Thursday, October 29, 2015

Related Rates Related to You

We did these problems today in AP Calculus.  Part of the problem I have with related rates questions is most of the time they seem so contrived and impractical.  Like, why do I care what rate the radius of the balloon is increasing given the rate the volume is increasing?  So, I had some fun with these types of problems.  The kids loved seeing their names in the stories.

I put them in groups and assigned one problem per group (making sure that if a student was in one of the word problems, s/he was in the group working that same question).  Answers are included so the kids could check themselves easily.  Then I had them make a poster.  These are some from last year:

Afterwards, I asked the students to read the other problems and then use the posters to write the solutions in their notebooks.

Here are the problems I used (I'm sure I stole several of them from other people, so let me know if I owe you credit).  I always change the names for each section.

Download here.

Wednesday, August 19, 2015

What they want is our time

Disclaimer:  I started this post a couple weeks ago and am just now publishing it.


It's August, and I feel like I haven't done nearly enough to get ready for the beginning of school.  Most of my summers have been spent in conferences around the state and/or planning for that new prep I'm about to take on.

This coming year (Year #7) will be my first year teaching exactly what I taught the previous year, and so I've let that be an excuse just to be lazy this summer.  That and I'm pregnant, which I feel is a valid excuse for just about anything these days.  And so now, it's August.  And because I'm prone to guilt, I've been feeling rather convicted about this laziness.

Until a student of mine called me up today.

Her reason?  She wanted to ask my permission to call me her mentor, because that's what she's been calling me all summer as she's counseled young girls at camp.

I don't do particularly well with flattery.  Don't get me wrong, I enjoy it as much as the next gal, but in the moment, I never know how to respond.  I'm trying this new thing where I just sit and listen and let the person tell me what they want to tell me.  Usually all I can muster up is a weak, "Thank you," or "I'm so honored..."  It all sounds so pathetic in light of their gracious words.

As I sit here, trying to remember exactly what this girl told me, all that's really coming to mind is her gratitude to me for taking time for her.  That's all.

I'm attempting to put my thoughts into words mostly for my future self, as a reminder.  Rebecka:  the hours you spend planning a single lesson or activity, it's all well and good (and necessary--the kids need to see this passion).  But the time you spend helping your kids understand how important they are to you...that's what they really remember.

So, my advice to both my current and future self:  Stop stressing so much.  Stop feeling guilty for taking time to relax and recuperate.  And start focusing on how you'll love on this year's group of kids.

Sometimes I think we live under the impression that we can't be too friendly or too nice or too "buddy buddy" with our students:  we're their teachers, not their friends; we need their respect.

Yes, we need their respect.  But, have you ever respected someone you didn't like?  Especially as a kid or as a teenager?

I want to take more time this year to ask about my kids' families, pets, hobbies, and jobs.  I want them all to know that I'm invested in them and that I care about them.  Because that's what they'll remember about math class.

I don't really care whether or not they remember the Fundamental Theorem of Calculus ten years from now.  I care about whether or not they felt safe, loved, and welcomed in Mrs. Peterson's classroom.  That's what I want them to remember:  that they were a priority.


So, as the first day of school approaches tomorrow (AH!), my prayer is that we would bond as a class and as friends faster than ever before.  That mutual respect, love, and admiration would abound.  That we would all recognize that every single person has something to teach us.  That we would be better together than apart.

That I would give my kids my time and my undivided attention.

Tuesday, June 16, 2015

What we did post-AP Exam

I still had a few weeks of class to fill after the AP Exam.  I definitely wanted the kids to still be working, but not necessarily on calculus and not to the point where they had tons of homework.  So, this is what we ended up doing:

1 day to go over released FRQs
1 week to work on Shoe Box Projects
3 days to work on End of Year Folders and fill out surveys
1 week to work on Serve + Create
1 day for goodbyes :(

Here's what we did for the shoe box project.  The kids were asked to create a rate FRQ and then make a shoe box scene that went with their story (like in elementary).  I think they had a lot of fun with it.  We basically just modified an Algebra 2 assignment, so if I owe you credit for this, please let me know!

Click here to download file

Here are some of their finished products:

This one had involved the rate at which Mrs. Peterson adopts cats vs. the rate at which she donates them.
If you can't tell, that's me holding to two cats...

For the End of Year folder, I asked students to correct all quizzes and tests from the semester (I asked this of them last semester, too, so they were expecting it).  Sure, this would have been good to do before the AP Exam, but it just fit better after.

I also had them fill out two surveys:  one that was just a general "What should I keep/change for next year?" (here) and then one that asked them fill in positive adjectives for each of their classmates (here), which I used to create Wordle bookmarks for end-of-the-year gifts (thank you, Pinterest). More on this at the end of this post.


Finally, the week before finals, I gave a totally non-math project, which I called Serve + Create (details here).  I told the kids that in the midst of both joy and sorrow, it's important to learn how to cope with change, and that two of the best ways I know to do that are (1) serve someone else and (2) make something.  So, that's what I asked the kids to do.  I gave them very little guidance.  I wanted it to be organic and come from them.


I wanted to take a day just to say goodbye to my lovely kids, many of whom I've seen every school day for the last two years.  So much is written on things to do the first day of school, but I feel like we are lacking in material on last day of school activities.  Especially if you have seniors, I think it's so important to make a big deal of the last day, because you accomplished a lot together.

So, for the last day, I first passed out my junior and senior letters, which were not too different from last year's letters (here).  One thing I did add was advice from the Class of 2015.  I gave the seniors a whole white board and about a week to add their advice/wisdom for us.  Afterwards, I took a picture and copied it to the back of each of the letters:

{This might be a good time to mention, again, if you've never used the app DocScan, I highly recommend it!  Covert pictures to PDFs easily.}

After passing out the letters, I read Oh, The Places You'll Go! by Dr. Seuss.  

Next, I passed out these bookmarks that had a word cloud with each of their names and the adjectives their peers and I had entered for them in the survey:

I used Word It Out because it was the first word cloud generator I found that wasn't blocked on my school computer, but there are several good ones.  I just had to play with the settings a bit.

I read each one out loud.  The kids seemed to love this.

Finally, I just spoke for about a minute (this is all my heart could handle) about what a great time I had being their teacher, and how excited I am for their futures and for the futures of the people whose lives they will certainly change for the better.  The last half hour kids spent saying goodbye to their friends and to me.  Lots of pictures were taken and some tears wasn't an easy day, but I very much wanted to make the last day of calculus something meaningful, for both the kids and for myself.

These are world changers.  Of this I am certain.

Friday, June 5, 2015

How I did homework this year in PreCalc...

I stole this idea entirely from the teacher who taught APSI last summer.  I was intrigued by it, so I implemented it in my PreCalc classes this past year.  My kiddos are begging me to extend the concept to AP Calculus next year because they loved it so much (you'll see why...).  I'm undecided.  I thought I'd write about it and get your take...

The premise of this homework set-up is that kids get rewarded for doing homework instead of being punished for not doing homework.  This is how I ended up doing it, which is a slight modification from the way the APSI instructor did it.

  1. Once a kid completes a homework assignment, I spot check it for completion and ask if she checked answers in the back of the book (assignments are due the day before quiz/test day).
  2. If the homework assignment looks thorough, I give the kid a hole punch on an index card (I have a star-shaped hole punch, but you could use a stamp, stickers, etc.).
  3. One a kid has ten hole punches, she gets a 100% on a quiz grade (I simply added extra quizzes, called them "Extra Credit Quiz 1," "Extra Credit Quiz 2," etc., and excused everyone from it until/unless she got 10 hole punches).
  4. That's it.

  • I will probably make these Extra Credit Quizzes worth only half a regular quiz grade next year (which should increase their overall percentage by 0.5-1 on average, instead of 1-2 percentage points on average).
  • My APSI instructor only checked assignments on certain days (and hence only checked certain assignments), but I found it easier just to let all assignments count towards the extra credit.  If I didn't have time to do homework checks one day, it wasn't a big deal--I told the kids to just remind me the next day.
What I liked...maybe even loved:

  • I hardly ever had to grade homework!
    • I still had to have at least two grades in a week, so I would take smaller in-class assignments for a grade (typically as a review of that week's warm ups).
    • Occasionally, I would give worksheets that I counted for "an actual grade" in the gradebook and not as a homework check.
  • Kids were super, super honest.
    • When I took homework for a grade, I saw kids half*** their homework ALL THE TIME.  You know what I mean.  Sometimes a kid would just miraculously go from Question 3 to Question 43...and hope I wouldn't notice.  Or, somehow they'd get the answer from the back of the book with no supporting work.  Yet, with this new method, kids would tell me almost daily, "I'm done with 8.3 but I still have two more questions on 8.4." Because there was no punishment for not finishing those two questions (and because they still had more time), they seemed to be much more up-front about how much work they had actually done.  This was good for me, sure, but I think it was also really good for the kids to voice what they still had left to finish.
  • I'm not sure any more or any fewer kids did homework when it was presented in this manner.  You'd think a lot of kids would just stop doing homework, but I honestly don't think it was any more than normal. There are kids who will do the homework no matter what and kids who will not do homework no matter what.  I don't think this changed that.
  • Kids felt less pressure.
  • I try to give kids as much time as possible to work on assignments in class, where they can ask me and their peers questions.  Because of this, they all typically have at least a very good start on their homework.  Is it really the end of the world if they don't finish every single problem?  Especially if they're working hard in class...? I'm asking in sincerity.
  • No one asked at the end of the year if there was any extra credit they could do to raise their grade.  Of course, I warned them at the beginning of the year that this was it. 
My hesitations:

  • Maybe some kids are falling through the cracks?  I'm unsure.
  • If I do implement this in Calculus, then something else has to change, because I'm currently not giving quizzes for a grade either.  Their entire grade cannot depend on tests!  One thing I do want to change is make their quiz corrections a grade (due the next day as opposed to at the end of the semester).  I've also thought about giving short MC assessments every Friday, which could certainly count as a grade.
  • Calculus is a different beast.  Most kids need to wrestle with concepts, and that takes time.  While I prefer that my kids do most of their work in class, they do need to set aside some of their own home time to really understand what's going on.
So...what are your thoughts?  Is this worth extending to calculus?  Or at least trying it?

I'm fairly certain that I'm keeping this method in PreCalc next year, but what about for Calculus?  Help!

Monday, June 1, 2015

Serve + Create

I've posted a lot about our AP Calculus AB final project (Serve + Create) on the One Good Thing Blog; it was a two-part project in which students were asked to (1) serve someone else and (2) create something they enjoyed making.  I haven't explicitly written what I gave the kids or where this idea came from; hence, some details about the project:

I gave the students four class days (there was also a three-day weekend in between) to work on whatever they wanted.  I told them that some of them would want to use this time for their final project, but most of them would probably want to work mostly out of class.  So, I didn't feel too bad giving a few "free days."  Several did work on their art project and several went to serve a teacher during these four days.  Others relaxed and played math games and worked entirely on the project on their own time.

This idea stemmed from an interview I listened to with Glennon Doyle Melton (here).  In the interview, she was asked how she deals with all the hardships she sees and reads about on a daily basis.  How do we get ourselves out of our own misery?  She said she always comes back to two things:  art and service.

I couldn't agree more with Melton's advice.  I had never realized that art and service were two ways I dealt with change and loss, too.  Thus, this interview was a catalyst to a project I've been mulling over for quite some time...


UHS AP Calculus AB Final Project

You’re almost done!  I recognize this can be a stressful and bittersweet time for both juniors and seniors alike.  While I hope you’ve learned lots of calculus throughout the year, there are things that are more important than mathematics:  one of those being—How do you cope with change?  There are two ingredients I want you to practice before you leave our class—service and art.  When life gets chaotic, one of the best things you can do is remember that there are others in this world who are suffering, and do something to help them.  Furthermore, creating something through an art medium is a great way to express yourself, especially in the moments when you’re feeling overwhelmed.  As a way to encourage you to practice both the art of service and creativity, I've made this our final project for the year (worth 25 points in the test category).

SERVE:  Think of something you can do that would positively impact someone else’s life in a significant way.  Spend no more than $20/person.  You may work in groups or as individuals. 

CREATE:  Create a piece of art that you’re proud of.  This is not limited to drawing or painting:  think outside the box!  Express yourself in a way that is unique to you.  Please work individually on this.

On Thursday, May 28, you will be asked to share both your projects with the class.  I do not want to stifle you in any way, so grading will be based on completion:  do the project and you’ll get full credit.

I'm so proud of all your work this year.  It’s been an honor to be your teacher!


I've never done anything like this, but the results were absolutely wonderful.  As I posted on the One Good Thing blog, here are some of the things the kids shared on Thursday.  They...

  • Helped teachers in elementary and middle schools
  • Played with and loved on elementary children
  • Made cookies, brownies, spring rolls (not even kidding) for the class
  • Sang a song for our class
  • Painted a picture only using spray paint
  • Made calligraphy signs
  • Passed out cards to fellow students with hand-written positive sayings and Hershey Kisses on them
  • Passed out burgers to homeless
  • Made origami
  • Wrote poems
  • Drew pictures
  • Mowed lawns
  • Visited nursing homes
  • Bought flowers for their moms
  • Threw a party for their families
  • Helped renovate a run-down church
  • Made a “Countdown to the 2016 AP Calculus Exam” for their calculus teacher (<3)
  • Made canvas art for their dorm rooms
  • Made canvas art for their teacher
  • Donated money to a student from El Salvador looking to pursue higher education
  • Made French food
  • Made a wreath for their room
  • Made food and cards for their teachers
  • Made shirts for their teammates
  • Made jewelry charms for their friends
  • Volunteered time to help coach the pom squad
  • Worked on a car for free
  • Made a “College Survival Kit” for friends
  • Made a poster to celebrate twelve years of friendship
  • Posted slips around school with motivation sayings for students to take
  • Made a Father’s Day platter
  • Bought reading glasses to accompany a family member going on a missions trip
  • Played the recorder for the class
  • Made paintings for a newly-married family member
  • Gave flowers to teachers
  • Helped at a cultural fair
  • Taught the class a hip-hop dance (this was a dream come true for me…so fun!!)