Not Quite the North Pole, but Almost as Fun!

When I first mentioned polar coordinates, did you immediately think "North Pole!" and then "Santa?"  (I know that's the way my mind works every time I think about polar graphs, especially at this time of year!) 

(And since we're talking North Pole, I'll share some KLas family trivia... I've told you that my sister lived in Alaska for a long time, and her wedding was almost exactly 8 years ago...happy anniversary Allison & Steve!  So when our entire family ventured to Alaska for her wedding during Thanksgiving, 2004, we had to go to North Pole, Alaska, shop at the Santa Clause house, and take a picture of the real north pole!)

That's my dad with me...& yes, there are geocaches close by!

Is that Rudolph, peeking around the corner?

Visiting the North Pole is oh-so-much fun, but look at the possible graphs you can make...doesn't that look like fantastic fun, too?! ;)  And you you will be able to create these graphs by the end of the week...no winter visits to Alaska required!

Great use for cardioid graphs!

Since our study of polar graphs and coordinates will be abbreviated, I wanted to provide a few resources for you to help with your studies, so here you go:

Written resources:

• Great examples from a professor at Lamar College
• Another math teacher's resources for students
• From the appropriately named "Math is Fun" website - examples of converting between coordinates
• How to create a polar graph using a table
• Using your calculator to create polar graphs
• An explanation and examples of all of the different polar graphs
• Free graph paper to download

Video/Interactive Resources (most require Java):

• Video tutorial of basics of polar coordinates and graphs
• Great interactive site to explain polar
• Interactive sites to create polar graphs (like our "web assignment") - found here and here and here

If you find another resource that might help a classmate, please list it in the comments below.  If you create a cool polar graph, take a screen shot and email it to me, and I'll post it here!

Aren't polar graphs cool?

I Used to Think... But Now I Know...

Last year, Mrs. Saxon found this quote, which is perfect for our discussion about YET:

“I may not be there yet, but I’m closer than I was yesterday.” – Author unknown

I love the way we've used the phrase YET in class, and I hope we will continue these kinds of reminders.

• Ms. Laster--my homework isn't finished.  YET!
• I don't understand what we're doing in class...YET!
• I don't think I'm ready for the test...YET!
• I don't want to do this assignment...YET!

I first heard this idea at a presentation by Dr. Carol Dweck, who wrote the book Mindset.  (Have you heard me talk about growth and fixed mindsets?  Haha!  Check out her blog!)  I think this idea is very powerful, and it has changed the way I'm thinking and working, not only at school, but also at home and with family.

If you're trying to change from a growth to a fixed mindset, Dr. Dweck has these suggestions, taken from her website:

1. Listen and realize when you are "hearing" a fixed mindset voice.  (I'll never make a hexaflexagon!)
2. Realize you have choice--to think with a growth mindset. (...YET!)
3. Talk back with a growth mindset.  (I'll get it if I continue to practice and if Kelly tutors me!)
4. Take action!  (Just do it!)

Do you have a growth or fixed mindset?  Actually, for some areas, you may have a fixed mindset (mine is sports!) but for others, you may have a growth mindset.  What are you doing to change your mindset?

If you have a fixed mindset about trig identities, what can you do about it?  OR what have you done about it?  If there is something else about our class that you have learned, please share it below in the comments.  Please respond to this post with:

I used to think_______ but now I know________

You may fill in the blanks with something about trig identities or anything else about our class.

Thank you for your time!  I know I'll enjoy reading your comments!

Sinusoidal Functions as Math Models HELP

OK, I know you can do these problems, but it definitely takes some practice!  I've watched several videos and found a few links to help you.  I also created a tiny "video" using the Educreations app.  You should be able to watch my videos just fine from your computer, but if you're on an iPad, you have to download the free app.  Unfortunately, this video does not work on an iPhone. :-(

• My video on solving a sinusoidal equation algebraically involving a cosine.
• When is Fiona an ogre vs. a princess?  Use this video to find out!
• Here's an explanation of a water wheel problem.  Thanks, emathguy!
• This PDF shows several problems worked completely.  The problems are even some of the same ones I've assigned, and at a quick glance, they look good, but I haven't checked all of the work.
• One more PDF of some similar problems worked.  I like this one because it shows a few distinct steps (looking for a max/min point, writing an equation as a sine or cosine, etc.) But again, I didn't work through all of the problems for correctness, so use at your own risk! :-)
• The answers to the "Practice Test" are the photos below, and all steps are shown for the algebraic equations:

The answers to your two practice worksheets are posted on EdLine.

Most of these problems (and the ones from the video) were taken from the green trig book (Foerster) section 2.12.  The odd answers are in the back of the book, of course!

If you find any other great hints, please share in the comments below!

---

From your comments on your exit ticket: one person asked for problems worked out completely, so I posted those equations above.  Another specific question asked about how do you determine whether your graph is a sin x or cos x (or -sin x or -cos x).

• If the first point you plot is a maximum point, your graph is most likely a cosine because your point is ABOVE the shifted x-axis.

positive cosine--starts at a MAX

• If  the first point you plot is a minimum point, your graph is most likely a negative cosine because your point is ABOVE the shifted x-axis.

negative cosine--1st point is a MIN

• If the first point says something about "the middle" (or the average, equilibrium, at rest, etc.) your graph is most likely a sine graph.  If the object then is pulled down (or something similar) your function is a negative sine.  If the object then moves upward, the function is a positive sine.

negative sine--"middle and down"

positive sine--"middle and up"

Cool Math Stuff

A cool thing to watch...
Vi Hart's work is amazing, and I bet she would approve of the word "mathmagical!"  Check out this great video that applies to our trig graphs.  What do you think...is pi wrong?  Should we use Tau?


I could spend hours watching all of her videos, but I know you'll love her Doodling in Math Class series.  Check 'em out!

A cool series to read...
A modern math superhero and professor, Steven Strogatz, wrote an incredible series a couple years ago called "The Elements of Math."  He includes a clip from Sesame Street, compares logarithms to power tools, and had the best titles for each post.  Each one of those articles brought my day to at least an 8! :-)

He just started another series, and the first article, Singular Sensations, was published this week.  I'm looking forward to reading the rest of his essays!

Do you know any other cool math videos, facts, trivia, posts, or links?

I Have Learned...

After two weeks of school, what have you learned so far?  Thinking specifically about our math class, what have you learned about how our class works, how to prepare for the class, how to complete homework, and how to prepare for a test?  What can you do differently this week?  How will you prepare for our next test?

Don't panic if your grade is not what you want at this point.  It's OK to make mistakes!  Learn from your mistakes!  Make new mistakes. :)  Do you have any favorite "failure quotes?"

“Success is not final, failure is not fatal: 

it is the courage to continue that counts.” 

~Winston Churchill

"If you fell down yesterday,

stand up today."

~H.G. Wells

Math Is...

I loved reading all of your Mathographies!  I will re-read them at the end of the six-weeks, at the beginning of the 2nd semester, and probably several other times throughout the year.  Thank you for all of your responses!  I'm looking forward to a great year with you all as my students.

Here's a wordle of your "Math Is..." responses.  Some of you created great similes and metaphors, by the way. :)

By the way, in our two classes, I think we have student representatives from every organization and sport.  I think you were about split 50-50 between which you enjoyed more: algebra and geometry.  (I'm more of an algebra person, myself.)  I loved seeing this comment in numerous papers: "Math is like a puzzle!"  I agree!

YES, I offer LOTS of tutoring, but you sometimes have to specifically get on my calendar...but I WILL find time for you.  And YES, I do offer some extra credit, but I'm still trying to work on my details and changing my philosophy about that.

I know we're going to have a wonderful year learning from each other!  I'm so glad you're in my math class!

My WHY!

This is what it is all about...this is why I teach!

Check out all of these graduation pictures, submitted by our faculty and staff.

Congratulations, Class of 2012!

P.S.--hope you're enjoying your summer!

Learning About Limits

Here's opportunity #2 for test corrections to post for points...and remember, it's all about the learning!

"I am always doing that which I can not do, 

in order that I may learn how to do it."

Take Picasso's belief to heart when you look over your test and make the corrections.  Please address the following in your post:

1. For each question where points were deducted, what mistakes did you make?  Were the mistakes arithmetic (added, subtracted, simplified etc. incorrectly); algebraic (made a mistake with solving an equation or simplifying); conceptual (missed an idea about limits); or careless?  Please be specific, i.e. on #11, I didn't know that indeterminate meant evaluate the limit and get 0/0, so I left that problem blank.  OR I made an algebraic mistake on #4 (d) and #9 because I didn't know how to factor those polynomials.
2. From the problems listed above, please summarize what you have learned from making the corrections.  How does Picasso's quote relate to making test (or HW or quiz) corrections?  How will this beliefs help you during the last month of school?
3. When is a time in our math class (any time this year) that you have been proud about your learning? 

As always, I look forward to reading your posts!  Thanks for taking the time to work and comment.  

All posts are due by Monday, May 7, 9 AM.

Kinder Than Necessary

No act of kindness, no matter how small, is ever wasted.

Ah, that is one of my favorite quotes, attributed to Aesop in his fable, The Lion and the Mouse.

Here's an opportunity to post about kindness, but not for points...just to share favorite quotes on kindness, acts of kindness you've seen or initiated, or thoughts about being kind. (Another great quote: Real kindness seeks no return.)  Feel free to comment anonymously, since this post is just about happiness, kindness, and positive-stuff.  


I'm already feeling the love.   Pass it on, and don't miss any opportunity to be kind!

Wherever there is a human being, there is an opportunity for a kindness.

The Importance of Being Bilingual

Students in my ESL class are ahead of me...they're bilingual, so they could have helped Lucy!




How has knowing another language helped you?  How many languages do you speak?