Posted by: rdkpickle | 03.29.2015


First full week of classes since the week before Valentine’s day! (No joke.) We just got back from spring break and finished up our unit on quadratics with graphing and applications.

Some good stuff:

MondayDesmos Polygraph!

I knew this would be a total blast, and it was. For those unfamiliar with the activity, it’s essentially a computerized “Guess Who” style partner game with a set of 16 parabolas. (Desmos has done some really smart things here, like starting off the activity with a practice round against the computer to see how the game works, and inserting questions between each round so that students can build vocabulary and get better at asking questions.) Other folks have done a great job writing up their experience leading this activity (see Dylan’s post here, which I now realize I should have reread Sunday night when I was prepping, oops) so I won’t go into details. For laughs, though, here was my favorite question asked throughout the day. Brilliant. :)

outsmarting the system

For homework, I asked students to read through some of the sections in their book on graphing quadratics and create a one-page “cheat sheet” synthesizing the important ideas and vocabulary. Here is one of my faves:

parabolas cheat sheet

Tuesday – WODB and Graphing Quadratics foldable

For Bellwork on Tuesday, I used a “Which One Doesn’t Belong?” question from the brand new, awesome site created a couple of weeks ago by Mary Bourassa. We had done one of these style questions before, and I’ve noticed that a wide range of students are eager to offer suggestions for why each one is different – not just the students who typically speak up in class.

wobd parabolas

After the bellwork, we made a foldable to organize all of the info about graphing quadratics that students had read about the night before. I had photocopied some of the info on already to save time, and called on students in the class to help us fill in definitions and work examples as we went.

graphing quad foldable 1

graphing quad foldable 2

graphing quad foldable 3

graphing quad foldable 4

Finally, we practiced graphing quadratics by hand, from start to finish by finding opening direction, width, axis of symmetry, vertex, y-intercept, and x-intercepts.

graphing quad class practice

Wednesday“Make these Parabolas” and groupwork

In our Algebra 1 course we don’t go into vertex form for a quadratic, but I thought my Honors students would pick it up pretty quickly based on their prior work with transformations and absolute value functions. So, I used this Henri Picciotto task “Make these Parabolas” as bellwork – first showing students a bit about vertex form with sliders on Desmos, then writing one equation of a graph as a class.

Screen Shot 2015-03-29 at 12.33.53 PMI turned them loose for about 5 minutes, and was super excited to see how many students were able to create the designs without any other instruction or help from me. (I even had a student ask me after class if there were more graphing challenges like this he could try. Don’t worry, I pointed him straight to Daily Desmos. :) )

make these parabolas 2

make these parabolas 1

make these parabolas 3

make these parabolas 4

make these parabolas 5

make these parabolas 6

After the bellwork, students worked in groups of three on a packet with some questions about graphs of quadratics that came from the textbook. This included some of the skills we had worked on the day before, some questions where they were given the graphs and asked to write the zeros, vertex, axis of symmetry, domain and range, and some pretty straightforward application problems.

On the homework for my Honors class, I included a couple of challenge problems I was hoping would help them to connect what we already studied with quadratic formula and the discriminant to the graphs of quadratics.

quad challenge

Thursday – Review (entire quadratics unit, including solving equations)

Friday – Test

It was a good week. Only a few weeks of instruction remain before we begin preparing for the Algebra 1 End of Course Test. I’m grateful for sunny days and renewed energy to tackle the last few topics in the course.

Posted by: rdkpickle | 03.18.2015


It’s spring break. (Hooray for warmer weather, longer days, and a pocket of time off to visit friends and get things done!)

Today I stopped by the school to accomplish a handful of tasks and managed to finally take some pictures of a few organizational things I have done this year that have made my class run more smoothly and my life a lot easier. Thought I’d share.

student mailboxes

student mailboxes

To cut down on time spent handing out papers in class, I created hanging file folders for each student, organized by class period. All graded papers are returned here, as well as copies of any handouts given when a student is absent. Additionally, I use the table space in front to lay out the day’s handouts and/or trays for collecting work. Students are used to taking care of picking up and turning in papers on their way in the door, before class starts.

agenda/homework board

weekly agenda

I’ve always posted the daily agenda for my classes, but this year I sacrificed some whiteboard space to posting the weekly homework assignments as well. (Sorry that everything is erased in the picture – spring break!) Super helpful for students who want to plan their week, absent students, etc. I used to post homework info online at my old school, but a physical board in the classroom seems to make more sense here.

index cards

index cards

At the beginning of the year, I had each student fill out an index card with some information – name, interesting fact, favorite song (title + artist), favorite book (title + author). I keep these in the containers on my desk to use for a couple of different purposes: 1) as equity cards, to randomly call on students to answer the bellwork (or other times I want to randomly select a student) and 2) to randomly assign seats when I group the desks into clusters of 3 or 4 by setting them out on the desks (students know to find their card.) You can also see that I keep the regular seating charts in this basket – we switch seats after every unit test.

homework binders

homework binders

I keep a copy of the answer key to every homework assignment (with all steps worked out by me) in the 2 binders at this little round table in the front of the room. I project the homework solutions daily as part of our start-of-class routine, but for absent students these binders are a way to ensure they have access to check their own work. It’s also been great to have them during the lunchtime enrichment period – both for students who want to get a head start on an assignment/see if it is going well and for those who really struggled/would like to look over the work. Again, at my last school I used to post answer keys online, but the physical binders work well here. Occasionally students will ask to take photos of a key to use for checking work on their own time – works well, and doesn’t require me to manage a massive online library of files like I used to.

That’s it! Back to break. :)

Posted by: rdkpickle | 02.25.2015

work worth doing

From the fantastic series finale of Parks and Recreation. I love everything about this.

“When we worked here together, we fought, scratched, and clawed to make people’s lives a tiny bit better. That’s what public service is all about. Small, incremental change every day. Teddy Roosevelt once said, ‘Far and away, the best prize that life has to offer is a chance to work hard at work worth doing.’ And I would add that what makes work worth doing is getting to do it with people that you love.”

“Now, go find your team and get to work.”
Posted by: rdkpickle | 02.16.2015

ode to the b-hall copier

your arrival was greatly anticipated:
in the math workroom, we cleared out books for you
had to rewire the electricity
(still can’t use the microwave at the same time)

every day, i arrive around 6:15, coffee and papers in hand:
you’re there, waiting
sometimes i’m first to turn the lights on – i wake you up
occasionally a colleague beats me to greeting you and
you’re warm to the touch

last year, in your absence:
i faced a long walk to the front office, jockeying for the 2 used and abused older models
often finding a line of grumpy teachers, no sympathy for the newbie to the school
who was running on coffee fumes and far too few hours of sleep
(they’d be copying exam reviews at 6:45 in september)

a-hall prospects were never much better
unjamming every third sheet of paper while
cookie store smells wafted in

my mornings begin just doors down the b-hall with you, calmly copied onto
reams of paper – white, pink, yellow, blue
your happy hum accompanies my own
(didn’t even know i needed you)
our enduring love runs 1 to 2 sided, stapled and punched

Posted by: rdkpickle | 02.12.2015

be mine

Happy (early) Valentine’s Day, from my very bored study hall students:


Don’t forget to send a Math-o-gram to your special someone!


Posted by: rdkpickle | 02.11.2015

odds + ends

We’re in the middle of a unit on factoring, and I keep thinking about how rare the factorable polynomial really must be in the wild, and how weird it is that we give them so much time and attention. Students must feel like the unfactorable polynomial is the rare find, when isn’t it really the other way around?

Sometimes I feel like we’re looking at math through a telescope, backwards, in the way we’re asked to spend so much time on certain topics as part of our current high school math curriculum. Who steps back and opens the other eye to ask “why have we focused our teaching on this? And why are we teaching it this way?”

I have gotten lots of really fantastic questions and noticeably increased engagement out of my students the past few weeks, even as the cold February days drag on and everyone is itchy for a snow day that won’t come. I don’t know whether to attribute it to the fact that we’re trekking into new territory after a 1st semester with many familiar topics from 8th grade math, to give myself some props for making better choices in planning good questions and activities, or to credit a level of comfort between me and my students that has finally been reached after 6 months together. Whatever the reason, it has been a good and exhausting few weeks of teaching.

The “Word Problem Wednesday” bellwork problem today was some dumb textbook question about hourly rate and flat fee to rent something, where the total cost and number of hours rented were given for two different customers. A pretty straightforward systems of equations problem that I was surprised to get more milage out of than I expected. Several students had a hard time setting up the equations to model the situation, I think because they are so used to being given the rate/slope and initial cost/y-intercept and varying the number of hours for input and total cost for output. They can build that kind of equation in slope-intercept form in their sleep. This problem had that flipped – the rate and initial cost were the unknowns. A nice moment happened in both 6th and 7th periods when one student in each class realized that a bit of logical thinking could get you the solution faster than the algebra; talking about this strategy after solving the system algebraically with elimination illuminated (I think) some nice connections between the context of the problem and the symbols on the page.

I’m pretty careful to speak precisely about mathematics when I’m teaching. So I was rather delighted yesterday when a student called me out after I asked if any of the trinomials we were looking at had a greatest common factor. What I meant, of course, was “do any of these trinomials have a common factor that we need to factor out as a first step?” but what I asked was “do any of these problems have a GCF?” All but one of my sweet and eager students answered back loudly, “no!” while one kid protested – “yeah they do, Ms. Kernodle. One?!” I’m pretty sure he genuinely felt he had knocked me down a peg or two, but in actuality I just needed a moment to file that great moment away for future use. [Besides, if my my mathematical ego was that fragile I’d be in a lot of trouble.]

We’ve really only seen quadratic trinomials at this point, but you can’t keep kids from wondering “what if?” So I’ve praised and highlighted (with squeals and trumpet noises) the questions like “will we only be able to factor these kind of problems if they look like that? What if that exponent up there on the x wasn’t a 2?” Yeah, “what if,” kid. Thank you for seeing a star or two through our telescope and imagining the night sky.

Posted by: rdkpickle | 01.14.2015

textbooks, etc.

Textbook adoption season has begun.

I can’t get into it, or have too many opinions. Mostly it just makes me sad – for all the things I wish I was doing in the classroom, for all the things I don’t feel empowered to do, for all the ways I feel I am underserving the young adults in my room every day — who deserve more from me. Who deserve more from us.

Dan quotes: “Children should not be asked to practice procedures they don’t understand.” (source)

I hear: “The real goal is for students to learn math well enough to solve math problems in the real world they live in, not on tests.” (source)

And then I get mad because that’s not the world I live in. Teacher evaluations are impacted by scores on state tests that sit shrouded in a cloak of complete mystery — talk about this test and lose your job — talk about this test and the world might end. State tests that will change next year. Students can’t graduate unless they pass these tests. We’re not PARCC or Smarter Balanced; we’ve made our ambivalence on CCSS quite clear. A new legislative session; an unclear future. I used to think these things couldn’t possibly matter – good teaching was good teaching and that was that. Protect the kids in my purview from whims of the day, teach math, engage their minds and all would be fine. But now I just sit and listen to buzzword bingo from a sales rep trying to convince our county to adopt a different textbook, convincing us this iPad app and “worktext” will be the solution. I teach students procedures without.r.t. whether they understand, and I am part of the problem.

What am I doing? Is it worth it? Is it having an impact? I leave school each day with a gigantic list of half-formed thoughts and half-done tasks. If there were 25 more Ms. Kernodles in room B-14, we might have a fighting chance. I hope you’re thinking. I hope you’re growing. See you tomorrow — I’ll be there with a smile and a plan.

Posted by: rdkpickle | 01.11.2015

regarding tomorrow

On sleepy Sunday evenings, it is helpful to remind myself that while a year is a long time, each day can only be lived once. Important that I show up tomorrow rested (caffeinated?), smile, and breathe. Important to set goals and work to meet them, push my students and myself, don’t shy away from tough moments, seek out opportunities for growth. Important that I see the big picture constructed from the small pixels of each day.

“If the product is the goal, then we lose the “we” in this thing we’re doing, whatever this thing we’re doing happens to be.

Once an object is made, a song sung, a story scribbled down on the back of of an envelope, it’s no longer us, merely an artifact of who we were. We become machines, we are machines, in our relentless chase to create the perfect product, make perfection a standard in whatever we do. We want everything to be professional, the new code word for standardized.

The us is in the process, the joy is in the doing.
A song is a song only as a song is being sung.”

— Michael Doyle, A Song Sung

“The meaning of a story has to be embodied in it, has to be made concrete in it. A story is a way to say something that can’t be said any other way, and it takes every word in the story to say what the meaning is. You tell a story because a statement would be inadequate. When anybody asks what a story is about, the only proper thing is to tell him to read the story. The meaning of fiction is not abstract meaning but experienced meaning.”

— Flannery O’Connor

“The only way to explain to you what I experienced when I first read Hemingway is to tell you to read those stories. And even then, you will read different stories. We may read the same texts, but the dhvani that manifests within you will be unique. Your beauty will be your own. If you reread a story that you read ten years ago, its dhvani within you will be new. Poetry’s beauty is infinite.”

— Vikram Chandra, Geek Sublime

I wrote about this before, but I need reminders from time to time. I crave tangible artifacts and struggle to let go and sink in to lived experience. There is joy in tomorrow’s Monday morning, sitting in a quiet classroom at 6:15 am, ready for a day that promises both routine and unique beauty – only to be lived once.

Posted by: rdkpickle | 12.17.2014

smart girls

I think I post this quote about once per annum:

“If you feel your value lies in being merely decorative, I fear that someday you might find yourself believing that’s all that you really are. Time erodes all such beauty, but what it cannot diminish is the wonderful workings of your mind: Your humor, your kindness, and your moral courage. These are the things I cherish so in you. I so wish I could give my girls a more just world. But I know you’ll make it a better place.”

- Marmee, Little Women

Additionally: (xkcd)

Although not permanently.

To ALL of the smart, beautiful, kind, uniquely talented young women I have been given the opportunity to work with each day – I hope you are able to cut through all of the noise, all of the pressures, all of the expectations – and find your own voice speaking with confidence and your own heart acting out in courage. You are all capable of achieving great things. It is possible for you to “change the world by being yourself.” Remember, “if you want to do this stuff, you won’t be alone.”

Posted by: rdkpickle | 11.13.2014

mediocre classroom action

As promised:

Today we wrapped a nice review of solving systems of equations. The 8th grade math curriculum has students spending quite a bit of time solving systems of equations, especially at the feeder middle school, where the teachers are very talented and the students are primed for algebraic concepts. This week, we spent Monday talking solving systems graphically (by hand and on the calculator), Tuesday solving by substitution (my favorite), and Wednesday solving using elimination.

Things that make me happy: students know their strengths and weaknesses. They have preferences re: solving systems, and they are willing to talk about them. They understand the pros and cons of the different methods. They can use mathematical language to describe these. This is good.

Today we: had a bellwork problem (#tbt – throwback Thursday – about writing the equation of a line perpendicular to a given line through a point.)


Had to check HW. I stamp if students complete on time, project the answers (fully worked by me) under the document camera, and students are supposed to check in pen and self-score, correcting any mistakes. We watched the (so great the lyrics are perfect!) “All I Do is Solve” song parody to recap the three methods.

I rearranged the desks with students in groups of 3. 1 paper per group. Discuss, record strengths and weaknesses of each method. Passed out individual copies and collected group work to throw under projector. Some great responses from students!

systems 12

systems 11 systems 10

systems 9

systems 8

systems 7

systems 6
systems 4

systems 2

systems 1

systems 3

(I only included this last one because they put under “graphing on the calculator” – “expensive” and Desmos is out to change all that.)

Afterwards, time spent practicing writing equations and solving systems for some (usually quite contrived) word problems. It’s a good day in my classroom when I talk A LITTLE and my students talk A LOT. That happened today, and while it mostly felt like lip-service because many of these skills were touched upon or even mastered in 8th grade math, it was a good day.

Quiz tomorrow. Inequalities in 2 variables next week. (New for all. On deck: Mathalicious Datelines. Duh.) A fairly typical day. Mediocre. Solid. I came home tired, ready for Friday and the coming weekend.

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