Yes, that is a baby chinchilla.
Technically, everything (including chinchilla babies) can be explained by math, so this relates. I did not just look up pictures of baby chinchillas just because I needed some cheering up; it was for a specific mathematical point.
Well, now that that explanation is out of the way, let's get down to what we actually did this week (sadly, it did not involve baby chinchillas in any sort or form). The class started out the week by completing our first CCC and moving on to limits involving infinity. I really like the CCC process because it utilizes and formalizes what students have been doing for years: teaching each other. It's something that I have never done in a math classroom before (in the previous years, we would just ask the teacher to explain), but it makes so much sense. I for one, am able to understand a subject or concept better if I teach it to others, so this is a great method for my learning. Apparently, it's also a scientific thing that this works.
Class this week covered three (or perhaps four, for reasons I will explain later) major topics. Like I mentioned earlier, we started out the week discussing limits involving infinity and all its related topics, like what f(x) approaches as x gets closer to infinity, horizontal/ vertical asymptotes, and end behavior models. End behavior models (EBMs) in particular troubled me a bit. The thing to remember is that EBMs do not describe the limit of the function; instead, they are simple functions that a much more complicated function "behaves" like as x approaches infinity. For example, if it we were trying to find the EBM of f(x)=x + e^(-x) as x approaches infinity from the right side, the first thing I would do is try to visualize what the graph would look like if x was infinity. In this case, it looks like as x gets larger, two things happen: the values of x in the function get larger, but the value of e^(-x) gets very, very small, due to the large negative exponent. This makes me think that f(x) looks more like x at larger x values because e^(-x) becomes negligible. In order to test this, I would state the model function g(x)=x and use the idea that it would be a right EBM for f(x) if lim (x approaches infinity) f(x)/g(x)=1. If you insert both functions into that equation, you get one, so the EBM was right!
Other than that, though, I think that this weeks' concepts were generally easy. Both continuity and limits are reviews of what we did last year in Honors Precalculus, although the salt-and-pepper graphs were new. Nothing too fancy.
As far as assessments for this week, everything went really well. I received my score from the review test and I did not miss a questions, so hooray! I can actually remember things! The quiz we took this week over 2.1 and 2.2 also went swimmingly. Although I did miss one question because of a careless reading mistake, I was able to figure out the "Cresswell's Cool Concept Corner" or whatever it was called. It might be just me, but after I figure out a math problem that I spent ages working through, I am always left with this enormous sensation of pride and accomplishment.
This week I definitely struggled with keeping up with the workload, especially in the last few days. I know that's not exactly a math concept, but hear me out. I did not procrastinate this week, or if I did, I procrastinated a negligible amount of time. So how come I have yet to finish two assignments? This does not sit well with me. I think a part of this might be that I know I will be able to get more stuff done at home than at school, but I end up having too much to do at home to get to the work. This is something I will definitely work on in the future. However, my participation in this class as a whole is pretty good, in my opinion. I really like what we are doing and how the class is structured, so I do truly feel like contributing to the conversation. Math is fun. I just needed to be reminded of that.
Technically, everything (including chinchilla babies) can be explained by math, so this relates. I did not just look up pictures of baby chinchillas just because I needed some cheering up; it was for a specific mathematical point.
Well, now that that explanation is out of the way, let's get down to what we actually did this week (sadly, it did not involve baby chinchillas in any sort or form). The class started out the week by completing our first CCC and moving on to limits involving infinity. I really like the CCC process because it utilizes and formalizes what students have been doing for years: teaching each other. It's something that I have never done in a math classroom before (in the previous years, we would just ask the teacher to explain), but it makes so much sense. I for one, am able to understand a subject or concept better if I teach it to others, so this is a great method for my learning. Apparently, it's also a scientific thing that this works.
Class this week covered three (or perhaps four, for reasons I will explain later) major topics. Like I mentioned earlier, we started out the week discussing limits involving infinity and all its related topics, like what f(x) approaches as x gets closer to infinity, horizontal/ vertical asymptotes, and end behavior models. End behavior models (EBMs) in particular troubled me a bit. The thing to remember is that EBMs do not describe the limit of the function; instead, they are simple functions that a much more complicated function "behaves" like as x approaches infinity. For example, if it we were trying to find the EBM of f(x)=x + e^(-x) as x approaches infinity from the right side, the first thing I would do is try to visualize what the graph would look like if x was infinity. In this case, it looks like as x gets larger, two things happen: the values of x in the function get larger, but the value of e^(-x) gets very, very small, due to the large negative exponent. This makes me think that f(x) looks more like x at larger x values because e^(-x) becomes negligible. In order to test this, I would state the model function g(x)=x and use the idea that it would be a right EBM for f(x) if lim (x approaches infinity) f(x)/g(x)=1. If you insert both functions into that equation, you get one, so the EBM was right!
Other than that, though, I think that this weeks' concepts were generally easy. Both continuity and limits are reviews of what we did last year in Honors Precalculus, although the salt-and-pepper graphs were new. Nothing too fancy.
As far as assessments for this week, everything went really well. I received my score from the review test and I did not miss a questions, so hooray! I can actually remember things! The quiz we took this week over 2.1 and 2.2 also went swimmingly. Although I did miss one question because of a careless reading mistake, I was able to figure out the "Cresswell's Cool Concept Corner" or whatever it was called. It might be just me, but after I figure out a math problem that I spent ages working through, I am always left with this enormous sensation of pride and accomplishment.
This week I definitely struggled with keeping up with the workload, especially in the last few days. I know that's not exactly a math concept, but hear me out. I did not procrastinate this week, or if I did, I procrastinated a negligible amount of time. So how come I have yet to finish two assignments? This does not sit well with me. I think a part of this might be that I know I will be able to get more stuff done at home than at school, but I end up having too much to do at home to get to the work. This is something I will definitely work on in the future. However, my participation in this class as a whole is pretty good, in my opinion. I really like what we are doing and how the class is structured, so I do truly feel like contributing to the conversation. Math is fun. I just needed to be reminded of that.