Archive for the ‘Videos’ 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.

This week’s video clip was brought to my attention by a senior from the class of 2011. He told me to check it out because it contains real life math that affects almost everyone in the United States.

I love this clip because it takes a number that sounds incredibly large, and changes it into a number that isn’t that spectacular. The United State of America, as well as countries around the world, use units of measurement that are common to everyday life, but if a person were to tell you the actual size of these units in relation to everyday objects, many could not. How big is an acre? How large is a ton? How big is a 5.8 earthquake? How big is a gigabyte? How much is a gallon?

My goal of YouTube Tuesdays in my classroom is a warm up and not a lesson that will devour the whole hour. Therefore, even though I would love to deal with all of the different mysterious units of measure, my time frame won’t allow for it. Instead, I am taking three units: an acre, a ton, and a mile; and then with these I have planned a short lesson. Hopefully, this will take no longer than 15 minutes of class time, and the students will have a better understanding of measurement when they are done.

To conclude the lesson, I have found another clip that uses the terms “acre” and “tons”, as it compares the amount of trash in the Great Pacific Garbage dump to things we Americans can relate to. Check it out below:

And here is the accompanying worksheet:

One thing that I have in my classroom that always baffles my young students’ minds is a digital binary clock. Students always look to the blinking lights and while some might notice a pattern, most of them have no clue as to its purpose. After a couple of weeks of having students in class, and once we have gotten into a rhythm for our daily routine, I then like to share how it is possible to tell time using this clock.

Usually, I go to the board and show them how the binary number system works, but then I fail to provide them with any practice in which they can show their understanding. This year, I plan on using a YouTube Tuesday to help illustrate the workings of the clock. Before I show them this week’s video, however, I plan on giving them a worksheet that helps them to understand what it is they are seeing in the video. As much as I love Vihart’s videos, it’s pretty obvious that she zips along in her videos.

To help them understand the idea of binary number, I will give them this worksheet (worksheet #3), which shows them the basics of binary numbers. While this worksheet was created for students in grades 3-5 to use for an entire 60 minute lesson, I intend to use it for a warm up for my high school students. It may be necessary to change some of the smaller numbers to larger numbers, just to make it more challenging for my older students.

Once, the students have a basic understanding of binary numbers, then I will show them the Binary Hand Dance, performed by Vihart:

I realize that after watching this video, that some of the number sign combinations are a bit controversial, but hopefully students will realize that when we count with our fingers, sometimes these things happen.

Also, if time permits, I would like to show them a clip from the TV show ancient aliens, in which they mention that the best way to communicate with other civilizations in the universe may be using the binary code.

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.

One of my fondest memories as a kid was watching David Copperfield with my family as he performed amazing magic tricks. One of the tricks, the Orient Express, amazed my little mind as I wondered how the heck he can know what I’m thinking when I’m at home and he’s in half way around the world.

The video that I found isn’t David Copperfield working his magic, but someone else performing the same trick. By using a clip of Copperfield I would have to sacrafice quality and also time, as the clip appears halfway through a longer video. If you want to see the original trick, then go here, and scroll to the 5:00 mark.

I also remember another clip of David Copperfield performing a similar trick. This one wasn’t as complex as the Orient Express, but it was still fun to participate in. Last semester, I showed this clip to my class and they were astounded by the results. “How could he know?”, many of them pondered. Even after showing it to them again, only a few students began to notice, but a few students were still left in amazement.

Since today is the first day of school, and also a Tuesday; what better way to get students involved and participating then to amaze them with interactive math? By opening class with the Orient Express Trick, I hope to capture students’ attentions. After they see the video, perhaps more than once, I will present them with a worksheet to do with their groups.

I remember using a worksheet that accompanies this clip when I was student teaching, but over the years I’d lost it and couldn’t find another copy on the internet. This morning I did a search and found a copy here, which was posted about a week ago, so it was perfect timing.

After we get done with the worksheet and discuss it as a class, I plan on showing them the second David Copperfield clip, with the goal that they will be able to quickly figure out why this one always works too.

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.