Nearpod “Best Practices” For Math Class v2.0

Folks often ask questions about how various apps and tools can be used “for math”.  I’ve always felt that, to some extent, math as a content area can be a tricky fit for apps, tools, strategies, P.D. etc. etc. when compared to other K-12 content areas.  To me, the most effective tech tools focus on making student thinking visible and easy to share from student to teacher, AND from student to student… which means, such tools have the potential to be effective in numerous content areas.  NCTM addresses the idea of effectively using “content-neutral” technologies in their Strategic Use of Technology in Teaching and Learning Mathematics position paper: 

“…Strategic use applies to both content-specific and content-neutral technological tools and in both synchronous and asynchronous settings…

Effectively applied content-neutral technologies increase students’ access to information and ideas and enhance student– student and student–teacher interactions to support and enrich sense making…”

It’s been several years since I posted about Nearpod “Best Practices” for Math, and in light of NCTM’s mention of “synchronous and asynchronous settings” I bring to you this post, version 2.0, to consider some additional ways Nearpod can enhance learning and communicating mathematics in our classrooms.


Student-Paced Pre-Assessments and Nearpod Reports

Class time is SO valuable.  I often try to maximize the time I have with my students by assigning a student-paced (asynchronous) Nearpod that addresses prerequisite material ahead of time.  Launching a student-paced Nearpod is easy – just choose “student paced” when launching a lesson from your Nearpod library.  The resulting student-paced code is valid for 30 days.

For example, I might assign a Nearpod lesson on solving 1-step or 2-step equations for homework before I plan to address solving equations with variables on both sides of the equals sign in class.  Providing “Draw It” slides in a pre-assessment gives me work samples from every student.  While sipping my morning coffee the next day, I download the Nearpod Report to check out my students’ work from the night before.  I’ll know what I’m in for in class, because I can see exactly what my students can do.

Whether one assigns an elaborate, comprehensive student-paced Nearpod lesson, or several simple “Draw It” slides asking students to do a problem or two, the value here is being able to see what students are up to before they walk into class.  To read more, check out this post.


Create a New Nearpod Lesson Using Student Work-Samples and “Draw It”

Let’s say you’ve assigned a student-paced pre-assessment lesson, and as you examine the “report” you find some interesting student work samples (to me, “interesting” often means “incorrect”).  While this student work can be very valuable in helping a teacher with instructional next-steps, there’s value in sharing this work with students too!

Several months ago, I started taking screenshots from such reports.  I use these “interesting” work samples as “Draw It” background images, creating a new Nearpod experience.  Launching this Nearpod work-sample showcase as a “warm-up” the next day, I ask students to “grade” the work they see by providing written, constructive feedback.  Not only do we have “interesting” authentic and anonymous work samples, we have students’ thoughts and feedback ABOUT these work samples to talk about.  As I share in this post

It’s one thing to feature anonymous errors on the screen at the front of the class and talk about them, and how to fix them, together.

Through this experience, I learned it’s another thing entirely to ask *each* student to analyze the work and take a stand on its correctness or incorrectness.

A screenshot of ONE student’s work is analyzed by ANOTHER student using Nearpod “Draw It”.

I don’t want to give the impression that this Nearpod strategy creates a silent classroom where every student is staring at a screen.  Seeing “real” student work, in and of itself, brings an emotional, invested atmosphere.  Students are always wondering if the next work-sample will be their own… and quite often, when that happens, students CAN’T HELP THEMSELVES… they yell out, “That’s MINE!  And I KNOW what I did (incorrectly) now!!!”  When I showcase the “graded” work samples, it’s quite shocking how many students hastily write “Great Job!” when work is clearly wrong!  The work samples and subsequent written student feedback serve as fuel to classroom discussion and healthy math arguments.


Nearpod “Draw It” iOS Includes a Camera Option!

With 1:1 iPads, the camera feature available in Nearpod “Draw It” has become an invaluable tool.  At any point in any lesson, I can launch a Nearpod “Quick Check” (<– steal and edit my template here) and in less than a minute, we have a gallery of student work to consider.  I often use this strategy to “spot check” homework.  Since students, in theory, already have the problems worked out, I start class by saying, “As I take attendance, will you go to Nearpod and send me a photo of Problem #4 from last night’s homework?”  By the time I enter attendance, I already have a work sample from every student.

At the front of the class, I scroll through every photo/problem.  Depending on each class period’s Nearpod culture, we leave student names visible, or we anonymize names.  (Note: 2 of my classes this year have been A-OK having their names attached to their work… and the other 3 classes, even now in March, prefer anonymous work – be sensitive to your own students here.) The first “lap” is a no-judgment lap.  Our goal is to look for trends (which can be correct OR incorrect).  Then we start talking about what we saw, and hone in on specific work samples.  I call this a “safety net” because we catch many misconceptions before students have a test or quiz.  We celebrate the mistakes because we’ve identified and fixed them in a timely way.  To read more, check out this post.

How are you showcasing student work for students to analyze and discuss?

What does error analysis look like in your classroom?

If you haven’t used Nearpod to examine student work, would you try it, in light of these classroom examples?

Posted in Algebra 1, Pre-Algebra | Tagged , , , , , , , | Leave a comment

MAD Fun: “The Sum Game”

About a year ago, Nathan Kraft blogged about a collaborative lesson design and experience to help students understand (and WANT to understand) the concept of mean absolute deviation.  This standard was added to 8th grade curriculum here in Texas three years ago, and the past two years, I feel like my MAD lessons could have been better.  Nathan’s post was exactly the boost I was looking for. Thanks to Nathan’s detailed lesson notes and student work samples, I designed this Desmos experience, and started class with it today.

Students went from ‘Monday groggy’ to actively engaged in about three seconds. First, I used Desmos’ new “teacher-paced gates” feature to limit students to only the first three screens.  The teacher simply clicks on the first and last screens he/she wants students to be able to access.

In pairs, I let them roll for a few minutes and pressed “pause” to bring everyone together.  So glad I did this – we were able to scroll through graph screens to see who “won” at their first stab at “The Sum Game” (that is to say, which partner got closer to a sum of 7).  P.S.  Using a pair of virtual dice on and the split-screen feature on our iPad Air 2s was nifty!

Split Screen!

The seed was planted that a sum of 5 ties with a sum of 9, and we were off with our second “teacher-paced gate”.  This time, student pairs only had access to screens 4, 5 and 6, where each partner “rolled” the pair of virtual dice to find two sums. So many interesting things happened here when partners decided on the victor.  For example, if one student rolled a 7, many students completely ignored the other rolls, establishing the 7-roller as the winner, period.  Some students started finding the sums of both rolls together to try to establish who won.  Some students computed averages, but averaged the two sums without regard to the distance from 7.  Again, I paused (They HATE when I pause without warning them!  They HATE when I pause WITH a warning!   They HATE BEING PAUSED… but it’s SO NECESSARY and helpful for class discussions!  Students be like, “AWWWWW!!!!”) and we addressed who won in each case. Check out some interesting explanations below that provided opportunities for class discussion.      

Next, it was time to transition from pairs to teams.  Students moved to teams of 3-4 students each, and had to “roll” the dice 10 times each, plotting their own sums.  I wrote the word “CHAMPS” on the board, and asked each team to write the name of the student who “won” in their group.  That winner from each team would advance to a class tournament from which an entire Sum Game class champion would be established.

MAD Symmetry!

“Teacher-paced gates” gave students access to screens 7 and 8, and off they went.  There was gnashing of teeth when a student rolled a sum of 2 or 12, and eruptions of joy with sums of 7.  Once the first team wrote the name of a “champ” on the board, I dramatically interrupted class and said, “Oh!  I almost forgot!  When you write the name of your team champ on the board, will you also write their score?  Thanks!” At first, this request seemed totally reasonable.  Then students started declaring winners, walking up to the board, and looked to me for guidance…

“Are we adding them up?”

“Should I write the average?”

“Can I just write how many times our winner rolled a 7?”

“How do I write the score?  Can you just tell us?”

My lovely, lovely students.  You know me better than this. 🙂

Student teams started to compare strategies for finding “a score” for their winners.  One class started the trend of simply writing down how many 7’s each “champ” got, and that was that. We were suspicious… did we really have a three-way tie?  Seemed unlikely… so we took a closer look at their line plots to see what the non-7’s were.

Then, it happened.  A couple of students erupted with the idea that every 7 should actually be worth 0 points… and that 6 and 8 should each be worth 1 point.  I couldn’t write what they were saying fast enough.  The class seemed to buy into this idea, and all of a sudden, groups were questioning the champs’ names that were on the board.  Kids started yelling (in a good way), “I *KNEW* I won!  My name belongs up there!” Everyone feverishly worked their own plots AGAIN, and we started seeing values next to the names of the champs that represented the average of the distances from 7.

I feel like we established important concepts to prepare for the MAD.  What transition would you include (in the Desmos activity or otherwise) to bridge this experience to calculating the MAD?

Each class had a “champ” today, but the real win was the entire experience.  Thanks again to Nathan for sharing so my students could play “The Sum Game” today!  If your students “play” too, I’d love to hear how it goes, and any feedback on tweaks you made to the lesson that worked well with your students!

Posted in Algebra 1, Pre-Algebra | Tagged , , | Leave a comment

Nearpod iOS –> Draw –> Photo –> Homework Check!

It’s true, I’ve probably mentioned this strategy idea 59 times before this post, and some may tire of hearing about it.  But I just. can’t. overstate. how much I love using it, several times a week even.  It’s just that I know how difficult it is to convey excitement and magic from one classroom to another by typing words on a screen… I just truly want you to experience it with your kids too.

I’m not a fan of giving too many problems for homework (quality over quantity), or the idea of “grading” homework (since homework is an opportunity to practice something new, we are still learning, and many have not yet mastered whatever the homework is about).  However, I do like to “spot check” a homework problem or two.

Yet, if I am the only one who gets to “spot” the problems, how does that benefit my community of students?

Enter Nearpod iOS app.  I like to choose one problem from the (paper, handwritten, old-school but good-school) homework that I’m most curious about so we can pick it apart.  As students enter class, a Nearpod code is already projected on the screen.  While I’m taking attendance, Nearpod is grabbing a work sample from every single student.  Each student quickly takes a photo of the problem I’ve chosen ahead of time, and submits it on a blank “Draw” slide.  I anonymize the work so we’re focused on the math, not who did it… initially, anyway.  As conversations begin, students inevitably reveal their identities so they have the opportunity to show AND tell about their thinking that’s on the big screen, even if… especially if… it was initially wrong and they want help.

My Algebra 1 students are brand new to solving quadratic equations by factoring.  No sooner did I project the first sample of student work today than my students literally started pointing at the screen, talking all over one another.



And this talking was on target.  Noticing that a quadratic equation HAD been correctly factored, but *poof* we’d lost the equals sign and it had become an expression by mistake.  Or, that someone factored correctly, wrote an awesome equation, but made sign mistakes when they applied the Zero Product Property.  We scroll through every work sample.  Every one.  And we have a class chat about each one, pursuing all of the wonderful questions and comments that the kids are almost jumping out of their desks to share.  We see trends.  Several kids have made the same mistake enough times, that when we see it again, we almost have a code word… the thing the teacher would write on a kid’s paper… we say it, in unison, as a class.  Today that word was, “Expression.”  Every time a student moved every term to one side of the equals sign, but dropped the ” = 0″ in the process, we identified that error as “Expression.”

Nearpod, I don’t know how you do it, but there’s something about this format that brings out an energy in my students that almost doesn’t make sense.  We are looking at equations and we are genuinely, seriously excited to talk about it!

Teacher truth-note: If we’ve ever taught this topic before, WE TEACHERS know our students are going to make these errors.  BUT THE KIDS DON’T.  This is the first time they’re doing this… they’re seeing this.  Let them think they are the only group of kids who have ever done this.  Give them the privilege of identifying and giving names to the errors they see.  Let their eyes be fresh to the math that we’ve been teaching for years… and maybe, just maybe, some of that math will seem a little fresher to us teachers, too.

I like to follow-up with a “Poll” after these great conversations, where students rank their current level of understanding.  Finally, I give them an “Open Ended” anonymous opportunity to ask questions, in writing, and showcase/address them before we leave Nearpod.

Students aren’t shy about sharing their opinions about the benefit of doing this feedback cycle.  We often have to do a bit more reteaching once the Nearpod portion has ended, but it’s VERY focused.

If you have the means to do so, please try it in your own classroom!  Steal my template here, and change the title slide to personalize it for your own use.  AND… stop back here and tell me how it went! 🙂

Posted in Algebra 1, Pre-Algebra | Tagged , | 5 Comments

“We All Fall Down” #MTBoS #MTBoSblogsplosion Week 4

I had the great privilege of attending the #CTCTM Spring Conference last weekend.  In my keynote address, I shared about how two things that bring me great joy (and challenges) collided right there in Waco… the endless list of home improvements at out own #FixerUpper #AustinFixer … and ways to “fix up” my own teaching.  In sharing transparently about my own practice with the attendees (half of whom were pre-service teachers, woot woot) my hope was to start a conversation about how to “fix up” what we do every day, even if that means starting small… starting somewhere.

Ready to see the BEFORE picture of our Fixer Upper?

My little family of three (hubby, son and I) purchased a “fixer upper” about a year and a half ago.  “Starting small… starting somewhere” has been the only way to (sanely) survive this process.  We’ve fallen down and have gotten back up repeatedly – from unexpected repairs, to downright horrific workmanship that had to be redone, it’s been a bumpy road.  And sometimes, I feel the very same way about teaching math.  Always a “honey do” list of things to “fix up”… Fall down… get back up!

Whether it’s my house or my second home (room 510), I will continue to get back up.  I’m encouraged and challenged by the #MTBoS community who shares trials and triumphs that shape me day by day.

So, without further adieu, here are several fall-downs that have a common theme for me:

Popcorn Spoiler

So pumped to try Dan Meyer’s Popcorn Picker using Nearpod as the delivery tool, I “set the stage” for students, expecting rich discussions, loads of work samples, and an all-around great 3-Act experience.  What I did *not* anticipate was that just about every kid would say (of the paper cylinders), “They are the same.”  Period.  Little to no math.  Except for the ones who showed math.  They found the area of both sheets of paper, looking at me like, “What’s the big deal here?  The papers are the same, lady.”  Sure, the whole point of the task is that students might think something about these cylinders is “the same” to start… but by the end… they should, in theory, have a sort of a-ha about volume… right?  Well, even AFTER I showed “Act 3” and asked students, just to be sure, which container would hold more popcorn… most STILL said, “They will hold equal amounts of popcorn.”  We had JUST WATCHED the final video, and they STILL said, with ZERO work attempted, that these cylinders would hold equal amounts… I was pretty much speechless at this point.  I didn’t know how to recover except to direct teach the whole. entire. thing.  Has this happened to you in the midst of a 3-Act attempt?  How did you get the train back on the rails?  (Other than my way, which was, just tell them.  Everything.  Do all the math.  Show all the math.  Just take over… while they watch… and still write down zero math…….)  I also had an experience where providing the necessary tools in person made for a much richer problem-solving experience than watching the videos.


Changes In Dimensions Flop

I gave students paper visuals and actual wooden cubes: a 1-by-1-by-1, a 2-by-2-by-2, and a 3-by-3-by-3.  I gave them a handout that facilitated, without telling, understanding how changing dimensions impacts surface area and volume.  I envisioned a classroom where students would build, play, discuss, discover, and generalize.  After watching groups attempt the task for 20 minutes or so, I gave in.  No one seemed to have a clue what we were doing.  I stopped the whole thing, took over, told everybody what I’d hoped they’d discover with some guidance, and basically felt like I’d wasted an entire class period.  I retaught the concepts the next day, directly, and from scratch.  Had I asked too much?  Or… should I have waited just a bit longer…?


If there are two things I can’t stand, they are:

  1. Feeling as though I’ve wasted instructional time.
  2. Designing a discovery/constructivist-type lesson only to take over and tell everybody what I wanted them to get out of it.

I haven’t figured this out yet, friends.  

When this happens to you, how do you handle it?

Posted in Algebra 1, Pre-Algebra | Tagged , , , , | 7 Comments

Teaching ^(Adolescent Humans) Mathematics #MTBoS #MtbosBlogsplosion

This week’s #MTBoS #MTBoSblogsplosion theme is “soft skills”.  In a middle school mathematics classroom, I’d dare to say this topic is *almost* as important as the math content itself.

The late Rita Pierson seals this truth in a simple sentence:

Ramblings and Reflections Regarding Soft-Skills and Teaching ^(Adolescent Humans) Mathematics

  • Sometimes, Embracing “Silly” Helps Learning Happen

What’s the first word that comes to mind when I say “math class”?  Probably not “creativity” or “silly” – however, there are some amazingly creative students sitting in our classrooms every day.  Sometimes being creative turns into silliness, but in these light-hearted moments, students feel safe, open to learning and building relationships with me and with one another.  Every class period has “their thing” that is unique only to their class.  Once we have that silly moment, it’s an experience to refer back to and giggle about for weeks to come.  This is the “stuff” students often remember about our classes (even more than that killer lesson we designed… sorry, but true!)

Several years ago, one of my classes went so far as to design and order class t-shirts.  We all wore them every test day, and it was a “4th period thing” that made *our class* special.

Strike a “duck lips” pose and sport your matching test-day t-shirts!


Here’s a day that math got silly, but learning still happened.  If I saw any of these former-students on the street tomorrow, they would be able to articulate some of these stories as moments they still remember from our class.  I’d bet money on it.

  • Ask For Their Opinions

Want to model “growth mindset” for students?  Ask them to “grade” YOU.  The #MTBoS graciously shares Google Forms they’ve designed to ask students for feedback.  Show students that you care about their opinions, and are willing to improve the class in any way you can, based on their thoughts and feelings.  Note: I used to do this only at the END of the year, but have started giving a “Teacher Report Card” mid-year, AND at the end.  That way, I can take action on suggestions during second semester, rather than waiting until a new school year with a new batch of students!

  • Listen to the “Invisible Subtitle” Rather Than the “Noise”

Just today, I had the opportunity to stop by the Nearpod #PioNearSummit here in Austin. Folks from all over gathered to experience a professional development session lead by Melissa Pelochino after lunch.  Probably the most profound idea she shared is that students often say something to us teachers (something rude… something that catches us off-guard… something that makes us possibly want to respond in retaliation) and that we need to look past what we hear (the “noise”) and hear the heart of the comment.  Here’s a post where I clarified the “invisible subtitle” to help me better understand a frustrated student. Instead of responding hastily when students are frustrated with what we expect them to do, try responding with, “You’re welcome.” 🙂

Years ago, I majored in “Secondary Education / Mathematics” but I’d often verbalize my major as “Secondary Mathematics Education” instead.  Funny, the play on words seems so obvious now.  Teaching humans mathematics… quite literally, the math is secondary, isn’t it?

How do you build trust with students?

What are some elements of classroom culture that evolve, spontaneously or intentionally, in your classroom?


Posted in Algebra 1, Pre-Algebra | Tagged | 2 Comments

My Favorites #MTBoS #MtbosBlogsplosion

Happy New Year!

This post is already late – whoops!  However, I can’t pass up an opportunity to share about a few of “My Favorites”.  If you haven’t heard, there’s a BlogSPLOSION happening in the Math-Twitter-Blog-O-Sphere (MTBoS) community, and you should join it!  More info here!

Two of my favorite tools for fostering student metacognition, dialogue, and error analysis are Nearpod and Desmos.  As with any tech tool, it’s not primarily about the tool, it’s HOW YOU USE IT.  Tools that help make student thinking visible, not just to ME but to my STUDENTS to analyze and discuss… are a win!


Favorite “New” Way I’ve Used NEARPOD 

Nearpod provides the opportunity to share static slides and interactive tools with students such that instruction and assessment become one and the same.  While I enjoy creating and implementing complete lessons using these tools, in more recent months I’ve found some fascinating, simple ways to use Nearpod (that I think you should try too)!

Using the “Draw It” feature on iPads, students have used student-paced Nearpod lessons to submit work to me.  I like doing this for homework, so that I have complete access to the Nearpod report before our next class.  A wonderful feature in the iOS version of Nearpod is the ability for students to submit a photo of the work they’ve done on paper.  This way, I have work samples from every student, and those who prefer to use paper can do so.

Before our next class, I like to take screenshots of students work samples from the “report” that are interesting (Note: Many times “interesting” means incorrect).  In a new Nearpod, I use these screenshots as background images for a set of new “Draw It” experiences.  To start our next class meeting, I launch a teacher-paced version this new Nearpod comprised of student work samples.  Students can draw on each problem and “grade” it.  Shocking moment: That moment when students “grade” an incorrect problem as being CORRECT!  To see this in action, read this post.


Favorite “New” Way I’ve Used Desmos CARD SORTS

Is it possible to love Desmos any more than we love it today?  In recent months, Team Desmos has added so many new features and improvements, it’s tough to keep up with them all!  I’m always so impressed with their willingness to listen to teachers regarding feature requests – Desmos is changing the course of history in the way mathematics can be explored and learned.  Period.

If you’ve seen a few of the Desmos creations I’ve been using with students, you’ll see that I love Card Sorts!  Rather than keep the feedback in the teacher dashboard to myself, I like to:

  1. Begin a card sort showing NO feedback on the teacher dashboard
  2. Project the teacher dashboard with student names anonymized initially
  3. Project the teacher dashboard WITH student names once a few “sorts” become entirely “green” (correct) so that these “experts” can provide peer help for those still aiming for “green”.

To see this in action, read this post.

I’d love to hear how you are using Nearpod, Desmos, and other tools to foster metacognition and error analysis with students!

Join the #MTBoS #MtbosBlogsplosion!

Posted in Algebra 1, Pre-Algebra | Tagged , , , , , , , , | Leave a comment

How Old?

The other evening, I was sitting with my husband and son at a candlelight Christmas service, singing carols and feeling merry.  One of the carols mentioned “shepherds” and right on cue, my 11-year-old son leans over and whispers… “There are 125 sheep and 5 dogs in a flock…”  (You Know Your Mom’s a Math Teacher When…)  It took everything in me not to burst into laughter right then and there.  I’m thankful for this holiday moment, as it reminded me to post briefly about the problem scenario – “How Old is the Shepherd?” (Which I may or may not have had my son experience as a guinea pig before presenting it to my own students…)

Perhaps I missed this post shared by Robert Kaplinsky because he composed it on my birthday, but I was thankful that Michael Fenton mentioned it to me in a recent conversation about teaching for understanding.  The minute I saw it, I knew I wanted to present the scenario to my students, and follow up with Robert’s fascinating video.  I also shared the video with my colleagues, who watched in amazement, and also decided to present the task to their students.  I’ll admit it… my colleagues and I were skeptical, thinking our results might be better… that our students wouldn’t fall for it.

However… I tried to put myself in the shoes of the students Robert interviewed.  I can imagine the 8th-grade-me feeling pressured to do math when presented with a problem, a white board, a dry-erase marker, and a one-on-one exchange with a teacher I respected and wanted to please.  Might that pressure have impacted students to number-pick without understanding, feeling the obligation to provide an answer?  If so, how could my colleagues and I reduce that pressure while creating that one-on-one environment where no one student could create a “spoiler alert” by calling out… “Hey!  This problem makes no sense!”

We decided to present the task using Nearpod.  We administered the task using a Nearpod-generated pin that fostered a “student-paced” format, and gave students the opportunity to draw and explain their thinking.  During quarterly exams before we went on break, after students handed in their tests, they completed the Nearpod task.  When students tried to come to my desk to discuss the task with a look of confusion, they didn’t challenge me when I said, “I’m sorry, others are still testing so we’ll have to keep a silent testing environment right now.  Please do the best you can.”

For the record, my poker face stinks.  I am amazed at Robert’s ability to remain respectfully stoic.  Even as students walked away from my desk, confused or frustrated, I had to look away to hide my cheesy grin – yet another reason using Nearpod was awesome, and frankly in my case… necessary.

Nearpod allowed my colleagues and me to maintain access to student responses using Nearpod reports, and comparing then during our PLC time was both interesting and somewhat disheartening… our students’ results were very much like those in Robert’s video.  When I looked at my Math 8 students’ responses, approximately 38% “made sense”.  When I looked at my Algebra 1 students’ responses… I was shocked to see that they, too, had a success rate of about 38%!

Here are some “Not Making Sense” work samples – incorrectly using division was, by far, the most common method I saw:



In spite of our attempt to try to lighten the pressure to provide an answer by using Nearpod as our tool of delivery, some students who smelled a rat clearly also felt obligated to give the math teacher “the answer”:




Some students called our bluff with grace and/or humor:



This information left us (teachers) asking a lot of questions about instructional next-steps.  One idea we had was to use student work samples to create a new Nearpod for discussion the next day in class before playing Robert’s video and asking the follow-up question, “What did you learn from this experience?”

After showcasing and discussing a variety of student work samples and showing Robert’s video, students gasped in amazement and started sharing about how they felt when presented with the task initially. MANY students admitted that they thought the problem was silly, yet felt obligated to do work and “get an answer” to please me or out of fear that I would “grade” it and they wouldn’t do well if they didn’t get an answer.  I’m also glad I asked them what they learned as a follow-up.  Check out a few responses from the Nearpod report at the end of this post.

While I’m left feeling like this experience was a square one in many ways, I know that I’ll be able to reference it during lessons, moving forward.

Have you used this task with students?  

If so, what were your instructional next-steps?

Want to use my initial Nearpod?  Grab it here.

Want to view my follow-up Nearpod?  View it here and create your own using your students’ work.

Posted in Algebra 1, Pre-Algebra | Tagged , , , , , , , , , | 3 Comments

Brain-Friendly Ways to Break It

Years ago, I had the pleasure of attending a workshop with Judy Willis.  Willis is a former neurologist who chose to apply her brain science expertise by becoming… a math teacher!  Though her time is spent educating educators now, her career path fascinated me from the moment she told her story in that workshop… dare I say 8 years ago…?  Additionally, many of her strategies impact instructional decisions in my classroom on a regular basis.  Willis knows what she’s doing.  How many days of PD can *you* say you still remember and apply, in detail, as you plan lessons… 8 years later?  Needless to say, I was an instant Judy Willis fan because her brain strategies worked, and continue to work, on me!

One strategy I intentionally use often is compare and contrast (see page 9 here).  Showing students what something *IS* and what something *IS NOT* helps deepen understanding.  For example, why introduce scenarios that are only “proportional-linear” when contrasting “non-proportional linear” situations serve to reinforce characteristics of *BOTH* concepts?

Recently, I used Desmos Function Carnival in a compare-contrast way.  In the past, I turned students loose in this activity by handing over a class code.  Being a (generally) compliant student myself, I hadn’t anticipated that many students would aim to “break” the carnival rather than trying their best to create a precise graph.  My first reaction when kids goofed around with silly graphs was frankly… disappointment.

Then I tried again, anticipating that they WOULD “play” and draw plenty of messed-up graphs.  I wrote this post to share how I shifted students’ focus from silly graphs to precise ones.  This is how Function Carnival has behaved in my classroom… until this year.

This time, students had been introduced to the concept of function the day before.  They had homework that required them to look at all sorts of wacky graphs, and determine whether or not they represented functions.  Rather than give students a class code from the get-go, I displayed Cannon Man on my smart board.  We watched him shoot out of the cannon, but this time I didn’t ask students to create a precise graph.  I didn’t even give them a class code.

I told them to ignore the green Desmos animation entirely.

Instead, I told them we should try to break it.

“Who has a favorite graph from last night’s homework that was NOT a function?  Let me draw that for you up here.  Now, talk to your group.  When I press PLAY up here, what is the blue Cannon Man going to do?”

Explode!  Gory and funny explanations all around… students begging me to press PLAY…a hush fell over the room, and then… this!

Our next non-function graph reinforced a deeper understanding of the “Vertical Line Test” that always shows up in textbooks but rarely makes conceptual sense to kids early on…

We chose several more non-function graphs from the homework for ME to draw… and then they started BEGGING for a class code so they could try it.

To summarize, I knew at least some of my students would want to break Cannon Man from the start.  Rather than meaningless graphs, we connected non-function homework problems to Cannon Man in motion.

To me, this was just as meaningful as the intent of the task to start.

Bonus: Check out a “Function or Not?” Desmos Card Sort, and other activities, by clicking the “Desmos Activities” icon to the right, or by using this link.

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Taking a Risk

My students are brand new to linear relationships, and it’s been so much fun watching them make connections.  We’ve been focused on applying slope to scenarios and writing linear functions in slope-intercept form given various info (a table, a graph with “nice” points, a slope and y-intercept, two points) and most of this foundational work has happened on paper. Yesterday, I took the opportunity to introduce students to two tasks to apply what we’ve been working on in novel and dynamic ways.

To start, I modified Michael Fenton’s “Match My Line” Desmos activity to create a “lite” version for slope-intercept form newbies. Match My Line (Lite Version)

While some students will just dive right in and try something, even if they’re not sure where to start, what I witness more commonly is students staring at the screen.  When asked, “Tell me, how is this going so far?” students often respond, “I’m thinking.”  Truth for some.  For others, taking the risk of typing something and seeing a line that doesn’t do what we wanted it to can be a scary step.

This might be surprising, as students take risks all the time with video games, and all sorts of techy and non-techy adolescent behavior in general.  However, I find that students need a bit of encouragement and coaching to get started, even with a seemingly non-threatening tool that’s simply going to graph the line one tells it to.  Prompting with some simple questions like, “put your finger on the place where you WANT the line to cross the y-axis” is enough for some kids to say, “OH!!!!!!!!” and get rolling with confidence!  Sometimes, asking a question like this reveals misconceptions such as putting a finger on the x-axis instead.  While Desmos has AMAZING built-in features on the techy Teacher Dashboard for students who have STARTED working on something, checking in on them in person can be the best intervention when they’re stuck or “thinking”.

And when the line goes through the points as they wanted it to, the reaction never. gets. old.  Cheers!  Arms in the air!  A sparkle in a student’s eye as they look at me and say, somewhat surprised at times, “… I did it…!”

Projecting the “Overlay” as students work is a great way to witness understanding… screen-shot-2016-11-23-at-8-55-19-am

…and even call out bluffs (with names anonymized) so we can help! screen-shot-2016-11-23-at-8-55-43-am

After students celebrated their “Match My Line” successes, we transitioned to a simplified “Marbleslides” task.  No emphasis on domain and range here – simply graphing some lines with slope and y-intercept in mind brought victories.  I love having the privilege of being the first to show students the capabilities of “Marbleslides”! 

They asked, “Did you make this for US?”


I just tell them Desmos is amazing, and we rock and roll. 🙂

Slope-Intercept Stars I’m glad we did the “Match My Line (Lite)” task first.  The more serious nature prepared students for the lighthearted, though equally mathy, marble launches.  I was especially proud of a gal who decided to plot her OWN “clean” points near the stars I provided to help her design a successful equation.

How do you encourage students to take risks when they’re not sure how to start?

What is technology’s role in promoting mathematical risk-taking?

Thankful for my students, and thankful for tools and resources that help them understand and enjoy mathematics.

Happy Thanksgiving!

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In The Moment

screen-shot-2016-11-11-at-8-29-12-pm The SAMR Model is a fundamental framework often used to help educators consider how and why to integrate technology.  Teachers are encouraged to aim “above the line” to provide students with potentially transformative experiences, rather than simply enhancing tasks with technology.  While this framework is helpful, I always find the four levels to be fuzzy.  I also question anyone who tries to force an app or tool into one of four levels… to me, it’s always been about HOW technology tools are used that determine the impact.

Additionally, I’ve sensed a bit of a shift in my own technology use lately.  While I find tremendous satisfaction in designing complete lessons using some of my favorite tech tools, there are plenty of days when I look at what my students are doing, and in the moment, I whip up a way to get the thinking that’s happening on sheets of paper and in small groups to a collection of student work samples that we can all talk about and learn from.  It’s not poor planning… it’s the comfort of knowing the tools I have at my access in a moment’s notice, and the confidence to know I can use them exactly when I need them!

Where do these in-the-moment discussions that technology makes possible “rank” in the SAMR model?  I often wonder.  From the outside, it may look like we’ve simply transferred a paper task to technology, ranking the whole thing “below the line”.  However, the discussions and a-ha moments that happen make me think there’s a bit more transformation happening than meets the eye.

For example, a-la-Open-Middle style, I asked students to create two tables of values and two graphs such that the first was proportional linear and the second was nonproprtional linear.  This quick prompt was part of a “foldable” I created several years ago.  In the past, I just walked around and looked at student work, or had several students share their work using the document camera.  However, this week as I watched students creating these representations in my first period class, I realized… I have Desmos Activity Builder now!

As they worked, it took me less than a minute to make this.  


Suddenly, their papers became rough drafts, and the finished product moved to Desmos, where we could anonymously examine every student’s work, explore every response using the Overlay feature… and even zoom WAAAAY in or WAAAAY out to see what was happening at the origin in each case.  Sure, I “substituted” a sheet of paper with Desmos, but I can’t accept that this was *only* substitution after all that creating, zooming, sharing, and discussing happened.


Showcasing Proportional Linear Relationships Using Desmos Overlay


Testing Desmos!


One evening this past week, I gave a “Desmos homework”, using this activity created and shared by Roxygirl Teacher.  Again, at first glance one might say this served as a worksheet substitution.


I intentionally gave the same class code to all 3 of my Math 8 classes, so we’d have a huge sample of responses to consider the following day.  In class, I projected the teacher dashboard in Desmos, used Sketch to work through a problem with students, confirmed the correct answer, then took full advantage of the “Summary” feature to examine student responses.  Discussions about equivalence, notation, and errors were fantastic!  More than once, students had OMG epiphanies that they had messed up.  They were thankful, as they have a quiz next week, and these discussions and comparisons of student work helped many students who, beforehand, didn’t know what they didn’t know.  Instead of hearing students complaining about mistakes, they were thankful for their mistakes, and the realizations that some had written every slope ratio upside down!  Some made sign errors repeatedly!  One student even represented every slope as two values separated by a comma rather than as a ratio.  And others… well… they just needed a re-count. 😉


Is it just me, or when you think you’ve seen every possible goof out there, a student comes up with a new one?  Sometimes we can’t anticipate every weird thing kids are going to do.  We try our best to be proactive, but there are some creative little buggers out there.  Tools like Desmos and Nearpod help us teachers to help our students better.

For example, I used Nearpod Draw It to spot-check several homework problems this week from an intro lesson with my Algebra students.  After students worked a problem in Nearpod, I clicked through every problem briefly, asking students to make the first lap about “noticing”.  After we quietly observed every problem (anonymously) we started to talk about trends, particularly in errors.  I saw repercussions of incorrectly generalizing “Trick” 6.5  in full force with these simple inequalities.  I was genuinely surprised by how many students fell for the “trick”!  Granted, I’m focusing on student errors here… plenty did well… but *they* needed to see this work and so did I!  Afterwards, I was able to generate a quick ThatQuiz assessment to check that our discussions helped dispel wrong thinking.

If we don’t invite our students to share their thinking, and provide an environment where they feel comfortable sharing, we’re missing out on many learning opportunities!



How do you empower every student to participate and share mathematical thinking?  

How do you handle student mistakes?

What are the best ways to address “tricks” that are being generalized incorrectly?

What is technology’s role in this process?


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