Math activity: The Counting Circle

One of my math goals for my children is to build a strong number sense, which is, in part, "fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons. (Wikipedia)." The Counting Circle is one way to accomplish that, so a couple of weeks ago I added it to our Morning Time routine. It takes about ten minutes each day.

The basic procedure is to decide what your students will count by and what number they'll start on (e.g. counting by twos starting at zero), ask for a volunteer to start the count, and go around the room having each person say the next number in the sequence.  I have anywhere from three to six people including myself participating at any time, but it will work just as well even if it's only Mom and one child taking turns.

The very first time we did this, we started at one and counted by ones -- yes, that means 1, 2, 3, 4, 5, . . . .  I did it that way because my non-mathy kids looked a little wary about what we were going to be doing, and I wanted to start EASY so the drill would be a success.  The next time we counted the same way, but every so often after a child gave his answer I asked, "What number is [two or three siblings down] going to say?" and another time I asked the person who said 5, "Who's going to say 10?"  and then, when we got to 10, asked that person who was going to say fifteen.

After a few days I remembered that in the article I linked above, the teacher wrote the answers on a number line, so I incorporated that.  We moved on to counting by 2s starting at zero, and counting by 2s starting at one.

Today, I told them to count by halves, starting at zero.  And then I did something kind of dumb.  I asked them if it would be okay if I just wrote ".5" instead of "1/2" every time because it would easier for me.  They agreed because they're good-natured like that, and we started counting.

Actually, maybe it wasn't such a bad thing, because sometimes they said ". . . and a half," and sometimes they said, ". . . point five," so maybe writing ".5" every time helped reinforce the fact that they're both the same.  Hm.

Anyway, it got a little boring until my 15yod said, with a smirk on her face, "Eight and two-fourths," and I wrote down exactly what she said.

Here's what happened next:

What I learned:

1. Slow down!  The point of the Counting Circle is to let the children think, not to get it done.
2. Write down exactly what they say -- don't take shortcuts just to make it easier on myself.  The excitement and creativity began when I wrote down 8 2/4 as my daughter said it instead of the faster 8.5.
3. Even when I think I've made a mistake it can turn out to be a good thing.
4. Definitely use the number line.  It makes it easier to keep track of where we are when I pause to ask a question, helps the children see and predict the patterns emerging, helps them learn different ways to write the same thing, and allows their responses to be more creative and complicated.