My Favorite Math Games & Interactives: Online & Off

A friend of mine has a couple kids in kindergarten right now.  He asked if I had any recommendations for "online computer games for arithmetic, patterns, creative math exploration."  Why, yes, I think I do!  Following is an annotated list of some of my favorite interactive online habitats for a wide range of ages, including parents.
 
However, I think I'll start with a list of activities that are not computer based.  I'll be the first to admit that I'm a little biased toward hands-on, not-virtual learning, especially for the primary grades; children's bodies really need to be involved in the  learning process, especially math.

Also, although my kid has some computer skills, she is basically raising herself as a luddite, which is fine with me for now.  She's never been drawn to the computer, even when I specifically show her something I think is fun or cool.  So, many of the games and interactives listed  in the online category, below, are places that I go to get activity ideas to adapt for her off-line lessons or to grow my own math understanding or just for inspiration.

OFFLINE FUN
I don't know where we'd be this year without the endless Shut the Box tournaments of last year.  I attribute at least half her mental addition skills to rolling two dice (which can make up to 12) and finding different ways to make the rolled number.

I attribute the other half of my daughter's mental addition ability to UNO.  It's a classic game that we played speed style all last year.  And, at the end, the winner got to add up all the points she won from her mother opponent who always remembered to chant the UNO Point Tallying Mantra: "Find your tens!"

Peggy Kaye's book Games for Math  has LOTS of easy and inexpensive ideas including Nine Men's Morris which is sort of like a more complex and moveable tic tac toe (strategy, logic).

Variations on "sort and count the change jar" along with "save and spend" from about the age of five means that now, at age seven, the child is a whiz at money math (also known as adding and subtracting 10s, 100s and 1000s).

And, of course, The Game That is Worth 1000 Worksheets from the Let's Play Math Blog -- for the littles all the way through high school.  This fall we used a version that was a combination of sums and differences.


ONLINE GAMES & INTERACTIVES (NOT JUST NUMBERS)
Some of these are for you, lots for them, and some for the whole family (like Scale of the Universe 2 and the triangle interactive!!)

National Library of Virtual Manipulatives: Truly a class act and a challenge for all ages. 

Math Pickle: This link takes you to a large library of interesting videos and ideas organized by grade level.

Kaleidograph:  I first found this toy and played with it online, and then I bought the real thing for Christmas. Both the online and hands-on versions are great but, no surprise, I find more meaning in the actual toy.

From my childhood memory bank, a classic Sesame Street clip with a lovely song: Two Little Girls and Their Little Doll House.  My adult eyes immediately saw one-to-one correspondence but my little girl heart remembered something different.



Scale of the Universe 2: I have no words for this interactive graphic other than just GO.  You can turn off the music if you want.

I've included this link to Planet Seed/Math Puzzles for Kids because I don't want to forget about it.  It was on a long list of bookmarks already.  Puzzle topics include combinatorics, algebraic thinking, topology, probability, etc. 

Games from Freudenthal Institute look great, and they even have a star interactive!

Make your own isometric dot graph paper here.  These and the other dot graph paper you can print out are fun to leave around the house so kids can make designs whenever the mood strikes.

Math cats!  Need I say more?

I personally love Symmetry Artist from Math is Fun and my daughter actually liked playing with it for a while. It's a great way to really experience the differences between line and rotation symmetries and you can print out the designs you make at the end.

And, you really cannot miss this triangle interactive from the Triangulation blog.  Truly.  Run, don't walk.

To close it out, here is a lovely and thought provoking classic Sesame Street animation with music by Phillip Glass called The Geometry of Circles.

Symmetry Artist: Exploring Attributes Through Design

I recently discovered how important the practice of identifying and describing attributes really is to math learning, especially at the elementary level.  Learning to discern similarities and differences develops mathematical thinking skills that can be used at all levels and topics within mathematics. 

Despite the thrill of discovering how this kind of thinking is used in my program Math in Your Feet, I was left with lingering questions about the differences between identifying attributes and using attributes in a design process.  I suppose they are two sides of the same coin, but I can't help thinking that being able to choose from an inventory of possibilities is the preferable skill-building activity in the long run.

I tested my theory on myself and my six year old daughter by using the Symmetry Artist at Math is Fun.  Maybe you've seen this before?  Check out all the attributes you can choose from to make your symmetry designs:

You can choose between reflection or rotation symmetry, with six to eight choices in each category.

Your pen has five choices.

Seven thicknesses.

And many, many colors.

There's a lot to choose from here, but the tool is easy to use, so you can easily change your mind and start over, or take out your last move or series of moves. 

While you experiment and play around you are also noticing relationships between the lines and shapes you make and observing the structure of the final design.  The addition of color serves to increase the complexity and interest in both the process and the product.

I suppose the difference between identifying attributes and using attributes is that one is a more closed process than the other.  I'm thinking that with a set of attribute blocks, for example, although you are learning to discern differences and similarities, there are really only right and wrong answers.  The benefit of this kind of activity is that you are actively using math vocabulary: thick/thin, large/small, circle, square, triangle, edges, etc.  This is all very useful but, as I said, a somewhat closed process in terms of inquiry.

In contrast to 'compare/contrast/identify' there's the process like the one you use in Symmetry Artist. Instead of simply identifying attributes, you are using this skill in context while thinking mathematically in an active way -- you are actually 'doing' mathematics.  By this I mean you are asking questions ("What would happen if I started my circle here?  What would the same design look like with nine iterations instead of four?  How'd that pentagon get there?"), experimenting with and analyzing your 'answers' (designs), erasing your answers, starting over, printing out the answers you like, asking more questions.... This is the creative process in action; it is also mathematics in action.

I love Symmetry Artist because it is a beautiful and fun way to play around with, learn about, and compare how lines, shapes, and iterations interact within these two symmetries.  Below I've put just a few of the designs my daughter and I recently made. 

As a first grader, my kid uses this tool primarily for exploration.  I started by explaining the different categories, but not much more, and she jumped in from there.  I, on the other hand, being aware of just how many choices I had, jumped in but soon got overwhelmed with too many questions which led to too much erasing and/or starting over, resulting in pretty much nothing to show for my efforts!  That didn't stop me from noticing a few things, however.  Take a look at what we did, see what you think and then go try it yourself! 

Here's my daughter's first design.  Notice that she set it for rotation, 'eight', pen, one color, and a medium thickness.  She 'drew' with abandon, and I was thrilled with what resulted, mostly because I would have never thought to do it that way!  As you'll soon see, my initial approach was a bit more measured.

Her second design was inspired by the first.  "I want to draw a sun!" she said.  I don't know if you can see it, but she started with 'four' red, then 'nine' red, then 'nine' yellow.

Here's the one I made as an example to show the kid what you can do with the tool.  I used 'five', circle, and some variations in thickness and color.  I love the almost-pentagon in the center where the five big circles cross.

The one thing during my experimentation that really thrilled me was that I noticed a difference between the process of drawing a design with a line of symmetry compared with what happened while using 'two' rotation.  Can you see it?

I know what it looks like, and how to describe it, when a two-person team transforms their percussive patterns using both kinds of symmetries, but there was something about using Symmetry Artist that made it stand out to me in a different way.  You are actually drawing one design and the multiples show up automatically.  There was something about seeing it happen in real time (moving patterns!) that I would not have noticed if I had been drawing it by hand, one reflection or rotation iteration at a time.  If I had been doing it that way (pencil and paper) I probably would have noticed something else altogether.

This is all just more evidence that you really do need multiple opportunities to observe and work with a math concept in a number of different situations to really understand it.  In the end, I think that both the act of identifying attributes and and the act of using attributes in a design process (choreography, visual art, tangrams, etc.) have something to offer each other. 

Because I am a teaching artist, dancer and musician, I am coming at math education from a different direction than many.  I am also a big picture learner, so putting math in context makes a great deal of sense to me.  What I am still thinking about are things like: When is it important to just teach math as math?  When do you move on to reflection on and representation of the math you've discovered during an open-ended exploration?  These are the questions that quite literally keep me up at night, and one reason that it's taken me so long to get this post the way I wanted it.  I suppose I may be overthinking things, but I really am curious about all this.

What's your experience with attributes?  I'd love to hear what you think about all this!