Archive for the ‘Math’ Category

If you ask a graduating senior, and most adults, what topology is, you will either get a crazy answer that it has something to do with maps or they may look at you with a blank stare in their eyes. Not many people outside the mathematical realm realize tht topology “is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing. It emerged through the development of concepts from geometry and set theory, such as space, dimension, and transformation” (Wikipedia).

While reading The Mobius Strip by Clifford Pickover, I decided that this video would be the first of a series of videos that I would show relating to topology. In the coming weeks I will be showing videos that relate to perfect squares, knots, and possibly some other topics that I discover while reading Pickover’s book.

Rather than come up with a worksheet, I’ve decided to present the students with a series of scenarios for them to try on their own.

  • If you cut along the middle of a Möbius strip, what do you end up with? Does Mr. Ug ever reunite with his dog?
  • What happens if you cut along a Möbius strip a third of the way in from the edge?
  • Create a Möbius Strip sandwich by taking two strips of paper one on top of the other, like two pieces of bread in a sandwich. Together give the strips both a half twist and tape them as if you were constructing a sing Möbius strip. What do you get?

Usually, I like to keep my questions short, because I find a lot of students are really intrigued by Moebius strips and they continue to discover on their own.

On a side note, I think it would be fun to crochet. Maybe if I ever learn how, I can make something like this.

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While going over past posts on Google Reader that I had starred, but not yet had a chance to look at in depth; I found this week’s video from Vihart on Math Mama’s Blog. In the past I have mentioned that I really like her videos because she does a great job of explaining difficult math concepts. While I like her videos a lot, my students have mixed reactions. Last semester when I showed my class the Snakes + Graphs video, a lot of my students grumbled and complained that not only did she talk way too fast, but she also was way too intense for them. The funny part about this is that many of those same students that complained were the ones that turned in homework assignments from that day with snakes drawn on them.

The worksheet provides an example similar to the one seen in the video. Rather than just have the students watch this method, they can experience it for themselves. I first included an example of the visual method that she presented in the video, but then I also included the every combination method and then went into a few FOIL problems. Rather than redoing examples, I took them directly from the Free Math Help website. I also included another multiplication method not talked about in the video, but rather taken from the book Rapid Math Tricks and Tips and pulled some of the examples from The Math Lab website. I included this method because it is what I use most often in class, and it’s always good for students to know how I am able to quickly find the answer to two digit multiplication problems without using a calculator.

While trying to find some fun stuff to do with my classes, I came across the textbook, “The Heart of Mathematics: An Invitation to Effective Thinking”, by Edward B. Burger and Michael Starbird. So I got to wondering, does Burger have any videos posted on YouTube? When I searched his name, I discovered that he has tons of videos posted that are similar to those on Kahn Academy, but then I came across one that was a bit different. I thought that this video was a great example of many of the mistakes that I see in my classes.

Because I would like to incorporate these videos into my classroom and have the students’ benefit from their content, I have also made a worksheet that the students will be able to do, with a little assistance. Since the video that Burger posted was intended for college Algebra, and since I only teach high school Algebra, I decided that #9 had to be reworked so that the students would get more out of it. So instead of looking at logarithms, which we don’t usually talk about until the end of their Algebra 2 course, I decided to include “Simplifying Fractions” into this space, since this is a common mistake that I tend to see in my classes.

Finish Up Friday

Posted: July 22, 2011 in Classes, End of Semester, Math, Real Life Math
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I usually reserve Friday’s for assessments using the Standard’s Based Grading (SBG) Technique. So whatever we have covered the previous week and that week, will be covered on Friday’s assessment. Since many of my students are eager to take the test and get it out of the way, I don’t want to over emphasize the warm-up problems for this day; but at the same time, I don’t want to eliminate them from their daily routine. Therefore, Friday’s will be a wrap up of yesterday’s warm-up problems.

My goal is to take the equations that each student submitted and put them on a word document so that each student can be expose to the different equations, with some being more abstract than others, and not have to worry about taking the time out of class to copy them all down. With these sheets organized into their notebooks, the students can then “reverse engineer” the concepts that others students have used and use them to better enhance their own problems in the future. Also, by numbering each problem, students can vote for their favorite problems, so that the person with the most votes either gets a prize or their name on some sort of trophy. The voting, although I haven’t figured it out completely, may either take place online using their Edmodo account, or it may be done by turning in paper copies with their votes. Most likely, I will use Edmodo, since this will allow me to quickly accumulate the votes.

Wednesday is Game Day

Posted: July 20, 2011 in Classes, Math
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So, it’s the middle of the week and a lot of the students are getting a bit antsy. Some are bored, others lackadaisical; whatever their mood, it’s time to get them out of their seats and have some fun with them. It’s time to play games!

While I have a few math games that I enjoy playing with my classes, I know that there are a lot of them out there. The game that I enjoy the most is Buzz, and my kids love to play it. My goal is to find games that are math related, worthwhile, and, of course, fun!

While you probably have already seen my YouTube Tuesdays, my goal is now to create YouTube clips that have accompanying math problems. While I know students like to watch video clips and not have to do anything with it, my job as their teacher is to help them retain the knowledge learned in these math videos so that they may use it in later math courses or in their lives outside of school.

Stay tuned for upcoming YouTube Tuesday math videos on this site. While some are already typed out, I plan on starting to reveal them once school starts up again. That way, my classes will be watching the same videos that I post to this site.

Monday’s warm-up will be devoted to basic arithmetic and mental math. Even though I teach lower level math classes, which typically include those students that lack the fundamentals of Algebra, there are those students in some of my upper level classes that lack the ability to do basic math in their heads. To overcome this handicap, I am going to teach them how to manually keep track of their score in bowling.

In the past, I have found that learning to keep score in bowling is a good end of quarter/semester activity, since it is fairly simple and it involves a fun simulated bowling tournament involving dice to practice their scoring abilities. Unfortunately, what I have found in the past is that after practicing with dice bowling and assessing them on their ability to score, is that many students still lack the knowledge and ability to keep score in a game of bowling.

Every Monday, they will have to score one complete game of bowling that I put on the board. Their score, which will be entered into the grade book and also used for seeding purposes for an end of quarter tournament, will be found by taking their score for the game and subtracting the actual score of the game. If their score matches the actual score they will earn 10/10 points. If their score is off by +/- 5, then they will earn 9/10. If their score is off by +/- 10, then they will earn 8/10. And so on.

Once most students are earning consecutive perfect scores, I plan on making it a bit tougher for them by telling them to create their own bowling score sheet so that it has a predetermined score. They will be mandated by a couple preset rules. First, their game cannot have more than one gutter ball in a row. This prevents students from creating a game and then when they get to the final score, writing in all gutter balls so that no score is added. Second, students must check to see if their game is correct by sharing it with a classmate and allowing them to score the game. This allows students the opportunity to see other students’ work and also it prevents me from having to give them a low grade because their score doesn’t work out. The students will need to understand all the concepts involved in scoring a game of bowling, plus they must use creativity and cognitive thinking skills. 

I realize that the first couple weeks might have lower scores then normal, but hopefully as time passes, their ability to score and also to do mental math will improve. I also feel that knowing there is a tournament at the end of the quarter will also help to improve motivation to learning and improving.