Mrschlorff's Blog

Reflections on Blogging

mrschlorff — Thu, 05 Nov 2009 16:29:18 +0000

Describe your blogging experience in this course. Do you think you will continue using your blog? Why or why not?

I really liked being able to carry on discussions with others through my blog posting. I think it is a neat place to have online resources as well as class discussions. I am not sure if I am going to continue this or not. Some of the teachers in the building have suggested something like this but with facebook (since the kids are on it anyway).

What did you learn about yourself and your abilities or interests in Math or Algebra?

Well I love math and have always enjoyed it. I realize that I sometimes do things very quickly and miss small details. I also have seen a lot of new neat ideas to talk about different ideas online, and with new types of technology.

Did you learn or discover anything you found particularly interesting through your course actives or your own internet research? Describe one interesting discovery and why you found it fascinating.

I thought the way that we were able to discuss ideas either in the blog posts or in the forum was amazing. I never thought it would work the way it did. Also, a lot of the online manipulatives were really neat, I have used some but there are so many out there and seeing them was a great reminder of what the web has to offer.

Do you think you will use journals with your students? Do you think you will use blogs? Why or why not?

I will continue to use journals with my students because it is so important that student can communicate. Without being able to communicate math doesn’t mean a whole lot. I would like to use blogs it just depends on if I can get the computers all of the time I need them.

Factoring Quadratics – in Your Own Words

mrschlorff — Thu, 05 Nov 2009 16:21:51 +0000

1.) Paraphrase how to factor:

Look at your last term, list out all of the factors that multiply to that number. Once you have a list of those factors figure out what adds to the middle term. For example (x²+4x+4), what multiplys to 4? Either {2 and 2}; {1 and 4} or {4 and 1}. Which of those sets then add to positive 4? {2 and 2}. Now we know the factors it is all about putting the pieces together. (x + 2)(x+2) or (x+2)².

2.) Did paraphrasing the words help you internalize the concepts more?

I really think that writing out in my own terms helps to understand the topics in a deeper way. The students tend to understand something that they write out, because they have ownership. The idea of factoring a quadratic is very hard so anything to help.

3.) How can you apply this type of exercise in a lesson for your own students?

I think journaling is a very important idea in the mathematics classroom. I think this would be a great journal. As well as this idea with many other hard vocabulary.

5-D-2: Applets

mrschlorff — Mon, 19 Oct 2009 14:10:55 +0000

I choose the following applet:

http://nlvm.usu.edu/en/nav/frames_asid_107_g_3_t_1.html

It is called Number Line Bounce and has the students figuring out how to add or subtract two integers using a number line. I use this in class when the students are working on an online portion to the class called ALEKS. The students have to get so many percent of growth in ALEKS and when they are done they can play this game. This really helps them with basic number sense and dealing with signs.

I really like most of the applets from NLVM there are so many things to use both independently with your students or as a whole class activity.

5-B-1: The Magic of Proportions

mrschlorff — Sun, 18 Oct 2009 01:56:37 +0000

When in the world do we use proportions? Well I think the questions shouldn’t be when, but where in the world do we use proportions. – EVERYWERE!

This past summer I went to Costa Rica and came across the following problem:

I wanted to purchase coffee for a friend back home, but I only had 40,000 colones. My friend wanted me to bring back as much as I could carry so I brought back 5 Kilos of fresh Costa Rican coffee. The price was 3,500 colones per kilo I wanted to know how much it was per dollar since colones doesn’t really mean much to me. I knew that the current exchange rate was 585 colones to 1 USD so I set up the following proportion:

This game me an idea that I was spending about 6 dollars per kilo of coffee so I spent 30 dollars total for coffee. With all of the traveling I have done I have found out how easy it is to convert money using proportions like that.

An extension to this problem and story is that when I went to pack the coffee I had to make sure my bag was not overweight, so not over 50 lbs. Well I had 5 kilos of coffee and the scales are set up in lbs not kilos. I had remembered that my bag weighed about 30 lbs on the trip down. I figured out that the ratio of lbs to kilos was about 1 to 2.2 and used that to set up the following proportion:

As you see I added an extra 11 lbs to my bag but 30 + 11 is still way less then 50 lbs so I was ok!

As one can see proportions are every were in the world and make traveling so much simpler if you can use them!

Evaluating Your Own Definitions

mrschlorff — Sun, 18 Oct 2009 00:01:38 +0000

After looking over my fellow student’s blogs I don’t think I would change much. I agreed and had very similar things down as they did. The one thing that I always debate on is if I would call an inequality an equation, and my thought behind it is that it is still showing a relationship. The only other thing I would change is that I would show an example of something that is not a function. I really thought that, that is a very helpful diagram for students.

Reading over my fellow classes mates posts really helped me to evaluate my definitions. I think that if students did the same thing reading over their friends ideas as well as mine they could easily see what is correct and what isn’t.

Equations and Functions 5 – A – 3

mrschlorff — Sat, 17 Oct 2009 23:48:22 +0000

Function:

A function is a relationship between two different items or numbers. A function has one and only one output for every one input. A great way to check to see if something is a function is on the graph; draw a horizontal line. If that line only goes through the graph one time it is a function.

The example below shows a function between number texts that a student sends and the student’s cell phone bill.

Each text that is sent cost $0.10. This student’s bill starts off at 25 dollars each month for phone usage and anything over that is texting.

Number of Text	Price of Bill
0	25
500	75
1000	125

Equation:

An Equation is two terms separated by an equal, less than, or grater than sign. Most of the time students think of it just an equal sign but really any sign that shows relationship can create an equation, it may be called an inequality but it still shows a relationship.

Examples of equations:

5x = 10

x = 5

5 = 5

Not Equations

My Reflection on Math Myths

mrschlorff — Sun, 11 Oct 2009 04:17:45 +0000

“To solve a difficult problem, work intensely, and don’t stop until the problem is solved”

This myth I did think was true while I was learning mathematics and I thought it to be truer when I was in my college career working on math. When I was in linear algebra in college I used to work and work and work until I got the problem. It isn’t until now that I know taking a break to let your mind think clearly would have saved me time and stress.

After I figured out that sometimes on really tough problems it just takes some time to think. I would be working really hard on a proof and until I sat back and did something else my mind wouldn’t be clear enough to figure it out.

I try to explain to my students that if you don’t get something, skip it and then come back. See if you can let your brain rest and think through the problem. Most of the times the students and myself get so frustrated they end up making the problem even harder then it was.

“There is always one best way to do a math problem”

I don’t think I ever thought that this myth was completely true but it was something I always wondered. Is there one way to do a problem that is the best. I don’t think so, I think there are many ways that might be equally as good.

Since I have decided that I do not believe this I am always trying to look for more then one way to find a solution knowing that it is a good solution.

I always try to explain to my students that as long as you can show how you got to your solution it doesn’t matter what path you took. I also try to show many different ways to get to the same solution.

Mathematic myths are out there and lots of students and even some teachers believe them. During parent teacher conferences I heard many times about how well either you get algebra or geometry. I wish there was a way have mathematical mythbusters show to debunk these myths.

Pascal’s Triangle

mrschlorff — Sun, 11 Oct 2009 02:50:50 +0000

One of the best ways to use Pascal’s Triangle is for Binomial distribution. When you have a quantity of (x + y) to the power of 1 your coefficients are 1 and 1. If you have the same quantity (x + y) to the second power it expands to x² + 2xy + y² which gives you the coefficients of 1 2 1 which is the third row in the triangle. If you take the quantity of (x + y)³ which expands to x² + 3x²y + 3xy² + y² which has the coefficients of 1 3 3 1 or the next row. That pattern continues and works for all power of the quantity.

Web Quest

mrschlorff — Sat, 10 Oct 2009 19:50:35 +0000

The first pair of search terms that I went with was: Fractals and nature and patterns.

I picked this first because I know teaching geometry that fractals and nature and patterns are linked in so many different ways. I teach a unit on the mathematics of snowflakes and the patterns of snow. There a great book titled Sacred Geometry which highlights how geometry became math and it says it is because of the patterns from nature. I went to http://www.miqel.com/fractals_math_patterns/visual-math-natural-fractals.html website and saw tons of pictures of fractals on leaves, drawings, shells, and rocks.

The second pair of search terms that I picked were:

“Fibonacci” and “Phyllotaxis” and “Prime Numbers”

Students always seem to have a hard time trying to figure out what is prime, what is the Fibonacci series and how does it work. I picked this because it links to mathematics in nature, you see prime numbers, and the Fibonacci series in things like leaves, pineapples and others.

This link has a great comparison between Fibonacci and prime numbers: http://www.flickr.com/photos/quasimondo/3784494627/

1. Were there ideas or concepts you were not familiar with? What were they?

I was pretty familiar with this idea but it was really neat to find a bunch of things that I can use in my geometry class. I have also seen the same type of connection of nature and patterns with a pineapple and the rotation that the diamonds make on the pineapple.

1. What images did you find particularly striking?

I always think that seeing a leaf that has patterns repeated over and over is art. I really liked this picture:

This picture is something that you would never think has mathematics in it but it does, look at how the patterns repeat over and over again.

1. Can you identify any manifestations of nonlinear patterns within your home or your workplace? What are they?

There are tons of patterns all over; one is the amount of traffic to work. Some days it is a very steady almost linear pattern and other days it seems like it grows quicker and quicker and quicker.

1. How can you adapt this webquest activity for your classroom?

Students love to use the internet and computers, I have them search for really tough concepts before we learn about them. This way students have a background information and a basic understanding of the concept.

Linear Patterns

mrschlorff — Sat, 10 Oct 2009 18:55:18 +0000

A linear pattern is a pattern that changes the same amount each time. So if you mow the lawn you may earn 5 dollars each time. How much do you get after mowing the lawn ten times? That idea is a linear pattern something that goes up the by the same amount, in this case five dollars each time.
Using Dictionary.com they defined linear equation as the following: “a first-order equation involving two variables: its graph is a straight line in the Cartesian coordinate system.”
To tell you the truth there is really no difference between the formal definition and mine. Mine takes out the language of first order and Cartesian coordinate system but just for a linear pattern all a student needs is the idea that the rate of change is the same. I really feel that it is important to have the students read the definition for the language but to then work with them on creating their own more meaningful definition.