Circles and Chocolate

We did a couple math projects this last week.  One was called Infinite Chocolate.  We were to take a candy bar of chocolate, cut it in a specific way, rearrange the pieces and then we had one piece left over- appearing to somehow from that arrangement, have more chocolate than we began with!

We gave it a try...

Here is the problem:

And our efforts to try it out:

Henry's observations from our project:  I discovered that it is impossible to get infinite chocolate.  At first it looked like we could do it, when we used the paper to begin with, it looked like it all worked out because we had the "chocolate bar" all put back together and one piece was left over.  But then at a closer look we realized there was one line of squares that was squished smaller than the other rows, so the left over brick was just the extras that had been taken out of that row.  The bar looked like it was put back together, but if you kept doing the cutting and rearranging, your bar would actually get smaller and smaller each time.

We also did some geometry work on circle making with a home made compass from a 

pencil and string.

Circle making with just a pencil and string was pretty challenging.  You had to hold the pencil just perfectly, and if you adjusted the angle of the pencil at all during your circle making, it would ruin the whole circle.  Henry says that the way he learned to draw a good circle was to draw it a fourth at a time.  Gwen found success doing it half at a time since it was hard to do the whole circle while holding the string and pencil, she needed to re-adjust her hands to make it work.