Math Monday:: Creative Computation

I know, I’ve been all about number patterns lately. Naturalist and I are drawn to finding the patterns, but Golfer prefers to do good ole’ fashioned number crunching. The more computations he has to do, the better. My goal was to find a way to make it so that we could join in with Golfer and still have fun doing it.

I personally feel a bit stifled when i look at all the math problems on worksheets, knowing that there is only ONE answer and I’ll probably get it wrong. Ditto Naturalist.

However, in current math theory, there is a push to help kids see that numbers can and ought to be played with. They’re encouraged to find their own solutions and come up with their own strategies to answers. Not having BEEN taught that way, I had no idea how to go about doing this.

BUT!

I checked into lots of different math skills books, workbooks, curriculum, etc. and one has stuck with us: Number Jugglers: Math Game Book & Math Game Cards

It is a spiral bound book that comes with its own deck of special cards, and all the activities inside (32 in all) use them. In the preface, the book states:

“Math can be a lot of fun. In fact, it can be downright exciting. Number Juggler math games are designed to let players start where they feel comfortable. Because the games can adapt to all ages and all ability levels, the same game can be fun for a kindergartner, for a sixth grader, and even for a college student. The math cards do not come with operation signs–the plus, minus, multiplication, or division signs that tell us what to do. When students see an operations sign, their brains seize on it…they see a plus sign and see addition. They see a minus sign and see subtraction. This limits their freedom to invent. In these games, we don’t want to restrict your child’s math creativity in any way. Looking at the numbers, children make whatever connections and relationships they can from their own store of math knowlege. This encourages players to make more and more complicated computations as they go along.”

What makes this book different from anything else I’ve seen is that instead of giving an operation to solve (5+5=? or 23-8=?) for the most part you have a target number (10, or 15) and you use 5 or 10 cards in any combination to get to that number. This really broadens the scope of math into a very creative, experimental and dynamic process. You’re not hemmed in to only ONE answer, or ONE way to do things…it’s up to you to solve it in whatever way you can or want to!

We’ve been using this book for 2 years now, and this hasn’t gotten old yet. The object is to make math sentences for every rung of a number ladder from 0 to 9. You are dealt 10 cards, and can use each card only once on any given rung, but you can use it again for the next rung. All operations can be used at your own discretion. At first, Golfer was the only one comfortable with using multiplication and division. Very quickly, Naturalist and I learned that you can get to a lot more numbers by using more operations than just adding and subtracting, so we started branching out, too. Golfer loves doing ‘acrobat math’, so will put together a string of numbers in complicated orders of operations…something like, 2 (2+2) + (8-5) -2 for the 9th rung. I was able to introduce the concept of parenthesis in math and the proper order of operations to him in the same game where Naturalist was doing only the most basic addition. But she’s a quick learner and was quick to catch on to the more varied possibilities on mathmatical answers.

By increasing or decreasing the number of cards dealt to each person, the difficulty can be increased or decreased. The same time we are playing it, Sassy takes her cards and puts markers on the rungs for whatever numbers she’s dealt. Then she tells me what numbers she’s missing and quickly looks through the deck to find them. I love that a pre-K girl, a 4th grade boy, and a 6th grade girl (and a mom!) can all play the same game with varied abilities, and each of us finds it fun!

This also reinforces basic math ‘rules’ in fun ways, like the balancing game.

In this one, we take our 10 cards and try to make a number sentence where both sides of the equals sign add up to each other, like this simple example (Most of these games can be played with playing cards, but I like their deck because there are the numbered dots on them, so kids can have them to count on if their number sense is still developing.):

9+6=10+5. Basic pre-algebra concept that even Golfer is picking up on. Of course, he loves to do his acrobat math and tries to use as many of his 10 cards as he can just for the sheer joy of using numbers. Naturalist enjoys using lots of cards just to be creative…which means she’s more open to learning how to do different operations so she has more options with her numbers. I’m trying to learn how to do math in a fluid, less stressful way. We’re all having fun!

As you can tell, I highly recommend this book. It’s been in our rotation for a couple years now, and as our math skills have developed we’ve been able to play the same games but with more sophistication. It truly stretches from K through at least Middle School ages, and adapts as we do.

A lesson the book taught me about math, especially teaching creative and divergent thinkers, is to open numbers up. Don’t give a problem where only one answer is right….give the answer with an unlimited number of possible questions that would fit it. Often during the day I’ll just shout out a number….”32!!!!” and the kids shout back whatever they come up with for an “answer”… “4 times 4 times 2!” or “64 divided by 2!” or “12 plus 12 times 2 minus 16!” With Naturalist I’ve noticed that she has less anxiety this way, because she’s not as afraid to get it ‘wrong’. When there are so many right answers, she focuses on finding a creative answer. If there is only one answer to give (like on a traditional worksheet) then it’s less creative and way less fun.

Try incorporating this open ended concept into your own math and see how much fun it can be!