## Buzz

Have you ever played the game “Buzz” when you were little?  It is a fun game for practicing skip counting and concentration.  I played many variations of it in elementary and middle school.  A few weeks ago we introduced the game in class and Katie took a real liking to it.  We have since played it with her on a number of occasions.  Here’s how it goes:

First, the “buzz” number is chosen (usually between 2 and 9).  Players sit in a circle and take turns counting by 1.  Thus, the first player says “one”, next one says “two” and so on.  Whenever a multiple of the buzz number is reached, instead of saying the number the player has to say “buzz”.  For example, if the buzz number is 4 then the game would go as follows: 1 2 3 buzz 5 6 7 buzz 9 10 11 buzz…

Now one might think that when there are just two players the game is not very interesting.  However, Katie still enjoys playing it and she makes new observations almost every time we play.  A few days ago we had the following conversation after playing a round with buzz number 5:

K: How come you say buzz on all the last numbers and I say buzz on all the middle numbers?

Me: What do you mean?

K: Well, I say buzz on 15, 25, 35 and you say buzz on 10, 20, 30, …

Me: So we alternate saying buzz.

K: Exactly.  Why is that?

At this point I go into an explanation of how numbers that end in a five are all odd and those that end in a zero are even – she already observed in the past that one of us says all the even numbers and the other one says all the odd ones.  After hearing my explanation she suggests that we start at one and let each number in order be the buzz number.

One doesn’t turn out to be very interesting (buzz buzz buzz 🙂 ).  With two we had already observed in the past that one person always says buzz while the other one says all the odd numbers.  So three is the first interesting case.  We get barely past ten when Katie interrupts the game.

K: Hey, it’s happening again.

Me: What is?

K: We are alternating saying buzz. Why is that?

Me: For the same reason as before 🙂 .

But that’s not a good enough explanation.  I attempt a better one, the details of which I will not go into as I’m not sure how much Katie got out of it.  We further observed that with 4 and 6, as with 2, only one person ends up saying buzz.  I then try to explain that this will happen with every even number.  I must have gotten a little carried away, and at some point Katie interrupted me to say, “Mom, can I say something?” 🙂

So here is the question that I have: There are many patterns to be discovered in math; which ones should we point out to kids, which ones should we suggest they should look for, and which ones should we just let them discover completely on their own?  My guess is that we should do some of each, but the more of the last kind the better.  However, sometimes I worry that we do too much of the pointing kind.  What do you think?