That's not omega!

That’s not omega!

“That’s not omega!”  I was shocked.  I am used to being challenged on many things: academic, worldly, and whether or not there are 3 minutes left in class or 4.  But omega?!  Of course it was omega!  What else would it be?  Does he not know that I majored in math in college?!  We know what (some of) the Greek letters are!

Unfortunately, now nobody is really thinking about angular velocity.  Thanks, Student.  : /

Honestly, I really didn’t know what else to say.  At some point, I remembered that Greek letters have capital and lower case, and he probably didn’t know that.  He was used to the capital omega.  We use the lower case one.  I know sometimes there is a reason certain letters are used.  I don’t remember which or why.

I wasn’t even annoyed with this kid.  (I know the face above tells a different story).  This was during my Advanced Algebra & Trigonometry class.  This class is designed for seniors who aren’t ready for calculus.  It is 7^th hour.  It was ‘fun.’  OK.  It really was fun.  They definitely tried my patience, but I really loved this class.  For the most part it was made up of seniors.  I love that.  They were good kids who were nice.  Squirrelly.  but good.  They made me laugh.  I found myself with a big smile frequently during this class.  They were great.

They also taught me a lot.  This time I realized that previous knowledge can be more of a hindrance than a help.  Student, for whatever reason, was familiar with a capital omega.  It, of course, doesn’t look anything like the lower case omega, and he thought I was crazy.  I could have told them w was the variable for angular velocity, and nobody would have said, ‘boo.’  I thought he was crazy, too.  Like I said, why would you even argue with me about that?  This distraction can be annoying in class.  Some students’ focus can only withstand so much distraction.  I need to work on my reactions.  Maybe I should have asked him why he thought that.  Then his reasoning would have been clear to me.  I could have explained, and then, you know, actually taught angular velocity.  (Don’t worry I did anyway!)

Also, this reminded me that we need to be aware of what is going on in their brains.  If he hadn’t voiced his omega confusion, it may have been something that was a constant distraction to him.  How often do our students suffer in silence?

Christmas Tinsel

Here is the assignment.  It does not look pretty.  The one I gave looked much better! 

I spent two years of college being an RA.  I hung streamers from the ceiling for several holidays.  I stole it from Andrea, the 6th floor RA!



I honestly can't believe it took me SO long to think of it.  During my 8th year of teaching I decided that I really should (and academically, could) decorate the hallway.  It was last minute, so my tinsel options were limited.  

I figured out how much tinsel I needed and how much was available at the local store (in two colors).

It was mostly estimation.  It was below the level for most students, but I still think it was good for all of them.



I loved it because it made the halls festive!

I think next year I am going to get Christmas themed scrapbook paper and cut 1-inch strips so the kids can make paper chains and hang them from the ceiling.

Christmas Lights

Here is my file.  It doesn't look as good as the Excel file I made, but I this is how it looks when I upload it here.  : /

I had kind of last-minute inspiration to do something Christmas-related at school.

I decided to do the 'estimation' activity and then I included a few other tasks in this assignment.



I got a ton of ribbon, but I guess I can do this again next year with the leftovers.

When we were done, I told the kids, "Uhh...  We are not actually going to hang these."  Some of them were sad or disappointed or indignant.  I decided they had a point.  I have two beams going across my room with lights.  (It is a really high ceiling above that.)  We hung the streamers across those two beams.  They were long enough they just hung there.

It did not end up being very pretty.  The colors were kind of strange and one of my students mentioned that it looked like the bad decorations of a gender-reveal party!



They were fun for a couple days, but we took them down quick.


I still want them to think even when they get a little antsy for holidays.  Also, I don't like to do this right before finals.  I like to do 'real' math then.

I drilled holes in the cups.  (My dad helped a lot.  Dads are the best!)  The kids pushed the balloon through the hole and then blew up the balloon.

Factors and Feathers

Here is the template and worksheet I assigned.
 

I do this to have some Thanksgiving decorations.  It is also a good time to review in Geometry and Advanced Algebra & Trigonometry.  It is a little below the level for College Algebra or Calculus.

I first gave the students two columns on a paper and had them 
1.)  Write the polynomial 
2.)  Write all of the possible factors of c
3.)  Write the factors of the polynomial
4.)  Write the solutions to the polynomial.

Then I had them trade with a person and check.

When everything is correct, then they got a half of a paint sample and they used a marker to write each thing.



I found a turkey clip art and just followed it.  It was a lot of cutting out.  My mom helped me.  (Moms are the best!)  

I took the pretty ones and put them together to make a turkey.  I tried to put the 'similar color palette' cards together.

City Map - Parallel Lines Cut by A Transversal

I found this idea a long time ago.  It's on Wikispaces.


I really liked it and have had my students do it two years now.  I altered it a little. 



They are more creative than I am, so I try not to restrict them too much.


I give this a little after they learn about parallel lines cut by a transversal.  It's not completely new to them, but some do struggle a little with where each of the buildings should go.  I tell them to make a fake map on a smaller paper before they draw it on the big one.




I do not require them to make large, good-looking buildings.  I know that many of them have much better maps if they're allowed to make simple figures.  If I was the student, that's the position I would be in.



I also hang the prettiest ones on the wall in the hallway, as long as most of their locations are correct!




One map had Mike Wazowski Rd and other animated street names.  Some of them like to have themes, but many of them are pretty standard.

One maps had This Street, That Street, Which Street, Where Street, and There Street, etc.  That may be my favorite!

The two intersecting lines don't have to be parallel, but it's easier if they are!

Your Name Here - Midpoints

Just like the "Thankful" words and the "Character" words activities, I have a Name-Activity where students calculate midpoints.



Actually, I think for the College Algebra class, they calculate distance, but it makes no difference.


When I do the Name, Character, and Thankful activities, one of them is for slope, one is for distance, and one is for midpoint.  I usually do the name first, and I do them in the order of Lesson number.
That's all with my Geometry students.
With the College Algebra students, I 'have' to cover the distance formula.  It's probably something I should just skip, but I don't like skipping things, so we do this instead.





With the Thankful and Character activities, I usually don't hang up each word.  I try to not get too many repeats and I only pick the ones that are neat, colored, and look good.

With the Names activity,  I hang every single one up.


I keep the same requirements for each of these assignments:


*Every letter must have only straight line segments.  No curves!
*Every segment must have a slope that is not zero or undefined.  (No horizontal or vertical lines.)
*Every word must be drawn in something other than pencil.


Sometimes, this may be a challenge.  

That is a "U."

Some students decide they don't like the way the name looks, so they redo several letters just to improve one.


**Generally, this activity is easier to do with all-capital letters.
**Sometimes letters can be a little tricky to make w/o vertical or horizontal lines.  These can be done by placing the letters at an angle and/or drawing them 'artistically.'



For these projects, the kids have to show work.  
That work must include calculations with the ordered pairs.  (That is the entire point of this project.)  
It has to be organized!


The name has to be at least 4 letters long.

King Frostine Wages War

 

I'm very proud of this.  I wrote it  a couple years ago during finals.  Finals are boring!  I had only done one lesson of this 3-lesson unit.  I was getting ready to do the rest when we came back from break in January.
I made up the story, but not the names or 'races.'  Don't sue me.  I'm not making money off of this!

Geometry, "Center" of a Triangle, a Task from King Frostine

You live in the land of Sunderedcounter in Intermedio Tierra where King Frostine rules over all of the Lilliputians.  You are the king's head mathematician.

John Hurt's voice

 

There is some disarray in the land.  King Frostine is ready to wage war with three nearby cities Crystalgarth, Sunderfen, and Sharpetide.  His plan is to use catapults to continuously launch water balloons at each city until they surrender.

The assault will go fine as long as the liliputians have access to a camp nearby.

King Frostine only has enough resources to set up only one camp as a refilling station.

 
King Frostine must pick the location of his camp very carefully.  The camp must be exactly the same distance away from each Crystalgarth, Sunderfen, and Sharpetide.


The reasons for this are political.  King Frostine's biggest supporters, Lemel Hailglow, Hazel Flameshimmer, and Bracken Goldtree, each prefer he focus on a different city. 


Lemel wants to attack Crystalgarth.  The mermaids from Crystalgarth are always singing limericks about the liliputians right outside Lemel's house.

Hazel wants to attack Sunderfen.  The dragons of Sunderfen are always dropping jello-filled water balloons onto Hazel's daisies.

Bracken wants to attack Sharpetide.  The centaurs of Sharpetide are always stealilng Bracken's pumpkins.

King Frostine must pick a location that is equidistant to each so he isn't showing any favoritism.





He needs your help.  You have taken a map of Intermedio Tierra and connected Crystalgarth, Sunderfen, and Sharpetide.  This has created a triangle.

 



King Frostine set each of your apprentices Brelynd, Jarthan, Tolbain, and Camnar the task to determine where the camp should be located.


 

Brelynd thinks we should locate it at the centroid.
Jarthan thinks we should locate it at the orthocenter.
Tolbain thinks we should locate it at the incenter.
Camnar thinks we should locate it at the circumcenter.

Which place should we locate the camp of water balloon refills?

Use geometry vocabulary to explain this.


If you're not a math teacher, then you can stop reading here!



The following pages contain a map of Intermedio Tierra.

Calculate the distance from the camp to each of the cities.

Brelynd thinks we should put the camp at the centroid.  Use this graph to locate the location (ordered pair) of the centroid.  Be sure to label the midpoint of each side of the triangle.  Use a ruler to draw the medians.  Graph the centroid on the map.

Jarthan thinks we should put the camp at the orthocenter.  Use this graph to locate the location (ordered pair) of the orthocenter.  Use a ruler to make a (GOOD) sketch of each altitude.  Remember altitudes are perpendicular, and should be labeled as such.  Make a (GOOD) estimate of where the orthocenter is located. Label the orthocenter on the map.

Tolbain thinks we should put the camp at the incenter.  Use this graph to locate the location (ordered pair) of the incenter.  Use a compass and a straight-edge to construct each angle bisector.  Remember to label the angles as bisected.  Make a (GOOD) estimate of where the incenter is located. Label the incenter on the map.

Camnar thinks we should put the camp at the circumcenter.  Use this graph to locate the location (ordered pair) of the circumcenter.  Use a straight-edge to sketch each perpendicular bisector.  Remember to label the sides as bisected.  Determine where the circumcenter is located. Label the circumcenter on the map.

I put the same graph paper map on each page.
It's easiest if you use a right triangle.