Sunday, July 28, 2013

The Ambiguous Case Activities



The ambiguous case is one of the most difficult concepts to get across to Geometry students.  When I teach congruent triangles, I think that some of the students are convinced that they can't use the ASS Theorem to prove triangles congruent simply because I don't want them to write bad words on their paper!  (No matter how many times I try to explain it!!!)

Then when you actually try to explain to Algebra 2 or Pre Calculus students the SSA case (have you noticed that it is never written as the ASS case? LOL) their heads start to explode!

I started my search online and came across a couple of things...

1) a really great explanation of the ambiguous case can be found at the regents prep center
  Ambiguous Case Explanation


2) A really great activity that even geometry students can use to explore the ambiguous case (see this link Ambiguous Case with Pipe Cleaners )  The basic idea is that you give the students two pipe cleaners to start with.  They must also start with a given angle - they use 30 degrees in this example.  Then students try shortening one of the pipe cleaners by 1 inch intervals.  After the students shorten the pipe cleaner a few times, they will get to a point where two triangles can be formed - in other words, being given an angle, a side, and a side does not guarantee that two triangles will be congruent.  Although not all geometry students are ready to see the trig involved,  (especially during the beginning of the school year when we study congruent triangles), I think that they can see by experimentation that two triangles can be formed in certain situations.  I am definitely trying this out this year!

Here are a couple of other links that I found for other possible activities.

3) Ambiguous case activity with paper fasteners and construction paper.  Ambiguous Case Activity

4) Here is a link to a calculator activity that you can use with your TI-Nspire - you could even just use it as a visual representation if you don't want to take the time for all the students to do it on their own.  Calculator Ambiguous Case

5)  Finally, here is a real world example from the CK-12 Book that would be a good starting point for your lesson.


Wednesday, July 24, 2013

Jumping On the Interactive Notebook Bandwagon


Perusing pinterest, teachers pay teachers, and lots of different blogs has led me to the conclusion that interactive notebooks are all the current rage.  But, are they right for me and my students?  Will high school honors students like cutting, pasting, and having things sticking out of their notebooks?  In addition, I can tell you right now even though I have been teaching Geometry Honors for (quite literally) 22 years (x3 classes per day most years) I am not organized enough to be able to make a table of contents with every possible thing I would want the students to put into their notebook.  I also am not quite sure that I can grade them...and by the way, how do I want to grade them???

But, they interest me quite a bit!  So, I am thinking that I will give at least some aspects of the interactive notebook a try this year.

I am thinking of things to try putting into an interactive notebook, and one of the first things that comes to mind is my calculus students.  I try to drill the convenient values into their heads...but their noggins are tough, and they just don't want to remember them!

So, here is a look at my first try at a "flippable."








What do you think?  What types of "flippables" do you use in your middle or high school classroom?

Have a great day!

Friday, July 19, 2013

Back to School Success in Secondary Linky Party!


Today is the day that always marks the beginning of the end of summer for me.  It is schedule pass out/picture day at they high school where I teach.  Kids have to come in and get their ID picture taken and then pick up what will hopefully be their final schedule.

Even though it's still July, after this day, I know it is only a couple of short weeks until we return to meetings and then the classroom. (Can't believe that it's August 12th this year!)

So, what better time to host a Success in Secondary Linky Party...feel free to post up to three items in this linky party...the only requirement is that they need to be appropriate for grades 6 - 12 - any subject is fine.

If you link up, please follow my blog if you haven't already :)


Thursday, July 18, 2013

Another Interesting Curve - The Ellipse


One of the topics that is often studied in pre-calculus is conic sections.  It is great to be able to give students examples of things that are actually shaped like one of the conic sections.

Today I want to focus on the ellipse.





The definition of an ellipse is "a locus of points such that the sum of the distances from two other points (the foci) is constant."

As you can see from the picture above, you can have students draw an ellipse by tacking two down two ends of a piece of string.  Then, students should put a pencil in the string as shown.  Carefully they move the pencil around the piece of string and they will trace out an ellipse.  That makes sense because as we see in the definition, the length of the string will remain constant.

But, the interesting part...where can we see ellipses in our lives?  


1)  Here is a picture of a park that is in the shape of an ellipse.  This park is in Washington DC and sometimes called President's Park South.  If you look carefully, you can see the White House at the top of the picture.  The National Christmas Tree is in this park.  This tree is lit every year by the President.




2)  We can also see ellipses in the orbits of the planets around the sun.  Although people once thought that planets orbited the sun in a circular path, we now know that the path is an ellipse.  Kepler's First Law says that planets orbit the sun in the shape of an ellipse with the sun as one of the foci (a focus is one of the fixed points that we mentioned in the definition above.)





3) The ellipse has a reflective property...If a tangent line is drawn at point P, the angles formed by that line and the lines PF' and PF would be equal. So, a sound wave that starts at one of the foci is reflected back to the other foci...this is called a "whispering gallery."  If two people stand at the foci, they can whisper back and forth to each other.

We went on a summer out to the Museum of Science and Industry in Chicago and visited their Whispering Gallery.



Have a great day!





Monday, July 15, 2013

Even High School Teachers Need Cute Decorations!

As a high school teacher, it isn't often I change my bulletin boards or anything hanging on the walls in my classroom.  I mean there is stuff there, but even I am getting kind of bored by it :)

So, maybe this year I will work changing it up a little more often.  One thing I want to try is some type of Post It to Prove It.  I got the idea from Jennifer Smith-Sloane's Blog Post (see it here.)

The general idea that you use this as an exit ticket - students write the answer to some question on a post it.  As they leave the room, they put their post it on the white board.  Cool - students see their work in the room and I see if they understand what we did!  With all of the back to school sales, I will have to stock up on post-its :)

In addition - I need posters - cute math posters!!

If you need some too, hop on over to my TPT store and grab this FREE new poster.



Fractions are Your Friends Poster

If you have suggestions for classroom decorations for me - please feel free to leave them in the comments.

Have a good day!

Saturday, July 13, 2013

Back to School Giveaway!

Today I am participating in a back to school giveaway by Live.Love.Math.



Hop on over and enter!

Live.Love.Math.



Friday, July 5, 2013

Ways to Greet Students


I found this pin on Pinterest, and it really makes sense to me.  I know that we are all busy during the school day, but greeting students at the door - with their name - is really important.  Having an activity that grabs interest as soon as students walk in the door is really important too.

As the school year gets started, one of my first challenges is to learn my students' names.  After a few days, I stand at the door and don't let the kids enter until I say their name.  I know I'm going to get some of them wrong at the beginning, but it lets the students know that I am working on it and that it's important to me that I learn them.  I have heard students in my class say at Christmas that such and so teacher doesn't even know my name.  That's not good!

But, as the year goes on, the beginning of class needs some variety.  I am not a big fan of Do Now questions - I have never been able to get that to work quite right...but I know that does work for some people.  What I like to do is to try to generate some excitement at the beginning of class - make students want to get there on time to see what's going to happen!

A video showing at the beginning of class of some interesting math thing happening is always a big hit.  Even if it's not necessarily related to the days lesson, it still generates interest.

I like the idea given in the pin above - give students part of a problem to solve.  It would be great if all students had a different part to the problem and all of the parts come together for one big solution.  This follows right along with give each student a part of a picture and have all the parts come together for one big picture.

A big scrabble game sounds like a great idea...how could we relate this to math - students are only allowed to spell math related words?  I have also made a bulletin board size copy of a math crossword puzzle for students to work on.

Here's a good one...give each student a random number when they enter the classroom.  Do something with the numbers during class.  For example, everyone with an odd number has to write a problem on the board (or demo on their iPad :)  or everyone with a multiple of 3 gets a free homework pass as long as they did today's homework...the possibilities are endless!