Is this thing still on?


Ahem. Mic check. One. Two. Three. Is anybody out there?

Holy cow—has it really been since 2015 since I blogged??? Oops. Time to dust off the ole wordpress and put some stuff out there.

I just returned from scoring AP Statistics exams and after re-connecting with some dear friends, have felt compelled to try and get back into the online math universe and post some stuff for other people to read. No promises for anything good–just stuff. I am going to *try* and blog once a week. We’ll see how long that lasts. Since we are in the midst of summer (glory, hallelujah) I am working on plans for the upcoming school year. I’ll be teaching AP Stats, Pre-calculus, and a new course called Financial Math. In addition, we are switching from trimesters to a hybrid block/regular schedule so, yay. I think.

Anyway…this post is about entrance cards.

Last year I taught precalculus for the first time and I knew (from talking to the calculus teacher) that one area which historically had been a problem for many students was that they didn’t truly know the values of the exact trig functions. They had been asked to “memorize” the unit circle but we all know what they did. I’m sure they took a couple of days to “build” it, either with paper plates and adding machine tape or with technology of some sort or with some other interesting method designed to help them see the values and understand where they come from. They were then told to memorize those values. The quiz to assess knowledge was probably a blank unit circle and they had to fill it in. Perhaps multiple times, perhaps only once. And BOOM. They “knew” the unit circle. And then class moved on to identities and perhaps referenced a unit circle value once in a while. I did not want my students leaving my class without at least making some attempt at doing it better than that. So…

I started with the fairly traditional “build-the-unit-circle” stuff; adding machine tape, paper plates, and lovely special right triangles to trace. We measured, labeled, discuss, identified patterns, all the good stuff. Then I said, “Now you have to memorize all of this.”  After all the moaning and groaning subsided, I shared a couple of memory tools that I knew or found on Pinterest and set them free to memorize. To help them practice as well as know that I really was serious about this, I decided to orally quiz them every day at the start of class. I created a set of flash cards (available below) and as students came to the door, I held one up. Initially I thought students would stand in line and wait their turn, but it ended up being a big cluster of people and the first person to get the question right got to go in. Everyone else had to wait for the next question. I cannot tell you how beautifully this worked. So much better than I had even imagined. Students knew it was coming. Every day. For almost two weeks. Some of them learned the values quickly, others took more time, but they all knew they needed to know this stuff. For those that were struggling, I was able to work with them one-on-one in the moment. Sometimes they just needed a little encouragement, sometimes we needed to revisit the memory technique they chose to use and see what misconceptions they had.

I did not use all of the flash cards–if you open the file you will see they include all the special angles around the entire unit circle. My goal was for students to know quadrant I and the axis angles, so I stuck with only those. The first few days, I only used cards with degrees/radians and had them practice converting the key angles back and forth. Then I added the trig values. Finally, I created some (sorry–just wrote on index cards) for inverse trig, prepping them to solve equations.

Trig Entrance Cards.Exact Unit Circle Values

Since I experienced such success with this topic, my first thought was, “How can I capitalize on this and use it more often, and in more classes, next year?” I realize this is only good for things that need to be available in “quick recall” format, but I’m thinking there are some skills precalculus kids need to be able to do that with. In stats, I’m thinking about quick vocabulary checks or basic formulas that need to be committed to memory. I know this won’t work for getting at deep understanding, but it gives students motivation to know at least something and I get to interact with each student individually EVERY time I use these. That’s a win in my book.

Here’s my current brain dump…I hope you’ll all add some ideas and suggestions.


Logarithms; Evaluating nth roots; Factoring quadratics and higher order polynomials;

AP Statistics:

Describing data (Shape, center, spread); Classifying data (categorical/quantitative); Estimating the center of a distribution; Which measures should you use for a given set of data (standard deviation and mean OR IQR and median); Interpreting slope, r, r^2, y-intercept; Choosing the right probability setting (and, or, conditional); which inference test; Should you reject/fail to reject the null (from p-value, from a critical value); Have a calculator available to check for basic skills (finding a 5 number summary, creating a histogram, finding mean and standard deviation, etc);

Thanks for reading. Maybe I’ll make it back next week.

Bellringer thoughts

I’ve been considering the use of bellringers in my classroom and have decided that I’m not a huge fan. I think the idea behind the practice is great (something for the kids to do to give me time to start class; a method for multiple choice practice; good review of prior content; a way to introduce new content), but implementing it effectively has not been a strength of mine in the past. I acknowledge that I need to be more intentional in ACT/AP practice, and have been pondering how I can use the first few minutes of class more effectively to meet the demands of multiple choice practice. [This is not a post to debate the pros and cons of standardized testing. It’s a plan to address the fact that they exist and that I live smack dab in the middle of them.]

Here’s what I think I am going to try out for the next 3 weeks (that’s how much time until the Christmas vacation).

My students are already arranged into groups of 4, 5 or  6, depending on the size of the class. I have no more than 6 groups in each section. I also teach Algebra 2 and AP Stats, so only 2 preps to consider.

As students enter the room, each one will get 3-5 multiple choice questions and I will have a timer running for 8-10 minutes. Students will work in their groups to agree on the solutions to each problem. Once agreement has been reached, they will submit their answers to me (either on an index card or using technology–I haven’t decided on that yet) and I will tell them how many they have right. They will have until the timer goes off to get as many right as they can. At the end of the time, they will get one “point” for each correct response. The team with the most points at the end of the 3 weeks will be declared the winner.


I’m hoping that the competitive aspect of it will motivate students to want to do well and that the group aspect of it will allow all students access to the questions and allow me use use some higher level questions that I might not normally attempt to incorporate into a bellringer. I am also hoping that the timer will keep me from letting this activity take over the class period.

I’ll give it three weeks and see how it goes!

#invertit-zero product property

I just returned from NCTM Nashville and wanted to put some things I’d learned into practice immediately before I forgot about them. One of those was from @k8nowak and the idea of inverting a lesson. Unfortunately (thanks to the lovely Nashville traffic) I didn’t make it to her session, but I was able to chat with a friend who was able to fill me in. The big idea, as I understand it, is to invert the order of a traditional lesson by giving students a “puzzle” then asking them to continue it or add to it. The generalizations or rules are saved for the end, after everyone is familiar with what is happening in the problems. Here is my version of it…

Our topic: the zero-product property

Students already know how to factor quadratics

What I did:

I started class by showing this this chart, and briefly explaining what it meant; namely, that everything on the slide was true, and that there were no problems for them to work out. Instead, I was giving them the problem, the answer, and what those two pieces of information told me about the graph of the function.


I asked them to study the chart silently for 1 minute, then turn and share their observations with their neighbor for 1 minute. Students then had a small white board on which I asked them to respond to questions similar to these:

Make up a new problem, solution, and graph that could be added to my list. [After viewing their responses, I selected 3 to add to the list above]

Make up a problem that would have 2 positive solutions. [Again, adding a couple selections to the list]

Make up a problem that would have a graph that opened downward. [Yep, add a couple more].

Make up a problem that would have one non-integer solution [Once we finally agreed on what-in-the-world I meant by that difficult vocabulary–insert sarcastic grimace- we had the opportunity to talk about why a factor of (x-1/2) is correct, but most likely would not present it self in that form. Students quickly figured out that it would be (2x-1) in most contexts]

After several questions and responses, and once I was fairly confident that the students knew what they were doing, we took some summarizing notes. Here’s the cool part: they didn’t really need me for this part. They knew what was going on and were able to put it in their own words. Rest assured math friends, I went over it, making sure we used good vocabulary and had solid examples to refer back to, but they had it.

So, from there, I asked them what they thought might be done to make the problems a bit more challenging. Because, let’s face it, that was pretty simple. It didn’t take more than 10 seconds for someone to say “put something besides zero on the right side of the equation” and about 25 seconds for someone else to say “give it to us un-multiplied” (we are still working on developing that vocabulary). Anyway, what a great natural sequence of events for me to give them more challenging problems. AND THEY WERE READY FOR IT!!

Just to complete everything properly, I gave them the following:

Circuit Training. ZPP

Thanks @k8nowak for sharing this approach and giving me a way to help my students “discover” mathematical concepts.

**Circuit training was a new term for a style of sequencing problems learned at NCTM from a session by Virginia Cornelius.

Preparations for a new year

It’s time to finalize preparations for the new school year. Sad that I am doing that and it is still July, but, oh well. That’s the way it goes.

Tonight I have been pondering my grading scheme and how to tweak it for class this year. I have done some hybrid versions of SBG in the past, but last year I felt like I drifted too far back into the world of traditional grading. Here are my thoughts for this year:

[I teach Algebra 2 on a trimester schedule. Algebra 2 is a 3 trimester course, but students move from teacher to teacher during the year. I may have a student for 1, 2, or all 3 terms.]

A student’s final grade will be portioned as follows:

5% ACT warm-up questions  M-Th students will get 5 questions to work on. Grades will not be taken. Friday students will have a “quiz” consisting of 10 questions similar (but not identical) to those completed during the week.

20% Cumulative Common Assessments  These tests will be given every 4 weeks (so there will be a total of 3 during each term); exams will last 2 days. I am either going to split the 2 days into multiple choice & free response OR calculator & no calculator. These exams are cumulative for the entire year and the grades are final. No reassessments are permitted. Obviously, this is the nonSBG portion of the course.

70% Learning Target Assessments  These will be given every Friday (?) and each LT will be assessed twice and reassessment will be encouraged (and required for scores below a 3 on a 4 point scale). I am struggling between whether or not I should average the two scores, count the highest score, or count the most recent. I know the reasons for using each method…averaging should make each assessment “count” so they actually study and prepare for it…counting the last score is a better indication of what they really know…counting the highest gives them credit for having learned the material at some point.

5% Soft Skills  This will incorporate tardiness, timely completion of assignments, classroom participation, etc.

Well, that’s the brain dump for now. I’m not sure I worked through anything, but at least I have a plan on paper and that’s a start. Sometimes that’s just what it takes to get the ball rolling.

Exit Ticket Stand-bys

Wow. Two posts in a month. Y’all better watch out. I’m on a roll.

My to do list from my brain dump is progressing rather slowly. I have managed to clean a majority of the house (at least the parts people besides me actually see) and put together a decent outline of a sequence unit for Honors Algebra 2. I’ve also read a couple of books and watched 4 seasons of Downton Abbey. Last week I attended the AP conference in Philadelphia. 

I have thought quite a lot about how to revise my Standards Based Grading plan of attack but have not come to any final conclusions regarding that topic. I am hoping to get some ideas while chatting with others next week at TMC14.


Much has been said and written about formative assessment and its implementation in the classroom. One of the big buzzes right now is the use of exit tickets as a means of determining what your student do (or do not) know at the end of a class period. In the past I have had good intentions of making this a practice, but never seemed to ACTUALLY make it work. Much of that is due to a lack of intentional planning. To help me combat that I thought it might be helpful to have a few “stand-by” options ready to use on a whim. This is my #madeformath submission for this week.

It isn’t anything elaborate, but I think am hoping it will make my life a bit easier this year. 

I took five end-of-class generic prompts and used posterboard to make signs that I can access quickly. Students can simply put their answer to a prompt on a post-it note and stick it on the poster on the way out the door. In addition to be ready to use with very little forethought, it also makes it easier to review the responses at the end of the day instead of trying to peruse them and get them out of the way before the next class comes in. 

I have punched holes at the top of each poster and, when school starts up, will put them on rings to hang either on the door or bulletin board. All I need to do now is prepare a prompt and stock up on a supply of post it notes.

Here are the posters:

#1 The Two-Minute Assessment

 2014-06-04 07.37.52 While perusing the Internet I learned of this assessment from Pam Wilson who blogs under the name Radical Rational. I loved the idea, but didn’t like using all my board space up for the assessment and having to rapidly remove them prior to the start of a next class. This poster has a place for students to put the following information about a specific topic:

     + = one new thing they learned

     ! = one thing they do not want to forget

     Lightbulb = one “aha” moment they had

     ? = one question they still are struggling with

I actually made two of these so I can easily use the assessment method twice in a single day 

#2 Stoplight

2014-06-04 07.38.14 Students can simply write their name (if you desire) on a post-it note and indicate they feel about the learning target for that day. 

#3 Ticket out the door

2014-06-04 07.38.25I think I originally saw a version of this on Pinterest. Each student is assigned a number and given a post-it note. They put their answer to the prompt on the space that corresponds to the number they are assigned. This should allow me to see more specifically who has a good understanding of the content and allow for effective grouping as necessary.

#4 twitter feed

2014-06-04 07.38.31 This simply asks students to create a twitter post that would be appropriate for the hastag #whatilearnedtoday. 

#5 Stuck

 2014-06-04 07.38.19 This simply asks students to consider the lesson and identify one thing that “stuck” with them. I am hoping I will be able to see if my goals for the day were translated effectively so that what stuck with the students was what I intended. 


As I worked on planning my first unit I have already found myself constantly thinking “what question or prompt can I pose that will assess the learning for that day?” I am hopeful that having these posters will keep formative assessment in the foreground of my planning.



Brain Dump

Mid July = time to get “serious” about planning for next year. Up until this time, I browse the Google, favorite tons of tweets, and e-mail myself tons of ideas that might be worth considering. Now is when I attempt to get real about reading everything closely and determining if it is a good fit for me and my students. 

I’m having a difficult time getting into that this summer. I’m not sure why, but for whatever reason I can find numerous other activities that I’d rather do. 


Nonetheless, here is my brain dump to-do list:

1. Finalize algebra 2 learning targets

2. Revise SBG format

3. Make a new bulletin board

4. Print and bind a teacher planner

5. Find a “killer” first day(s) motivator for Algebra 2 students


This certainly isn’t everything I want/need to do, but I’m hoping that putting a list to “paper” will give me focus so that the remaining part of my vacation is restful but also productive.

Hope your vacation is time well-spent for you!

The MTBoS Challenge

So, I’ve been blogging for a while (although *ahem* not consistently, as I’m sure you can tell) and participating on Twitter with some cool math folks who affectionately refer to themselves as the MathTwitterBlogOSphere, aka MTBoS. You can read all about them and their initiative here.

This post is supposed to address the following prompt:

  • What is one thing that happens in your classroom that makes it distinctly yours? It can be something you do that is unique in your school… It can be something more amorphous… However you want to interpret the question! Whatever!

Knowing me, I’ll end up on the “whatever” end of things, but here goes.

Uniquely my classroom: Wow. That’s a hard one to nail down. I’m uniquely me, and I try to bring that to my classroom. It’s like a package deal. I’m corny, geeky, and usually slighty nuts and I think that’s what my classroom looks like on most days. I tell my students on the first day of the class that they “don’t know it yet, but they just walked into their favorite class of the day.” So, they don’t all feel that way by the end, but a majority of them do. Or, at least, they don’t hate it.

As far as MTBoS goes, almost everything I do is stolen borrowed and revised, so y’all won’t find it unique, but to my school, I think I’m pretty radical. I do my version of Interactive Notebooks with my Algebra 2 kiddos and use Standards Based Grading with them. My learning targets drive the classroom, the notebooks, and the assessments so I like to think I’m pretty aligned.

I guess the ONE thing that I do that is truly unique is the opening week interaction between me and each student. You can read in more detail here but basically it is just a simple (albeit slightly time consuming method) whereby I can build rapport and know my students better. I didn’t think it was all that radical, but after posting it on this blog and hearing other people talk about how they used it, I’ve decided it must be rather unique.

And there’s the baby dice. Funny how easily amused high school students can be.

2012-08-22 18.36.28

Sometimes, this job…

Disclaimer: there is nothing related to lesson plans, teaching ideas, or anything professional in this post. It’s personal.

I teach. I love teaching. I love seeing a student “get it” after struggling. I love designing new lessons. I love scouring the MTBoS for ingenious ways of presenting material. I really do. But not today.

Today I’m sitting in ICU with a dear family member who is struggling to move from this life to the next. She barely knows I am here with her. I want to be her for her and for my husband, completely. But the job I love weighs on me the whole time. To even be here, I had to spend 3 hours writing lesson plans and figuring out what I could leave that a) the students would have at least a shot at being able to figure out and that b) wasn’t a ton of busy work. While I’m here, I get e-mails from parents wanting to know why their kid is failing and from students who want to know when they can retest. I still have to spend 3-4 hours completing a professional self-reflection as part of the new, *improved* teacher accountability that my state so fondly embraces. I have to pour through transcripts for students who need to take an end-of-course assessment…even though I have asked them who needs to do so. See, we can’t even deem them responsible enough to know what courses they have failed and repeated. I have 3 stacks of tests to grade, because that’s what I left them to do last week while I was here. And, I have to be ready to go back into the classroom Thursday, which means more lesson plans and idea development.

Thank goodness I have students who are patient, and who, at least on some level, know what my family is going through and are willing to endure the boring lecture and who are willing to at least try everything I leave for them to do. If I wasn’t blessed with those kids, I’m not sure how I’d even handle this situation.,

I love my job. But sometimes I really do wish I could escape and just take a month off to take care of my family. I have enough sick days. But I can’t make that many lesson plans. Real life just kind of sucks at times.

Legos, Dirtbikes, and Desmos

So, I’m supposed to be working on chapters 3 and 4 of my dissertation, but once again I find myself sidetracked and in need of something else to do to clear my mind before I go back to the statistics and joy that is APA formatting.

I teach Algebra 2, and we have implemented the CCSS for math. We’ve been messing around with the standards for the past few years, so it really doesn’t seem all that novel to me now. It still bugs me that the end-of-course exam we give doesn’t really seem to be all that aligned to CCSS, but that’s a blog for another day.

Last week we finished our brief lessons on systems of equations (after all, that topic is in 8th grade and algebra 1 now, right?) and came to the days of linear programming. While I find LP problems somewhat fun and cool, history has shown me my students most definitely do not share this admiration for the subject. So this year I decided to bring in a new tool. Enter Desmos.


My blogging skills are incredible sucky, so I don’t know how to make this a hyperlink. You can get using  As soon as I get smart, I’ll hyperlink it.

Anyway, I’m all, like, excited to show them LP on Desmos. Especially NOW that you can find intersection points by simply clicking the mouse. Totally cool, right?!? So, we went through the lego furniture problem (courtesy of @fawnpnguyen) and the NCTM dirtbike problem and the kids are hooked on Desmos. Oh, and they can do LP problems like no body’s business. Here’s what it looks like:


So, I’m happy. Until I remember the blasted end-of-course test. And now I’m mad. And frustrated. Isn’t one of the “mathematical practices” to use tools strategically? Now c’mon, you can’t tell me that using Desmos for this crazy long process called linear programming isn’t strategic. Do the kids still have to be able to write the objective function? Yep. Constraints? Yep. Graph the stuff? Yep. Find the vertices of the feasible region? Yep. Determine which one offers the optimal solution? Yep. Isn’t that the point of LP? I think so. So, I have about 60+ kids who, for possibly the first time in my career, really understand LP AND who understand the best tool for the job. Yet, I fear they will not score well on the EOC because they will miss a sign when they are solving a constraint for Y so they can graph it. Or they will miss a sign when solving the system for the intersection point. And since the test is all multiple choice, well, you know where that leaves them. With the wrong answer. And no credit for any of the work they really do understand.

Stain stick, Band-aids, and Sharpies

In an effort to keep up the blog, I felt I needed to post something. Sadly, I don’t have any *oh wow, that’s a great activity* ideas to share. Things are just kind of blah right now and I know I need to fix that, but sometimes stuff at home just trumps lesson plans and that’s been my life lately.

So, instead of a great lesson plan or a cool classroom activity, I’ll just share what I’ve learned in the last 2 weeks.

If you want to win over a bunch of high school kids, have Sharpies on hand, keep band aids in your desk (if you want bonus points, get the ones with cartoon characters on them), and have a bleach pen or stain remover handy at all times. Crazy right? but I swear, I’ve had a half a dozen kids buy into my class because I had these things on hand when they needed them. It didn’t cost me much. It’s all stuff I use anyway. And it wins them over. Everytime.

If you want your high school kids to be on your side, TALK TO THEM. About stuff that isn’t your subject. Or even school related. Ask them where they work. Find something they like and act like you’ve never heard of it so they can feel smart. Currently the topic of my classroom is Duck Dynasty and Frog Giggin’. Sure, I have a remote conception of what both of these are, but what does it hurt to let a few students think they are enlightening me to something they think is awesome. They respond well. Everytime.

Finally, I’ve been reminded this week to laugh. Not at people, that’s mean. Laugh at yourself. Laugh at funny jokes. Show a funny video if you can’t find anything else. This life is short. This job won’t last forever. Heck, this day won’t even last very long. Those kids are only mine for an hour a day (thanks for the reminder @fawnpnguyen). I have to make it count.