The delights of a new class

This Wednesday began my sixth year working with sixth graders at Jordan Catholic School doing Enrichment Math. I am fortunate to have 23 students signed up for this 7 am class. What a great bunch of children. We're off to a promising start. Most of the students and I have not met each other before. I asked the children whose siblings have been in any of my classes to raise their hands. That accounted for six. Then I asked which children were sitting at a desk where the name tag on the front corresponded with their name. That gave me another ten or so. The rest I had to work on the old-fashioned way - saying their names over and over to myself while trying to visually tie it to the name I see in my mind. I pride myself in learning my students names within a two or three classes.

After I passed around permanent metallic markers for the students to use to write their names on their brand new calculators (and the face plates), I went over the usual routine of the class. As we are at a Catholic school, we begin every class with a prayer. I ask a student to come forward, ask for prayer requests (intentions), and then lead us in a prayer of his or her choosing. When we asked for prayer requests, the first girl called upon said, "How about the Our Father?" I tried very hard not to laugh. I shook my head and said, "I'm sorry. I didn't mean to ask for your request of the top ten greatest prayers of the Holy Catholic Church. I meant for you to say something like 'My big toe hurts.' or ' My mom is having surgery.' or ' My dog is old.'" Fortunately we all had a good laugh and continued on. Thankfully the girl leading prayer chose to end with the Our Father, so the request was not in vain.

The worksheet I handed out had the numbers 1, 3, 5, 7 , and 9 printed prominently at the top. I wrote the numbers on the board and asked the students to tell me what they knew about these numbers. "They're single digits." "They're odd." "They skip a number in between." I asked if anyone could tell me how many prime numbers were represented. The answers were all over the map. I asked if anyone could define prime. They kept getting closer and closer. One student said, "It's a number that can be multiplied by one." Nice try, but all numbers can be multiplied by one, but I think I understood where the student was headed.
I asked them to draw a little house.
_______
/______\
|______|
|______|

We put the number in the attic and the factors on the floors. Like so.
_______
/__3___\
|__1x3__| Notice that three is a two-story house.
|__3x1__|
All two story houses are primes.

Notice that one is not a two story house.
_______
/__1___\
|__1x1__|

What's up with one? It is unique. Singular. Neither prime nor composite. I asked the students to look at the word unique. How many wheels does a unicycle have? How about a unicorn? We live in the United States of America. Out of many one. We are one. I then point out that zero is another unusual number in this respect.

Then we test out all the other numbers on the board to see how many stories are in each house. Five and seven follow the same pattern as three so we tally up two more primes. Then we look at nine. Uh, oh. Three times three can only be written once. Then we have the other two facts (remember all numbers can be multiplied by one). Then I point out another interesting fact. Houses with an odd number of stories have a special name. Squares. Then I draw a 3x3 square on the board next to a 1x1. Any number times itself makes a square. (At this point I know that they have not studied this concept, but I like to show them this visual point.)

Ah, now we have three primes, two squares, and one composite to add to our list of what we know about these numbers. We haven't even talked about natural numbers, whole numbers, integers, or rational numbers. They will get that later in the year. As I check to see that students are taking notes, I add, "All that and we haven't even begun to look at what the worksheet is asking us to do."

It's time to hold on to your desks as we take math apart. We get to explore the inner workings of numbers and deconstruct the language that we use to describe mathematical realities. We are off on another grand adventure, and I am so privileged to be the tour guide.