Trading Worksheets for Desmos

Michael Fenton has come up with some very creative ways to use Desmos.  The “Match My Graph” mini-challenges on his blog provide students with opportunities to create and revise their thinking with immediate visual feedback from their graphs.  With Michael’s permission, I placed the hyperlinks to the challenge tasks into ThingLinks so I can embed them on my teacher website for students to easily access (and you can too if you’d like).

Much better than static worksheets if you ask me. ;-)

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

What is a “Math Coach”?

Screen Shot 2015-01-24 at 7.59.02 PMFrom 2008-2011, I served as a “math coach” in Pennsylvania.  The position was grant-funded, and there were no guarantees (or expectations, frankly) that the position would last beyond the first year.  The timing was perfect – I had been at home with my son for his first 3 little years, and we *both* were ready for a change of scenery.  As he toddled off to daycare/preschool, I read “The Math Coach Field Guide” while I waited to be approved by the school board and start my new job.  I was pumped!

My role was very specific, which helped a *lot* in defining my days.  I worked primarily with teachers who were elementary certified and were teaching Pre-Algebra to grade 6 advanced students or Algebra 1 to grade 7 advanced students.  I was there to help with content, lesson planning, creating resources and assessments, co-teaching, and modeling lessons.  I administered, scored, and tracked assessment data.  I worked with some of the kindest and most cooperative teachers around, from new-to-the-profession teachers to I’m-retiring-next-year teachers.  We had a 1:1 laptop initiative at the time, which made the experience that much more amazing.  The students were “our” students.  Though I didn’t have my own classroom, I still felt that sense of relationship and ownership since my role was so focused.

We had a 6-day-cycle model, so I’d spend 3 consecutive days at each of the two schools I served, staying in contact with the teachers at the other campus, and sharing resources with them across town.  It was a precious time in my career.

Year 3, the grant funding disappeared, but a unique set of circumstances found me serving at a third middle school in the same district the following fall.  I thought my time of employment was ending, and instead, I had a new batch of teachers to work with.  Every morning, I had my very own Algebra 1 class first period, and the rest of my day was dedicated to a math coaching role.  This time, I worked with all math teachers in grades 6, 7 and 8 who’d have me, rather than only working with Pre-Algebra and Algebra 1.  I worked in an emotional support class once a week and was treated like a celebrity.  I worked with teachers who would love nothing more than for my perky self to exit their not-so-sunny space, teachers who embraced co-teaching from day 1, and teachers who were happy to have me stay by the sidelines as they ran 100% of the show 100% of the time.  The classroom is a very personal space, and my role varied greatly from classroom to classroom, but I did my best.

I also started to remember how much I adored having my own classroom.  That crew of Algebra 1 students that was *all mine* made me think that if my “coaching” days came to an end, it would be a welcome transition for me.  And that’s exactly what happened the following year.

I credit my years as a “math coach” and my supervisor at the time, Julie Victory, with helping me see the value in blogging.  I was required to keep a log of my days as documentation, and what began as merely a recorded schedule morphed into a reflective document that I still enjoy reading every now and again.  The only math blogger I knew of during that timeframe was Dan Meyer, and even though I was composing a daily log, I never saw my daily happenings as worth sharing with a readership.  In time, as blogging seemed to become more of a “thing” I landed here.

Every educator in a “coaching” position has a unique role and set of circumstances.  I’ve wanted to compare notes with others who serve in this type of position, so I tossed a Google Form out to Twitter.

* Responders serve anywhere from 1 to 40 schools.

* About 1/3 of responders also teach their *own* students while roughly 2/3 of responders do not teach any classes of their own.  (I always wonder about this – for me, having one class of my own every day made me feel so much more connected)

* Responders have many responsibilities!

Here’s the Google spreadsheet with snappy graphs in the tabs (compliments of @MrVaudrey – colorful charts are kind of his thing). At the time of this post, I had 13 unique responders, and I hope more folks contribute.  I’d follow every one of these fine folks on Twitter if I were you. :-)  Still want to contribute to the spreadsheet?  Here’s the Google Form.

Posted in Algebra 1 | Tagged , , , | 4 Comments

Nearpod Popcorn Picker (Student Responses Too)


I’m not going to lie.  It was disappointing that my students so easily fell for Dan Meyer’s Popcorn Picker problem today.  A *very* small subset of students realized that, just because the sheets of paper had the exact same area, this did not translate to the cylinders having the same volume.  It took awhile for students to even connect that filling-with-popcorn related to filling-the-3-D-space-with-popcorn.


They definitely were duped by this image.  The photos seemed to confirm to them that their wrong thinking wasn’t wrong.  They fell for every trick today!


Using Nearpod to gather and share student responses was a boatload of fun.  They were SO engaged and excited!  But in the end, even after seeing Dan’s Act 3 video, they were skeptical.  At this point the lesson turned into more of a direct instruction experience.

*I* talked them through using the circumference to find the radius of the base.

*I* proceeded to find the area of the base of the first cylinder using our newly found “r”.

*I* found the volume of the first cylinder using our newly found “B”.

Then, *they* referenced my math-teacher-y structured work and found the volume of the second cylinder.

The energy was there.  The engagement was there.  The curiosity was there.

The correct math was not there.

Perhaps doing more of these tasks will help.  So, I’m doing a different task tomorrow.  We’ll see how it goes.

Click the link below to see some pages from the Nearpod report from one of the classes today.  I’m so glad I was able to capture these responses.  No students can opt out of the 3-Act process when they’re held accountable in this way… not that they would want to opt out!  :-)


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


Screen Shot 2015-01-17 at 10.24.32 AMIt’s been fun getting to (virtually) know more and more math Tweeps in the #MTBoS.  One such bud, Jon Orr, tagged me to compose a #10GoodThings post to reflect on “good things” that are happening with my little corner of the world (usually known as room 510 – and I really am tucked away in a little corner of our middle school, ha!)

I’ll try to keep this concise, but if you know me at all, I get kind of excited when I talk about teaching and learning and what I get to do every day.  Here are some “good things” that happened in 2014, and even as recently as yesterday.

In no particular order…

10) The other day, I gave in to the “rabbit holes” of Facebook and found myself taking a quiz with the premise “Can we guess how long you’ve been teaching?”  My results were “Have you been teaching from 0 to 5 years?”  The description followed about how my answers implied the enthusiasm of a new teacher.  So… I’ll take that.

9) I can’t even sit down to write this list because I’m continuously in conversation with math Tweeps in another browser tab.  I love that!

8) My students have become “math authors” of interactive eBooks.  Their work has been featured by Book Creator, iTunes U, and soon, will be included in a (paper, physical) book about student-created media using iPads.  Stay tuned!

7) I’ve gotten to meet, work with, and learn from truly legendary professionals I respect.  In 2014 I got to hang out with Dan Meyer, Andrew Stadel, Kyle Pearce, and Robert Kaplinsky at events like NCSM and iPadpalooza.  I’ve learned from Dylan Wiliam, Carol Ann Tomlinson, Ramsey Musallam,  Judy Willis, Sugata Mitra, and I’m sure I’m forgetting a few!  Having the chance to have in-person experiences makes the continued virtual communications richer.  I hope to meet more Tweeps in person in 2015! (ISTE? iPadpalooza? NCTM Regional Nashville?)

6) I’ve seen colleagues who teach in my corner of the hallway trusting my nudges to try new tools with their students.  When a colleague nearby sees successes with Nearpod, Socrative, ThatQuiz, Kahoot!, etc. with their OWN students, we have these “I-get-it” happy dance moments that I cherish.

5) I’ve continued to work with and create lesson content for Nearpod, an app I believe has amazing potential to impact student learning and develop that precious math metacognition.  If you’re not using it… you should be! :-)

4) My students feed off of my passions, and give it right back to me.  That cycle of I’m-not-sure-what’s-going-to-happen-next, and not taking ourselves too seriously (especially when we goof) seems to make math class perpetually fresh.  There’s a lot of love and energy in room 510, and I’m glad students know I adore them… and feelings (dare I say) are mostly mutual.

3) My week-at-the-spa (so to speak) was ADE Institute 2014 in San Diego.  I mean, getting to hang out with educators from literally the entire WORLD for a week of learning and hands-on exploring was an experience I will never forget.  When I compare it to the “spa” I mean figuratively – ADE Institute is a week where I didn’t have to think about making meals (that’s for sure!), errands, bills, or any other mundane real-life stuff.  I could be professionally selfish for an entire week, and soak up that energy that only a room full of worldwide, passionate, Type A+ educators can muster.  I am WAY too high strung to spend a week at a spa – I’d be bored!  ADE is like a brain spa… and you should apply if you want to drink some of that ADE Kool-Aid.  It’s good stuff.  Plus, I had a few seconds of fame on the big screen – that was pretty cool.

Screen Shot 2015-01-17 at 10.12.39 AM2) I helped my son create an advocacy project last summer so he could help educate others about severe food allergies.  He exported his book as a video on YouTube, and you can watch it and hear him narrate it here.  It’s been shared all over and has helped skeptics understand what it’s like for folks who have to consider food allergies 24-7.

1) I have the best “cheerleader” and encourager right here in my house.  My husband is always pushing me to be better, do more… and he keeps it real.  It’s nice to have a former high school math teacher and current ed-tech nut right here next to me.

What are your #10GoodThings?


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

Nearpod Homework Reports: Worth the 40+ page PDF

Screen Shot 2015-01-10 at 5.48.48 PMI had a field day with data after assigning several Nearpod lessons using the “homework” feature this week.

What’s great about the homework feature is that students can take on the lesson and embedded activities and assessments at their own pace.  Afterwards, I get a comprehensive report of every quiz question answer (with pie graphs), draw-it slide of student work, open-ended question response, etc. from every student.  That translates to a pretty hefty document to review!

Screen Shot 2015-01-10 at 5.49.20 PMI look for trends in the report and share my findings with students the next day.  Generally, I have the pie graphs from the report displayed on the smart board as students enter class.  This gives them a general idea of their performance as a whole group.  They expect this, and it frames our homework review and conversations well before the late bell even rings.

One tidbit I had to share with students came from the Nearpod report from a review lesson on translating expressions.  Knowing students were heading toward tackling the TEK below, I wanted a bit of a simple language lesson review to come first (given that we’d just come back from break and all as well):

8.8(A) Write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants.

What was SO interesting to me was students’ errors translating subtraction expressions.  Sure, we expect newbies to translate “five less than a number” in the wrong order, but the Nearpod report showed that the question type made a difference.

For example, when asked to translate a subtraction expression from “words” to “math” using an Open-Ended Question, 89% of the students typed the correct expression.

Screen Shot 2015-01-10 at 5.52.06 PM


When asked to translate a similar subtraction expression in a multiple-choice question… well… this happened.

Screen Shot 2015-01-10 at 5.55.33 PM






Yes… that says 50%.

Half of my students took the bait and chose the “trap” answer choice.  I had a great conversation about this phenomenon with my students.

1) They reasoned that having four answer choices makes you “have to think less” and that it’s easier to be “swayed” to choose a popularly wrong answer.

2) They reasoned that you have to “think more” when answering an open-ended prompt.

3) They reasoned that taking multiple choice tests is a skill/game, and proceeded to ask me to propose to administration that I should teach a course on test-taking skills and strategies, and that they would sign up for it.

Ha!  Well, I’m not sure a test-taking course is in the cards for me, but this little doozy surely made my students more self-aware, dispelled the myth that multiple-choice test = “easy”… and also affirmed that perhaps multiple-choice is not the best way to assess mathematics understanding… or is it?  Did my students “get it” and then proceed within minutes to “not get it”?  Did they feel a false sense of security when their first gut-instinct answer was one of the four choices in the multiple choice question?  Why did this happen?

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

2015 First Day Back

I spent the first half of my day at a high school math textbook vendor fair.  Having a substitute felt awkward – it was tough to NOT be in my classroom to welcome students back and crack corny jokes about how we hadn’t done any math together since last year ;-)

IMG_9236I knew they’d be in a fog, in denial of the horrific alarm-clock that sounded to start their day today.  After completing a Google form with their intentions of “New Years Math-o-lutions”, I needed them to DO MATH, with or without me, and I wanted access to their work and scores.  Now I’m gleaning Nearpod reports, ThatQuiz scores, and Google Doc spreadsheets to assess the damage that 17 consecutive days off may have done to my students.

We have some work to do.

But at least I know what I’m in for.  The painful bliss of assessments using iPad!

For now though, I want to steer this blog post in a different direction.  One of the Google forms students completed today was a reflection and follow-up of our Book Creator project.  (Read all about the project here if you missed it.)  Before our break, with such focus on semester exams, I didn’t feel like I’d given students a chance to provide feedback on the project.  I need their feedback.  It gives me the reality check I need to make the project better next time.  I want to know what they think worked, and what they’d change next time.  Here are some of their responses, with some of my favorites in bold print.

P.S. Any time I ask students questions like these… I’m so glad I asked! :-)  Definite themes in their responses.  We didn’t just learn about math.  As a matter of fact, MOST responses are about all of those life skills folks need to be successful 21st-century employees.  I’m so glad they were able to recognize and articulate these responses.  I also chuckled at the self-awareness epiphanies that occurred when students had to listen to their own recorded speaking voices.  Don’t miss the suggestions for improvement as well, which I will take to heart for… Book Creator Take 3!  (Did they *truly* need more time, I wonder… or did they need to *manage* it better…?  Hmmm…)

Q1: For YOU, what was the most valuable lesson learned by completing this project and creating a math eBook?

It helped me remember things from the previous chapters
Getting to learn more about the subject of my eBook
I learned about some very helpful and well explained websites that could help me learn some math concepts that I don’t understand
Teamwork is needed in all situations… Even math!
I got to learn more in detail about my subject and others that I was confused on.
How to get things done in groups when there is a deadline
To always go back and look over things you learned in the past so you don’t ever forget them
That everything has to be your best work and detailed.
I learned a lot about how to participate in a group
Better understanding of the topic I wrote my book on
Time management!
Work swiftly and work well
Choose partners wisely
I learned that communicating is really important when working in a group.
Knowing how to make an online book
Learning how to show something many different ways and explain it
I learned how to work with a friend and still get the work done efficiently.
How to met deadlines and guidelines better
Math can be fun when you explore different ways to share Math
Math is really fun when you make it your own thing.
I learned to valuable lesson of team work.
It provided us with an understanding of how our fellow classmates are and an understanding of the different subjects
Teamwork makes the dream work because without it you will be too busy arguing than working but don’t pick your friends because then you might be conversing with them than working
To work better with others and divide and concer
I learned to work with different people
That you can work together as a group to create A very valuable project.
Identify, write and graph direct variation
My own voice is actually quite irritating.
Learning to study more efficiently.
There’s tons of resources to learn math.
That I have to work hard and stay concentrated
To be patient
Linear functions
How to use book creator
Always double check your math
Making a book is difficult
A voice recording is what you sound like to everybody else
Teaches me to be brave enough to make a book that my peers have access to.
That if you work with others when creating the book you can get more ideas
That there is so much math left to learn.
that making a project helps you understand the topic more
If you stay focused you can finish things quicker and more efficient
How to graph functions correctly
I feel like I really mastered my topic.
Making a project really helps to better my learning on the topic


Q2: What suggestion(s) do you have that might improve this project for future students?

A more detailed rubric
Less pictures, more videos
Having a more detailed story board
Groups of two
Groups of 2-4
I think this was an overall great project but maybe if we had more explaining and maybe less things on the rubric to complete then it would have been a bit easier.
Give them an extra day because a lot of groups barley finished
More time
Less time working on books and more time just studying
I don’t have any suggestions it was a fun project!
Maybe show them on the smart board so everyone learns together
I think it would probably be more helpful to myself if we started the books earlier and studied for the test longer.
None (thought it was fun and challenging)
Go over the rubric several times
To have less points taken off for minor mistakes
Have fun! It really shows if you enjoy making a project.
Maybe give a little bit more time.
More time for better results?
Maybe just a little more time and find a way to let us use that video app rated 12 and up
I thought that this project was well directed and I can’t find anything wrong with it.
Nothing it was perfectly fine.
More time
None, I liked the way it was.
A little more time
longer time
Give them one more day.
It’s great I have none.
I don’t have any suggestions
Let us trade topics
I think it would be better if you could use online videos with citing your sources.
Be able to use photos offline instead of draw
Have more time in class to work.
Posted in Algebra 1 | Tagged , , , , , , , | Leave a comment

Some Top 4’s – Another “Reflecting on 2014″ Post

Reflect‘Tis the season for reflection and hopefully a bit of relaxation.  I’ve taken a break from math and ed-tech the past few weeks to spend QT with family (some days I took a break from just about everything… darn you, flu).  Exhaling is good – this post was an appropriate read for me.  Balance is important.  When you’re passionate, sometimes balance is tough.

Before I place my teacher-hat back on my head next week, and hit the ground running for another semester, I wanted to pause and share a few favorites from 2014.  Every year I work with students, blog, and spend time reading others’ blogs and tweets, I get more excited to try new things and improve.  So many folks and tools have helped equip me to be better so my students can be better.  I’m grateful to continue learning and growing, and I’m thankful to be a small piece in the vast Math-Twitter-Blog-o-Sphere.

Some 2014 Top 4’s

Top 4 Events Spent Connecting With Other Educators IN PERSON in 2014

SXSWedu 2014


iPadpalooza 2014

ADE 2014


Top 4 Math Playdates

Big Nickel

Ice Bucket Challenge

Radical Nearpod Art

Kahoot Meets Desmos


Top 4 Tools for Assessment 






Top 4 Tools/Strategies for Student-Created Content

Explain Everything

Book Creator


Story Time 


Looking ahead to 2015…

Top Tools I Want to Use in 2015



Desmos Polygraph Activities

Freebies from NCTM 


Events I Can’t Wait to Spend Connecting With Other Educators IN PERSON (Will you be there?)

iPadpalooza 2015

ISTE 2015

NCTM Nashville Regional Conference 2015


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

Book Creator Student Math Authors: Take 2

Last May, my students took Book Creator for a test drive.  As the school year came to a close, student-authored review eBooks seemed like a worthwhile task to try.  Students learned a lot about working cooperatively, using new apps, and presenting mathematics using unique strategies in ways that would potentially teach someone else.  It was a good thing, and you can read about it here.

Since then, I tried firming up the project a bit by structuring my expectations, designing a detailed scoring rubric, and housing necessary resources neatly in an iTunes U course (you can find it published on iTunes here!)  This time our purpose was to create multi-media lesson books – study guides, if you will – that collectively address the learning targets we’ve studied in Algebra thus far this year.  These guides are to serve as an additional resource to help all algebra students prepare for semester exams, and more importantly, deeply understand mathematics and be able to effectively communicate about it.

IMG_8923This time, I required a specific number of student-created videos, recorded sound clips, and images in each book.  I made storyboarding mandatory, which encouraged students to research and review first, making the math content unquestionably the #1 priority of the project.  I allowed students to work alone, in pairs, or in groups of three students.  I divided up the learning targets, printed the target spreadsheet, chopped and folded up each target slip of paper, and had students randomly draw topics for their books.  While some elements of choice were taken from them, they still had plenty of room for creativity and choice through designing the pages, using various apps to create media, and deciding who to work with (if anyone).

As students enrolled in the iTunes U course and began carefully considering the provided resources in their self-chosen groups, I knew the quality of these books would be improved from my first run with Book Creator last year.

With a deadline of 11:59 p.m. tonight, books are still rolling in ;-) and as I review them, I’m sharing them through a ThingLink so students also have real-time access to their work and the work of their peers.  The eBooks are not perfect, and many have those algebra errors that might make us cringe a bit, but remember this is the first time most of these students have created something like this.  This is evidence of their thinking.  These books represent my students’ voices in ways they couldn’t necessarily share them in the past.

A highlight you won’t want to miss is a student’s book who (not surprisingly) chose to work alone.  I have to bend low to hear her voice at all when she speaks to me in class, but her voice and personality (and artistic illustrations) can certainly be heard (and seen) in her book.  Don’t miss her Direct Variation guide listed as #13 on the Linear Functions spot.  (scroll down… follow-up below…)


On 12/12/14 as students received their scored rubrics and written feedback comments and suggestions from me, they wanted to continue editing and improving their books.  This ThinkLink serves as a “working document” of sorts as students resubmit their books.

Before handing back rubrics, I let students know that some projects may not be embedded in the ThingLink yet.  Reasons ranging from too many math mistakes to distracting (think: silly) visuals kept some submissions from being included.

What was interesting to me was how quickly students navigated to the ThingLink to see whether their book had been included.  Immediately, buzz ensued and I heard outbursts like “YES!  Ours is there!”  versus “Oh man, we didn’t make it…”

My observation was that students cared more about whether or not their books made the cut than they cared about their “grades”.  I found that to be very interesting.  I conferenced with each group as a follow-up to talk through my rubric comments (and interpret my horrible cursive if they couldn’t read it, HA!) and we decided together what changes needed to happen in order to make better books.

I love that they want to improve and correct their projects.  Learning. Is. Happening.


Posted in Algebra 1 | Tagged , , , , , , , | 9 Comments

Bottling Up the Perfect Balance

I feel like, as a teacher, I have a lot in common with the video gaming industry.

We both want to draw kids in to a challenge.

That challenge has to be feasible but not too easy.

Students have to be able to try things, possibly failing miserably at first.  They have to want to try again, and make adjustments to improve, while also gaining valuable, timely, dare I say instant, feedback.

I wish I could bottle up this perfect balance and use it every day I work with my students.  Sure, many teaching days are very good, but some are truly magical.  I had one of those I-want-to-bottle-this-up days today.

The task was simple and open-ended.  I got the resource as part of an online Algebra EOC (end-of-course) Exam training I completed when I moved to Austin. On paper, it doesn’t look like much.  In practice, it was just, wow.

IMG_8874Using a graphing calculator and/or Desmos, students were asked to create three equations whose graphs would intersect to form a triangle in a standard viewing window.  From there they were asked to create other polygons.  A parallelogram?  Trapezoid?  Pentagon?  Others?  Students were also asked to record the linear equations and sketch a picture of each graph.  They’d recently completed a unit on linear functions, so they had plenty of background knowledge to get rolling.  They work in cooperative groups of 3-4 students, and they absolutely ran with this thing.

The conversations were amazing.  Kids were crossing their arms in the air to visualize what lines might look like before graphing them.  They talked quickly.  They talked loudly.  They struggled a bit, but began crafting equations to graph.  The academic vocabulary in use was spot on.  As the TI calculators graphed each line a bit more slowly than students would have liked, they literally crowded around the calculator screens and cheered when the lines appeared as they’d hoped, and “awwed!” when the graphs didn’t turn out as planned… but they were ready with a new plan and made adjustments until they got what they wanted.

At one point I literally had a crowd around me, every student with a graphing calculator in hand, wanting to show me what they’d created.  These 8th graders were on fire.

What’s a recent task or lesson your students have tried that made you wish you could bottle that energy up?  How can we make many of our days “magical”?

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


The last day of classes before Thanksgiving break, I set up my iPhone in an attempt to record some time-lapse footage in each of my classes.  Since middle-schoolers can smell a camera a mile away, there was nothing secretive about my set-up.  My intention was to capture samples of some of the “normal” goings-on in my classroom.  For example, these snippets show how we use a Nearpod “homework review template” to facilitate mathematical discourse, share work efficiently from EVERY student, do a bit of authentic error-analysis, reflection, and as needed, reteaching.

Screen Shot 2014-11-28 at 12.45.06 AMWhat I didn’t anticipate was just how valuable this simple footage would be for me for reflective purposes.  It was an efficient self-observation.  In mere seconds, I can see habits and patterns in my own practice that could use some improvement.  Was I at the front of the room too much?  Did I circulate to every student group often enough?  Were the students on task?  Was that kid really reading a book long enough for me to notice it in a time-lapse, yet I didn’t even notice in real-time!?!  It’s amazing what seeing your students and yourself on camera can reveal, even in this speedy format.

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