Rational Numbers

Rational numbers are numbers that can be expressed as a ratio of two integers.  Algebraically: a/b, where b ≠ 0.

Rational Numbers Practice: http://www.clcmn.edu/kschulte/mathworksheets.html

Rational/Irrational Practice: http://www.regentsprep.org/regents/math/math-topic.cfm?TopicCode=rational

Irrational Numbers

Irrational numbers are numbers that cannot be expressed as a ratio of two integers.  They cannot be written as a terminating or repeating decimal.

Rational/Irrational Practice: http://www.regentsprep.org/regents/math/math-topic.cfm?TopicCode=rational

My Mathography

In first grade, I remember that my teacher giving me more and more math to keep me occupied as the other kids finished.  She did this for three of us.  Eventually, she gave us different math books to work from.  In second grade, my teacher introduced me to Roman numerals and that was my math enrichment for the year.  Then, in third grade, they began to ability group us, and I was in some form of accelerated math through high school. 

What I enjoy about math is how it all fits together.  It’s just this nice neat little package of information.  It is all inter-connected and somehow related.  To this day, I’m still discovering connections between things that I before had never even bothered to examine.  Usually, I discover these when I’m speaking with students and answering their questions.

What I didn’t like about math was the instruction I received in high school.  Knowing the rules can only take you so far.  When I got to trigonometry, I was continually in situations where I didn’t know what rule or what equation, or what anything I should do to solve the problems.  Rules are only good when you know which one to follow or use.  It’s the ideas behind the mechanics that allow people to apply them in new, unknown situations.  That’s true problem solving,

As a kid, I hated having to sit through those seemingly unending church services, but loved anything that had to deal with sports, especially throwing something.  The church services actually led me down the mathematical trail that I’m still on today.  To keep me quiet and occupied, my mom used to write down math problems.  I loved it!  The only thing that would have made me happier is if the pastor would have begun talking about the Pirates rather than Pontius Pilot.  Also as a child, we had a dart board in our basement and had about 20 darts.  I used to throw all the darts and then add up the score.  (I wish that I had known about the doubles and triples back then…I could’ve learned multiplication much sooner!)  My dad had some accounting ledgers that he’d found somewhere and given them to me because I loved numbers.  I’d try to add them differently every time I threw.  I discovered a lot about numbers just by working with them.  That’s what I think kids are missing today, playing and experimenting with numbers.  Do kids play darts today???

I can’t honestly say that I ever had a favorite math teacher.  I did have a favorite professor, Dr. Werner, but she didn’t teach math, per se.  She came to Slippery Rock right at the beginning of my master’s program and I had her for many classes.  One of the first classes I took with her was Problem Solving.  She taught us to look into the problems and identify the underlying concept.  Most times, problems can be extended beyond what the book expects the student to do.   Patterns often occur that students can discover.  Then, it is my job to extend them beyond the point where one can just simply count, necessitating the use of algebra and writing equations that will solve for any value.  (It’s amazing how many times Pascal’s Triangle is used in math books!)

Math was always my favorite subject.  Unlike reading, I was good at math, had success, and who doesn’t enjoy something they are good at?  In high school, math was not one of my favorites.  In fact, I quit math after trig and didn’t take a math at all during my senior year, but used it in physics.  It wasn’t until a few years ago that I decided to take a math beyond trig.  I took a Pre-Calculus course at Slippery Rock and was actually good at it, very good, in fact.  After almost failing out of trig in high school, I’m proud to tell you that I missed only a few points during the entire class (which was way harder than what I almost failed!)  I was quite surprised to learn that math was easy when you knew the ideas and where the material comes from.  Being able to make connections between ideas was the key.

Tree stands, Washers, and Vacation

Tree stands, Washers, and Vacation: 

 

How are these three things related?  Well, just tiptoe through the following anecdotes to begin your mathematic journey. 

 

Recently, I was assembling two tree stands that I purchased for the upcoming deer season.  I took one look at the plastic washers that they sent along with the bolts and knew that I needed to replace them with metal washers.  So, I went to the hardware store.  The washers were $2.39 per pound, a unit rate.  Figuring I would buy some extras, I just grabbed a few handfuls and put them in a bag, then weighed them.  I had 7/8 of a pound.  However, I only had a few dollars with me…you other teachers know how that is, I’m sure.  So, doing a quick estimation, I figured that 1/8 of a pound would be about 30 cents.  Therefore, I had just over $2 worth of washers.  Add in the 6% tax, and I had a decent amount of change returned from my $3.  If my better half was there, she’d have dug through her purse for a few minutes trying to find exact change.  However, I don’t mind the change…I save it as a vacation fund for the girls, which will set off its own math problem when June rolls around… 

 

Here’s how that goes.  When they were younger and not exactly astute mathematicians, I’d give the youngest all the change.  She had the assignment of dividing the change into two groups.  Then, her sister got to pick the pile of her choice.  The youngest got the pile left over.  It’s amazing how quickly kids become great mathematicians when proper motivation is supplied!

Integer

Working Definition: all the whole numbers, positive, negative, and zero.

Book Definition: all the counting numbers, their opposites, and zero.

Integer Practice: http://classroom.jc-schools.net/basic/math-integ.html

Welcome!

Hello everyone!  My name is Shawn Sowers and I’m a sixth grade teacher.  I have two goals for this class.  I’m currently teaching two math courses, one eighth grade level and one seventh grade level.  By taking this class, I’m hoping to better prepare myself to move to our new middle school (it is supposed to open in 2010) and hopefully move up in age/grade level.  I’m hoping to some day teach Algebra I as well as the normal middle school math curricula.  I’m also hoping to get a better insight into how middle school teachers teach for meaning when time is such an issue.  Right now, we have math for 70 minutes a day, and I’m able to accomplish quite a bit in that time.  However, in the regular middle school day, classes are 45 minutes.  I wonder how I’ll “be as good” with 25 minutes less per day?!