Informal Derivation of Pi

7.GM.5 Understand the formulas for area and circumference of a circle and use them to solve real-world and other mathematical problems; give an informal derivation of the relationship between circumference and area of a circle.

I gave the students hula hoops and some coasters, and next year I might save some container lids or something to create a few more things for them to measure and work with. Then i gave them strings and measuring tapes (there were measuring tapes in some of the manipulative kits I found at the end of last year!) and had them figure out the relationship between the circumference and diameter. They all came pretty close to pi, which was cool.

I need to review the instruction sheets I gave them to make sure the language is as clear as possible, or else create an instruction video.

I liked this activity and the students seemed to as well, but it’s frequently really challenging for my students to reverse the direction of the problem. They have the idea that circumference/diameter = pi, and some of them even got that pi is like a unit rate, or a very specific variable, but they can’t seem to remember the process that circumference = diameter * pi. I need to think of more ways to extend this activity to help with that.

Tacit Knowledge and the I-We-You Trap

Long story short: I became a mathematics teacher like my forefathers before me.


Basically, I went and took the Middle School Mathematics certification test. And because this is how my life works, that’s what I got hired to teach. But I have an admission to make – I like teaching math, but I really struggle with it.

Most of my mathematics knowledge is tacit knowledge. I don’t think about problem solving, particularly not at the pre-algebra level that my students are learning at. I just solve the problem. My parents described the situation as having a lot of power, but not much finesse. So my challenge is turning that tacit knowledge into something that I can share with the kids.

There’s also a huge problem in the culture of education right now, which you probably know about if you are reading this. Your measure of success, career stability, and financial value is a test score. The test is written and graded by a gigantic corporate entity that apparently has no experience whatsoever with children in general and seventh graders in specific.

There’s a standard approach to mathematics instructions that has been used in the classroom for over a century -I’ve read about it being called I-We-You, or sometimes it’s called Gradual Release of Responsibility. Basically the teacher explains the concept, then we solve some problems as a class together, and then the student is expected to solve the problems. Despite it being the prevalent practice, it’s not actually the best practice. Kids and adults hate and despise math and are missing out on the best part of it because they are so caught up in algorithms and computation and I-We-You.

The practice that’s considered most effective is You-You All – We. In this sequence, a student takes a problem and tries to solve it. Then they work with a small group to discuss their solutions, and then the teacher leads a whole group discussion of solutions. If there are textbooks written this way, I don’t have one. (Actually I have no textbook whatsoever).

The two problems with this approach are as follows: 1. This approach takes time, which, when I consider the number of standards I am supposed to teach them and that they may be  tested on, I am not sure I have. 2. If kids are used to I-We-You they seem to be incredibly resistant to trying any other approach. Frequently attempts at doing so end in tears, even for students who do well in math. Sometimes particularly for students who do well in math.

Or maybe I’m just doing it wrong. It’s not like there’s anybody who can tell me if I am; ¬†it seems like these are pretty uncharted waters.



This Blog Not Dead

Okay. So it’s been a busy couple of years.

I have not been teaching preschool, or doing before-care.

I moved to Indiana and taught special education for two years. I know there are special educators who blog about their practice, but I actually don’t have much that’s positive to say about either experience, in a broad sense.There’s a reason that people burn out of special ed so quickly, and it isn’t the kids or their parents.

Now I’m teaching math in an urban school setting. I don’t think I’m an expert in math instruction at all – in fact, I really struggle with it, because it’s not what I majored in. But there are good moments and terrible ones and I think I am learning.

More later.

This Morning In Yellowstone

The nice thing about AM club is that we can pretty much do what I want. There’s no curriculum or expectation for learning – my job is just to keep the kids occupied and safe for the morning. The downside is that there’s no paid planning, so mostly I just keep on my toes.

I got a text from my mom this morning saying that they were on Geyser Hill in Yellowstone. Texting isn’t exactly forbidden at my job, in fact, Imageit’s how I communicate with my offsite supervisor. So I read it to the kids, and then we wrote back and asked for pictures. In the meantime, we talked about Yellowstone and geysers and watched some videos of geysers erupting and a quick clip on how they worked. My dad sent some nice photos and tomorrow I will bring in my laptop so we can watch a video he made of our trip to Yellowstone back in 1995.

The reality is that it’s 2012, and people have smartphones and no one wants to keep them locked in their closet or stowed away in their purses. There are too many ways they can enrich what we do as teachers and care providers, and if we don’t have them in our pockets, we will miss out on the best opportunities to use them.

Helicopter Tag

I just wanted to share a cool activity some girls and I came up with as an exercise in compromise. One really wanted helicopter during free play and another wanted to tag, so we came up with something for both of them.

Basically, it starts like tag, but first person who gets tagged picks up a rope and spins for helicopter. When somebody misses the jump, the rope gets dropped, and everybody scatters because the person who missed the jump is it. Play continues in this pattern, although a child who is dizzy can ask a rec leader to take their turn spinning the rope for them.

It was a nice example of a compromise where things turn out better than anyone originally thought.

Helicopter, for the uninformed, is basically a group jump rope game. One child spins the rope, low to the ground. The other kids stand in place and try to jump over it. It can be played with a short jump rope, but if you have a bigger group, the best thing to use for jump rope is the kind of clothesline that feels like a computer cable, but has no wires inside. They’ll have it at your local giant hardware store for cheap.

Teachable Moment: Graphs and Charts

A teachable moment: chart about our lunch beveragesAt the end of the school year, I started eating lunch on Wednesday with some of the older preschoolers who were staying for our afternoon “Reading Ready, Math Smart,” program. Basically we are our sack lunches, cleaned up, and sang some reading and math songs I had on my iPhone. A pretty exciting thing happened on one of those days, though. We were all talking about what flavor juice we had for lunch, and the kids were trying to keep track of how many of each kind of juice was represented.

It seemed like the perfect opportunity to teach them about making a chart, so I strode over to the pad, grabbed a marker and drew a chart, with a picture to indicate each flavor, and then a face for each kid who had a juice box. We talked about it. One of the other teachers came in with her pop, and we added that to the graph.

Without much thinking about it, we had just hit Illinois Early Learning standard 10.A.ECa. And that was way more interesting than fruit snacks.


We wanted to hand out medals at our end-of-year picnic, so we chose an Olympics theme for the last week or so of school. With the Summer Games happening in London this year, we thought it was a great time to get the twos (well, threes now) some background knowledge so that they could enjoy the games with their families this summer.

We’ve had a lot of sports books out from the library this year, and this was no exception. Petra filled up the book nook with titles on summer sports. I went online and found some nice clips from past Olympics and a video of this year’s torch-lighting ceremony in Athens.

Several of the little boys were fascinated with the freestyle wrestling and we had a lengthy if basic conversation about how this was stuff for watching, not doing. I explained that the Olympic athletes had special training to keep from getting hurt. Maybe I should have just skipped that sport altogether, but in my defense, those were some fascinated kids.

We did two craft projects relating to the Toddler-Made Olympic TorchesOlympics. I didn’t get a picture of the first one, but it was pretty basic. We took Styrofoam cups and dipped them in different colors of paint and made our own pictures of the Olympic Rings. I did this with one child at a time so that we could talk a little about the whole thing while we worked.

Petra came up with this amazing torch craft. Basically, it’s a Styrofoam cup with the bottom cut out and taped to a paper towel roll (masking tape). The kids wrapped the torch body in tinfoil and then glued in the tissue paper to be the flame.

When their parents came to pick them up, we sent them out of the door holding their torches while we sang the Olympic theme. “Dah DAH dah dah dah DAH dah.”

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