|Hero's 2nd rocket.|
The first rocket he made didn't work because I forgot to tell him that we'd be working with only a limited number of shapes - the ones that can make a hexagon. The second one did much more nicely. But it became clear as we tried to do the worksheet that he needed some of the foundational ideas still, so that's what we mainly worked on.
First, we looked at the number of each shape he'd used. Hexagons were our "whole," the shape we called "one." The rest of them, we looked at in terms of how many hexagons could we make. This worked out nicely, since he chose to count the hexagon first. Next, we looked at the trapezoids. Since Dragon(3) was (kind of) also playing with the shapes, he got some exposure to the names of the shapes as well. We decided that each trapezoid is half of a hexagon, and that 4 trapezoids make 2 hexagons. This gave us a chance to write a couple of fractions: 1/2, 1/2, and 2/2. I forgot to show him the 4/2, which is probably ok. But things got really interesting when we got to the rhombuses (rhombi??). This posed a challenge: figuring out the denominator. We've talked about the denominator several times, but it hasn't really stuck, and he needed more help with the concept. At this point, we pretty much abandoned the worksheet to work on the concepts he needed to solidify.
First, we more firmly established our base:
A yellow hexagon = 1. Surprisingly, this took a moment to establish. It didn't click into place until I started talking about how we can trade the other shapes for a hexagon, the way we trade with our Cuisenaire Rods. Then he had the ah-ha! moment and things were much more clear.
So, a yellow hexagon = 2 red trapezoids = 3 blue rhombuses = 6 green triangles.
We wrote this out like this:
1/1 2/2 3/3 6/6
And at the end, I went through and did this:
1 = 1/1 = 2/2 = 3/3 = 6/6
And we kind of lined the numbers up with the shapes so he could see it was true.
We've done work with "Names of a Number" before, so when I told him these are all different names for one, he understood, and at that point I felt like he had the concept, so we went back to his rocket again. He'd used 2 rhombuses, and that now made sense to him as 2/3 of a hexagon, so I asked him to make the same shape in triangles, and we figured out the name of that as well.
2/3 = 4/6.
At this point, I mentioned the terms "equivalent fractions" and "improper fractions," though I don't really expect them to stick. We did, however, note that the root of equivalent is "equal" and that's really what we're saying: equivalent fractions are equal.
I could tell that we were close to time to be done, but I wanted to try going one step further, and I gave him 7 triangles and asked him to figure out the name of the fraction they represented. It took a few minutes, but he figured it out.
Pattern blocks are so much fun. Hero has made some beautiful and intricate pictures with them in the past, and today when we were done working, he made this one again. It's one of my favorites. The more of math that I re-learn, the more that I believe that playing around with shapes and patterns like this is immensely valuable. I hope that in the next while as we're messing around with fractions and pattern blocks that he makes some more pictures that I can share.
And, browsing around through comments and links, I found this amazing list of picture books with math in them. I could spend so much $$$ on books! There's a couple in the fractions section that are sounding pretty interesting. I need to order more pattern blocks and Cuisenaire Rods anyway, now that there are usually at least 2 kids playing with them during math time.
I love it when math is play. I think I need to make me some "math cards" and just keep them. I'd play these games with the kids more often if I didn't have to go through and sort the cards before we could start every time.