Choral counting

In music, a group singing in unison is called a chorus. In mathematics, one can be part of a similar group but it is choral counting, and instead of singing it is counting together. I had the opportunity to participate in choral counting recently in my mathematics class. My professor began the class by explaining that choral counting is like “skip counting” or saying a multiplication table. The difference, however, is that we were to say them together as an entire group - and were to do the 19s. I was not the only one who gasped audibly at first, never having practiced the 19s. I was pleasantly surprised, however, how it went.

She gave us a few minutes to prepare silently on how we would say our 19s, and we collectively began to search our minds for patterns, having been preconditioned to the existence of patterns by our previous lessons. Fortunately, it was not that difficult to find one after due consideration. When we began the count, our class was able to make a decent showing, having discovered that 19 is very close to 20. One could mentally add 20 and quickly subtract one to equal 19.

As we orally counted, my professor wrote the numbers down on her flip chart for us to see. The surprise came when she stopped us after we had only counted five 19s and asked us to look for patterns. We quickly stared at two obvious patterns. She had written 19, 38, 57, 76, and 95. The ones read: 9, 8, 7, 6, 5, and the tens read 1, 3, 5, 7, and 9. We were anxious to see how this pattern would continue. She did ask us to continue, and each time we went a little further in our count, though we always started at our beginning number 19 in order to keep the rhythm.

Besides the patterns we first noticed, we saw others emerge to join them. The ones counted backwards from 9 to 0 and then started all over again with the same numbers. Likewise, in the tens the next five numbers repeated the numbers 1, 3, 5, 7, and 9, but then it changed. The next two sets of five were 0, 2, 4, 6, 8 and again repeated the same 0, 2, 4, 6, 8. Later, at home I continued with this pattern and noticed there was an extra transition number 9 and then it went back to 1, 3, 5, 7, and 9 for the next two sets of five numbers. I became so excited in my exploration; I looked further and found still another pattern.

Now I saw there were five different numbers in the tens, five different numbers in the one hundreds, five different numbers in the two hundreds, and then there were six different numbers in the three hundreds. Interested in how this would play out, I continued and found three more groups of five numbers and then another group of six numbers. I learned that different multiplication tables provide different patterns. I also had the opportunity to later facilitate a couple other choral counts for both second and third graders and saw that they too became very quick at noticing patterns, but that is another story…