We have started the Keys of the Universe Geometry album, and so far, so good.
A lot of it was just review in the beginning, but it led to some great work.
Going over the concepts of Congruent, Equivalent and Similar led to looking at our fraction circles. We don't have any metal insets, or metal anything here, so I have to improvise with some of the ways I present these concepts. Luckily he's had access to these things in a classroom before, so my information is just one more way of looking at it.
The fraction circles were a way for him to explore equivalency, and he used two 1/2 circles.
While he had those out, he started fitting other fractions into those halves. He's done this work before, but it was fun to explore it again. He made notes in his math composition book to indicate how many 1/10s can fit into 1/2. He traced the 1/2 and then traced 1/10s inside of it and labeled it. Then he did the same with 1/8s. I asked if it would work with 1/7, and he said no, and then we tried 1/5s, but that didn't work either. When he had the 1/2s finished, I asked, "So, if four 1/8s will fit into 1/2, how many will fit into one whole. Of course this was easy work for him, but I was happy to review it and see where he is with fractions. (Who needs tests?)
Then he asked if there was division with fractions, because he's been working on long division for a while now. He likes it, and still seems to want to keep going with it. I can see that he is still working through the steps for long division and needs my assistance sometimes. He sees all of the numbers and starts to get confused. I'm trying to find a better way to explain it, but haven't found anything yet that will isolate just the numbers he needs to focus on at that moment. I encourage him to cover up whatever he isn't using, but it is difficult. He has worked with the tubes, but I can't justify spending the money on them. I don't think we would use them for very long anyway.
We've worked with word problems, so he understands the concept of division, it's just setting it up on the paper and working through it a step at a time with all of those numbers on the page that are getting him tripped up sometimes. I want him to get used to doing this, because when he gets deeper into algebra I don't want the string of numbers and setting up those problems to be overwhelming.
But I digress.
Once he was finished working with the fractions, we moved on to Geometry Sticks. At first he was resistant, and claimed we had done that work before. We had never done it before, but he remembered it from school.
I started at the beginning anyway, and followed the album. By the time I had constructed a few polygons, he was starting to become more receptive to the idea. He clearly understood what a polygon is, and I asked him to construct one. He wanted to use as many sticks as possible.
I kept saying, "Oh, I don't know. Do you think this will work?" He insisted that it would. When he got to the last piece, and he probably used about a dozen sticks in various sizes, he had to zig and zag them to get a closed end.
We ended with the quadrilateral.
Next we will explore the Triangle, and talk about how it is the shape that constructs.
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