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August 02, 2015

Copy-Paste (the hard way)...

The children had been thrilled with being able to animate the moon going round the earth and wanted to show the solar system with the earth going round the sun. 

Thanks to Arham I had recently seen a video called Earth's motion around the Sun that indicated some of the complexity from the simplistic info that children had:

We looked at it and the children felt that it would be interesting to get an object to move in an elliptical path and replicate the earth going round the sun.

The circle was more or less straight forward with moving and turning in each step, but an ellipse...I talked to them of using Geogebra to draw the curve they wanted e.g. an ellipse and then "copy-pasting" it in scratch. Of course the issue was not drawing a shape, but to get an object to travel along the curve so it needed to be true to the curve.

I started with a simple case if x+3 = 5, we went over the story and I reminded them that the answer was not important, it was a trivial case and we were trying to get a method that would help the computer do a repeated simple task till it reached a condition. Also to have a simple condition we changed this to the expression x+3-5 and substituted values of x from -3 to 3 to find when the value of the expression goes to zero giving us the correct x.

We then attempted to solve 2x+3=6 i.e. 2x+3-6 and check when it becomes 0. But, it did the following:
For x=-3-->-9 ; x=-2-->-7 ; x=-1-->-5 ; x=0-->-3; x=1-->-1;  
      x =2-->1  ; x=3-->3    ; x=4-->5    ;x=5-->7 ; basically missing 0. What would then be the way of capturing where the answer lies. The idea that came to the children was that the result of the expression changes direction. Naturally, the last result will need to be remembered, but how do we check if something has changed direction. 
I asked them what they had learnt from integers that might help them do so crisply.They could not quite figure out how to go about it and when they couldn't quite connect after struggle I guided them into the product of integers and checking if the result it positive or negative. Of course here we get the closest integer number, but if the equation is large even though we don't have the decimal parts the curve looks good enough.

We then moved to a real equation x+y=3 and for each value of y we swept x...Once it worked for a line we just moved to the curve and only needed to handle the boundary conditions. 

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