09.29.07
Posted in Co-op class, The creative side of life at 5:29 pm by Meg
Hubby helped me decide on the theme for the third Map Club. He thought the kids would enjoy learning about non-Euclidean geometry and studying Taxicab geometry. It looked really fun, but at first I wasn’t sure how I was going to develop sessions at all three levels. It took a little playing with, but I finally came up with a structure for the classes.
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The pages’ abilities are all over the place. I decided before I could even introduce them to coordinate systems, I needed to work in one dimension. In fact, I ended up deciding their class goal would only be to introduce the girls to a coordinate system.
So we started off with a number line (I printed them each out a numbered strip) from 1 to 20. Our guessing game focused on the terms ‘greater than’ and ‘less than’. The person who was ‘it’ would chose a number and then we’d go around trying to guess what it was. After each guess, she’d tell us whether her number was greater or less than the guess. The girls enjoyed it and it gave them some idea of order and location.
From there I explained who Rene Descartes was and that he is credited with developing the Cartesian coordinate system. Earlier in the morning a couple of the older boys had drawn a large grid on the driveway and using it as a visual, I explained that each line represented the same distance.
We then used the grid to play an oversized version of Animal Crossing 
from Stenmark, Thompson, and Cossey’s book Family Math.
We first played it without any walls, so they could understand the what they were trying to do and then I drew in the walls and they played again until we ran out of time.
The idea of the game is that you roll a die that just has the numbers 1, 2, or 3 and then move in a straight line that number of spaces. When you run into a wall, you need to stop moving and then on your next turn change direction to continue on your way. The goal is to reach the opposite side.
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For the knights, I started with Descartes’s quote “I think, therefore I am.” and asked them what they thought it meant. After a short discussion, I explained he was a French philosopher and a mathematician (and even a lawyer) and that unlike today when we tend to think of these as separate areas, during the Renaissance period people would be interested in a board range of ideas.
We then went over the grid (which I had now added labels to the axis) and we discussed it’s 3 characteristics: origin, perpendicular axis, and a scale for measuring distance. We also went over how to name a point (x,y).
To use the grid, we first played another game from Family Math called Hurkle. For this game, whoever is ‘it’ chooses a point and then when another player guesses, they have to tell them what direction their point is from the guess (north, west, northeast…). The kids quickly figured out that by having everyone stand on the point they chose helped narrow down where the next choice should go.
After playing that for long enough for each kid to be ‘it’ once, I discussed that on typical grids the distance from two points is a straight line. But that wouldn’t work for a taxi in a city unless it could fly like a bird, so I explained how taxicab distances are measured. We then went around again, but this time instead of indicating direction, the person who was ‘it’ would give the taxicab distance to their chosen spot.
To finish coordinate systems we ended with a discussion of 3 dimensional systems that are used in ‘real’ life. They came up with examples from GPS systems to aircraft systems.
Since we had a few minutes left, I gave them another puzzle dealing with movement. The Konigsberg Bridges problem was solved by Euler (or actually not), but it kept them busy for their last 5 mins.
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By the time of the squires’ class it was getting hot. I think it actually hit close to 90 and we were in the sun. It definitely had me dragging a little.
But we jumped in with Descartes’s quote and why a Renaissance philosopher was also a mathematician. I started by introducing them to the grid by playing Animal Crossing and then we discussed the Cartesian coordinate system and how to name points. From there we played Hurkle, had a similar discussion about measuring distance, and then played taxicab.
And with that, their class was over.
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09.24.07
Posted in Co-op class, The nuts and bolts of it at 9:45 am by Meg
When the first class ended, I had no idea what the next class would entail. It was some point over the weekend before I finally figured out an idea.
Since we covered counting, we could look at measurement. I quickly settled on only focusing on measuring length.
As I worked out different activities, I quickly decided that this would be an outside class. (And believe me, I was watching the weather report for any chance of rain.)
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My classes ran in the same order, so I started with the pages. I started by asking them what we can measure and it was like pulling teeth to finally get one to respond with ‘a rock.’
Okay, ‘what can we measure about a rock?’ After some nudging and guiding we touched on mass, volume, and length.
Then I approached how we might start working on a common unit. I had them line themselves up by height and we talked about how comparison was fine, as long as everyone was together. From there we went into some history of units, ending on feet.
So, we first all lined up and counted out 10 heel/toe feet across the driveway to see how they all varied.
Our next activity was to trace and cut out everyone’s foot so they would each have a ‘foot ruler’ to measure with and we measured each other’s height and then the width of the driveway.
So we discussed the need for standardization and the fact that most towns would post how long a ‘foot’ was for their town. Which then expanded into national standardization and the stories about Henry I setting them.
Lastly, we talked about measuring longer lengths. I took an exercise from my college level survey class years ago and had them count paces between two stakes set 100 feet apart. We then roughly calculated their pace length and used that to measure the width of the driveway.
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My oldest class, the knights, was next.
We started by discussing the history of units used for measuring.
How the body was the basis of small units. The inch was the width of a thumb or between two joints on the pointer finger, and was set at 3 barleycorns (pre 1066 England). The foot was either a natural foot (shoe included), 36 barleycorns, or set by the Romans as 12 inches. And we touched on digits (width of a finger, .75 inches), palm (3 inches), hand (4 inches), shaftment ( a palm with the thumb at a right angle to the pointer finger, 6 inches), span (fingers outstretched, 9 inches), cubit, yard, and fathom.
That the mile was a 1000 paces of a Roman legion (which was 2 paces by our standards).
We then did the same pacing exercise as the first class, but used the result to measure the length of the driveway.
From there we discussed how we might measure longer distances and I introduced how surveying was done a generation ago using transits and poles. While I couldn’t borrow a transit from the local engineering college, I did find this fun little exercise for them to try.
From there we talked about chains and rods and how their length was set by the mile.
And I split them into 3 groups. Two groups each had a 9 foot chain. (a real chain is 66 ft., but I didn’t want them to have to deal with so much, let alone have to buy that much for the class), the other group had a modern chain, or measuring tape. 
I then gave each group a sketch of the property and asked them to measure distances. They spent the remaining time surveying the property.
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As before, my last group gets a blend of activities from the first two classes.
They started with the ‘What can we measure?’ question (with much better results) and we compared heights, made ‘foot rulers’ and measured the width of the driveway with them.
We discussed some of the history, hitting on points closer to the details of the older class, but not as complete.
They then did the pacing exercise and paced the length of the driveway. We followed with the thumb trick and discussed using chains.
Lastly, I split them into two groups and they used the chains to measure the length of the driveway.
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09.17.07
Posted in Co-op class at 9:14 am by Meg
Some of the people in the group are discussing putting together a yearbook this year. (I will not volunteer, I will not volunteer) OTH, Boy likes the idea and is all gung ho to be involved with it. (I will not volunteer, I will not volunteer)
So, while he doesn’t participate in the co-op classes, he’s tagged along these first two weeks in order to get some pictures. And I thought I’d share a few.
The first class we are calling Apprentices. It’s really a preschool/kindergarten class. These kids have one teacher for the morning, though she has a bunch of helpers.
The next oldest class are the Pages. It’s all girls right now which makes for an interesting dynamic - very quiet.
Stirring and carving soap for crafts
Measuring their feet for math
Then come the Squires. This class is mostly boys and while very attentive, you have to watch for the hanging from the ceiling tendencies (No, they are very well behaved)
Making soap
Measuring feet
Discussing a medieval village and building a castle for it.
And the last class we are calling Knights. This is the largest group and can get the most rowdy with the interplay of some of the personalities. (Girl included) But they have fun doing the stuff and hanging out.
Crafts
Math
Building the castle and hanging out
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09.14.07
Posted in Co-op class, The nuts and bolts of it at 11:56 pm by Meg
You may have remembered me mentioning that our co-op is now doing a math and science club class. Well, yours truly is teaching it.
Last year Girl participated and I was a drop and run parent. Convenient, but I felt somewhat out of the loop. So this year I offered to do something. I first thought recorder because the family that was doing folk music had moved and I’ve always thought it would be fun a have a little group to teach to play. Then I saw this post and realized that it seemed right up my alley without stepping on anyone’s toes. I also considered some hands-on basic science stuff, but T had that on her list of possible classes.
So, last month we had an organizational meeting and there was no interest in music - oh well. Math got a lot of interest and so did science; so did the renaissance thinkers class that T really wanted to teach. So, I offered to do 6 weeks of math club followed by 6 weeks of science club. And the moms loved it.
oh shit. Now I had to actually come up with a game plan and make it work.
Needless to say, I’m flying by the seat of my pants. I’ve got 3 1 hour classes to fill every Friday and they are diverse enough to make each one different.
The pages are 6 to 8 years old; the squires are 9 to 11; and the knights are 12 to 17. The skill level in each class is all over the board and I think the worst are the knights. Girl at 13 is probably one of the most advanced (Boy doesn’t participate) and some of these kids have trouble doing multiplication without a calculator. And I’ve told the other moms that while I hope to teach them something, I’m not doing a ‘math class.’ These will be fun little activities. Go Meg!
Anyway, last Friday was the first week. I decided to start with a basic - ‘How we count and counting systems’ to get an idea of the kids and their skills. And it worked! and the kids seemed to have fun. I came home flying and Hubby suggested that I write up what we did, so I might keep track of the information.
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My first class was the pages, the littlest kids. Mentally I built their class around the beginning reader How Many Feet? How Many Tails? I had each kid bring in a stuffed or plastic toy for class. I figured that not only could we do a counting game that the book suggests, but that they would feel more secure coming with a ‘friend’ along.
I had seven in the class (though another join us shortly) and I started by using the ‘buddies’ to show primitive counting systems. We put the buddies into sets of two and I explained that they would count by 2+2+2+1, and that this would only work up to about 10. Then we changed our orientation and I pointed out the next step of counting by fours, and then grouping sets of fours.
Then we talked about why someone might count in sets of 5, 10 or 20 and I touched on counting systems of early cultures in the Western Hemisphere. Finger counting from the Great Plains, the Inca’s quipu system, and the Mayan dot and bar system (most of this is from Zaslavsky’s book Number Sense and Nonsense ).
Ahead of time I had taken some leather thongs and made myself a quipu necklace. After I explained the system, I had them try to read the numbers on each piece. To help them ’see’ the Mayan system I had made each kid a bag with a handful of pokemon tokens (for pebbles), toothpicks (sticks) and pennies (shell for zero). We then used the pieces to show their age, at which point I then drew the patterns on the white board and discussed how writing numbers developed from using pebbles and sticks.
While we were on pebbles, we shifted to Asia and I showed them an abacus and told them they were just pebbles strung on wires.
Lastly we shifted to Egyptian hieroglyphics and Roman numerals (just a light introduction) and I closed the ‘lesson’ part with discussing where our numbers come from.
For the last 10 mins. I read the book and then we lined up the buddies and tried to play the grouping game. The 7 and 8 year olds caught on pretty quickly, but we ran out of time for the younger kids to really get into it.
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My second class was the knights, the oldest group. I introduced the idea of counting by explaining that the term calculus comes from the Latin word for rocks and since we were modeling pebble counting systems, they were doing calculus today.
And, because I know this group will try to sidetrack whatever the ‘plan’ is, I told them that if we got through everything that I wanted to, they’d be making a computer before we were finished. It definitely got their attention.
We quickly touched on the base 2 counting systems and the quipus. With them I spent more time on the Mayan base 20 system. They not only wrote their ages (with the same baggies of pebbles, sticks and shells), but we also worked on the Mayan’s base 20 place value system and how to write larger numbers.
We then jumped to Asia, but before we talked about the abacus, we played with the Chinese rod numerals and they used the toothpicks to write different numbers. I then picked up a Chinese abacus and the Russia one I had borrowed and showed them the differences and we did some simple arithmetic.
From there we jumped to the Babylonian’s base 60 system and discussed ways in which we still use a base 60 system.
Lastly, we looked at Egyptian hieroglyphics for numbers up to 1000 and I talked about how the Romans modified that system to get the Roman numerals we know. And we discussed where Roman numerals are still used. We finished our discussion section by discussing where our numerals came from and how long it took the Europeans to accept them.
We then talked about computers.
I set it up by touching on the base 2 idea, explaining that that was all a computer really understood. And I mentioned base 16, since some of these kids are dabbling in coding and have seen the hex codes for specifying colors. But then I explained that what were really going to do is make an old fashioned grad. student computer, the sort of thing that was used as recently as WWII and designing the bomb.
You see the word ‘computer’ originally meant a group of people solving a problem assembly line fashion. It was actually a job title. And when you were doing a calculation you would have two groups working the same problem. Now in real life the computers would be doing major calculations, but for our sample I made it easy.
I split the class into 2 groups and then gave out cards with simple arithmetic operations. Each group got the same cards in the same order. Then I gave the first 2 people the same starter number and they did their step and passed the result on to the next person.
We got through it twice before we ran out of time and neither time did both groups get the same result.
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My last class is the squires and I’ll admit that I plan for the two extremes and then mix the squires’ class from the different activities.
For the squires I introduced the term calculus, we discussed counting by twos, and then all 3 counting systems from the Western Hemisphere. We did play with the Mayan pebbles and sticks. And while we did model a number over 20, we did not get any larger than that.
We also played with the Chinese rod numerals and modeled a couple of numbers and then discussed the abacus and how it was used.
From there we discussed Egyptian hieroglyphics and how they became Roman numerals. And I ended the discussion by explaining where our Indo-Arabic numerals come from and when they became the norm.
Our last 20 mins of class was spent with each kid making their own abacus. 
These are actually modeled on a Japanese abacus since that takes less beads. It’s half a form board with the holes prepunch by me. Each kid got a little more than a yard of plastic lace, 5 blue beads, and 20 white ones. They laced it up by zig-zagging back and forth and then we tied the two ends together.
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