Pie Are Not Square. Pie Are Round.

I have to credit my brother-in-law Adam for the quote in the title. Today we messed with Math, and I desperately need to blog these things, or my progress reports will be a struggle. I was awakened this morning to a parade of three pairs of eyes, no, make that four – can’t forget the dog – staring hopefully at me, and three excited little voices fading into my brain. It was 8 a.m., and they’d already set up the Catan game board, and were really REALLY hoping I’d come play with them. Brian and Ian and I had played it for the first time ever the night before, and it was apparently a hit. So, I got up and played with them while I ate breakfast. The game involves adding (dice), resource allocation, planning and strategy, so it’s one more learn-as-we-play opportunity. It’s a lonnnng game, so I played until Orbit could wait no longer for his walk.

Next, I tossed some compasses and protractors, paper, pens, and pencils on the table and told them to fiddle around with them and see what they came up with. Here is what followed:

Elijah (6) first made an eye shape.

Then he made a happy mouth shape, and did some math on it. He’s still working on getting numbers going the right direction, incluing the 12s that look like 21s. I remember having a hard time getting letters and numbers the right direction.

Isaac (8) made a circle and then chose to measure angles. He noticed that 180 degrees is a line, and that angles can go even bigger than that. I used that to give him a brief lesson on acute, right, obtuse angles, straight, and reflex angles. Again, more number backwardsness, and a new word for it, no extra charge.

Ian (9) made a circle and set about trying to figure out how to measure it (see a backwards numbers pattern here?). Here was the first attempt, which he scrapped.

This photo is a little while after his first efforts, which I’ll try to explain. First, he made a circle, and then marked the center and the radius. Then he took the straight ruler and marked out one inch on the paper. Next, he took the protractor and measured one inch to span about 20 degrees. He then laid his protractor on the circle and marked off every 20 degrees around half of the circle, to make 9 equal sections. He doubled that to get 18 “inches” around the circle. He measured the diameter at about 6 inches, so he told me he measured his circle and that it was “18 by 6 inches.”
I was impressed that he got very close to discovering the Pi ratio, without even knowing it. So, that’s where I picked up the conversation. We used his circle and another smaller circle as examples. I got out string and a ruler and had him measure the circumference with those. Then I had him note the two diameters (reminding him of the names of the circle parts, by the way). I showed him how dividing the diameter into the circumference — of any circle — always results in this special number “Pi.” Since Pi is a number we can always trust, we can use it to easily find circumferences with the formula circumference = Pi*diameter. I then showed him how that was related to the first math we did of circumference/diameter with some math tricks by dividing both sides by the diameter to end up with Pi by itself on the other side – just like it was when we first measured.

As a side note, I wish I had taken a better picture, because I also want to point out that his second attempt to measure the circle was actually to draw a bunch of straight lines touching the circle, with each line being slightly more angled than the last as he went around the circle. For a visual of what I mean, look at this site. I pointed out how he can actually end up drawing a circle using straight lines with that method.

Well, back to the Pi discussion, just for fun, I went ahead and showed him how to find the area with Pi*radius squared. Here’s an awesome video that explains why that works.  He interrupted with another thought as he drew a wobbly shape. Like this:

Then he proceeded to explain and illustrate how this wobbly shape could actually be seen as a smooshed circle. I’m no mathematician, but I surmised to him that we could probably take a bunch of radius measurements, short and long, from the odd shape. To introduce the concept of averages to him, I showed him how we could add all the radii together and then divide by the number of measurements we took to find what might be a reasonable estimation of the “potential circle’s” radius. He was really into all of this. But by this time I could tell he was being mentally pulled away by the glee of his brothers playing.

 

 

 

Here are some snapshots of other things we’ve done recently.

Elijah figured out how to make cool shapes with MagnaTiles

Ian continues to make contraptions with whatever he gets his hands on.

Elijah likes making cool structures with these clippy toys. Clearly I’ve lost the capacity to keep names of things in my head.

Ian built and has been programming this Makeblock Mbot robot.

I do have a third child. But he’s a middle child. He often refuses to have pictures taken. But he does things too. He likes to draw, read, do his music, engage in imaginative play, build with Lego blocks, play educational computer games, and so forth. And his wit is ridiculous.

Isaac is still taking piano, and now is also doing the recorder. Ian really took to the recorder and has also picked up voice class, which he seems really into. Elijah is not terribly enamored with music yet, but Isaac teaches him piano sometimes. Now and then he toots the recorder or bangs on my drums or plays with sounds on the keyboard. Hopefully we’ll bump into something he will stick with before long. Elijah IS crazy about chess, however, and has a fantastic attention span for it and other typically time-consuming games.

I think that about sums it up for now. Dinner beckons to be make.

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