So now that the school year has hit, my schedule and routine has slowly gotten back to its rhythm.

Which means that so many of the things I made time for during the summer have just gone away.

Today, I was just thinking how disappointed I was in myself. After all, over the summer I became a full-fledged Tweeter, networking with others in both tech and gifted education. I joined Diigo, sharing math and other educational links with colleagues on the Internet. I kept up with Google Reader, searching out blogs and websites that would be of benefit to my teaching.

Where all is my time going? What exactly am I doing? How am I working to develop as a teacher?

All my haven’ts and my shouldn’ts were starting to pile up in my mind like papers on my desk waiting to be filed.

**WARNING: THINGS GET MATH-Y FROM HERE DOWN. IF YOU HAVE A MATH PHOBIA BE AWARE THAT IT’S QUITE POSSIBLE YOU MAY BEGIN TO FIND NUMBERS INTERESTING.
**

Enter my fourth graders, who are working through a unit on measurement. Let the record stand that the teaching of measurement puzzles me. Kids – even accelerated ones – still lack essential foundations needed to truly understand concepts of area and perimeter. I’ve been working for the past year or two to tease it out. And when I do, I’m going to shout it from the rooftops.

But I digress.

The kids came in today with their homework. They had to create animal “pens” on graph paper with perimeters of 56 feet. I was all excited to let them compare the rectangles they had drawn so we could move on with the next part of the lesson: comparing dimensions and looking for patterns.

But here’s the kicker. Obviously, I didn’t spend enough time telling students to draw RECTANGLES. We had all sorts of 56-foot long fences, only about a third of which were actual rectangles. Some of them were pretty wacky, if I say so myself. My heart sank. I couldn’t tell the kids they did the assignment *wrong*. Because they didn’t. Time to think fast.

And then I realized those crazy shapes would fit right into our discussion later this week about how to most efficiently use that fencing to create pens of the greatest area. Of course they could make crazy fences, but they’d sacrifice space.

Whew! One down. Score one for Mrs. Levin. And I didn’t even have to claim my mess-up on the assignment.

I thought I was coasting along pretty well until the kids had to take the dimensions of rectangles we recorded on the board, put them in order and point out patterns. We had four rectangles to consider: 14×14, 20×8, 10×18, and 8×20. It was obvious to me they were supposed to arrange with the dimensions going from smallest to largest. Then they were *supposed* to notice that as one dimension got bigger, the other one got smaller. I did everything I could to steer them down that path.

Then came a couple of stubborn ones who decided that no, they would arrange the dimensions by the *DIFFERENCE* between the two. They could write down the order, and they could describe how they figured it out. But patterns? They couldn’t find any. Because on their lists, the dimensions didn’t go in order.

And then it hit me. The patterns* wouldn’t* show up for them. At least, not today. But when we start comparing the areas of these arrays later this week? That’s when it gets good! These kids found a way to arrange the rectangles from most to least square. Some pretty sophisticated thinking from ten-year olds, if I say so myself. And patterns? Judge for yourself. Look at the areas of these rectangles with the same perimeter:

1×9=9 square units

2×8=16 square units (7 more than above)

3×7=21 square units (5 more than above)

4×6=24 square units (3 more than above)

5×5=25 square units. (1 more than above)

See the differences? Notice how they are odd numbers going down? 7,5,3,1? You can try that with any group of rectangles. It will work. (I’d like to think that I could take credit for this discovery, but I have to thank another fourth grader for sparking the same investigation three years ago.) I can’t wait to lead this year’s fourth graders down this path. Maybe they’ll have another fork in the road for me.

SO…

Where all is my time going? What exactly am I doing? How am I working to develop as a teacher?

Oh yeah. I’m teaching. More importantly, I’m learning.