Thank you, and "See you later"

To my 2012-2013 students:

I wanted to take a few minutes (before Baby Kirch takes over my life) to do what I usually get to do in person every year - celebrate the year and thank all of you for being such great students and people.

From the first day back in August, I know many of you walked into class not knowing what to expect, and being worried by the rumors you heard about my class or the flipped classroom or just math analysis in general.  I didn't know you, and you didn't know me.  First of all, thank you for being open and willing to try a new way of teaching and learning (not that you had a choice...and I know some of you took a while to come on board, but better late than never!).  Your positive attitudes and willingness to work hard helped this year to be so successful.  Throughout the course of this year I think I can confidently say that I had the privilege to get to know each and every one of you individually and that you had the opportunity to get to know your classmates in a deeper way than what you expected.  You have all touched my life in one way or another and I am grateful for that.

I am so proud of the growth I have seen you make as both students and as young adults.  I am so proud of the challenges you have overcome as I have required you to do things you've never had to do before (make videos, have a blog, learn in a new way...).  And I am so proud of how I have seen you learn more than just math skills to memorize, but how math concepts are so interconnected and applicable in life.

More than math though, I hope you take with you from this class those important life skills I tried day in and day out to model for you.  The importance of integrity.  The value of hard work.  The skills of collaboration.  That is what will stick with you, long after you have forgotten that solving an SSA triangle means there could be 0, 1, or 2 solutions (what, we learned that? Yes :)).

We have had our good times and our hard times, our ups and our downs.  I will never forget our last day and how much time and work you put into BK's surprise shower and the appreciation I felt from all of you.  I will always remember the Polynomial End Behavior Dance (that my husband is now famous for) and all the songs I "made" you sing :).  I still remember announcing to you that I was pregnant and having half of you claim you'd already known for a while (so much for secrets!).  There are so many more moments and inside jokes I could continue to mention but just know that I really enjoyed this year with all of you.

While I hope you have learned a lot from me, I hope you also know I have learned a lot from you.  So thank you for allowing me to be a part of your lives this last year.

This isn't goodbye, it is "See You Later"... because I sure hope you will make at least a few treks up Kirch Mountain next year to say hello!

"End of Year Final Exam" details

Your end of year final is worth the last 100 points of your final exam grade.

It should be very easy to get a full 100 points (and raise your grade by getting a perfect score on a test!).  All you have to do is the following:

1. Complete Part 1 (blog post), done well and thoughtfully. - 50 points

2. Complete Part 2 (test creation) and work well in groups, staying focused in class. - 50 points

Keep in mind that 50% of your final exam grade is based on completing the assignments (blog post and test creation), whereas the other 50% is based on the quality of your work.  

• Your blog post should be well-written, thoughtful, grammar-checked, make sense, etc.  
• The tests you create in groups should be neatly done, organized, and easy to read.  
• In addition, your work ethic in class on the days you are given to work on the tests will affect your grade. If you are on task, focused, working well with others, and getting your work done, you can earn the full 25 points in that category. If you appear to be lazy, not participating, absent, not helping your group, etc, you will lose points.

Grading Breakdown:
25 points - Completing Blog Post
25 points - Quality of Blog Post
25 points - Creating one (sr) or two (jr) tests in a group
25 points - work ethic, focus, and participation in class on Wed, Thurs, Mon, and Finals Day
------------------
100 points final exam

PART 1: 

Students must do one last post on their blog.  They will need to submit the link to a Google Form like always.  The submission form link is here.

This is due no later than class time on Thursday, June 6th, 2013.

The post is a letter to a Math Analysis Honors student in my class next year.  

1. What do you want to say to them to help them have the most successful year possible?  
2. How can they best adjust to the flipped classroom and learn to work with all the technology I require of them?  (do you have any specific tips for them or experiences you could share?)
3. What can they expect to be different from their previous math classes?

There is no length requirement but it should be thorough and answer all 3 questions.

I found this quote online and thought it applied to this situation:

Source: reddit.com

If you participated in the “Spring Break Extra Credit Video” assignment, you can embed your video in this post.  You can also record their thoughts on video as well.  However, the post CANNOT be just a video - that is just supplementary.

PART 2: 
The sign-up document link is here. (see below for viewing only of live doc)

The math portion of the final exam for Math Analysis will consist of students writing tests for the different units from throughout the year.  This is done in groups and thus there should be plenty of time to work together, collaborate, and get it all done during class time (not having to bring any of it home!!). However, if work needs to be distributed to be completed at home, please make sure that happens!

Here is what each test must consist of:

1. Students will be put in groups of 3-4 students.  No more, no less. Must be same class period. Signups are first come, first serve on document above.

   
   

   *For best use of time, these should be chosen and signed up (see link above) BEFORE class ends on Tuesday!!

   
   
2. Students must print “Test Templates” for their chosen units from the class blog.  They will need two copies of each Template per group. 
   
   

   **For best use of time, these should be chosen and printed BEFORE class begins on Wednesday!!

   
   
3. Same number and type of questions as their original test for that unit . They must get the original tests from their portfolio.  Original test questions can be borrowed from Ms. McMullen during the class period (ask me for location if needed).
4. On one template, students will write the problems only (directions already on test).  This should be written clearly and neatly by the group member with the best handwriting.  This should be written in pen.
1. They must make up their own problems.  They cannot be ones from original test or from SSS.
5. On the second template, students will write the problems in pen as well (identically to first copy) and will then solve it neatly step by step in pencil on the test.  Work should be done on separate paper first so the copy you turn in is neat, readable, and steps flow clearly.

**For best use of time, students should be splitting the work up among group members and sharing the load. Not all 3-4 students in the group should be trying to write ONE problem or solving ONE problem...big waste of time! However, problems should be checked for clarity and correctness by more than one person in the group.

The requirements are as follows:

SENIORS: Must complete one test between Wednesday and Thursday in a group.

JUNIORS: Must complete one test between Wednesday and Thursday in a group.  Must complete a second test between Monday and Finals Day of the following week in a new group.

There are 16 possible tests.  

• Units A-B
• Units C-D 
• Unit E
• Unit F 
• Unit G 
• Unit H 
• Unit I
• Unit J
• Unit K 
• Unit L 
• Unit M 
• Unit N 
• Unit O 
• Unit P 
• Unit U 
• Unit V

What is Calculus? Answers to your questions...

What is YOUR biggest question about Calculus right now?

15 of the 69 submissions asked some form of the question: "Is it hard?"

• How hard will this really be?
• Will I be able to handle it?
• Is calculus hard?
• is calculus going to be as confusing as it sounds?
• is it very difficult?
• is it as difficult as it sounds? 
• Will it kill me?
• Is it going to be a lot harder than math analysis? 
• Will I survive?
• My big question is, how difficult is it really? 
• Why is it so hard?
• On a scale of 1-death, how difficult is calculus? 
• on a scale of one to ten how much harder is it?
• Is it really complicated?
• Is this stuff going to get easier? Because it looks extremely confusing and impossible to do right now
• My response:  Yes, it's hard.  But it's also awesome.  The way things come together and the cool real-life problems you can solve once you understand the basics of calculus is WAY cool!  It gets easier with time and repetition, and understanding will come... trust me :)

Or, like 5 of you asked, "What is the most difficult part?"

• what will be the most difficult thing about calculus 
• What is the concept most students struggle with in Calculus?
• What is the most difficult thing about calculus?
• is it complicated as it sounds? im kind of nervous about this.... :(
• Why does it seem so complicated, but so simple.
• My response: This is different for everybody.  But in general, just wrapping your head around the concepts
• My biggest question about Calculus right now is, How long does it take to understand the basics of Calculus?
• My response: There's not one answer to this.  It will come with time.  I always tell my students the story of how I visited my AP Calculus teacher as a freshman in college and sat in the back of class finally understanding something he taught me the year before.  Not saying that I was lost for the whole year, but some parts of the conceptual understanding take time.  And sometimes you need to see the whole picture before some of the small pictures make sense.
• I'm just overall confused so I can't give just one question about it. i think I just need a class discussion to get a better understanding. 
• My response: I wish I was there!  Miss you guys!  We can Google Hangout or Skype whenever you want...well as long as I'm free ;)
• how long will it take to understand derivatives and what would you rate as the level of difficulty?
• My response: You will just understand it a little this year - there's not enough time to delve into it.  But, next year you'll catch on :)
• why is calculus so complex?
• My response:  It's not, once you grasp it.  Seriously though... I took it in high school, 3 semesters in college, and then tutored it for 4-5 years after that.  It was so awesome and cool once I saw the connections between everything!  It just takes time...

Or, "Will it apply to me?"

• Does calculus apply to bioengineering?
• Will this help me if i'm pursuing a degree in computer science?
• How can we use calculus in real life? Will there be a career that relates to calculus?
• Will I need it for my career?
• My response: Yes. Calculus applies to everything :).  Well, most things.  Well, most things in the fields of math or science!

• Is calculus very related to physics? 
• will we have to apply physics with our understanding of calculus?
• My response: Yes... in so many ways!!!  If you are taking both courses next year you should really see the connections.

• does everything we see was impacted by calculas somehow
• My response: Calculus is everywhere :)  You just won't know it until you learn it

• what are some real life applications?
• My response:  AP Calculus will be awesome for you :)

• What do all these terms actually mean and how do they apply to real world?
• My response:  Sounds like you are ready to start Units U and V!

From those of you who I'm assuming are so happy trig is over...

• Is Calculus as confusing as Trig?
• Will calculus be as challenging as using fundamental identities to simply expressions?
• My response:  Certain parts may be, but they are different types of math (although highly interconnected!). Calculus does not have you proving or verifying identities, if that makes you happy.

• Is Calculus based on geometry more than algebra and trigonometry?  
• My response: All three...can't really pick one.

• Will the unit circle or anything related to it be involved with calculus?  
• My response:  Knowing the UC will help you

And those of you who have written more in math class this year than in your English class...

• I know that Calculus requires a lot of writing responses, but are the answers always have to be in the write up response form or is it just for certain topics?
• My response: You won't be doing as much formal writing in calculus until your AP exam, but being able to explain your thought process either verbally or in writing is still important.  A lot of calculus will still be algebraic processes - but the understanding behind that is where the true beauty lies.

And many other great questions I'm excited to see you learn about in the next month and all next year!

• Are there various types of problems we need to be aware of?
• My response:  Yes, but in Units U and V we are just going to focus on a few

1. Finding the Slopes of Curves - YES, lots and lots in Unit U!
2. Calculating the Area of Bizarre Shapes - YES, you will get introduced to this in Unit V Concept 5
3. Justifying Old Formulas - A LITTLE, but not a big focus this year
4. Calculate Complicated X-Intercepts - NOT TILL CALCULUS!
5. Visualizing Graphs - A LITTLE, but the big ideas NOT TILL CALCULUS!
6. Finding the Average Value of a Function -NOT TILL CALCULUS!
7. Calculating Optimal Values" - A LITTLE, but the big ideas NOT TILL CALCULUS!

• How is that you can zoom in to a curve to find the slope? 
• My response:  If you zoom in so much, eventually it looks straight.  Try it with your graphing calculator - if you graph any sort of curved polynomial and zoom in on just one point over and over again, eventually all you see in the screen is a straight line.  Same idea

• My biggest question is on how we will use the derivatives and integrals.
• My response:  You will draw the symbols over and over again until you can do it sleeping.  And then it will be summer break.  Just kidding :).  I hope this question is answered in about a month after you finish U and V.

• I want to learn about limits and what exactly they are. 
• My response: Oh yay!!!  Just wait for class on next Friday then!  Starting in Unit U Concept 2-8, limits are your new BFF (sorry Unit Circle...)

• does it deal with infinite numbers?
• My response: Um, yes.  Did you read the material? ;)  Just kidding (can you sense any of my sarcasm in this blog post?).  Calculus deals with INFINITY all over the place!

• how to use the formulas and apply them to the problems.
• What do all these symbols mean ..?
• My response: You'll learn...patience my dear child, patience...

• Does Calculus use similar formulas to that of algebra or geometry?
• My response:  Everything you've learned will come together... so I hope you've learned it well!

• How fun will this be?
• My response: Amazingly fun.  Best time of your life.  Except I won't be there to share it with you :(

• Will we be introduced to things we have never seen before?
• My response: Yes. And it will be scary.  Really scary.  Just kidding - it will be awesome and new and exciting because I think some of the math we go over so many times it's not fresh anymore... and now there will be NEW and exciting stuff!

• Does calculus have many formulas to memorize?
• My response: Yes.  Once you learn what derivatives and integrals are, you will learn the shortcuts and have to memorize a lot of them.

• how does this apply to the whole world and where i will be using it 
• My response: Calculus is everywhere. :)

• How does differential calculus, which deals with the derivative, correlate with integral calculus?
• My biggest question... what are derivatives and integrals used for. I've heard so much about them, yet learned so little."
• My response:  Derivatives and Integrals are "opposites" of each other.  In fact, before learning the term "integral", you will refer to it as the "anti-derivative".  The real life applications are quite different - while derivatives can be used to find instantaneous velocity and acceleration of objects, integrals are used to find areas and volumes of weird shapes.

• Will we be working with chain rule this year? (:
• My response:  Not this year... but next year!

• Will there be shortcuts that will make our lives easier when solving Calculus problems, and if so, will these be taught to us?
• My response:  Yes.  Shortcuts exist.  You will not be taught them this year, but you may discover them.  If you discover them, Mrs. Contreras has been told to NOT tell you if you are right or not ;).  Next year you will learn the shortcuts... but you must understand the LONG WAY first (sounds like my whole class, doesn't it?)

• This year, in math analysis, it seems as though we only dealt with ideal situations rather than irregular. How different is next year going to be???
• Is Calculus a lot like what we learned this year just a lot more complex?
• So it's like math analysis but more complex?
• My response:  Good point!  That's because Algebra is "more regular, less real" because it's easier to comprehend.  All of your skills will still be used, but now you will be applying it to different types of situations that are not so ideal... and seeing that all the skills your teachers have made you learn finally are worth it!

• how much content will we cover in calculus?
• My response:  A lot. But it's all awesome.

• If we have to split the complex figures about to find the values for them, couldn't we still use formulas we learned from before to solve them by putting them into shapes we know?
• My response:  Hmmm you might want to use that knowledge on Unit V Concept 5.  Good starting point!

• What's a derivative
• My response:  Unit V Concepts 1-4 will be your best friend!

• Can you teach me how to calculus? 
• My response:  I'll do my best on my videos...

• what is the basis of calculus? Meaning, where did the derivative and the integral come from? how/where did they originate?
• My response:  Sounds like a great question for Google :)

• How complicated are derivatives and what level of trigonometry is involved?
• My response:  Derivatives - understanding them is hard at first.  Solving them is basic algebra.  Trigonometry - certain parts of calculus will have you use trigonometric formulas instead of algebraic formulas, but it won't be as big of a focus as it was this year.  Remember, this class was NOT "pre-calculus" for a reason.  It was "Math Analysis" because it's a combination of "Pre-Calc" and "Trigonometry".  So, we had quite a long time on trig because that's what the course entails...

And to those of you wondering if I actually had a plan with what I was teaching you this year :)

• is it just an extention on pre calc?
• My response: It IS extensions on Pre-Calc... but it's not JUST extensions on Pre-Calc... it will go further than we were able to ever go.
• Will some of the concepts that we learned this year be in Calculus also?
• My response: Yes... all the algebra skills we've used you will use again... but the most easily transferrable concept is the DIFFERENCE QUOTIENT WOO HOO!!
• Where do you start in order to begin understanding the concepts of calculus? 
• My response: Right where I'm having you start :).  We will first learn about limits and how everything in calculus deals with infinity in some form, and then tie that into derivatives.  Lastly, we will see how the area problem is set up... but we won't go into the calculus of it yet.
• Will all the material of calculus tie/ relate with each other to make the learning process more understandable? 
• My response: I think it does.  I hope you at least see the connections between the concepts I am having you learn in U and V.
• Is everything we already know building blocks? Or will it be thrown out the window as calc deals with new ways of finding answers.
• My response:  It's all building blocks.  I wouldn't teach you something without a purpose...it may take a while to see all the connections, but they are there.

PLEASE POST FOLLOW-UP 

COMMENTS AND QUESTIONS BELOW :)

Trig is...

If you haven't added your thoughts yet, please do so here.

Unit T Test "hints" from class Wednesday

Today I went over some pretty important stuff.  While studying and completing your Practice Test (12 graphs; you do not have to do the review problems!) make sure you consider these questions...

PART 1: Unit Circle and Parent Graphs

• You must be able to accurately draw all six trigonometric graphs (no shifts, parent graphs) on a labeled axis very quickly.

(Big Thanks to Noemmi G. period 4 for the video!)

PART 2: Shifted Trigonometric Graphs and their parts

• You will not be filling out complete templates for every problem.  Instead, you will be given 12 functions and I will ask for a certain part or two for each of them.  Namely, I will be focusing on:
• Period
• Sin,Cos,Sec,Csc - 2pi/b
• Tan,Cot - pi/b
• Amplitude
• Sin,Cos = |a|
• Sec,Csc = no amplitude, BUT we use the amplitude of |a| from cos,sin (respectively) in our graph
• Tan,Cot = no amplitude
• Domain
• sin,cos = (-inf,inf)
• csc,sec = x cannot = asymptotes... and to find the asymptotes you have to be able to see the graph to see where sin,cos = 0.  Plug into the formula x="first one" +/- HALF THE PERIOD(n)
• cot,tan = x cannot = asymptotes...and to find the asymptotes you DO NOT have to do any graphing! Just use the formulas b(x-h) = pi/2 (tan) and b(x-h) = 0 (cot) and then plug into the formula x= "first one" +/- THE PERIOD(n)
• Range
• sin,cos = have to graph it and see where the highest and lowest points are; start low to high, will always be [y,y]
• csc,sec = have to graph it and see what is going on.  Will be (-inf,y]U[y,inf)
• cot,tan = (-inf,inf)

PART 3: Free response questions

• Three questions found somewhere within the "Big Questions" will be on the test.  There will be space to draw a picture up top and then plenty of writing room :)

FINAL EXAM - UPDATES AND REMINDERS

Your final exam will be taken the first week of May.  Here are some dates for you:

Monday, April 29th - work on review packet in class

Thursday, May 2nd - review packet is due by the end of class.  You will not be physically turning it in to me that day, but I will be checking to see if it is complete.

Monday May 6th-Wednesday May 8th - take final exam in 3 separate parts.  Monday and Tuesday will be the "Math Analysis Part" which you can use your portfolio on.  Wednesday will be the "CST part", which is no notes and no portfolio.

You will be turning in all your review packet work to Mrs. Contreras on one of those three days (she will let you know when).

I do understand that May 6th-8th are also AP exams.  Most of the exams are in the morning and you should be back for class in the afternoon.  In the instance that you miss one or more days of the final exam, Mrs. Contreras will plan ONE make-up day after school that first week.  You must show up to the make-up day or will receive a zero on that part of the exam.  No exceptions - she will not be offering multiple opportunities for irresponsibility or forgetfulness.


Review packets can be found here. 

You must print your own copy of the review or view on your electronic device.  All work must be done neatly and numbered and will be turned in before the exam.

• Parts 1 and 2 cover "normal" Math Analysis material and you will be able to use your portfolio for it.
• Part 3 will cover CST questions for your summative exam, which reviews Algebra 1, Geometry, and Algebra 2.  Plan to ask a lot of questions on these problems, especially the Geometry ones because it has been a while!

Answer keys and help can be found here (will be updated as I add more; please let me know if you want me to work out any of them) 

• 2011-2012 "Final Exam Chat" document - lots of great questions answered here from our discussion last year. 
• Algebra 1 #90  http://edcr8.co/IfYaoe
• Geometry #90 http://edcr8.co/J0oqiL
• Geometry #91 http://edcr8.co/J0olvD 
• Geometry #92 http://edcr8.co/J0olM1
• #10 2nd semester finals review
    http://edcr8.co/IgV2ol
• Algebra 2 #39 http://edcr8.co/IgZ2VT

Unit R Test - Concept 2 (#36-37)

A couple of notes on these problems... and a great opportunity I wouldn't pass up.

• Most of you lost up to 20% of your test percentage on these two problems alone (they were worth 10 points each)
• Edmodo note sent out with names of students who got 20/20 in this section and do not need to do anything.  You will have to log in to view the note here. 
• Drawing the triangle appropriately and correctly was worth 6 of the 10 points for each problem (3 points each triangle).  This includes:
• Correct quadrant
• Correct signs (+/-) for each side length
• Left and Down is negative
• Up and Right is positive
• Hypotenuse is always positive 
• If you got the correct answer randomly without the correct triangles to support it, you did not receive credit because you could "randomly" get the right answer without the right signs on your triangles.

With that being said, 

Please go back and review Unit R Concept 2, as well as how to draw appropriate quadrant triangles. See picture below for review.

Because knowing how to appropriately draw triangles is essential for your success on the Unit S Test as well, I will allow you to come in and re-do #36-37 on Tuesday at 3pm.  Sorry, with my schedule, you will only have from 3pm-3:30pm on Tuesday alone to do this, so please make plans accordingly.  It will only be 2 problems so I can't imagine it taking more than 10 minutes.  You will not be able to do this at lunch, I will have ONE TIME when you can come take care of it so you must adjust your schedule accordingly.  The only exceptions are my seniors with no 6th period, who will be able to do this at the beginning 6th period. You WILL NOT be able to use any notes, but I will project the 6 sum and difference formulas on the screen.

You must print this page and bring it with you on Tuesday after school.  The top portion must be filled out before arriving after school.  Nothing else can be written on the page.

You can make up #36, #37, or both.  You will receive your tests back Tuesday in class to check your specific scores on those concepts.