to make a given other unit. For example, 1+1=5 if you add wheels of a bicycle (2) and wheels of a tricycle (3).
“Clap, drum and shake it” and “Meadow count” are about gross motor mathematics. In particular, the units are formed out of large movements, then multiplied into patterns – sort of like a dance!
On our Facebook stream, people discuss their metaphors for teaching, inspired by the “square thoughts” picture Zekeria Karadag shared. Pei-Jung Lee sees herself as a humble servant to the desire of learning. Yelena McManaman paves a road, or at least adds lines to it. Think Magnet likes the quote, “”Education is not the filling of a pail, but the lighting of a fire.” What is your metaphor for teaching?
One of my eccentric hobbies is collecting creative Hundred Charts. The number system we use today is the pinnacle of thousands of years of international research and development. Hundred Charts help us notice some of the patterns that went into this incredible invention. This fresh addition to my collection comes from a young girl named Nomi. Her dad Dor Abrahamson helped Nomi develop the idea into this neat puzzle. Can you figure out how it works? Hints are below the picture.
Hint 1: think of the sum of digits.
Hint 2: think of the number of numbers with each sum.
Sharing
You are welcome to share the contents of this newsletter online or in print. You can also remix and tweak anything here as you wish, as long as you share your creations on the same terms. Please credit MoebiusNoodles.com
More formally, we distribute all Moebius Noodles content under the Creative Commons Attribution-NonCommercial-ShareAlike license: CC BY-NC-SA
Talk to you again on January 30th!
Moby Snoodles, aka Dr. Maria Droujkova
Posted in Newsletter
