Goldfish riddles

There are ten goldfish in the bowl.
Four goldfish are orange. How many are not orange?

It's Fun Math day. Today we did goldfish riddles. Who doesn't like a good riddle? Especially when you get to eat the answer. I made up simple math riddles for the fine young gents to solve, riddles like, "There are twelve goldfish in the bowl. There are twice as many red goldfish as green goldfish. How many red goldfish are in the bowl?" Goldfish riddles introduce the concept of solving for an unknown,and math language like "twice as many" or "one more than." (And, note to self: "Riddles" sounds waaaaaaaaaaaaaaaay more fun and game-like than, say, "word problems.")

Goldfish riddles is a perfect example of activity-based learning. I didn't sit down with the gents, pass out pencils and paper and say, "Time for algebra!" I sat down with a bowl of colored goldfish and said, "Let's play a game! It's a riddle game. Let's see if we can figure out the riddles." Embedding concepts and skills into a hands-on experience allows children to experiment, to learn concepts informally, and to experience those concepts in a concrete way before they're ready for more abstract learning.

In activity-based experiences, my job is not to instruct, but to guide; a little bit of teaching, a little bit of trying. How do we measure "twice as many as" anyway? First we figure out what it means, that's where the teaching part comes in because I knew what those words mean and they didn't. Then we tried putting one green goldfish in the bowl followed by two red until we got to twelve goldfish altogether. Does our answer match the rules of the riddle? I don't have to say "Yes, that's the right answer," or "Nope, that's wrong." Instead they get to decide....does it follow the rules set out in the riddle? Are there two red goldfish for every green? And do they add up to twelve altogether? Well, then, is it a match? Eat up! (Or let's try again!) As they crunched up their own fish bowls, I drew a picture of the answer for extra reinforcement and to keep myself from eating up the next riddle.

With simpler problems, first grade gent had a chance to be the guide. "That's easy. Six!" he replied to the riddle at the top. "Show your brother how you got that answer," I replied. He had to think back beyond the memorized math fact, 4 + 6 = 10, and show the way to the answer. Beautiful.

First grade gent is a math lover like his daddy. I think I'd have to lock this kid in a box to keep him from learning. I got out a pencil and paper to show him the "real math" (his words) behind the riddles. I don't expect that he'll start doing algebra tomorrow, or even next year. He's just a bright but typical first grader playing around with math ideas. The beauty of these kinds of activities is that not only do they make learning fun and spark his interest, they lay a foundation for more formal abstract learning later. When it's really time for him to start learning to solve problems like 2x + x =12 he's already experienced this concept. He's had practice hearing the language of math and turning it into a sovable problem. He may not even remember playing goldfish math by then. But the seeds have been planted.

I expect that we'll be playing goldfish riddles a few more times over the next couple weeks and revisiting it from time to time for the rest of the year. It's a game that takes practice to learn how to play, with a little more prompting and guidance initially in order to teach the task of playing in addition to finding the answers. It's a flexible game. We don't have to use goldfish. We can use m&m's or counting bears or acorns or beans. We can play anywhere, for as long as we'd like. Because it's Fun Math.

(A huge nod to Family Math for Young Children, Coates and Stenmark. We really like this book. It's chock full of Fun Math, hands-on real life activities and games. I based our goldfish riddles on the Bean Soup activity, and would have used the riddles from the book and probably used beans too because that's what it said in the book except that I couldn't find the book and we were out of dry beans. Oh well. The goldfish were tastier anyway.)