Putting Pascal’s Triangle into Formal Terms

Posted in 1 on October 7, 2009 by coltswet

Pascal’s triangle I notice is a large triangle containing many smaller triangles in its interior. The two outer edges of the triangle are made up of the number 1.  As we move down a level from the peak we create new triangles.  Now you must follow a vertical line from the peak of this outer triangle to the bottom of the triangle to understand my next explanation.  Each time we move down this vertical line from the peak we get a larger number. This number is determined by adding the sum of the previous interior triangles steps. For example, The first number after following our vertical line down the center of our original outer triangle is 2. We get this total by adding 1+1, which is the first two steps that bring us down to this level of our vertical line. The next number on this vertical line is 6. We get this sum by adding the previous 3 steps sum which is 1+2+3. So each time we take a step down this original vertical line we add another step in our sum.  Once you determine the pattern, you can repeat this process to expand outward in the triangle.

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Working with the definition of linear patterns.

Posted in 1 on October 5, 2009 by coltswet

Nontraditional patterns are simply patterns that do not follow a repetitive format.

Linear Patterns- A pattern that moves in a straight line and is easy to notice.

Formal Definition of a Linear Pattern- A linear pattern is said to exist when the points examined form a straight line

My definition and the researched formal definition of linear patterns are very similar in the fact that they both mention a straight line.  The word Linear tells us that were evaluating something that is in a straight line.  Pattern tells us that were looking for something that is repetitive.  The only difference that I noticed is that in the formal definition they mention “points”, which I presume they are talking about on a coordinate grid.

I could explain to my students that in order to determine the linear pattern, we must look for the repeated process throughout a graphed line.  We must look at the rise compared to the run of a line that is graphed.

My Reflection on Math Myths

Posted in 1 on October 5, 2009 by coltswet

There are many myths that have accumulated over the years in math classes.  Two of the most common myths that I discovered while reading an assignment in this course that I no longer agree with are; Boys are better than girls in math and there is only one way to solve a problem.

Myth 1:Boys are better than girls

While a student in school, I noticed that in many of my upper tier courses the class was mainly made up of boys.  At that time, I was unaware of what was taking place but I believe that it was mainly because that’s what we were told and female students looked at it as a boy’s subject, so they did not pursue it as heavily. I also feel that boys did better in math because it was “quick” work and not a lot of explanation.

Now as a teacher, I am noticing that my female students are really overcoming this myth.  I believe now that we put a lot of emphasis on writing in math such as open-ended response questions, female students are starting to excel more than boys.  I also feel that the stereotype of math is only for boys is being overhauled due to the fact that math is a stronger focus for getting into college and starting careers.

I always tell my students that any student can be successful in math as long as they are willing to pay attention, practice, and ask questions.  I also let them know that math is very important for being successful in their future.  In this day of age, women are competing with men in every field, which means that no subject is only one gender.

Myth 2: There is always only 1 good way to solve a problem

While a student in school we were always taught that you needed to follow a certain process to find an answer and if you were unable to do so, you would not excel in that area.  This had a very negative effect on me as a student, because I sometimes did not find it easy to work on a problem using the method of the teacher.  I would struggle to focus on the lesson’s because of this and often lost credit for not showing work.

Currently, I teach my math lessons using the PowerTeaching approach.  In this approach, the teacher teaches a lesson showing the standard approach to complete a task.  However, encourages students by expressing to them they can use different methods to complete the task.  Part one of the lesson is called Active Instruction.  Part two of the lesson involves students working in Team Huddles where students work together to complete their task by way of the teachers methods or their own.  This allows students to learn a concept using multiple approaches.

By using this approach, I have encouraged students to by all means, use whatever approach they are comfortable with to solve a problem.

PUMAS, an interesting site!

Posted in Math Stories on October 1, 2009 by coltswet

At this website, teachers may find outstanding activities and thoughts on how to present a concept to students. The one activity that I thought was great was called “Two Answers are Better than One”.

In this activity students are encouraged to use estimation as a first step before finding the eventual exact answer.  By estimating, you are able to determine what is reasonable before you actually calculate your final answer. This website also gives great examples that you can model for students to help with estimating and finding an eventual answer.  I also like the name of the title because its “catchy” and reinforces the importance of checking for reasonableness.  A concept that many of our students often don’t use, which allows them to sometimes make careless mistakes.

Understanding the Inverse Property

Posted in Glossary on October 1, 2009 by coltswet

There are two types of Inverse Properties. The Inverse Property of Addition and the Inverse Property of Addition.

The Inverse Property of Addition is when you add a number and its opposite resulting in zero. Therefore, in order to understand the Inverse Property of Addition, you must understand a numbers opposite.

Examples)  5 + -5 = 0   or A+ -A= 0

The Inverse Property of Multiplication means to multiply a number by its reciprocal. Therefore, to fully understand this property you must first understand what it means to find the reciprocal of a number.

Examples) 7 * 1/7=1  or A * 1/a=1

Notice that in each example the first term is not written as a fraction, but as a whole number.  I could write 7 as 7/1 as well.

My Mathography

Posted in 1 on September 24, 2009 by coltswet

I remember when I was in elementary school that math was my favorite subject.  I really enjoyed it because I was impatient and math was able to be done quickly.  I was a very competitive boy and we used to play a game called “Around the World”. I was the kid to beat and often circled around the class for the entire game.  The kids called my the “math wiz”.  It really motivated me to do well.   Once I entered into sixth grade, I was put into a group called the “math league”. Here we began to work on challenging math problems that involved words.  At this point I began to no longer enjoy math as much.

The first thing I learned in math was how to add and subtract.  I remember learning to identify patterns as well.  The way I learned how to do these things was by mostly coloring and drawing.

My favorite teacher of all time was Mrs. Kraybill.  She was my favorite because she was the one who taught me how to play “Around the World”.  I also enjoyed being in her class because she used a lot of competitive things to motivate me as a student.  She also taught in a way that we were able to do group work, which at that time I thought was so we could talk, but now as a teacher I realize it was to share our thoughts and ideas with each other.

Math Stories from this past week and forward

Posted in Math Stories on September 23, 2009 by coltswet

Recently, my wife and I have been building a sunroom addition on the back of our house. This past weekend I was finishing up the siding and because of the angle of my roof I had to cut the end of the siding on an angle.  I knew the length of what I needed of the siding, however,  it had to be cut just right because the last foot or so needed to be angled due to the slope of the roof.  I didn’t have the proper skills of a construction guy, so I thought about how I could determine the proper slope “cut” so that the siding would fit behind the j-channel.  As a math teacher, I told my wife we could use the Pythagorean Theory to help determine the length of the cut from the top of the siding to the end. So I figured it out as this.  My piece of siding was 12 feet long and the piece of siding would fit perfectly up until 8 feet 8 inches. At this point the slope came into play for the remaining 14 inches. So I used the Pythagorean theory and set my problem up as such:

12″ squared + 14″ squared = the length of my slope squared.

144 + 196= slope squared

340= slope squared

Slope had to be 18 1/3 ” long.
I am so proud to say that the first thing I tell my friends when they come over to see the final project is that I successfully completed the siding myself, without the help of my neighbor who owns his own remodeling company!!!