Flatland

This week we learned all about geometric figures. Plane, point, line etc. When I was in AP Lit senior year of high school, I had the *joy* of being assigned a book called Flatland, which is literally about 2D geometric figures, living on a plane. Now every time I hear about points, lines and polygons I have horrible flashbacks to that book. Hence, the title of this post. Anyway, back to the real reason for this post. I remember back in middle school first learning about geometric figures, and doing it all on the computer, it was actually quite fun. This time around it was still online and still quite fun. One of the most interesting concepts to play with is angles. Especially when you get to or more involved. An angle is made up of two rays that stem from the same endpoint (not to be confused with an angel, which a spiritual being believed to act as an attendant, agent, or messenger of God, conventionally represented in human form with wings and a long robe). The most common angles are acute angles > 90, right angles which are 90, and obtuse angles which are < 90 and A ray is a part of a line segment in which one end has an endpoint, and the other end goes on for infinity (I always remember drawing arrows on the infinity end to demonstrate that fact.) I think for every student, the moment when you realize how angles react and compliment each other, theres a moment of logical wonder. One of the best representations of how the angles interact is when you introduce vertical angles. These types of angles are created by the intersection of two lines. When you add all the angles together, you get 180. The angles opposite each other have the same degree value. Its great to demonstrate these by having one of the lines rotated around, and watching how, despite the fact the angle values change, they still stay equal. It's always fun when you get to discover math by "playing" with it like that. Here is my vertical angle example from class:

Notice how angles ABD and CBE are opposite yet equal. The same goes for angles ABC and DBE. Also notice how angles ABD and ABC add up to 180, as well as ABE and DBE. 

Probability

This week's lesson was on probability. For example, the probability of spinning a 10 in the game of life, the amount of green skittles in a bag, rolling a 6 on a die, flipping a coin, etc. Something I found really interesting was what is called a probability tree. It's a way of representing the different outcomes of two or more "events' (ex. flipping a coin than rolling a die) and writing it out to show the probability of each set. Going with the example of a coin and a die, you start with the two outcomes, or branches, of the first event, here it would be either heads or tails, each with a 1/2 probability of being flipped. From each of those braches, you branch out the outcomes of the rolle of the dice, in this case we're only using one die, so the heads would have six braches, 1,2,3,4,5 and 6, and the tails would as well. Each of those outcomes would have a 1/6 chance in occurring. To figure out the probability of lets say getting heads and rolling a 4, you would multiply the two probabilities together, 1/2 x 1/6 = 1/12.  The tree would look something like this:

Glog Reflection

This was one of those assignments that was cool in concept but not in practice. We had to make an online "poster" type thing called a Glog. It's really hard to explain, if you've ever messed around with any photoshop type program, it makes more sense. I could basically describe it as an online scrapbook page experience: lots of little images and whatnot to play around with for effect. When I started, I got really excited to get all creative up in this bitch, but as I got deeper into trying to put the damn thing together I got frustrated. I dont know what was wrong with this website, but I had to keep reloading the page because the flash sucks. Maybe thats why it's still in beta, I dont know, but I spent more time waiting for the page to reload, or load, or wonder why the entire thing was just white. I basically had everything I wanted to put on it all ready, screen shots, text etc. The problem was the actual functioning of the flash. It loads super slow and half the time when I left the page for a different tab, to take a screenshot and whatnot, it caused the glog I was working on to crash. Thank goodness for the autosave or I would have been screwed seven million times over. I was ready to bash my face into my keyboard by the end of the night, I just wanted it done. I eventually had to open glogster in Safari and it worked better, but it was frustrating that it wasn't compatible with Chrome. And even then, it took forever to upload my images. I would love to try this again of the flash worked correctly. So you can go check out this "masterpiece" by clicking the following link 

-->Coordinate Glog<-- 

If I had more patience with the internet and flash, it's be SO much prettier. But hey, it gets the job done I suppose. Yay graphs....... yeish.

Cups and Beans

So this week in class we practiced one of the more fun ways to teach the basics of algebra, what my professor calls Cups and Beans. It's a great way to show you need to keep the problem "balanced," that whatever you do to one side to solve the problem, you need to do to the other. You set up cups and beans on a "scale," cups are x, black beans are positive while green are negative. I'll use the given sample problem x-3=-7

You start with setting up the problem:

Next, you determine what needs to be added or taken away to isolate x, in this case, +3 to cancel out the -3 on the cup side. When adding the beans, you need to add one bean to each side simultaneously, one bean in each hand:

Here's the problem with the +3 added to each side:

When you add a positive 3 to a negative 3 you get 0, so the next step is to pair the beans and remove the zero's:

The final step is to simply solve for x:

Here are a few more examples

x+4=-6

This one is a bit simpler, you dont have to add anything, just take away the same amount of positives from each side

x+5=8

It makes more sense when you practice yourself, and its more fun the more you do it. This particular method was review to me because I learned it in the first portion of the class I took last semester, but it's still as much fun as I remember. I really do think this helps understand algebra better. I even showed it to my mom, and her reaction was "Ahhhh, fun with math!" So there you have it. Cups and Beans

First Post About..... Me?

Whoever thought a math class would require such a literary themed assignment. Writing and math. Oh, joy. My two favorite things to do. At least this makes the class WAY more interesting than your typical math lecture. So, to begin, I'll talk a little about myself (because I don't do that enough in class). I'm a 20 year old (soon to be 21, yay) college student finishing my last semester at OCC before transferring to U of M Dearborn in January, something I'm very proud of, and would never have dreamed for myself back in high school. I'll be going for my Bachelors Degree in Elementary Education with Early Childhood, minor in Language Arts (or reading, or both I suppose). That will make me able to work with infants up to 5th grade. I would also like to get a masters in High School Language Arts WAY later on. For now I'm also working at a daycare in Rochester Hills, and though the traffic and drivers out there drive me insane, as do some of the kids sometimes, I love my job. It makes me sad I'll have to leave once I transfer, due to needing a full time student status to stay on my step-dads dental insurance, and to get scholarship money. I'm glad I can work somewhere thats related to what my futre goals are. Ideally I want to teach Kindergaren or Preschool. I also want to move to Arizona.