Using Desmos on iPads… for the Algebra 1 EOC STAAR Test… Take 2

This week, our Algebra 1 students took their STAAR End-of-Course exam.  This round marks year 2 of Algebra 1 students being permitted to use both a TI handheld graphing calculator and the Desmos Test Mode iPad app in light of this TEA calculator policy change that went into effect last school year.

An annual tradition for my Math 8 students (who recently experienced year 3 of TI and Desmos Test Mode access for state testing) and now, my Algebra 1 students, is to give a quick 3-question follow-up survey.

I asked three questions:

  • In general, which tool do you prefer?
  • Name a few math lesson topics for which you like using the TI Graphing Calculator more than Desmos Test Mode.
  • Name a few math lesson topics for which you like using Desmos Test Mode more than the TI Graphing Calculator.

Though my Algebra 1 sample size this year is very small (36 students to be exact) this round marks the first time that not a single student answered the first question by saying they prefer the TI calculator…!  This hasn’t necessarily been the case with Math 8 students annually.  You can see their preferences by checking out this post.

Here’s a side-by-side comparison of this year’s Algebra students and last year’s sample size of 49 students.  Additionally, you can check out the unedited and anonymous responses from this year’s Algebra 1 students regarding their favorite concepts to explore using each calculator.

Algebra Calculator Survey Yenca 2016-17

What struck me most was that we’re paying over $100 a pop for a calculator because it can graph stuff, but these students aren’t actually using the TI handheld graphing calculator for that purpose…!

Hands down, these Algebra 1 students use Desmos for graphing, and the TI primarily for quick calculations using the four basic operations.

More calculator commentary here and here and here and here and here and here and here !

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

Using Desmos Polygraph to Establish “Intellectual Need”

Have you seen Dan Meyer’s fun little “Pick a Point” geometry task?

If not, watch this before reading on.

Today, AFTER I’d already introduced polynomial vocabulary (not the most interesting topic) I had students play Desmos “Polygraph” with tasks created by John Stevens and me.





And then it hit me.

I just passed up the opportunity to establish intellectual need.  I *TAUGHT* the vocabulary, then used Polygraph to practice it.

Which was fine.  First, I used a Nearpod lesson to introduce the vocabulary.  The Nearpod lesson continuously asked students to create polynomials with varying characteristics.  They clearly applied the vocabulary and created a variety of polynomials (correct and incorrect ones) that far surpassed your average textbook’s bone-dry examples, while creating interesting and misconception-revealing non-examples.

Nearpod Draw It Prompt: Create a monomial with a degree of 5. #nailedit

But… couldn’t I have applied Dan’s “Pick a Point” strategy on a grander scale, asking ALL students to play a round or two of Polygraph with little to no vocabulary to lean on… first?

The answer is yes… I could have… and probably,  I should have… and definitely, I WILL do that next time. 🙂

What math topics and concepts come to your mind that might benefit our students more if they’re given a shot at a Pre-Polygraph and a Post-Polygraph once “intellectual need” is established?

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

Teachable Moments

Five minutes before the end of class yesterday, a student made an interesting claim while everyone was working on something else. She said, “Did you know that by the time you’re 90 years old, you will have been asleep for 9 whole years?!?!”

I told her I hoped not, and that 30 years would probably feel a whole lot better.

Every nearby student was shocked by my claim.  Absolutely disgusted and disappointed. How could I say that?  Could THAT much time be devoted to dozing?

We had a quick chat about the ideal average of 8 hours of sleep per night, and they quickly realized that, of their 13 short years on earth, they’ve already been asleep for over 4 years. While I saw students’ faces droop at the realization, they sure were motivated to explore this side conversation.

So… who’s going to turn this idea into a Desmos Activity? 😉

Speaking of… I had a math moment with my pantry this week.  I was rooting around for a snack and was suddenly struck by the number of boxes and packages that show dilated food stuffs.  Most were enlargements, but one cracker was a reduction.  I put my munchies on hold and grabbed my phone to snap a few photos, and this was born.  It’s in draft-mode, and I appreciate the feedback folks have been sharing on Twitter, and/or any edits you make and share back.  I’m hoping to have this polished and ready to go for my 2017-18 students.

Now, about that snack…

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

Highlights from #NCTMannual San Antonio

Glancing through the NCTM Annual program, I could almost feel my arms and legs being pulled in no less than 4 directions for any given session timeframe.  Respected colleagues in our community shared their expertise and I’m thankful to have had the opportunity to learn from so many folks who continue to do great work.  Here are some highlights from my experiences in San Antonio.

Classroom Dessert: Putting Assessment into Students’ Hands

John Stevens and Matt Vaudrey showcased alternative ways to assess student understanding by encouraging student choice.  Whether students preferred to show what they know through a paper-pencil task, a creative video, or a work of original art with accompanying written explanations, student work-samples featured unique ways to arrive at the same goal – learning!

Looking for ideas?  Check out the list of ideas John shared in the photo below.  Even more here:

Math Task Makeover with Desmos Activity Builder

Bob Lochel, Michael Fenton, and Jed Butler provided before-and-afters of some all-too-familiar textbook spoilers and worksheet ho-hums such that Desmos Activity Builder up-leveled student experiences!  Check out the latest support resources for teachers at and a visual summary of the session through one of many amazing sketch notes shared by Karen McPherson!

“Noticing and Wondering” as a Vehicle to Understanding the Problem

Annie Fetter helped attendees realize that there is a part of problem solving that good problem solvers do naturally.  We educators need to put natural structures in place to help students problem solve.  One way to do this?  Withhold the numbers at first – give students a chance to seek relationships and patterns rather than rush to “the answer”. Everyone can “notice” and “wonder” about something visual.  Does it take time?  It sure does, but this time spent upfront reaps rewards once a lesson progresses since students have already done so much of the “work” up front. Noticing and wondering is not a time zapper… it’s actually a time saver!  All students are “doing something” – it’s not a strategy where “fast kids” get the answer and the others are just waiting for them to tell the answer.  Annie’s pointed reminders about the power of “noticing and wondering” are already impacting my lesson plans for tomorrow!  Watch Annie in action here:

Mathematical Mindsets: Creating a New Future for Math Teachers and Learners

Jo Boaler continues to press on with her math revolution!  I was thrilled to hear her speak in person, and I think my neck is still a bit sore from nodding in agreement with her philosophies and findings.  Visit and be prepared to spend a few hours there.  Check out my favorite slide from her talk below.

Open Educational Resources: Designing a Middle School Curriculum

Kate Nowak, Ashli Black, and Bill McCallum shared about the process and progress of developing a cohesive OER middle school math curriculum set to be released in July 2017, so stay tuned!  Attendees got an exciting sneak-peek in this session.  I can’t wait to further explore this work.  To learn more now, check out the math curriculum tab at Open Up Resources using the link below:

Looking Forward: What’ll Be Possible in Math Ed in a Decade?

Eli Luberoff, the CEO and Founder of Desmos, emphasized the importance of our students’ ability to solve non-routine problems as we dive into future careers.  Eli addressed the purposeful use of technology in our math classrooms to assist our students in preparing for their own futures, even claiming that our math classrooms are one of the most important places on earth!  Feel the weight of that honor and responsibility for a moment!  Additionally, Eli proposed the use of a tool like Desmos Marbleslides to meet unique differentiation needs of our students because of the “low floor, high ceiling” nature of these tasks.  Finally, in WWDC-Desmos-Style, Eli let us play with the latest and not-yet-final-draft of the new Desmos Geometry construction tool at  I wish I could have recorded the audio of the attendees during this time.  There were oooo’s and ahhh’s and even moans and groans of delight as teachers began imagining how this tool will change the ways students explore geometric concepts.

Using Digital Tools to Give Every Student a Voice

With a foundation set on NCTM’s Position Statements regarding formative assessment and technology integration, we explored how connecting a math standard to a #MTBoS resource by using a technology tool can give every student a voice in class.  Check out a self-paced experience by visiting and use the code FHBNX (valid through April 2017).  Feel free to participate if you weren’t able to make it, or if you were in the session, to provide any feedback you’d like to share to help me improve upon the delivery of these ideas!  It’s challenging for me to share about something I experience with my students in my classroom in a conference setting where the attendees aren’t 12-14 years old, and I’m looking to get better at this!  Also attached below is a handout that includes links to take-away resources to use and/or edit for your own classroom use. NCTM 17 Attendee Notes Session 529 Yenca

Fun fact: Our live Nearpod session code was GIJOE.  I thought for sure someone at Nearpod was messing with me, and had created that code intentionally.  It turns out, the code was generated randomly.  The probability of that happening is (1/26)^5 folks… or as a decimal…   Perhaps I should go buy a lottery ticket.

 Math Is Power Not Punishment

Dan Meyer used Guershon Harel’s paper as inspiration to pursue the idea of creating the “intellectual need” for the mathematics we explore with our students.  I’m pretty positive we’ll have a video of this talk to share later.  You know Dan – his talks can be tough to describe in a blog post.  You’ll want to experience this one for yourself. (Will post a link later).

The Struggle is Real: Tasks, Academic Status, and Productive Problem-Solving

Geoff Krall challenged us to think deeply about “productive struggle” and how we promote productive struggle to students who’ve been conditioned otherwise.  Geoff’s take on the topic is that it takes a wholistic approach of three elements: Quality tasks, Academic safety and Effective facilitation strategies.  Visiting is a great place for folks to find an abundance of quality tasks.  Additionally, we explored this Open Middle task in Geoff’s session and got surprising results that sparked conversations lasting beyond the session!

Empowering Digital Collaboration in 3 Acts

I finally got to meet Cory Henwood!  We’ve respected each other’s work in this realm of digital collaboration for several years, and it was a treat to experience his session.  The benefits of using digital tools to capture and share student thinking are worth considering.  Additionally, Cory shares a boatload of resources at


One of my proudest moments to date in my 40ish years on the planet may well have been having the opportunity to share at #ShadowCon17.  At LEAST a Sagan of thanks to Dan Meyer, Zak Champagne, Michael Flynn, and NCTM leadership for the opportunity and support you’ve offered to help us four Shadowcon-ers to prepare for this experience.  I look forward to continued work as we launch our free online courses this fall.  Sign up here.

Of course we attend professional conferences to attend sessions and soak up the goodness like a sponge, but I would be remiss if I didn’t mention my favorite part of this conference: CONNECTING WITH YOU!  “You” includes so many familiar faces that, until this conference, I knew from a tiny Twitter photo and a vast collection of work through blogs and shared resources that have made my teaching practice and my students’ classroom experiences all the better.  I can’t describe the feeling I felt when I first walked in to the #MTBoS game night on Wednesday evening and finally got to high-five and hug so many awesome folks in our community.  I was so giddy, I had a hard time sleeping that night.  I was overwhelmed with joy, humility, and frankly, as a colleague of mine, Nadine, describes the feeling… cognitive crushes, ha!  

I love your brains, I love your work, and I respect you immensely.  

P.S. Check out the Global Math “My Favorites” from NCTM sharing-session here:

Check out another great NCTM reflection from Kim Morrow Leong here.

Valuable presentation advice compiled kindly by Dan Meyer here.


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

Using Desmos on iPads… for the Math 8 STAAR Test… Take 3

This past week, we completed our third lap of using the iPad app “Desmos Test Mode” on the Math 8 STAAR test (with the option of also using a TI handheld graphing calculator).  If you’d like to see what we’ve done in the past to lead up to this moment, check out this post and the included links for nuts-and-bolts.  Most folks who get in touch are curious about how we’re securely using iPads.  We “lock them down” using Casper Focus, which disables the camera in the iPad and keeps students only in the Desmos Test Mode app during testing.

To keep with tradition, I asked the same questions of students that I posed to my Math 8 students in 2015 and 2016 post-STAAR:

I asked three questions:

  • In general, which tool do you prefer?
  • Name a few math lesson topics for which you like using the TI Graphing Calculator more than Desmos.
  • Name a few math lesson topics for which you like using Desmos more than the TI Graphing Calculator.

My sample size was 62 this round.  Here’s a summary of their responses to the first question:

If you’d like to see which math topics were preferred for each tool, check out these anonymous responses.

Math 8 Desmos Survey 2017

Having three years of survey data now, I thought it might be interesting to see the graphs side-by-side… so here you go.

With variations in sample size (and frankly, pretty tiny sample sizes) it’s tough to say whether a shift is happening here.  Still interesting to examine, no?

Finally, a graph combining the responses of all 188 students I’ve surveyed over the past three years:

I’m not surprised by these results (though I really didn’t expect these results the first time I asked in 2015).  Math 8 is more of a “sampler course” curriculum-wise where a hand-held calculator has been the preferred tool each year.  (A little bit of Algebra, a little bit of Geometry, a little bit of number stuff, a little bit of data, and some financial topics).

However, Algebra 1 students seem to value the beauty and ease in working with multiple representations of functions that Desmos provides.  Of note, my Algebra 1 students’ results from last year can be found here… and we’ll see what my current Algebra students say in May!


Get over to today and play around with their *ahem* new “plaid” feature.

I’m guessing this feature will only last through today…


Plaid Mode, Anytime… it’s a thing. 😉


Posted in Algebra 1, Pre-Algebra | Tagged , , , , , , , | 1 Comment

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. (NOTE: Student-paced lessons are included in GOLD membership and above.)

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 , , , , , , , | 2 Comments

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?

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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?


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