homeschooling,  lisp,  mathematics

Moving levers and looking at how everything ties in together

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One activity that followed quite naturally from making a Golden Ratio Gauge was to make a pantograph. A pantograph is a mechanism to copy pictures or maps, using levers. We built one out of lego and one out of k’nex. The k’nex one was slightly easier to use because we mounted the stationary pivot to a giant k’nex building and didn’t have to worry about holding it in place. The lego one was easier to build. I took a picture of it, and had my seven year old label the picture for me. Labelling the picture gave us a chance to discuss how it works. What part moves what? The two inner sticks provide the effort to move the third-class levers on the outside. One of the levers moves the location of the pivot for the other.

The kids don’t know it yet, but tomorrow we’re going to build the pantograph again to discuss angles. Which angles become obtuse at the same time? Which ones become acute when the others become obtuse? We’re also going to talk about how having a longer stick changes the size of the copied picture and why that is. I want them to think about the similarity between the length of a lever and the distance points on different sized gears have to travel.

We were at a playground recently and I couldn’t resist snapping a shot of one of my guys on a digging machine, so I asked him to label the picture too. Like the pantograph the digger has one pivot that moves.

I’m teaching the children to remember the different classes of lever through the mnemonic “Ple” (Plee). The pivot is in the center for a class one lever, the load for a class two and the effort for a class three. (I prefer to use “Ple” than “fle” or “flex” because I find the “f” confusing. Does it refer to force? Or to fulcrum? By using pivot, load and effort I avoid that confusion.)

I sense the need for some lego play building different arms and grabbers. Its always bothered me a bit that the diggers in the park end up digging a big circle only. I’m thinking it would be worth sitting down with lego and trying to devise a model of a stationary digger with a bit more flexibility. I want to try to challenge the children to think one step ahead. If one part moves, then how will it affect that movement of the other parts?

In some ways the skill of looking through the chain of implications (such as how one lever’s movement affects the next when they are connected in some way) is the same as needed for some of the algebra questions my oldest has been practicing recently. In algebra I ask “if Mary has twice the number of marbles as Peter, and Peter has three less than a third of the marbles as Joan has, and Joan has 21 marbles, how many does Mary and Peter have?” When we were studying gears I would draw out a gear train and ask him to calculate how the different axles turn at different speeds. It is like in computer programming when a variable is passed through one function that calls another function and another before returning a result. It is about breaking things down into steps and figuring out the best tool to use for each step.

I’m also wondering about doing some graphing of how levers work. I might lay out some simple levers on a piece of graph paper and get the kids to record how the numbers change if we move the lever. I might be able to use it to explain rotations in geometry.

I am working on learning how to do programming in lisp and realizing that the geometry will come in handy for programming the graphics in games. I think that is how I’m going to “sell” it to my children. We’ve done some simple graphing of shapes and looking at how adding numbers to the x or y coordinates makes a number move in straight line. I want to keep going, and if I get the chance I want to program a small computer game where they have to put a set of coordinates through a series of transformations to make a simple polygon match up with another polygon. Would anyone be interested in using such a computer program if I write one? I made rough plans the other day for how to do one but I haven’t gotten up the ambition to test if my idea would work.

There is so much to learn. I think in many ways this is an incredibly fun period in history for homeschooling in because the internet provides such easy access to so much information. I remember as a child watching movies or reading about something and wanting to learn more about the history or science of something and having to content myself with the tiny bit of information available in my parents used encyclopedia. Now so much more information is at my fingertips.

I know some people think the easy availability of information makes it less important to learn things. Why memorize anything when the information can be googled? I think we should memorize things because we don’t always have access to the internet, the internet has a lot of misinformation too, and because facts gathered online are different than facts understood through playful experience with them. Most of all though, I think we should learn so as to develop a love of learning and an interest in always looking one step further. What would it mean if….? How could this be improved….? Why does this work…?

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