09.14.07

Math fun - week one - Counting

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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