All right, next page, variations and extensions. So awesome, this is great! So finally, we're actually drawing a graph. I don't know if I think this is a variation. And I don't know, for me, that seems like a really critical part of the activity of the lesson. On the other hand, we didn't actually have really explicit learning outcomes. Remember, it just said skills, problem solving, so maybe not. Maybe it isn't a goal that students learn how to take a drawn model of roads and houses and represent it as a graph. So maybe it is an extension, but that's one of the benefits of having those learning outcomes. But I saw this graph and I was like whoo-hoo, excited. Except then I was like, wait, is this the right representation for the thing that we saw? Let's go back and look. All right, I got a 4 across there and a 5 across there, a 6 here and a 4 and a 3 there. I'll kind of try to keep that in my head. All right, I have a 4 across here No, was this the, no, how many houses do I have? One, two, three, four, five, six, seven, eight, nine, ten. Do I have ten nodes here? One, two, three, four, five, six, seven, eight, nine. What, why are you showing me a graph that almost looks like the one that we were doing, but isn't exactly? I think that's sloppy. As a teacher, that means I already have to know that houses are represented as nodes, and the edges are the weight of the tiles. And they tell me that here, but it should be the same graph that I'm using. Let's be nice, okay? However, after this is pretty good. They talk about, they give the terminology, graph, and it's in italics. And so this is good because it helps me if I'm not an expert in computer science graph usage to understand how computer scientists use and mathematicians use graphs, and how they might be different in a different area. So that's really cool. I guess I would like to see an activity where the students themselves were engaged maybe in building one of these graphs. And this does say variations and extensions. This really mostly talks about me, the teacher. They jump right ahead, it sounds like, asking the students. Here's what the students are doing. By the way, be nice, students, discussion. They're asking for a discussion. That goes a step beyond the step we're missing, which is how do you actually represent a drawing in the notation of a graph. And so I feel like that's missing in this particular case. All right, so you may have gotten to this and been like, wait a minute, a section called what's it all about? And it's the very end. I may have thought that way, too. However, if you think back to it, as not this isn't a textbook, this is a lesson plan. You're a teacher. Are you going to do this activity tomorrow or next week? How much time do you have to read it? If you have to read all of this stuff, okay, where we really get into the detail of defining what a minimal spanning tree is. Big, long word there and all of this, maybe that's not the best way to engage. Maybe you want to see quickly, again, that overview and what students will be learning and what you'll actually be doing with them in the classroom. And then this is something that you go to that maybe you can even read in front of students to summarize sort of the full detail of all of this. And maybe your students don't need to know all of these things. Just in particular, I really think that they come back to the examples of the electricity, gas or water. Seeing these things in English is one thing, but come on, it's a graph. Could we have some images? These are real world networks. It would be really nice, and I think very important, for students to be able to see some of these networks to really connect what they all are together. In the third paragraph where it talks about minimal spanning trees, they actually get into a really, really important point here, which is that a lot of what we talk about with networks and computer science isn't actually really about minimal spanning. It's about route finding, right? And that, it turns out, is a very different problem in computer science, from minimal spanning trees. Minimal spanning tree is a good way to start and get people understanding about representing things. But it's a very easy task relative to route finding. And so I feel like they didn't really clearly call out the difference here. And as a teacher, wanting to sort of remind myself and review, it's like, graphs, graphs, graphs, right, we did a bunch of things around graphs. What is the difference between the muddy path that's easy, minimal spanning tree, and the challenging how do I get Google directions to find the shortest route from one place to another or with planes? And so that would be really nice to have them pull out. Finally, cool, solutions and hints, sort of. Okay, these are the solutions and hints to the variation extension. I can honestly, they didn't actually show me, if I go back and remember, they did show me some solutions up here. But they never actually really, well, okay, two possible solutions are shown below. Are those the only two solutions? Boy, I'd really like to know that, because what if a kid comes to me and says I didn't have one of those, but mine is as good as those. It's just as cheap. Okay, maybe I can sit there and count. But it'd be really nice to just be assured if these are the only two minimal spanning trees, just tell me that. So I feel like there could be a little bit more in terms of solutions given here. It's nice to know, let me go back to here. It's nice to know the answers to the variation and extension because these are actually quite detailed. But it might also be nice to have a link out to maybe a Wikipedia article where they explain this in a little bit more depth. So that either I, or I could have the students who are advanced maybe spend sometime reading a little bit more about.