Triangles are Forever!

I haven't posted to the blog in a while, but that is about to change.  Today we began the unit on triangle congruence, which is the underpinning of the rest of the course.  Nerd that I am, I had a great time proving beyond the shadow of a doubt that the measures of the angles of a triangle add up to 180˚.  Here is the solution to today's Challenger.    Can you come up with a check of the problem to make sure the answer I got was correct?  Tell me about it, and you shall be rewarded......

Check out my new Voki - and follow her instructions!

Halloween is over, but I love these cupcakes!

On Logic, the PSATs, and Opportunity

Today in Geometry, we delved into the study of Symbolic Logic and one of my inquiring students asked why we study Logic if we will never use it.  Using what teachers refer to as a 'Teachable Moment,' I spoke about a liberal arts education and the value of learning how to prove something to be true, step by step.  But I have been thinking further on this all day, and I want to add something to my argument.  First of all, we study Logic to develop what we call Habits of Mind.  I truly believe that it is always worthwhile to learn something that teaches us to discipline our thinking, and to impose some order on the chaos that is in our brains.  I have done this as an adult (and do so continually), and find the process both intellectually and personally rewarding - that moment when something becomes more clear because I have worked at it, and then I own it.  A small personal challenge met, a victory all my own.  And the more that I do this, the more I challenge myself and work at learning new things, or clearing up old misconceptions, the better I get at it, and the more I grow.  If you think learning stops once you graduate high school, or college, you are wrong - you can be a lifelong learner if you choose. 

Tomorrow morning the sophomores and juniors will take the PSATs.  Right now, I am sitting with my daughter who is a junior in high school, going over some practice questions, and she is stressing and complaining. "Why do I have to do this?  Why study?  Why cram?  What good will it do?  I'm stressed enough as it is."  I agree.  The night before the exam is not the time to prepare. You can prepare for tests like the PSAT and the SAT, but with time and effort, and you can improve your scores.  Are the tests stressful?  Definitely.  What do they mean about you as a person?  Probably not much.  BUT they can be the key to the opportunity, and for this reason, it is important to pay attention to them.

Everyone knows getting accepted to college is challenging and competitive.  And once you are accepted, going to college is expensive, even if you go to a public institution like SUNY or CUNY.    ANYTHING you can do to improve your application or resume, or make yourself look just a little better might be the thing that earns you notice, admission to the school of your dreams, acceptance to a travel program or internship, or scholarship money.  So while college may seem very far away, and the PSAT may not seem to be important, remember that we don't always know how significant something is until after it is over.  Another reason to do the best you can do, as often as you can do it.

So get a good night's sleep (no chatting/Facebooking/texting until 2 am!), eat a good breakfast, and don't forget your pencils tomorrow.

One last thing:  you are not a test score.  This may seem to contradict everything I just said, but realizing that your exam scores are but one facet of the total package that is YOU may put things perspective.  So try your best, but remember there is A LOT more to you than a number.  I know that, and I hope you do too.  

Good luck, Geometers and Living Mathematicians! 

Parallel Lines, Parallel Universe

How great are 3 day weekends?

I was walking around this afternoon trying to find examples of parallel lines and angles in the real world that might help my students see the relationships better (yes, this is really what math teachers do in their spare time).  All the examples everyone gave in class came back to me - the lines in the sidewalk, the train tracks, the painted lines that divide the street into lanes - there seems to be no end to models of parallel lines in the real world.  And I was thinking how abstract this concept may feel to some students, but how important it is in the physical world that lines that are meant to be parallel actually are (studs in construction, for example, and walls in houses).  While there are many examples of buildings that use lines that aren't parallel in their design to beautiful effect (as above),  we still need the floor to meet the wall at a right angle.

Here's a question - are the frets on a guitar parallel?  what about the strings?

See you tomorrow -

Ms. M

Points, Lines & Planes - oh my!!!

I was so impressed today with everyone's focus on the basics of geometry - all of the students seemed to be working hard to internalize the concepts of these very important building blocks, taking copious notes and making lovely sketches.   I know that if we can take good care with this beginning the material, the rest of the year will be much more successful for everyone.

At the moment, I'm a happy math teacher.

Addendum to Day 2

It's almost time for Project Runway (one of my family's favorite shows!).   If anyone reads this tonight and watches the show,  look for examples of symmetry and/or scale, and make a post or send me an email - more extra credit!!!