Yesterday I told the kids that we were going to do math without the math book, and that I’d teach them to count to one. I’ve been Counting to One with fourth graders for a few years now, but I put a new spin on it this year.

One of the teachers I work with had a great idea for teaching decimals that she mentioned in a meeting the other day. She said that the place value blocks that come in units, tens, hundreds are easy for the kids to understand as decimals if we call them something that they look like, that represent something less than one. She said she calls them cake, slices, pieces, and crumbs (there’s no block for a crumb, but they can picture it). I tried it, and now we have something concrete to talk about when we use these things for decimals.

The Conventional Approach

The math books all start off with decimals by showing a place value chart with one’s, ten’s, hundred’s, etc. And we are supposed to “review” this before we introduce the new decimal stuff. By review, they usually mean we talk about it, and the kids write some numbers that you say, and then they find out if they’re right.

In my experience, this kind of review is great for affirming the knowledge of the kids who already know it, and for reminding the rest that they never got it to begin with. After this review part, according the manual, we move forward with the lesson.

The achievers are great at following directions, and they remember everything you say, even if they don’t know what you mean, and they figure it out after a while. The kids who didn’t know what you were talking about to begin with just copy what you’re doing, and they don’t hear anything you’re saying.

They might not ever figure it out because they learn to expect nothing. You’re told to provide examples of decimal notation by showing the students how 45 or 27 or… any number of little blocks out of a a hundred-square grid should be written .45, or .27, or … whatever, and then you’re supposed to tell them how to read the number, and you do some examples.

This routine is known as Teaching Math. But the low performing kids in this imaginary movie don’t have a reciprocal routine for Learning Math. Unfortunately for the real kids in my classroom, now, I have a Pacing Guide. The pacing guide is there to make sure I stay on the same page with everyone else and complete the program.

How, I wonder, is administering a program the same as teaching? It feels strange. I’ve never had a Pacing Guide before. Raise your hand if you think I’ll stick with the pacing guide. That’s right.

I’m just the teacher. Accountable to the program. The memo is somewhere near my desk if I ever want to read it. The cover says Pacing Guide. I read that.

The result of the Teaching Math routine is that you get a sixth grade girl in your class one year who tells you that a decimal is a number with a dot, and that’s all she knows about decimals. The girl was unable to write a number for a picture prompt showing half a glass of water. For her, the glass was way more than half empty.

Cake, and Fuller Glasses

When I counted to one a few years ago with my class, they got it, but we didn’t have the cake and the slices analogy. A good analogy is a big help in talking about something later on. By definition, analogies travel well, and they keep for a long time. When we call .17, seventeen hundredths, it just doesn’t have the same imaginative punch as 17 pieces of cake, or alternatively, one slice and seven pieces. Of course we use both forms. The mathematical and the analogous, and the kids learn to code-switch.

To accomplish the job of counting to one, I passed out the blocks and some grid paper. I have a bell. I explained that the flat 10X10 block was the cake pan. The little cubes were pieces, the long sticks of ten were slices. When I rang the bell, they added a piece of cake to the pan, and wrote the number for it. Every time we got 10 pieces together, they’d trade for a slice.

Ring! .01, “one one hundredth.”

Ring! .02, “two one hundredths.”

Ring! .03, “three one hundredths….”

Every now and then we’d stop and talk about the patterns they saw in the numbered grid they were recording in. The bell ringing kept them engaged in the conversation so we’d all be looking at the same thing. I told them we were factory workers, operating a cake-making machine. They put up with my nonsense most of the time.

“Hey, these are like regular numbers,” I heard a several times.

Some kids said things like, “I notice all the numbers in each column start with the same number.”

There was a lot of exclaiming and hand raising as various people announced discoveries of the obvious.

We actually counted past one cake. They need to see what happens when there’s a whole number. We didn’t go past 1.1, one cake and a slice because they all got it.

“Hey, we learned math today, and we didn’t even do the book!”

“I’m so glad you showed us this, Mr. Noon.”

“I understand this now. It’s easy!”

Dessert

Today I pulled out the wimpy number line worksheet (I just made a typo, worksheep, that I kind of liked better than the real word) with decimals, and they filled it in - no problem.

One little girl told me, “Yesterday I told my mom that we learned how to count to one. And she said, ‘At least they aren’t rushing you.”

That mom has a sense of humor. And the kid said, “I wanted to see if she could guess what I was talking about.”

It was a good lesson.

Later on, at lunch time, another little girl who has no confidence in her ability to do math was looking at a poster of the multiplication table, and she said, “You know what, Mr. Noon, I just noticed that if I want to multiply three times five, I don’t have to look at the whole chart, I can just look at the three’s and count down five of them. See, it’s fifteen.”

This quarter, math is mostly about getting rid of that poster.

When they notice things on their own, they like to tell you about it. I’m feeling optimistic, despite the Pacing Guide.