May 112013

I am trying to put some order to my to-do list this summer, as well as create some structure for all the work. I want to avoid creating a broken, fragmented summer where I accomplish nothing but spend a lot of time spinning my wheels.

First off: Trainings, conferences and travel I am planning.

1. A training given by my district on CCSS changes to Algebra 2, 10-12 June. Kind of important since I signed up to teach the new CCSS Algebra II STEM changes at our August Mandatory PD session. It will be a great three days in June, and a great way to start the summer.

2. The Silver State AP Institute in Las Vegas 24 to 27 June: Really looking forward to this institute given by Josh Tabor to the experience AP Stat teachers. It says he is going to work with Fathom a lot, which is good, I have no experience with Fathom. I am interested in seeing what the new additions to GeoGebra can do as far as stats teaching, so I will work with both programs and see what I can do to crossover.

3. A fun trip to Chicago for some family time around the 4th of July, and then a week later a motorcycle trip to Portland and Montana. That will be a blast! It is always good to see mom, sister & family in Portland as well as family in Montana.

4. TwitterMathCamp 2013 from 25 to 28 July! Yay. Last year it was amazing and hands down the best PD I have ever done for myself. I am very happy to be going again. Looking forward to developing relationships with more teachers and building stronger relationships with the ones from last year!

5. In addition to all that, I signed up for a MOOC on Coursera on the Philosophy of Mathematics starting in July and going through August.

Whew, that is a lot of traveling, and it will definitely keep me hopping. But in addition to traveling and learning, I want to really dive deep into a some books and synthesize some ideas.

My reading list, in no particular order is:

The Art of Problem Posing by Stephen Brown and Marion Walter

5 Practices for Orchestrating Productive Mathematics Discussions by Margaret Smith and Mary Kay Stein

Common Core Mathematics in a PLC at Work: high school by Gwendolyn Zimmerman et al.

Common Formative Assessments: how to connect standards based instruction and assessment by Larry Ainsworth and Donald Viegut

I have some other sitting on my bookshelf that I want to revisit, but those are the 4 that I absolutely want to get through this summer.

The thread I am working on is connecting classroom practice to better questioning, learning how to ask and guide better questions, and then teach other teachers in my department how to ask better questions.

This is a big chunk, but I think it is important to developing a better math program and math classroom.

I will post here on the books and conferences.

Apr 132013

I have been mulling this question over for a while now, since last summer at least. It is a offshoot of the time I spent working with Exeter materials at an Exeter summer institute, and if anything the question has grown in my mind to the point where I must answer it for myself and act on it.

Here is the newest version of my question: If much of what and why we teach math the way we do is arbitrary, then why not change to make it easier to learn?

Now of course, there is a HUGE set of presuppositions / assumptions just in asking the question. First, I assume that much of what and why we learn math is arbitrary. Well, I don’t think I am that far off the mark. Let’s look at Algebra 1 as a course first. Honestly I am in good company with this thinking.

Grant Wiggins (author of Understanding by Design) and his thoughts on Algebra 1

I agree. Algebra 1 has a huge failure rate because it is very abstract, meaningless content. We don’t really ever see why we are doing it, we are just learning to manipulate variables and constants around. Grant gives a small part of Lockhart’s Lament (pdf), and it is worth linking to (and reading) completely. Again, the ‘why’ of ‘why do we teach it this way’ is completely arbitrary. Which is why we get political science professors arguing that Algebra is unnecessary because it is hard in the NYTimes. That Algebra is a gateway topic is not in question. It is. The content is essential for future jobs and future success.

If we look a the content, we see arbitrary stuff all over. Heck, just look at the old y=mx + b. Why “m”, why “b”? There is no good answer. Do a google search and get 33 Million hits, none of which can definitively tell us why. I find the answer from the Drexel University Ask Dr. Math to be the most grounded answers, which you can find here for m, and here for b. And I LOVE the answer given here by math historian Howard W. Eves in Mathematical Circles Revisited (2003), where he suggests that it doesn’t matter why “m” has come to represent slope.

“When lecturing before an analytic geometry class during the early part of the course,” he writes, “one may say: ‘We designate the slope of a line by m, because the word slope starts with the letter m; I know of no better reason.’ ” via

I totally agree. In other countries they use other variables for the same meaning (scroll down), so clearly the “agreement” that we all must use the same convention is not universal. There are so many conventions in math that are purely arbitrary. Since they are arbitrary, we must feel free to throw them away when they interfere with good learning and teaching.

So the second question, and a very important one, is: How could we teach math differently to make it more understandable?

One thing I think is important is to connect the vocabulary / language / processes of linear functions with other polynomials / transcendental functions. After all, look at the amazing similarity and simplicity of understanding the transformation processes.


Don’t believe me that every single function listed has exactly the same transformation rules? Try this little GeoGebra applet I whipped up. Think about that for a second. When I have shown this to math teachers I get two reactions, “Well duh” and “OMG, I never thought about these like that.”

The teachers who see this as obvious are the teachers who are much more experienced and have taught for many years and have spent the time looking at the math. The crazy thing is that very few teachers have told me they teach this. Why not? Because it isn’t how they were taught, it isn’t how the books phrase it, it violates the conventions of math teaching. So they know it, but ignore it.

And don’t get me wrong. I am not suggesting this is where we stop teaching, we use the exact similarities as a springboard to bounce into the other types of functions. If the learner of math knew this with strong understanding, then the rest of algebra becomes a close examination of each type of function (which is all the different algebra courses are anyway.)

The Common Core Curriculum has mixed up the order of teaching these functions, but the fact that all algebra is just an examination of the skills (which are essentially the same, find ones by multiplying by the inverse, find zeros by adding the inverse) needed to solve, graph, and understand how each function is used.

The last question I have is: Why do we, as teachers put up with this, and what are we going to do about it?

I think the CCSS gives us the perfect opportunity to demand better from textbook publishers as well as our professional development opportunities. We, as teachers, need to be willing to throw the ‘conventions’ away and teach better.

Will it make a difference to the failure rates of algebra 1? I don’t know. but how can it hurt? How can it hurt to strongly connect all of algebra through trigonometry with an unbreakable thread so learners know that what works for one type of functions will work for every other type of function too. It shatters the concept that Chapter 3 doesn’t relate or have anything to do with Chapter 7. That is what learners think now.

Apr 082013

Today is the first official day of Spring Break (Monday) and so far I have had an eventful weekend. I started by flying to Los Angeles and attending the 5th of the series of AP Workshops they have had. These are the one day workshop where teachers can attend and get some additional tips, hints, and prep for their AP classes.

They definitely inspired me!

I flew down on the districts dime. They offered to send myself and one other teacher to this workshop and paid for flights and hotel for us. This was very generous and even though the workshop was not offering Statistics I felt I could not refuse the offer to go and spend the day doing some calculus. I am glad I did. I spent the day talking to teachers from LA who work in very urban to not so urban schools about how to teach better. I also got a chance to speak with Don who works for the CollegeBoard and has some amazing insights into the AP process. More on that later.

First: This was the FIFTH in a series of these workshops for the LA Unified School District. Think about that. They have had 5 so far, and one more planned. If you teach AP, you are getting some great professional development. But it goes beyond “if you teach AP”. I was in the ‘little to no experience’ calculus room by choice, and in that room there were 7 others who DID NOT TEACH CALCULUS at all. One very eager teacher taught 10 years of geometry and 2 years of algebra 2, but wanted to make sure he was teaching correctly to help develop calculus learners. Another young teacher was in her 3rd year of teaching, and wanted to make sure she was still fresh and current on all levels of math.

Think about that. The depth of teachers LAUSD is developing by opening the sessions up to teachers who want to learn but are not currently teaching calculus is amazing. When Washoe County does their one workshop each year I doubt that it is this widely attended. I went once, but have not gone the last two years because of speech and debate meets being scheduled the same weekend. The one I attended was 100% only current AP teachers. What are we losing by limiting these?

Second: Some tips gleaned about what works for the “urban learner.” I won’t try to define what that means, but suffice it to say that LA has its fair share of them. Some of the tips here are pretty normal. A couple I never thought of. Worth the price of admission right there.

  1. Go over new material BEFORE questions about homework. <insert dopeslap here> DUH! What happens when you get lots of questions about the material from yesterday? You end up rushing the lesson for today. Which leads to more question tomorrow. Which leads to rushed lessons, and then you are always behind and the learners then learn to use that to their advantage and never let you get caught up.  Teach first, THEN go over homework if you need to. Teach first.
  2. Warmups in groups of 3 to 4. The urban learner has been trained NOT to be the smartest or the standout learner. The standout outside of the classroom is the mole that gets whacked (to use my own notes and putting it in different context.) Group work for the warmup allows them to talk about content without being “that kid”.
  3. Meet with parents at the beginning of the year in an AP class. Tell them what the expectations are. Let them know that there needs to be a homework time where NOONE watches TV in the house. Stress the importance of learning. Set the example. Have the parents form a support group of their own. Stress the importance of constant vigilance on homework and learning. Let the parents know there will be very stressful days for their learner. That is okay, support them.
  4. Encourage learners to build study groups by assigning problem sets from old AP exams that are due as group work. Start off by having 2 to 3 week deadlines. They need time to learn how to work as a group. Eventually shorten it to 3 to 5 days with more problems in the problems sets. It is about managing their workload and teaching them how to learn and talk about content.
  5. Praise often, and praise the right stuff. Look at a problem the learner did. Notice they did 85% of the problem right but made a consistent mistake. Point that out. Show them how much they know, and how little they really got wrong. The “100% is correct or nothing” mentality built by the “urban learner” is devastating to learning if they don’t see the progress.

These were the biggies. It is about creating culture of success in the classroom.

Finally, the next thing I learned was the importance of hammering the gatekeepers and using the AP Potential report. The AP Potential report is why the school district pays for every sophomore to take the PSAT. We get a report that itemizes for each learner what AP classes scores like theirs have been successful in AP classes. For 24 different AP classes.

I wonder if that report lists more than 60 learners for AP mathematics. Because that is how many learners are taking AP mathematics at my school out of 2100 learners. This means that at my school, only 2.9% of the learners take AP math of either calculus or statistics. Pretty sad, actually.

I am going to get a copy of our AP potential report so I can look at it and start pushing for AP math at my school. I am also going to share that with all the other AP teachers. I may ruffle some feathers but it is time to push, challenge, and ruffle some of the gatekeepers feathers.

Mar 212013

Nevada is one of the SBAC (Smarter Balanced Assessment Consortium) states, and the SBAC has released some questions on their website in a way that shows us how the test will look and work when it is fully released.

Guess what, I can’t get it to work at school. Why? The district is standardized on IE7, which is too “old” of a browser for the SBAC, and Chrome is too new. I had it working in Chrome one day, and then Chrome updates and it is broken again.

So, I go home and using Firefox I can get it to run. Great, how do I now get this info to my department? I know, I will use Snagit and make captures of the screens. …. Not so much. One question is actually animated. Great, I will use Snagit and make a video! Yay.

Here it is. The 11 released questions for the High School level proficiency CCSS exam. Please don’t judge the voice over. I sound like an idiot.

Dec 312012


My friend Anthony created a blog post the other day saying he was looking for the CCSS in Excel format instead of PDF format. He did all the work to create the file he needed, which made me feel a little bit bad.

You see, I have had exactly what he needed for the last 6 months, easily. I too, prefer to search and work in Excel. It is just an easier and faster platform to search and copy/paste from.

So, with that in mind, here are my files.


The main difference between my file and Anthony’s is the way the standard are presented. Anthony’s files are all in one tab, so searching / filtering for a complete strand is easier, while mine are broken up into different tabs for each grade level. Depends on what you need.  I have also indicated STEM standards with a “+”.

The one thing I have not done is changed all the standards to include the Cluster designation. That is something I need to do still. Besides that, the formatting is slightly different, but they are the same. I just felt bad he had to do all that work when I had what he needed all along.

I wonder how much other stuff is on my hard drive that other people can use?

Nov 272012

In which the CCSS website makes changes to the notation of the standards without really communicating it.

So today I am working on the Exeter Project, aligning questions to the CCSS, and one of the persons I am working with is using this notation for the standards that confuses me greatly.

After some research, I discover that there are TWO different notations for the SAME standards! What the hell? So I do some further research and find out what is going on. I was so irritated that I had to write this up and ask for help.

First, let’s compare the website to the PDF for a grade 8 standard.


which is compared to the PDF below:


Hmm, one says the standard is Math.Content.8.NS.A.1 while the other says the standard is 8.NS.1.

Okay, the Math.Content is throw away, but where does the extra A in the first standard notation come from? Any guesses? After a bit of research and finding a memo on it, I discover the extra A means, “Know that there are numbers that are not rational, and approximate them by rational numbers.”

No joke. Read it for yourself.

… In math, however, cluster headings have an important design function in organizing the subject matter and in adding important meaning to the individual content standards; math cluster headings are also proving crucial in implementation efforts. Therefore math cluster headings have been given identifiers (such as A, B, C, for example). By this means, the identifiers preserve links between standards and clusters, which is necessary to ensure that applications using the system can preserve the meanings that arise from considering the cluster headings and the individual content standards in conjunction with one another.

To differentiate the Common Core State Standards from state standards (in other domains or as part of the optional, up to 15 percent standards additions), CCSS is now added to the front of the dot notation identifiers. For example, what appears in the PDFs as RL.2.1 is officially CCSS.ELA-Literacy.RL.2.1. It is assumed that educators will continue to use the shorter RL.2.1 in conversation, but the official dot notation identifier will contain the CCSS component.

The publication year of 2010 is provided in the metadata and XML for the standards but is not included in identifiers. Any future refinements to the CCSS will be appended with a revision number, for example CCSS.ELA-Literacy.RF.4.4r2, or, reflects the second revision, or third version of CCSS.ELA-Literacy.RF.4.4.

Great. We haven’t even fully implement the CCSS, and we are already forcing down a new naming structure.

At the high school level, this ends up looking like this:


vs the PDF:



Why does this matter? Why does it upset me and cause me some heartburn? Because if I am doing a search for a standard, and I am using the official PDF standard, I search for A.SSE.1a and I will find some problems / lessons. However, now the CCSS group has doubled the amount of searching work for me, because I also have to search for A.SSE.A.1a in order to get full results.

Computers are very literal, and they are NOT going to give me results for both searches.

To make matters worse, the CCSS group says explicitly that they expect teachers will continue to use the shorter version (and I don’t think anyone in their right mind will add the useless CCSS.Math.Content.HSA to the front).

Aren’t the CCSS FOR the teachers and learners? Clearly not. It is clear the standards are being written for someone not in the the classroom and using them daily. If they were, we would have one nomenclature to use that is consistent and easy to search. These standards are only in implementation for about a year and we already have a bifurcation of nomenclature.

Seriously, can we fix this? Teachers need 1 name, 1 set of search terms, not two. What happens next year when they decide to add a third for whatever reason?

This is ridiculous.

So what do you think? Which name should we, as teachers, use for these standards? Which one will you use? Which one should I use for my project?

 Posted by at 8:57 pm  Tagged with:
Sep 162012

Where to start.

I have been thinking and working with the Exeter materials quite a bit in the last 3 months. I have come to see the value in the methods and the questions, and the way the questions cycle from lower levels to higher levels.

But I have to say I don’t see the Exeter curriculum as a magic bullet. It isn’t. There is no such thing as a magic bullet for math education. There is a lot of hard work. There are a lot of relationships to build with learners. There are many hours to put into lessons that engage learners to think deeper about the mathematical issues.

The Exeter Curriculum is a part of this process, not the end of this process. It is not something that will solve any problems. It is however, something that will help me, as a math teacher trying to improve my classroom, to engage learners, to develop deeper thinking, and to push the high standards of the Common Core into classrooms.

I am not confident of the efforts offered by the textbook publishers. Here are two examples of why:

If the CCSS is going to actually impact the classroom in a positive manner, we can’t take the same ol’ same ol’ materials and just slap on a new label. We need to structurally change and improve what we are doing.

That is where the Exeter Curriculum can come into play and help, and it creates the next problem I, as a public school teacher have. And this goes back to the first post I made, Exeter we have a problem. I had flashbacks of Apollo 13 as I wrote it because it is relevant. As the quote goes, “Houston, we have a problem” and the problem was absolutely centered in that little capsule. The experts who developed the program were on the ground and could go home safe and sound at the end of the day, but those astronauts needed to step out of their comfort zone and do something above and beyond.

As a public school teacher, I am in the same capsule. Our comfort zone has been stripped away and completely new standards pushed on us. We need to step up, or step out. It really does come down to that. The old guard who doesn’t want to change will be forced out through the new “evaluation” procedures that also have been forced down our throats by people who have no clue about education.

Okay, so the stage is set. Nothing I wrote above will change. Stop complaining.  What the heck am I going to do about it.

The Plan (or WCWDWT):

As part of our evaluation process I had to create a Professional Growth Plan. The plan I proposed and was approved was to take the Math 1 Exeter Curriculum and align it with the Common Core State Standards as well as simultaneously give the problems keywords and strands.

In addition, I have spoken with the two very nice and enthusiastic gentlemen from who have the technical background to take the entire project, upload it to their website, and host the problem sets, alignment, stranding, keywords, AND make it all searchable, selectable and downloadable for FREE (and that is free as in air).

What Can We Do With This? We can create a database of problems that are rich. We can create a database of problems aligned to the CCSS that are searchable, selectable and downloadable for use in the classroom by math teachers around the world.

What can we do with it then? That hasn’t been explored. We have to create the foundation before we can build the building. I have spoken with someone at Exeter and they are interested in the project. Of course, they can not help much. It isn’t their burden to take on, it is ours (and now mine!).

I have another teacher at my school who has agreed to take on this with me. She is absolutely crazy to do so, which means I am completely insane.

Aug 262012

Okay, all along I was promising a massive file upload for all the readers who want the Exeter materials. I will explain what each group of files are for as I go.

All files are in WORD or PDF format, and all are in a zipped folder. Downloading and unzipping the folders will speed up your access tremendously. All in all there are 44 megs of files here. That does not sound large, but word files and pdfs are incredibly small these days!

[The placement tests were posted on Exeter’s website, but they didn’t realize they were made public. Links to that page have been removed. If you are a teacher and would like the files, let me know.]

The progression at Exeter begins with a Placement test to determine what course the learner should be enrolled. These are released Placement tests from Exeter:

Released Placement tests
After being placed in the correct course, the learners then start in on the problem sets. I have 2 years archived, but I would love more if someone has them.

Problem Sets 2011-12

Problem Sets 2012-13
The current year is 2012-13, so the archive is an August download of the new materials, including the change logs. If someone has the change logs for the 2011-12 or the files for previous years, I would add them also. The live location for the current year’s materials can be found on their site.

I do have solutions to the 2009-10 problem sets (I was given these without the actual problem sets) and solutions to the 2011-12 problem sets. Will I post them? No. I know I would not be happy if a teacher posted solutions to all the problem sets I created. That is the one thing I won’t post.

During the class the learners are in, they will do hands on activities, and use Geometers Sketchpad to explore math. The Instructor of the Exeter sessions I attended was nice enough to share these. They are all written by Exeter teachers, so no poaching and claiming them for yourself. Please attribute them accordingly.

Hands On Activities 2011
(Both Word and PDF documents!)

GSP Document and Sketches
GeoSketchpad misc
If you are looking at these thinking, “Dang! That is a lot of material to go through!” You are absolutely right. The 2 docs for Alg 1 are 59 pages combined, the Geo doc is 62 pages, and the Alg 2 Hands on is 69 pages. Right there are enough docs to keep a person busy in class for a long time, and you would be learning terrific math as you go. In the GSP Document and Sketches folder, there is a document called “2011 gsp.doc” It is 101 pages of GSP constructions.

So the learners are working problem sets, they are working activities and extending their learning beyond the problems and being active with the math. Now it comes time for some assessments.

Math 1 tests
Math 2 tests 
Math 3 tests
These are all in word format, so you can edit and use them in your classroom if you like. These tests give you some idea of how Exeter assesses their learners. Something you should know is that every one of these assessments are open notes. Every problem set they have worked is available to them on the exam.

Finally, the year is over, the faculty get  together and evaluate the problem sets. What worked, what didn’t, what can be improved. And the writing committee collects all those comments and distills them down into a commentary on the problem sets for the rest of the staff. Then the rewrites happen, and the new problem sets are published, and the cycle starts all over again.

Commentary 2011-12  [if you would like the commentaries, and can demonstrate you are teacher, please email me or comment and  I can email them to you. The files have been removed at Exeter’s request.]


And there you have it. This is the cycle of development of the Exeter curriculum and materials. The vast majority of the work is done by the writing committee, compiling the commentaries and editing the problems. That is a huge task, and I would love to have a serious discussion with someone at Exeter just about that. Heck, I would spend a week with them just asking questions about the writing of the questions, let alone working and thinking about the problems themselves.

I hope this is of some help to other teachers out there.

Aug 102012

I am planning several posts on this week’s time I spent with a math teacher from Phillips Exeter Academy. This first one, though, will be radically different from the others, and it is because I have to vent a little and lay out a difficulty I had today.

Today was the last day of the Exeter training, and it started with me staring at my computer at 6:45 am this morning thinking about the day ahead and looking at my notes from yesterday. Then I looked at my Google Reader and I read a post on Common Core that brought me to a realization.

As public school math teachers … we are screwed.

Let me explain how I reached this epiphany.

It is impossible to work on the Exeter math problems and not realize how carefully they are constructed and well developed the curriculum. After spending time with an Exeter math teacher and developing a deeper understanding of the Harkness Method they use (never once did this phrase come up, but the methods used by the instructor were clearly modeling the method) a person can’t help but really develop a strong affinity for their curriculum, which they GIVE away for FREE!

Okay, I really like their curriculum. It is rigorous, models real life situations constantly, allows learners to develop strong understandings without memorization, has multiple entry points for learners to develop strengths and and is completely free.  Point one to my depression today.

My state, like 44 other states (Utah backed out this week) is adopting the Common Core State Standards. This fact is point two to my depression. You see, when those two points are combined we are in a heap of trouble. Pearson and McDougal-Littel (among others) are developing many programs they are chomping at the bit to sell to our admins, and we all know they have a direct line through media and other means to our principals and curriculum directors.

And what does Exeter have? A curriculum that is fabulous, and is not aligned to any Common Core standards. They have the experience to build what is hands down the best math curriculum we could possibly use, and they give it away for free. They are not going to be lined up at our Admin Retreats pumping their product (but all the publishers had a booth at our local Admin Retreat this week, I looked.)

The next time textbooks are adopted who is going to be at the table? Pearson? Yes. McDougal? Yes. Exeter? No. Who has the better curriculum that will BEST meet the requirements of CCSS? Hands down, Exeter.  Are our admins going to even consider a curriculum that isn’t handed to them pre-aligned and packaged for the CCSS? No.

Who are our admins going to listen to; the missing voice of Exeter, or the loud and well funded voices of the textbook companies? Right.

And the worst thing is that this is NOT Exeter’s problem. They just write the problems. They write them for their own use and then make them available. They can not and SHOULD NOT be expected to advocate for their curriculum in public schools.

But, Exeter, WE have a problem.*


*I think I have a solution that I will write about after I detail some great stuff from this week. I am not sure my solution is achievable, but I don’t think we have a choice.

Aug 062012

My district (Washoe County School District in Nevada) puts together blueprints for us each year. They change a little from year to year, but generally don’t have tremendous changes. This year, of course, being an exception because of the Common Core State Standards (CCSS) that we are required to roll out.

The page I linked to above is to the general Assessment page on my district’s site that contains the current blueprint. It has not been updated for the current year, but it will. Below are the current blueprints for:

I really didn’t like this format for Common Core. It was very book reliant, and focused too much on what our old (3 year old) books wanted us to teach instead of the new standards. I took those blueprints, and turned them into a scope and sequence document that looks like this:


Now we have the topic, the subtopics, the recommended days (based on a 55 min class, 5 days a week, which is NOT my schedule, but easier to communicate across schools w/ different schedules) and the standards listed.

If you want the PDF of the document for Algebra 1, Geometry, and Formal Geometry for my district for comparison purposes, here it is.  If you want to make your own, here is the publisher file for you as well.


Next, I have some consensograms for you. @Druinok posted a link from Pinterest about using paint chips from your local hardware store as consensograms. Which reminded me, I have many consensogram blanks on my website! For instance, I have this:

image (I actually have each one of these separately, but posted a pic of all 3 together to save space.) Or this one:

image (which is what I use) or :

image or even the really interestingimage

All of these are in PDF or Word format on my website: on the left hand side. They are listed as “Consensograms” because that is what we called them in the SLF (or Student Learning Facilitator) Program.

I use the 1- 5 card. I had 30 or so laminated up by our Student Company and cut out. Then I put a paperclip on the top, and the learners slide the paperclip to where they are at. When I ask for “How you doing?” or some such question, they slide the clip and show me.

If I make more, I will put on the back, A B C D E so I can also have them show me their answers to multiple choice questions that I use for AP Stats Warm-ups.

And those are my 2 #Made4Math contributions for today!