How the Desmos Guide to Building Lessons Changed How I Teach

If you know anything about me, you know that I am a Desmos junky.  A couple of years ago I had the privileged of being chosen for the first Cohort of Desmos Fellows, and that has truly changed how I teach.  One of the most important things I took away from my visit to Desmos HQ was the idea of understanding how Desmos designs their activities.  If you are a Desmos user and haven’t read their The Desmos Guide to Building Great (digital) Lessons, you really should.  It will give you some great insight into how to implement the activities that Desmos has designed with your classes, and also make you rethink how you design custom activities using Desmos.  The following are a couple of highlights for me:

  1.   Incorporate a variety of verbs and nouns – have you ever done a worksheet where you had to solve 30 equations?  Why?  Wouldn’t it be more useful to estimate a solution, or compare your results with another student.  The monotony of doing the same routine many times does not have great results.  Also, as we change the math verb, there is the indirect consequence of changing the nouns that go with it.
  2. Create activities that are easy to start and hard to finish – this has a lot of effects for me as a teacher.  When I design custom activities I usually think on this and also the idea of “asking for informal analysis before formal analysis” at the same time.  I want the activity to start off by giving every student a chance to start off with confidence in activity to get them “hooked”, but I also want the activity to progress in such a way that we make a “leap” by the end of the activity so students understand how they grew during the activity and they can see what they learned.
  3. Connect representations – this has been a point of emphasis in my teaching the last couple of years.  It is extremely important for students to make the connection between an equation, a table of values representing solutions to that equation, and the graph of the equation.  Before being chosen as a Desmos Fellow, I did a really poor job of making these connection, but now it is something I am constantly reinforcing with my students.  Also, this is something I think that separate Desmos from other platforms.  The ability to see how changing an equation immediately changes a graph, or how.

Desmos continues to be my favorite tool in the math classroom for many reasons.  The graphing calculator is the most effective and intuitive one that I have found.  Also, the activity site has activities that have allowed me to have high level math conversation, that I previously wanted but could not create.  Desmos helps me create discourse in the math classroom, which has lead to more success and understanding for my students.

New School Year

Well, another summer has come and gone, which means I am about to start my 19th year in teaching.  Over those year I think I have progressed into a pretty good teacher. My goal is to never become stagnant or content, and to always look for ways on improving and challenging myself.  With this in mind I am looking forward to some new challenges this school year.

For the first time in my career, I will be co-teaching a class.  I have little to no expectations about how this will go.  My co-teacher, Mrs. Juhr, is a great teacher in her own right, so together I think we will have a lot to offer the students in that class.

In 2 weeks I will have my first LARGE professional development about Desmos, which I am a super excited about.  Desmos has reinvigorated me as a teacher, not only have I adapted my teaching to include it, but also being part of the Desmos Fellowship has given me a great community to support me as a teacher.  I am excited for this new step in my career, and I am super excited to spread the Desmos word!

Also, I am working on an article for the NJEA Review.  I am a math minded person, so writing has never truly been my strength.  Expressing my ideas and thought to such a large audience is intimidating, I definitely do not envy the editor for the article, but I am excited to share how I use Desmos as a tool in my classroom.

The 2017-18 school year is only a couple of short weeks away.  I am excited for the challenges and the opportunities it will bring me.  More importantly, I am excited to meet and work with a new group of students.  Hopefully I teach them some math, a little bit about life, and help them understand that life is a journey better shared with others.


Desmos Graphing Project

The last couple of school years I end the school year by assigning my 8th Grade Algebra 1 students a graphing project. I have gotten a lot of positive feedback about it, and also many teachers ask me what I have my students do, so I took that opportunity to write a little blog post about it.

I’ll start off by talking about why I like (actually I LOVE!!!!) the project. It is an awesome way for students to showcase all the different types of functions we us in Algebra 1. I also like to make the connection between art /life/math, and this is an excellent way to make those connections. I also think it is just a fun way to end the year in math, and students usually think it is pretty fun to. Lastly, I LOVE DESMOS… (which you probably know if you follow me).

I usually see teachers debating whether to have their students do the project inside of an activity using or just using the graphing calculator.  For me, it undoubtedly inside an activity, here are some reasons why:

  1.  I love watching the progress of the students, and the teacher dashboard allows me to do that very easily
  2. When students get stuck, I use the teacher dashboard to hop into their graph.  Then I show them what they need, but they still have to go back to their own graph and perform what I did
  3. Autosave – when students are working inside the activity, its like they are working in a google doc and autosave is on.  Not true in the graphing calculator.
  4. It elminates “constructive find and use as mine” technique for the project.  I HATE assuming a student is guilty of cheating and then investing my time trying to figure it out.  Students can quickly google, find, save, and make graphs they find their own and turn them in.

Next you will see some examples of work my students have done.  They are just pics, but keep in mind I make all graph have moving parts, thus students must learn how to use sliders.



Below you will find the link to the activity I assigned my students this year. Please, don’t ask me for a rubric.  I am a very liberal grader with this assignment, and I do not try to take points off.  It is supposed to be a fun way to end the school year and show off what they know and have fun with math.

If you have more questions, there are plenty of us that are Desmos Fellows that love to talk about our projects.  You can find me on twitter at: @MrCorleyMath and @AlgebraDesmos


4 ways of multiplying polynomials


I recent made a tweet  of a pic from a quiz from one of my students on the topic of multiplying polynomials, more specifically multiplying binomials (see pic).  I was stoked because the students actually used all 4 methods I modeled for students during class.  As a math teacher, when possible, I try to model all of the different strategies for different problems.  When I posted the pic, I got a lot of likes and comments, and some people weren’t familiar with all of the techniques, which led to this post.

Below I will talk quickly about teach technique:

Box Method (see problems 10 and 13) – this to me is the most important/useful method with great connections.  Later we will explore factoring trinomials, where I will use this model again.  It’s a nice tool for visualizing the idea of all 4 multiplications, and some students like the organization that goes along with it.  Also works well with more complex polynomial multiplication.

Distributive Property (see problem 12) – Probably the method I saw used least by my students.  I’m trying to figure out how to make students value this method more, we do talk about it again when we discuss factoring by grouping.  I think the first step shown by the students is something the students don’t think is useful.

FOIL (see problem 9) – I know, I know, I probably shouldn’t use it.  I HATE showing students a method that does not work in all cases.  My fear is that if I don’t at least acknowledge its existence, it cause issue with their higher level math teachers depending on that teacher’s method.  I over emphasize that it only work for binomial x binomial, and relate it back to the distributive property.

Stack and Multiply (see number 11) – I had a bunch of people on twitter mention that they never saw this method, which sort of shocked me.  I am not sure where or when I learned this method, but is one that a bunch of students LOVE.  I also think it is useful, because it expands upon their prior knowledge of multiplying 2 digit numbers.  Usually when I present this method to students I first show them the problem on the left, and students mention that their most common mistake was the “carrying”.  I mention that this method is similar, with no “carrying”.  I like this method because the students are familiar with the process.  I also like the idea that, similar to place value, like terms are lined up vertically.  IMG_20190208_092207

I also included an example below that might answer a couple of questions you might have about this method for more involved problems.  IMG_20190208_101724

As a teacher I try to give my students as many methods as possible, and let them choose which one works best for them.  I also try to make my students aware of the pros/cons of each technique.  I teach 8th Grade Algebra 1 in a K-8 district, I rarely get time to articulate with the teachers these students will have in high school.  By presenting my students various techniques I hope to give them the skills and knowledge to succeed in mathematics in the future.

Sink or Swim in Middle School Algebra 1? Why are we throwing students off the deep end?

I am not the strongest of swimmers, nor have I ever really been a strong swimmer.   I spent a lot of summers in Ocean City, NJ, during those summers you could find me boogie boarding most days.  Although I wasn’t a great swimmer, I felt pretty safe due to the safety net of having the boogie board with me.   Til this day, I am not confident in my swimming skills.  A long swim in the deep end, or swimming back from the sand bar without a boogie board still causes some anxiety for me.  This is because I never improved my skills as a swimmer.

In this blog post I am going to express some of my ideas about middle school students taking Algebra 1, more specifically, I am going to address those borderline students who are pushed into an Algebra 1 by parents, administration, previous teachers, or even themselves.  Although there are definitely reasons to discuss whether any middle school students should be taking Algebra 1 (check out SFUSD APPROACH) , what most concerns me are the students that are placed into Algebra even though they may not be fully prepared.  Most of our attention in education is on our high level learners and our low level learners, the choice of math class for these students in middle school is usually straight forward and needs little debate.  It’s those kids in the middle where the decision becomes a little more challenging.  Their decisions are the ones we need to spend more time on.

Currently our school uses a pretty extensive rubric to decide the placement of students in advanced mathematics in grade 5-7 and eventually into Algebra 1 in 8th grade.  Some of the categories in this rubric include PARCC score, NWEA MAP score, grades, and teacher recommendation to name a few.  Once the scores are entered into the rubric the students are organized by their scores, and then a line is drawn.  Those above the line get advanced math and the others don’t.  Question that come to mind to me are:

  • Where and how do we draw the line?
  • Is this the best method?
  • How much do we weigh the categories?
  • What happens to students who are below the line one year, and above another?
  • What happens to students above the line one year, and below another?

The last question is the one that I am interested in.  These are the tough decisions!  As educators, we want to give every student every opportunity to SUCCEED at the HIGHEST LEVEL;  but this is not a cut and dry decision.  When we push students to advanced math, like Algebra 1 in middle school, we also need to make a plan and be ready to adapt when they show us signs that they are NOT READY.  If we don’t, the effects of being PUSHED to a level they are not prepared for could have some unexpected and severe consequences.  

If you know any Algebra 1 teacher, within the first couple of weeks of school you will undoubtedly hear them complaining about their students not having the skills they need to succeed in their class.  My first chapter in Algebra 1 is solving equations, a topic they should have a prior knowledge and understanding of.  During those first couple of weeks of school I usually start to identify students I think might not be ready for what is being asked of them in Algebra 1.  I usually give students the first month of school before I start to look at the rubric that was used to place the students in Algebra 1.  Those students I identify and have concerns about are always just above that arbitrary line in the spreadsheet used to determine Algebra readiness.  As I do more exploring, I usually find that some of those students were NOT in ADVANCED MATH the previous year, and were pushed in.  I also usually find students who were in ADVANCED MATH but struggled.  I am also reluctant to say, when I do more investigation I usually find these borderline students had grades on the PARCC and MAP test that indicated they did not have a strong grasp of the concepts they needed to succeed in Algebra 1.  I am not a huge supporter of standardized test, but when you have several pieces of data supporting this idea, it is hard to deny.

Our school has a policy that you must maintain an 85% (B-) in Algebra 1 to stay in the class, 2 marking period of below 85% and you are placed into an 8th Grade Math class.  Usually I start making contact with parents within the first marking period expressing my concerns, usually I refer to some of the data from the rubric as a way of supporting my concerns.  I hear the same lines from the parents almost every time:

  • I will tell them to try harder
  • I think they are capable, just give it more time
  • If they don’t start doing better soon, I will get them a tutor
  • They have always been good at math, so I’m not sure what is wrong

What usually happens with these students is they continue to struggle in Algebra 1.  I usually have frequent conversations and send numerous e-mails updating parents on the students’ progress.  During this time the student usually looses confidence in math, gets frustrated, and their grades and learning continue to decline.  It usually takes several months for either the parents to realize the student is misplaced, or for the school rule to kick in to change their placement.  This to too late!!!!!  By this time the student is turned off by math, has lost confidence and now has to deal with the stigma of changing math classes half way through the year.  All this happens because there is this idea that students NEED TO BE IN ALGEBRA 1.  Why?????  I am so confused by this rationale.

If you asked me 10 years ago about those borderline students, I would say keep them in Algebra 1 and if they struggle, have them retake it.  There are some problems with that way of thinking:

  • Will the student actually retake Algebra 1, or will they be PUSHED forward again?
  • What happens to their confidence?
  • How does retaking a class affect them academically, socially, and emotionally?

Now my thought process is much more in line with long-term goals and the social/emotional decisions that go along with it.  I now believe that if a student is borderline,  they would benefit more from gaining confidence and building their skills by not being pushed into Algebra 1.  Also, as standards have changed, we see more Algebra in the 8th grade standards.   I will once again share the link from SFUSD who eliminated Algebra 1 in middle school altogether, and postponed Algebra 1 until high school for all of its students.  It was a very BRAVE move, but led to more success for its students.  I think the goal of middle school math should to build a solid foundation in problems solving skills and build confidence in mathematics, so students are ready to perform in high school and beyond, even if that means delaying concepts like Algebra 1 until high school.  When our students do not have a SOLID FOUNDATION, we are setting them up for failure.  

As I think about the pros and cons of pushing a borderline student into Algebra during middle school, I think the cons heavily outweigh the pros.  To my knowledge there is no study that Algebra 1 in middle school is an indicator at success in high school or college.  Also, we have to be aware of what we are LEAVING OUT, when we put students on the advanced track.  That is something that is rarely thought about.  Those topics that we breeze through quickly, or worse yet, skip over, are the foundations idea for us to build on.

I leave those of you that are parents, teachers, and administrators who decide the placement of your middle school math students with 1 question:


Thanks for listening.  I appreciate any feedback or discussions.  I don’t have an advanced degree in education or mathematics, I am just a humble 8th grade math teacher who is concerned about his students.




A couple of days ago I made a simple tweet about how we should not be using PEMDAS anymore.

It was not meant to pass any blame, but rather just let teachers know that we should not be teaching students “tricks” that are misleading.  The tweet was motivated by an event in my Algebra 1 class that day.  I was doing the Four 4’s activity, and we were analyzing some incorrect answers.  We were discussing why they were incorrect, and I asked how many steps there were in the order of operations, and of course, I was told by many students that there were 6 steps.  Guess that was my main motivation for my tweet.

I was SHOCKED at the number of responses I got to this tweet.  It seems like many teachers are also frustrated like me.  Here are some responses that hit home.







I wondered:

  • Who started this whole PEMDAS thing?
  • Did it actually help students with the understanding?
  • Who is still using it?
  • Why do people continue to use it?
  • Is there a better option?

I would like to start off with a quick and easy change that I saw recommended.  Moving away from a six letter term, to a 4 letter term would make a little more of a connection.  Cathy Yenca (@mathycathy) shared a link that used GEMA:

  1.  G – grouping
  2.  E – exponents
  3.  M – multiplication and division
  4.  A – addition and subtraction

If you need a “cute” phrase to go along with it:


Do I think using GEMA could make a difference?  Yes!  Do I think it is the solution?  No!  Ultimately it is left up to us, the educators, to create an understanding for our students that they can build upon and refine as they progress through mathematics during their education.

Now, the tough question, how do we ensure that people stop using PEMDAS and creating this confusion?  Marian (@DingleTeach) mentioned that by 5th grade her students are already familiar with PEMDAS.  How do we, as a mathematics community, communicate to others that they are causing harm, and that a change needs to be made?  We are not blaming anyone, regardless of who is causing this issue.  I assume they are doing so with the best intentions.  I would love to send an alert out to all educators/parents and anyone else that may be assisting our students in learning math and say “STOP using PEMDAS!!”  But how does that happen?

I was amazed at how many people reacted to my tweet.  Maybe if we all take it upon ourselves to open the lines of communication with others in our schools, community, and social media, we can make this little change in mathematics education that seems to be affecting many of our students and our instruction.  Lets not just complain, or pass the blame, but rather make a plan to make a change.

Twitter account for Desmos Algebra 1

So…….I had an idea, partially a little bit selfish on my part.  Create a place where Algebra 1 (and possibly 8th math and Algebra 2) teachers can share ideas on how they use DESMOS to ENERGIZE their class.  In addition, it could also be used as a place for math teachers to share graphs, activities, and ideas in a more “intimate” setting.  If any of the following things interest you, I recommend that you follow @AlgebraDesmos on Twitter:

  • You would like to grow your PLN to include some amazing Algebra 1 teachers.
  • You love sharing how you use Desmos in your classroom.
  • You would like to see how others use Desmos in their classroom
  • You have question about a Desmos tool specific to Algebra 1
  • You would like to have others offer ideas about your Desmos Algebra 1 activities
  • You only heard Desmos…..and that was enough

I chose to start this during the spring with the intentions that the numbers of followers could grow and we would have a nice group when the new school year started.  If the account grows would love to lead some chats too.  Please join me in celebrating the beauty of mathematics, Algebra 1, and Desmos!

My thoughts on standardized testing

Standardized testing can be a truly polarizing topic in the world of education.  There are some that think the data we get from the results is a valuable resource for guiding instruction and other think it is a waste of time and adds unneeded stress to our students lives and wastes valuable instructional time.  As an educator, I can truly see both sides of the discussion, so I guess I will take a moment to express my thoughts.

I think standardized testing is an important part of our education system.  Whether we are talking about playing an instrument, working out at the gym, playing sports, saving money, or basically anything else in life; it is always important to measure our growth to see if we are accomplishing our goals.  I feel like measuring growth of individual students, schools, and even individual teachers is important.

I do have several issue with our current methods of standardized testing.  I don’t think we need mandatory state-wide testing to occur as frequently as it does.  I live in NJ, and testing happens in grades 3-8 and also HS.  That is too much!!  In my opinion it would be sufficient to have statewide testing 3 times during a students path: once in elementary, once in middle school, and once in high school.  In between those, I believe individual school district could have bench mark assessments to measure growth.  I also have issues with how and what we are testing.  During class I am supposed to have my students work together and collaborate, many classroom are set up with students to work together, but standardized testing happens and they have to sit in rows and be quiet.

Don’t even get me started on the tools students are permitted to use or given on these test.  My Algebra 1 students are provided an embedded graphing calculator on their standardized test, similar to the one I used 20+ years ago in my math class (with the big pixels and all).  If we want to measure if they are ready for college and the real world, we need to be giving them tools they will be using when they get there.

As we evaluate standardized testing moving forward, we really need to consider many things.  Change needs to happen!!!  We need to incorporate administrators, teachers, parents, and students and give them all a voice to make the change.  NJ has promised to move away from PARCC, which is nice, but maybe we need to rethink standardized testing as a whole before we make a new plan.

PARCC’s Choice of Graphing Calculator

I am a teacher in the state of NJ, where we currently give the PARCC exam (although our new governor says we are going to move away from it.  In this post I am going to refrain from my opinions of the actual test, but I will quickly mention that I understand both sides of the debate about the test.  Regardless of my thought, it is a test my students have to take, and although I don’t “teach to the test”, I do try to give my students tools they need to succeed in their math classes in the future and also on any standardized test they may cross during the educational journey.

The majority of my students are in Algebra 1, therefore they take the Algebra 1 PARCC exam.  In NJ passing this exam is a graduation requirement,  which adds another level of stress and importance to the exam.  During the exam the students have an embedded graphing calculator available to them, and this is where my objection occurs.  The graphing calculator offered to them is a TI – 84 plus silver edition .  This is calculator is very similar to the graphing calculator I used in high school and college over 20 years ago….still featuring all those amazing pixels!!  Why would PARCC choose this calculator????  There are several online graphing calculators that are far superior to the one offered on the PARCC, my favorite being Desmos.  Desmos is a much more intuitive tool to use, has much better resolution, has more features, and also has accessibility features for students who need them.

Below is the graph of the same equation in both Desmos and using the TI calculator provided on PARCC.  First of all, which one is more visually appealing?  Also, I would like to point out that on Desmos you can see both the equation and the graph on the screen, TI it is 2 separate screens.  In addition the tools and interactions with the equations and graphs are far more intuitive with Desmos.  There are many other benefits to using the Desmos calculator….too many to mention in this forum.









One of the most frustrating aspects of PARCC’s decision on the graphing calculator is the related cost to the schools and the students.  The cost of these TI calculators is around $100, which seems like a high amount considering that over the last 20 years that haven’t improved their technology much.  Not only is Desmos a free website, but is also has a free app available for all devices.  It is amazing to me that schools and students have to spend around $100 for a graphing calculator, when there is a far better tool for free.  If PARCC changed its choice of graphing calculator is could be using a better tool, and could save the schools and students its testing money.

If you or somebody you know works for PARCC, TestNav, or Pearson and would like to discuss this, please reach out to me.  If you are a NJ teacher or administrator let the DOE or PARCC directly know that their choice of graphing calculator is UNACCEPTABLE!


Professional Goals for New Year

Recently I have gotten overwhelmed by the amount of teaching tools that I have heard about on twitter.  I would love to incorporate all of these tools into my classroom, but I first have to investigate them, then have the courage to use them in my classroom.  I try to keep my instructional techniques current and up to date, but with 2 toddlers at home it can be a bit of a challenge getting the time and energy to investigate new techniques.  Go to conferences can also be very expensive, and out school has a limited budget for professional development.  I would love to go to more conferences, and observe other teachers using these techniques; but the time and money to do so is so limited.

The topics I am committing myself to spending more time exploring in the new year are:

  1.   Clothesline Math –
  2.   3 Act Math –
  3.   An exploring and incorporating more Open Middle –

Explore and incorporating these are part of my professional new years resolutions, I think it is important for teachers to always be looking for way to improve their craft!

More time in math

How much time do students spend each day in their mathematics class?  Is it the same across each school, state, or even country.  Do students have the same amount of time in English class (or Language Arts, Reading, or whatever you school calls it)?  If we want to get better at something at life, don’t we usually spend more time working on it?

These questions should lead us down the road to understanding why students need to be spending more time each day in their mathematics class in school.  A couple of years ago my school change from 42 minutes of class each day to now 80+ minutes each day, and I feel like my students have greatly benefited from it.  We hear stats about how the US if falling further and further behind in topics like math and science, but how are we changing instruction.  It seems like we keep pushing higher level material into lower and lower grades, but when are students given time to grasp and understand the key concepts so they can apply them to higher level concepts.  If we want student to understand math better so they can become better problems solvers we need to give them MORE TIME!!

When my school made the change several years ago to 80 minute class periods, it was a very difficult transition for me.   For years I had a routine I used in my class every day, that I rarely veered away from, because I wanted to optimize every second of class.  I did a warm-up, went over the previous nights HW, gave my students notes, I modeled examples, we did guided practice, and started HW.  That was basically how every class went, because I felt that a routine gave me the best chance of using every minute possible so that I could cover the wealth of standards I need to.  I knew I wasn’t being creative, but I felt this was what was necessary to for students to learn all of the standards.

Now my class is completely different!  HW is optional, I place some practice problems with answers in my google classroom if students need it.   I do not follow the same routine every day, which is very freeing.  I now have time to let conversations drift away from the main topic, and create better understanding of how different parts of math work together.  I have time to do DESMOS activities, which are some of my favorite things to do in class.  These activities help create a need for mathematical vocabulary and new mathematical skills, and help me create discourse.  More importantly, more time in class gives me more opportunities to build connections and relationships with my students, which makes them enjoy class more and makes for a better overall learning environment.

More time in class has definitely helped my students, but also increasing the amount of time I have spent being engaged with mathematics has made me a better teacher.  Over a year ago I was selected to be part of the first Desmos Fellowship , which has given me a great boost in my career.  I met some amazing people through this fellowship, and now have a great community of math teachers to lean on when I need help.  It also inspired me to be more active in social media with other teachers, these interaction have lead to some pretty amazing lesson in my classroom (Check out #MTBoS and #ITeachMath on twitter).  Finding this time can be challenging, but giving up Facebook was a good trade off.

If we want our students to succeed to a higher level in math, I think the solution starts with giving them more time in their math classes in school.  In my life experiences, to get better at something you have to make a time commitment to it!