A Fork is not a Spoon

In my last post, I shared briefly about workflow and tools during our continued COVID-teaching time. This. Is. Hard. Teachers across our nation and globe are finding themselves teaching under varieties of circumstances with challenges that test our every limit. When it comes to using technology to help students learn mathematics, tool CHOICE has always mattered… and the WAY those tools are USED has also always mattered. But we find ourselves in unconventional, long-haul circumstances where teacher-SURVIVAL (literally during a pandemic, and with respect to our practice) can matter as much or more than making best-case-scenario pedagogical choices. We’re doing our best, where we are, with what we have, with the deck we’ve each been dealt, given the same 24-hours each day. (I happen to be “in-person” teaching students in-the-Zoom and in-the-room simultaneously, masked behind plexiglass barriers. It’s still surreal, even though I’ve been in this modality for 4 months now.)

I just finished listening to a recent episode of Justin Reich’s TeachLab Podcast featuring Dan Meyer in the Failure to Disrupt Book Club series. A question posed by regular guest Audrey Watters had me leaning in to my laptop with raised eyebrows (at the 36:19 mark):

“… Dan can you talk a little bit about… the kinds of things… features… that you would say no to?What is something… teachers want that you’re like, nah, we ain’t gonna do that…?”

SPOILER: The “very big” feature request from teachers in recent months involves the desire for more auto-grading.

Dan goes on to say,“…By design, we (Desmos) have not exposed to students whether they are RIGHT or WRONG… That’s been intentional.”

Listen in (38:00 minutes) as Dan elaborates on the WHY. His responses resonated with me. For me, hands-down, Desmos has been the absolute best tool to help further mathematics education with our students’ “creativity and connection to other students” in general, but ESPECIALLY during this pandemic. Desmos Activity Builder provides a platform for students to experience mathematics in dynamic and even playful ways that simply cannot happen without technology. Desmos can help encourage student discourse that aids in building a community of learners who see math, not as static, but as something we can explore, test, attempt to break, and more deeply understand together.

That being said, I have never “graded” a Desmos activity.*

Perhaps being dealt the deck of teaching synchronously in-the-Zoom and in-the-room shapes my lens here. I have students who show up, log in to Desmos, and participate every day. Since we share the same time and space, whether in-person or virtually, I use Desmos activities to drive our live lessons. For us, Desmos is an experience, not a summative assessment. If students were to join a Desmos activity, and ask that age-old question, “Is this GRADED?” it would break my heart a little. They never ask me this because it’s not something we’ve ever done. Yes, we teachers are expected to put grades in our grading software programs. This is a deeply-ingrained part of “school”. For me, Desmos is just not the best tool for that. A fork is not a spoon.

I have the UTMOST RESPECT for the droves of teachers who are teaching themselves and others Desmos CL (computation layer coding language) in order to make Desmos Activity Builder “grade” student thinking. And I am a firm believer that many of the tech tools we have at our access can be used in unconventional yet effective ways, so using Desmos for grades isn’t right or wrong, it’s a use-case choice. I have seen some AMAZING Desmos assessments out there that use the platform to ask students deep questions, while taking advantage of providing students with access to so many of Desmos’ strongest features! KUDOS TO YOU! For those looking to assess understanding quickly, not necessarily using the strengths of Desmos along the way, I’m thinking about you right now… those trying to use Desmos activities for “learning checks” that are graded for you. When a tool has to be undone like a knotted pretzel and forced to do a thing that should be easy to do, maybe it’s not the best tool for that thing we are trying to make it do. A fork is not a spoon.

I’m not here to judge anyone’s tool choices or uses, *ESPECIALLY DURING A GLOBAL PANDEMIC* but I would like to propose another option for graded assignments. I’m looking for solutions to our many teaching challenges too, and here’s one that has helped me to assess AFTER our rich, shared Desmos experiences. It’s not pedagogically perfect, is certainly NOT new, but I think it might be an option to consider for folks who simply need a tool that provides students with opportunities to practice, demonstrate understandings, and quite frankly, “grade” stuff efficiently.

Check out my tag cloud to the right, and you’ll see “ThatQuiz” listed. This pandemic has propelled me to learn and understand ThatQuiz’s capabilities more than ever before. ThatQuiz does some automated things (generates skill quizzes based on constraints, for example), but it’s also a creation platform. You can make of it what you’d like. It auto-grades. I like using it to check understanding. With password-protected student logins, class data is collected over time in a user-friendly way. The teacher can even set a threshold (for example, students must earn 80% or will be prompted to redo) which propels students to seek help too. ThatQuiz has always been free, and promises to remain free forever, and to exist forever, so it’s worth a look if you’re new to it. Is ThatQuiz the utensil you might be looking for? Check out this brief video, go explore, and keep being your awesome teacher self.

*The only Desmos Activities I have “graded” were longer-term projects that use the Activity Builder as a platform. 🙂

Posted in Algebra 1 | Leave a comment

Reflect and Share: Workflow

Why do I blog? Simply stated, I blog to both reflect and to share. However, in recent days, weeks, months… heck, we’re almost to the point where I can say for a whole YEAR it has been tough to just sit down, center myself, and reflect or share. My heart has been in a constant state of heavy for almost a whole YEAR, and I pray 2021 will turn around (SOON PLEASE) for the better in EVERY possible way…!

We began our 20-21 school year 100% remote. I’ve been back “in person” teaching since mid-September, with what began as roughly 60% of my students “in-person” with me and 40% joining synchronously from home on Zoom. As the year has progressed, I’m closer to 75% “in-person” and 25% on Zoom now. The numbers change daily because the circumstances change daily. We’re working one day at a time, masks, plexiglass, and all.

It’s taken some time to figure all of this out. Workflows have become more important than ever, and I’ve come to realize that workflows can vary greatly even when folks use the exact same tools. While my timing is likely waaaaaaay off here, as many of us have probably established things by now, I’ll share and hope that you’ll share back, so we can all be better!

Google Classroom

One thing I’ve realized is that saying one “uses Google Classroom” doesn’t always mean we’re using it the same way. I’m not sure many people use GC the way I do, and I’m sure I’m NOT making the best use of GC’s capabilities! However, my students have expressed appreciation for the way I keep things organized, so this has sort of been working, even if it’s unconventional.

My Classwork area uses each math unit title as the GC Topic. Each day, I use a Material under the current unit Topic to create a brief daily agenda. In this agenda, I include the day’s objective, and any links / codes / PDF resources students need. I schedule the daily Material agenda to post each school day at 8:10am, roughly 30 minutes before the school day actually starts. Students only receive one e-mail & one post from me per day. Each Material I post is initially organized by lesson topic, but includes the date as well since it is scheduled to post on the relevant day… so it’s organized for students both by lesson topic AND by date.

Essentially, we visit Google Classroom to start each class and see our objective(s) and agenda, and then we swiftly leave Google Classroom…! In general, students are leaving GC to participate in a Desmos Activity or Nearpod or Socrative or ThatQuiz… and all of these tools already have a built-in workflow. I’ve never really invested in Google Forms or Google-y assessment tools, so, I need you to help me in this area!

Desmos Classes

Speaking of Desmos Activities, they are A-MAZE-ING for in-person and remote students! I created Desmos Classes when the option became available in recent months… and again… I don’t think I’m using these classes in a conventional way either, ha! I created my Desmos classes by class period, but I do not “assign” Desmos activities to integrate with Google Classroom because I don’t “grade” Desmos activities… we use these activities to learn and explore during live lessons together, not for grades… so, as a part of my daily GC Material “Agenda” I include the already-assigned Desmos student activity link(s) each day. Farewell to sharing codes students must type in, they just click the link and go!

My students don’t even know that there is an actual class code or link that gives them access to all of the assigned activities (at least YET… I imagine I’ll share this at the end of the year, if not sooner…) they just click on the link(s) each day in GC, and I get the blessing of having activities organized by class period… and even better… seeing that precious ROSTER of student names in real-time to ensure everyone is logged on with me, in the room AND in the Zoom…!

Graded Stuff and Not-Graded Stuff

During live lessons, we use Nearpod and Desmos Activities to drive our lessons. Students participate in the lesson activities every moment of the class period, and their thinking/work (often anonymous) is shared to promote dialogue and exploring multiple methods. I’m able to keep tabs on student progress in real time, and intervene just-in-time. Sometimes, student-paced Nearpod and Desmos Activities are assigned for homework as well. These are also not graded. (Note: I’ve created and collected resources for both tools and shared them in the sidebar to the right on my blog here, or you can visit my editable Nearpod lessons here and Desmos Activity Collections here.)

Additionally, sometimes we’ll play a live Kahoot! to review and reinforce concepts, and often, I’ll post Kahoot! challenge codes in Google Classroom for some asynchronous optional practice, review, and competition as well. (Note: I’ve created standards-aligned Kahoots! and shared them in the sidebar to the right on my blog here, or you can visit this link for Math 8 and this link for Algebra 1.)

Our “graded” assessments this year mostly live in two tools – ThatQuiz and Socrative Pro. While ThatQuiz’s platform is a bit dated, lacking bells and whistles of any sort, I really like this platform for assessing along the way. ThatQuiz can generate a skill quiz based on constraints set by the teacher, teachers can visit the Browse option to edit and assign assessments created by other teachers, and teachers can create assessments from scratch under the Design option. At the start of the school year, I create password-protected classes where each student logs in to find ThatQuizzes that have been assigned at whatever date and time the teacher chooses. There’s a running dashboard of student progress that can be viewed by any date range chosen, and the teacher can hammer down into each score to see precisely which questions students missed. One can even decide options like, do we want ThatQuiz to save student work/progress along the way, or not? Do we want students to receive feedback upon submission, or the grade only? Do we want to give students only one attempt, or let them redo the assignment with a set a threshold, such as earning 80% or higher? I love the flexibility ThatQuiz provides! (Check out my tag cloud for lots of ThatQuiz posts and ideas —->)

For summative end-of-unit assessments, we use Socrative Pro. While we are limited to having open-response and multiple-choice questions, we use our class time with Nearpod and Desmos to dig deeply into student work, taking our time as we progress through each unit of study. When it’s time for a summative assessment, we’ve taken the philosophy that students should have the freedom to choose the methods they like best, and complete exams that mimic the ultimate summative assessment *that they will still have to take this year ahem* the STAAR test. Summatively assessing an entire unit with roughly 45-minute class periods is a challenging task… and creating unit assessments using Socrative Pro makes things a bit more feasible. I also like that questions can be scrambled, and answer choices can be scrambled, to encourage the “integrity factor”. 🙂 And just like Classes in Desmos Activity Builder, Socrative Pro permits that oh-so-valuable class roster for each class testing room, so the teacher can see at-a-glance who has and has not logged in to the assessment at hand.

All of this being said, in an effort to streamline things for students and families, we’ve narrowed down our tools to this bunch:

Google Classroom —> Daily agenda and materials

Nearpod & Desmos Activity Builder —> Live lessons and occasional asynchronous homework

ThatQuiz —> Smaller assessments along the way

Socrative Pro —> Summative unit assessments

Kahoot! —> Optional practice & review

What am I missing?

If the activities and assignments students complete are in tools with built-in work flows already, convince me why I might use GC Assignments rather than only Materials in my Classwork? Or, is this an instance of… if you started using Google tools initially, and have invested time creating goodies there, you’re more apt to use them…? As you can see, I don’t use Assignments in Google Classroom at all… and perhaps that’s okay…?! Or, maybe, YOU know something I’m not seeing, and you can help me see it…? 🙂

More Sharing

I’m honored to have had some unique opportunities to share about teaching and learning with technology the past few months. Check out some highlights below.

Eanes ISD Math Teacher Tackles Remote Learning (Spectrum News)

Making Math Moments Podcast: It’s Not About Tech, It’s About Good Teaching

Kahoot! Academy Teacher Takeover: Teacher-of-the-Week Cathy Yenca

mmhmm blog: “Mathy Cathy” Yenca: Why visual learning matters for math

A mention on #DesmosLive around the 30-minute mark!

Math Teacher Lounge (presented by Amplify + Desmos)

Posted in Algebra 1 | 3 Comments

First Quarter SY 20-21

Whelp, would you believe we’ve made it through the first quarter of this (don’t say it… don’t say it…) UNPRECEDENTED school year. For me, the year started with three weeks of 100% virtual learning. All teachers and all students learned from home using Zoom initially. Then, those of us with health waivers continued to teach from our homes while colleagues went into our buildings to serve 25% of our students in-person, and 75% who remained at home. Then, our phased-in plan required all staff (even those with health waivers from doctors) to go into our buildings to serve the 52-ish% of our student body that would join on-campus learning. Now, we have roughly 64% in-person, and still meet with our remote learners on Zoom, simultaneously.

via GIPHY

There’s literally been no time to blog. Twitter pals using #MTBoS and #iteachmath and @Desmos have saved my sanity and provided just-in-time resources and ideas during this one-day-at-a-time pandemic teaching lifestyle we find ourselves in. It’s all about survival right now (literally and figuratively) so, here are some highlights from Twitter that summarize Q1 of the 20-21 school year for me. Happy scrolling, and thanks a MILLION to all who continue to create and share, helping us all get through this temporary insanity.

First Day of School (At Home For All)

Go-to tools (in “regular” teaching times too, but ESPECIALLY now)

THE MULTI-TASKING IS REAL.

Desmos Amazingness.

https://twitter.com/mathycathy/status/1298667865218981889
https://twitter.com/mathycathy/status/1307149714274439168
https://twitter.com/mathycathy/status/1304576433638043648

Add “TECH SUPPORT” to the 4,297 hats teachers are already wearing.

https://twitter.com/mathycathy/status/1307676818586185729

The fear of initially entering the school building myself was VERY REAL.

P.S. It’s still real. Every day.

S.E.L. is not just a three-letter acronym.

https://twitter.com/mathycathy/status/1309284855843303425
https://twitter.com/mathycathy/status/1313638529403105286

A kind word goes a long way. SUCH a long way.

Creating resources to fit the times has been a TON of work, and a TON of REWARDING and SO-WORTH-IT work, at that. Some days, I’m really proud of the activities! Other days, the activity is honestly more like a worksheet-turned-Desmos-so-I-can-see-what-everyone’s-up-to… I’m okay with that.

https://twitter.com/mathycathy/status/1314929511197220865

LOVE the idea of creating what I’d call a “Metacognitive Card Sort” in Desmos Activity Builder. I’m using these to help students on our review day before unit assessments. While they already have a “test review”, I feel like this puts perspective to our “learning targets” and encourages students to take a stand on various question types. It also helps them formulate specific questions for us to address during our review time together.

https://twitter.com/mathycathy/status/1317861539722964994

Matt used this idea for post-assessment reflections too – neat-o! Encouraging students to think about their own thinking is always a good thing!

Thanks for scrolling! In closing, if there’s anything you might need for Math 8 or Algebra 1 kiddos, please know that I’m always adding things to my posted Desmos Collections! Like, literally almost daily at this point!

Check out my Desmos Collections by scrolling up and clicking on the “Desmos Activities” image at the tippy top of all the stuff on the right side of this page —–> and help yourself to anything useful there (Kahoots and Nearpod lessons too!)

Be Well, Stay Well, and here’s to the second quarter of SY 20-21.

…And remember to find some humor in each day!

https://twitter.com/mathycathy/status/1316786034693353472
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Back-to-School From Home

The summer of 2020 felt sort of like “the summer that wasn’t”. We didn’t do any of our usual traveling or visiting family. The days sort of ran together much of the time, with the exception of watching the news TOO MUCH, taking lots of walks around our neighborhood, and the occasional delivery of groceries on the front porch. Just as the end of the 19-20 school year was mushy and abstract, this “summer” felt similarly mushy.

However, this summer, more than I can ever remember, professional development online was ABUNDANT. From Twitter to Facebook groups to webinars to online courses and conferences, educators leaned on each other from far and wide, both for moral support and to learn how to make some lemonade from all of these lemons. One of my favorite experiences was the week-long offering from teachers at Stanford Online High School, who shared candidly about all they have learned to effectively teach students remotely (the recordings are still available here). Desmos webinars, the Apple Distinguished Educator month-long Festival of Learning, the Kahoot EDU Summit, and the Pennsylvania Council of Teachers of Mathematics conference were just a few of the many offerings. The perpetual tug-of-war pull between watching the often hopeless news, to learning hopeful strategies for future students, all the while seeing teachers caught in the middle of so much of the mess was, at times, exhausting and paralyzing.

After a week-and-a-half of ZOOMING with colleagues for our district-level PD to prepare for the reopening of online school, it’s been great to reconnect. While we’re juggling a lot right now, we’re as ready as we’ll ever be, and tomorrow we get to meet a new crew of students! I’ve never felt so ready, and simultaneously *not* ready, for the start of a new school year. I’d imagine students feel similarly.

With so much literally out of our control, sometimes it can be therapeutic to control the things you can. For me, that translates to being productive and creating and organizing things… then sharing them with others! Here are some resources I had the pleasure to play a part in creating / curating over the summer, to help with this moment and the days ahead. I’m grateful that so many folks spent the summer creating and sharing amazing resources day and night! We make each other better.

Math 8 and Algebra 1 Desmos Activity Collections

Kahoots for Math 8

Kahoots for Algebra 1

As we seek to build relationships with our students while juggling online teaching, in-person teaching, or some combination of the two; our own families, our own physical health and our own mental health; politics, the news in general, pandemic statistics. public perception of our profession and EVERYTHING ELSE that 2020 continues to throw at us, I urge us all to take a breath. We must be intentional regarding our self care. We don’t have to be perfect.

Be well, stay well, and let’s do this!

Have a happy and healthy new school year, one day at a time…

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Bringing SY 2019-2020 to a Close: Reflections… and Desmos

Several weeks back, I packed up my classroom. Frozen in time, everything was set up and ready to go for teaching on Monday, March 23, post-spring-break… that day had LOOOONG come and gone, though my classroom was ready to propel to the “normal” routine. I couldn’t wrap my heart around why I was packing everything up, even though my brain knew full well that I had been quaranteaching for WEEKS already. My gloved hands went into autopilot while my exposed eyes fought back tears in my eerie, empty, silent classroom.

Here we are, staring down the last week of school. The official school calendar says next week is the last week of school. It always did. Normally, if we’re being honest, most of us would have had a countdown of how many teaching days were left until the coveted ***LAST DAY OF SCHOOL***. While we usually count the days down out of jest and sheer exhaustion of end-of-year testing, field trips, and all the wonderful interruptions that make the end-of-the-year enjoyable and terrible all at the same time… this year, it feels flat. Abstract. Really, really sad.

Wishing we could meet for class for one final farewell is not uniquely my wish… MANY teachers’ hearts out there have yearned for this for over two months now. Though technologies are amazing and have maintained the learning and community-building to a degree, there’s nothing quite like the heartbeat of the classroom… IN PERSON. I’m grateful! We’ve accomplished A LOT! It’s okay to celebrate that and be thankful for our Zoom-time and technologies while also feeling sad, tentative for what’s to come, and even angry… about ALL of it.

When I need to do something with a pile of feelings, I create. I have to make something. Something that will potentially make things better. Content creation is my outlet. It makes me feel like I am countering the blahs with joy and practicality.

After cleaning out my “real” classroom, I made this. I kept seeing this virtual classroom Bitmoji idea on social media, and scanned past it… but after packing up my classroom in real life, creating a virtual one helped organize some things NOW while also providing an editable platform for next year, when we meet in person and/or virtually. I used Apple’s Keynote to create the bones of it… the things I really don’t plan on editing. I used the actual paint color of my classroom walls, used a photo to fill a shape with the actual floor tiles, and included some cherished pieces, like my MISTAKES art canvas and my carved wooden MRS. YENCA name sign given to me by my husband’s Nana… who is the ORIGINAL Mrs. Yenca for whom it was carved! 🙂 It’s a busy and silly Google Slide full of hyperlinks and animated GIFS, and making it was therapeutic. Google “Virtual Bitmoji Classroom” for tutorial ideas galore.

I’m hoping that students have also found creating to be therapeutic. That’s why my PLC-mates and I have assigned Desmos Projects to every class the past few weeks. You can access and read about project ideas for Math 7, Math 8, and Algebra 1 here. In other tabs on my MacBook, I’m watching them work now, as I type, and these open and creative tasks never disappoint!


Next week, I’ll have one final Zoom meeting with each class. We’ll begin with a showcase of students’ graphing projects to celebrate their work and progress! Here are screenshots from the work they’re finishing up in Math 8, Algebra 1, and Math 7 respectively.

When I cleaned out my classroom, I grabbed the stack of “WHO I AM” papers that students had completed on the first day of school. I didn’t know what I was going to do with them yet. Generally, I return them to students on the last day of school. They barely remember ever filling them out, and are always surprised to read about how their interests have changed since August. And we all have a good chuckle at their hand-drawn self-portraits!

I was compelled to create something for my students, given that I wouldn’t be able to hand these back in person this year. So… using Keynote to sort out the portrait images, I created custom Desmos Card Sorts for each class! Students will attempt to match their peers’ (and their own!) names to their self-portraits, sketched on the 1st day of school this year. I wonder how many of them will even recognize their OWN creations! It’s going to be fun and light-hearted… creating it has left me a little heavy-hearted too.

AND… thanks to the Desmos Educators group on Facebook, I found @rachael_degnan’s end-of-year reflections activity, modified it for my middle schoolers, and tacked the self-portrait Card Sort screens at the beginning of the activity (the ability to COPY and PASTE screens between Desmos Activities is a DREAM FEATURE).

Here’s Rachael’s original End of Year Reflection activity, in case you’d like to use or edit it too.

Maybe **I** need a teacher-version of a Desmos End-of-Year Reflection Activity… there’s so much to process about how we “got through” these virtual teaching days, and even more uncertainty regarding how school will operate in the fall. Let’s all promise to give ourselves permission to rest, and not try to anticipate every “what if” the next school year might bring. Reflect, celebrate, and rest in knowing we’re all doing the best that we can.

Hope to be back here safely.
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Desmos From a Distance

Here in Texas, we received official word from our governor that our classrooms are closed for the remainder of the school year. We knew this was coming. It still stings. Such an abrupt ending to the communities we’ve built since August. I can’t believe our before-spring-break farewells were actually the last time we’d meet in room 510… heartbreaking!!!

Meeting twice weekly on Zoom from home sure helps! We’re keeping our communities and curriculum rolling in the best ways we know how. It has been exciting and exhausting to transition to 100% online learning. I lost a LOT of sleep the first few days, and worked well into the night hours trying to adjust materials I had, or create things from scratch, to make them more distance-friendly. Even when we regularly use technology tools in our classrooms, it’s with the assumption that our students are ALSO right in front of us! That we can run around the classroom and LOOK at what they’re doing, and CHAT with them one-on-one, in small groups, and as a whole crew. Online learning has been a blessing and a challenge.

Looking ahead to the rest of this Maypril of a school year, I have some Desmos projects and enrichment activities up my sleeve. Since I teach three math courses, I thought I’d share the resources I’ll likely use for each class here in this post.

{Math 7}

Math 7 students will use tables of connected points in this Desmos FIRST NAME Art Project. The included checklist could be modified to include point values if one chooses to ‘grade’ the project. Thanks to the ability to copy-and-paste screens from one Desmos Activity to another, this mash-up includes modified screens from other activities (credit given in the project description). Students are also asked to capture and submit a photo of a graph paper ‘rough draft’, thanks to the ability to add an image to a Desmos graph!

Looking for a prerequisite or follow-up activity that helps students use Desmos tables for graphing… and fun? Try Mini Golf Marbleslides!

To revisit ratios and proportional reasoning one last time, while previewing the concept of scale factor (which will be addressed in Math 8 next year) students and families will choose a favorite recipe, then use this Desmos project to scale it up as if they were feeding our entire class… and me!

My PLC-mate Lauren and I have been throwing around the idea of a recipe project, and thanks to the Desmos Educators group on Facebook, and friends on Twitter, we got the help we needed to include some self-checking CL tables. Once students scale up the recipe, they’ll add their recipe AND scaled-up recipe to a Google Slides presentation, which will serve as a virtual class cook book to end the year!

{Math 8}

This will be the third year my Math 8 students will use linear functions, and a whole lot more, to create their Pet House Linear Projects! This year, I added a screen where students capture and submit a photo of a graph paper ‘rough draft’ since we won’t be in the classroom together. If you search for this project online, you may also find modifications folks have made that include other features and some fancy CL (computation layer)!

As a prerequisite to Pet Houses, perhaps Marbleslides: Lines will help students get reacquainted with linear functions?

To encourage students to explore functions beyond linear, here are two enrichment tasks that can ‘run in the background’ as students build their Pet Houses. I also use these for my Algebra 1 students! MARBLESLIDES CHALLENGE SETS!

{Algebra 1}

While the Pet House Project focuses mostly on linear (but never stays there, ha!) this Des-Draw Algebra 1 project explicitly asks for quadratics to be included… and nudges students to explore inequalities as well as functions beyond linear and quadratic.

As a prerequisite to Des-Draw, maybe Marbleslides: Parabolas will help students get reacquainted with quadratic functions?

Lastly, these BREAKOUT activities might be even MORE challenging in a distance-learning environment, but I have them in my virtual back pocket nonetheless. Differing opinions were shared about trying to combine the Zoom Breakout feature with a Desmos Breakout activity… you never know until you try…?! What do YOU think?

What? You’ve never heard of Jay Chow’s DESMOS BREAKOUT ACTIVITIES?!?! Launch one for yourself, try to ‘break out’ as a student, and you’ll quickly see why these activities have become a few of my favorite ways to promote practice, review, and deeper understanding of concepts.

Breakout Desmos – LINEAR!

Breakout Desmos – QUADRATIC!

These activities are literally the tip of the iceberg as far as what’s available. Googling “teacher Desmos *insert math topic*” will provide even MORE options for you! I hope your end-of-year Desmos-From-a-Distance experiences are successful for you and your students! Thank you to ALL who have contributed to the creation of so many rich (and fun) Desmos activities!

Posted in Algebra 1 | 2 Comments

How To Be an Online Teacher in X Simple Steps

JUST KIDDING! That catchy title doesn’t begin to give justice to the hard-working colleagues I have the pleasure of planning with… the ones in my PLCs locally, AND the global ones who have been sharing about their experiences to help all of us be better.

I am BY NO MEANS posting ANY of this to say “Here’s How To Be an Online Teacher”… this is me saying, this is what I have tried in my 2-whole-days of experience, mostly because I’d love to know how YOU are doing this, and how I can do a better job because you’ve already learned or realized something that I’m not yet seeing.

{UPDATE 4/9/2020: Check out this news feature that showcases some of the resources mentioned in this post!}

Okay, my tongue-in-cheek post begins now.

Step 1: PLC Planning

PLC with teammates via ZOOM, e-mail, and/or texting at all hours. Calm each other down when technology behaves questionably. Share resources so we can all survive. Document all lesson plans in a concise report (see mine below… HAHAHAHAHA)

Step 2: Consolidate the Plans

Interpret chicken-scratch and transfer to index cards, labeled by day/class period. Realize the resources listed actually need to be located… find, create, and/or share needed resources* {see more about resources at the end of this post}. Brew a cup of coffee. Brew another.

Step 3: Digitize

Transfer index-card ideas to Numbers spreadsheet. Include links to aforementioned resources. (This process digitizes my plans, and helps me think about how to also rewrite my teacher-plans into student-friendly plans to be posted for them later…)

Step 4: Zoom

Set up Zoom meetings for each class, being mindful of all settings. Use a photo of my classroom as the virtual background for a personal touch!

Step 5: Rearrange the Furniture in Your Home

Realize that a Zoom Virtual Background does not stop household noises or the flow of humans through the open dining room. Rearrange the dining room and bedroom furniture. Ensure every worker-and learner-from-home has his/her own room… with a DOOR.

Step 6: Schedule

Close the bedroom door. Copy-and-paste student-friendly, digital post from Numbers spreadsheet into Google Classroom for each pertinent class (I teach three different courses), remembering to create unique links for each activity for each class for each day, including details for accessing each Zoom meeting. (Each time a class meets, I’ve been plopping everything into one announcement in GC and scheduling it ahead of time to post 30-minutes before each scheduled Zoom meeting.)

Step 7: Post Agenda

Post a concise agenda-version of Google Classroom student-post on Google Calendar for parents to access and view.

Step 8: MEET WITH THE KIDS!

Watch Google Classroom post your announcement at the scheduled time… and launch the Zoom Meeting (anyone else get butterflies in their stomachs when they do this the first few times?!? I was as nervous as the first day of school, pressing that button!)

Rinse and repeat from now until the unknown end of all of this…!

For reference, here’s what my schedule will look like each week! A MILLION THANKS to my colleague Georgia for helping our entire department take a more general schedule and streamline it purposefully to this! 🙂

This planning process has honestly felt like I am creating never-ending sub plans, because of the level of detail needed to ensure that we maximize our Zoom time together, that we present concepts using what we perceive to be the best tools within our realm of familiarity to meet the objective(s) at hand… it really is A LOT.

NOT COMPLAINING, just the facts!

As a matter of fact, I couldn’t be more grateful to be safely grounded at home with two of my favorite humans, while also having the opportunity to continue to teach and connect with my students through a schedule that has been thoughtfully set up by amazing district leadership. We can keep on moving and shaking with curriculum, while adjusting expectations and demands.

Step 9: Just Breathe

Eat something. Drink water. WASH THOSE HANDS. Get away from the screen. Go outside and breathe the fresh air. Stop hitting “refresh” and looking at that map for a bit (I’m talking to myself here!) Exercise. Take a walk. Chat with friends and family. Don’t try to do it all right now… (Also, talking to myself…!)

Okay, GO! Tell me of the magical ways you’ve streamlined your planning while not sacrificing quality in the process!

*The resources created and shared by other teachers and me have made the distance feel much closer! I meet with my students “synchronously” for roughly 20-30 minutes during each of our class meetings.

My first goal is to see their faces, chat a bit, and have a light-hearted exchange before getting to the math, the same way we would if we were in “real” class together. I used this Desmos activity during our first Zoom meeting, and here are more! One day, students introduced their pets (lots of folks have shared this idea on the Twitters – thank you!) I got to virtually meet the most ADORABLE hedgehog!!! We are also having theme days. The other day, we wore sunglasses. I have hat day, favorite color day, and even…. bring-a-roll-of-toilet-paper-to-class day coming soon, ha! I also have some fun tasks planned, where having everyone unmuted in Zoom and just calling out when they “see” it will break the ice and start class in a novel way. Here’s one such resource!

I’ve also been using our synchronous time to do a “micro teach” and ask students to do a problem or two. When written work is important, I use Nearpod. Having the entire iPad screen to draw and write math work makes Nearpod an ideal tool… and being able to see these work samples, LIVE while using Zoom and Nearpod during our together time, is priceless!

I also like to post a short “quiz” at the end of each Nearpod, because Nearpod allows the teacher to share the quiz results of each individual student through their own, personal pie graph! AMAZING to be able to do this in the classroom when we’re all together… AND now, when we’re all safe in our homes! Here’s one such short-and-sweet Nearpod, where we compared-and-contrasted the simple and compound interest formulas and concepts, worked two problems together during Zoom, students took a very brief to-the-point Nearpod “quiz”, received their pie graph results from me, and were released from Zoom to work on a PDF homework assignment asynchronously for which I immediately posted my key (so they could check work and get feedback before our next class meeting).

I’ve also been using Desmos Activity Builder to create “micro-teach” experiences during our Zoom time. Desmos is great for designing inquiry-based lessons that guide students towards noticing patterns in math and making generalizations.

Desmos is also a fantastic place to share short direct-teach videos and ask students follow-up questions that can be seen from the teacher dashboard asynchronously. I’ve been using my OKIOCAM in conjunction with QuickTime or Zoom to create these brief videos for my students. I’ve also had success using a Desmos activity synchronously with the entire class to get started, then using Breakout Groups in Zoom to give students some time to work through more challenging screens together. I can virtually visit their groups while simultaneously watching their work using the Desmos teacher dashboard! Here is a brief lesson I used with my Math 7 crew this past week. Here is a follow-up I will use with Math 8 this coming week. Here is another brief activity I used with Algebra 1, where using Zoom Breakout Groups for the last two screens was ideal!

I can’t thank the math community enough for continuing to create and share resources and experiences during this time in history!

Posted in Algebra 1 | 1 Comment

TRUE or FALSE? Independent Events… and Socrative

Years ago when I had the pleasure of serving as a “math coach” in the Bethlehem Area School District in Pennsylvania, I learned a clever way to expose students to independent events. A colleague of mine provided his students with lined paper, asked them to number from 1 to… 10 maybe? and told students they were being given a pop quiz!

Then, the teacher began verbally providing students with the “quiz questions”…

Teacher: “Number 1… TRUE or FALSE?”

Pregnant pause.

Teacher: “Number 2… TRUE… or FALSE?”

Students: “…TRUE or FALSE what? What do you mean?”

Pause.

Teacher: “Number 3… TRUE… or……. FALSE?”

Students: “WHAT THE ACTUAL HECK.”

Eventually, students would giggle and play along, realizing, literally, they were simply being asked to make the choice… do you choose TRUE or FALSE?

After the verbal “quiz” was over, it was time for students to “grade” their own papers… against an arbitrary answer key that had been previously created by the teacher. After students scored these so-called quizzes, the teacher would ask if anyone got a “perfect paper”. Literally no one did. But, it was a wonderfully silly segue to consider probability… what’s the probability a student could earn a “perfect paper” on this arbitrary quiz? (and subsequently… NO WONDER NO ONE ACED IT!)

I thought it would be fun to spend 10-15 minutes giving my Math 7 students a similar scenario today, our first day back from break, but I added a few twists. Rather than create that moment of what-the-actual-heck, I opted to tell students outright that I had created a TRUE or FALSE quiz with my own fake answer key… and their job was to guess what answer I chose for each of 5 questions. I didn’t want students to get distracted in silliness at the start – I wanted to challenge them to essentially attempt to read my mind. They were on it.

Rather than provide paper, I’d used Socrative to create my arbitrary TRUE or FALSE quiz and “answer key”. Using the Teacher Paced option, I still verbally asked the question five annoying times…

Me: “Number 1… TRUE or FALSE?”

Me: Number 2… TRUE or FALSE?”… and so on.

Students made their choices in Socrative on their iPads. I didn’t reveal the “correct” answer to any questions along the way… I just paced it to give a sense of don’t-dilly-dally… make a gut-instinct choice and let’s move on…

They were quite anxious to find out how they “did” on this “quiz” ! Before I revealed the class results, we worked through the probability of getting a “perfect paper” on the board… 1/32… would *anyone* ace this thing?

Student: “That’s only, like, 3% or so… that’s not very good!”

Now… the reveal! Here’s a portion of our results! Surprise! NO ONE “ACED” IT!

IN FACT…

Someone actually earned a ZERO!

What happened next, I did not expect.

Students: Let’s do it again! I want to do another one!

So they asked for another chance… AND… they asked me to make it only FOUR questions this time… how cool is that?

We established the probability going into Round 2 ahead of time… kids still expressed concern that 1/16 was close to only 6%-ish… but they had hope!

On the spot, I created a brand new 4-question TRUE or FALSE quiz in Socrative, and launched it as a student-paced activity so they could just zip through it… after all… we only had literally 4 minutes of class left…! No time for drama, just give me the data!

The reveal… WHOA!!!! Only one student aced it, but you’d think someone won the lottery with the way the class, and particularly that student… erupted!

The bell rang, the first school day of 2020 came to a close, and though that winter break was much needed and appreciated… I’m so glad to be back with these kiddos.

Happy New Year!

Posted in Algebra 1 | 1 Comment

How We Do “Four Corners” to Move & Talk About Mathematics

Search for the terms “Four Corners Classroom” online and you’ll find variation after variation of this cooperative learning strategy. The way we do “Four Corners” in my little corner of the world has evolved over the years. It’s one of those strategies I use so often that I dismiss it as “normal”… but maybe, this versatile strategy is just what you need to get your kiddos moving and talking about mathematics when we return to the classroom (and this turkey coma wears off).

I know my Math 7 crew will benefit from a little refresher regarding circles and circumference, so I’ve created a Four Corners for them to try when we return to class next Monday.

Creating a Yencafied Four Corners Resource

Create four similar-but-different problem sets that address the math concept at hand.  Use an icon to differentiate between each of the four sets.  This can be something novel (symbols that indicate different types of weather, animals, card suits, etc.) or the icons can address math concepts (use various, relevant math shapes or symbols, as in my example that follows here).

Copy the two Four Corners sheets, one sided, and cut vertically down the middle.  Distribute one half-sheet per student such that no two students in a cooperative group receive the same problem set.

PRO-TIP: To help with this process, I suggest having TWO copies of each of the two pages.  When placing in the photocopier top tray to run copies, stack the pages such that page 1 and page 2 are stacked on top of one another.  THEN, stack the SECOND copy of page 1 and page 2, but rotate these two pages 180º, then place these two sheets under the first two sheets.  Set the copier to collate, and voila! Cut the entire stack vertically down the middle, place one half-stack on top of the other, and you’ll have a beautifully mixed stack guaranteeing that groups of 4 or less will NOT have any duplicate sheets within the group! Every kiddo receives a different problem set!

Now that you’ve created, copied, collated, and cut the sheets, it’s time to use them with students!

First, students work on their own half-sheet silently and individually for a few minutes. When appropriate, consider allowing students to reference any resources they have handy.  When students try to collaborate within their group, they’ll soon find that their own paper is different from every other group member’s!  The first time one uses this strategy, students are very much caught by surprise that each paper is unique!  Once this strategy becomes a regular occurrence, students know their papers differ from the start, and simply get right to work independently.  {NOTE: Just as with Numberless Word Problems... students who attempt to collaborate are placed in a position to discuss big ideas and relationships, rather than specific ‘answers’… which I LOVE and did not anticipate when I first started doing this…} Meanwhile, I walk around and peek over shoulders, but I say nothing… I just observe what they’re trying, and how they’re progressing. MANY MANY times, students say to me as I pass by comments like, “Oh! I know what to do!” or… they look at me longingly and say, “I totally forget how to do this…”

    ≅    ~    ≈    

After some time has passed, and some students have completed the task (it’s also okay if some haven’t fully finished) allow students whose papers contain the same icon/symbol to meet in each of the four corners of the classroom.  I verbally and on-the-fly assign an icon to a classroom area/corner so students know where to meet and talk with the folks who had the same problem set from the get-go.  Students take their papers and writing utensils to the new location to collaborate with their group.

NOTE: This is a neat-o opportunity to assess students’ knowledge of whatever math symbol/icon was used to create four unique groups.  On my example here, I’m wondering whether students will know the difference between congruent, similar, approximately equal to, and not equal to… they will likely ask peers quickly to determine, “Which symbol do I have?  Which one am I? Where should I meet with my group?” Sneak in a review or mini-teach on notation/symbols/shapes/any math visual you use to create the four groups… or just have fun and use icons of four different animals instead, ha!

Once all students find their corner of the room, they discuss, compare, and correct their own papers as needed.  I never ask students to remain standing, but they just DO! They need to be able to walk around and chat with one another, comparing their papers. Everyone is standing and moving around! This is a great time for me to listen in, and notice if any groups are arguing and justifying their positions on any particular problems.  The idea is that ALL students in that group come to an agreement, papers are modified as needed, and that ANY student’s paper within the group could be chosen by me as a “sample answer key” for their problem set. I often ask each group to decide upon a paper from their group that they consider to be an “answer key” and bring it to me. After I have an “answer key” from each of the four groups, everyone returns to their own seats.

Once everyone is seated, I present each of the four “answer keys” using the document camera. Another variation is to have each group send a representative to the document camera to present their group’s agreed-upon “answer key” paper to the class.  I have also been the one to randomly choose a paper from each of the four groups… in theory, if everyone has discussed the problems, and made any necessary corrections, it shouldn’t matter whose paper I use.  However, I am careful NOT to reveal the name of the person whose paper is being showcased at the front of the room, unless our class culture has reached the point where anonymity is not a concern.  Ideally, though, I’m NOT the one presenting the problem set, but rather, a student (or several) from the GROUP is explaining the problems to the class.  During the presentation phase, students at their seats are encouraged to respectfully ask questions of those presenting, and additional conversations and corrections often occur as a result.

Ideally, we usually spend 10 minutes or so on this whole process. It’s a great little exercise in retrieval practice, collaboration, movement, and presenting to the class!

This Four Corners strategy can literally be used for anything!  

A pre-assessment… a warm-up… a review… a lesson closure activity… a great way to start a Monday morning to see if Friday’s math is still in their brains…

literally ANY TIME.

I love that this sort of activity promotes both MOVEMENT and STUDENT DISCOURSE.  It’s a variation on “YOU DO… Y’ALL DO… I-DO-or-intervene-as-needed”.  Sometimes I make up my own problems from scratch… other times, I use ancillaries that have versions A, B, etc. of homework or practice problems as my inspiration for the four problem sets.

How does “Four Corners” look in your classroom?

Grab the PDF for my circles Four Corners as an example, and share back when you create something awesome!

ANOTHER NOTE: The circle diagrams on my Four Corners example here were created using Apple’s Keynote first. I used shapes and text boxes to create the first circle on a slide, then duplicated and edited it three additional times to create four slides. I tried sneaking in letters on each circle that represent texting lingo or silly words, and I researched common circular objects when I chose each radius measurement. I’ll be curious about the everyday objects students think about! Finally, I exported the four Keynote slides as images, and dragged each image into the two-column Word document, where I added the questions. #KeynoteForMath

Posted in Algebra 1 | 6 Comments

Goldi-Desmos and the Three… Layers? {I’ve got nothing}

Okay, so my attempt at a clever title is lacking here, but the idea in my brain still stands and seems sort of valid.

Last Friday, my Math 7 crew needed support transitioning back to the curriculum after several days of end-of-quarter review activities, and taking a district “quarterly” benchmark test. Given that it was a 4-day school week, and three days prior were dedicated to the aforementioned tasks, it had been an entire week since we’d talked about equal ratios and started exploring the concept of “proportional”. The previous Friday, students had explored several scenarios to compare and contrast linear proportional and non-proportional relationships using tables of values (one where someone earned an hourly wage, and one where someone had already saved some money and was saving another consistent, additional amount, weekly) and hinting at what graphs of these relationships might look like.

Fast-forward to a week later. I wanted students to build on the tables and patterns we’d explored before, and continue to extend these to graphs.

“… that was too big…”

As a warm-up (that subsequently took 2/5 of the class period) students were given an empty coordinate plane and a few strategically-chosen ordered pairs. We tried to recall vocabulary like “origin”, how to label the axes, which quadrant was which, and how to plot a collection of ordered pairs that, if graphed correctly, would form a beautiful hexagon. Taking a lap around the room… I saw graphed polygons… and… other… things. It certainly didn’t hurt to address graphing ideas with these kiddos. I knew at this point that if our goal was to explore proportional and nonroportional relationships, graphing them by hand was an additional skill-set that we’d need to surely revisit.

“… that was too small…”

On the other hand, the instructional resource we use (a.k.a “the book”) simply states… “If the graph makes a straight line through the origin, it’s proportional.” These sorts of “quickies” are what students latch onto, without understanding more deeply the WHY. If we provide already-done graphs on worksheets to students and ask, “Is it proportional?”, and all they say is, “Yes, it goes through the origin” or “No, it doesn’t go through the origin”… this “quickie” explanation can extend to when students examine tables of values too. If their thinking halts here, and they don’t see (0, 0) in a table, they can make false assumptions.

On the back of the coordinate plane 40%-of-the-class-period warm-up, I copied this resource from Illustrative Mathematics. Students had discussions in their groups, ensured that they’d “answered the question asked” at the top of the prompt, and we had a share-out. Yes, the “line through the origin thing” is true, but I wanted to be sure we hadn’t lost the idea of relationships (Are there patterns between the x-coordinates? y-coordinates? Are equal ratios happening?)

This prompt came from Illustrative Mathematics Grade 7.
I tried finding a direct link to post here, but I couldn’t find it anymore.

“… that was JUST RIGHT.”

Lastly, I asked students to do what often is “the magic word” to seal understanding… “create”. I used Apple Classroom to navigate students’ iPads swiftly to student.desmos.com and used Teacher Pacing on this activity to limit their access to screen 1 only. Students talked in their groups as I asked them each to “create a proportional relationship you think no one else will.” They were excited to zoom in and out, seeing that this coordinate plane was quite different than the others we’d seen on worksheets today. LOTS AND LOTS of space to create!

Something happens in the room when students are provided with an empty table and are asked to “create”. Many take pause. Some initially stare at the iPad, as if making a wrong move will break it. Others dive right in and look at the graph happening simultaneously… and “play”. The feedback the Desmos graph immediately provides encourages them to keep going with their patterns, or revise ideas. What I loved most about watching them create patterns in these empty tables was… many students did NOT start with (0, 0) as their first point! For some, that was an afterthought that *I* asked them to add at the end to see if their line segments continued to the origin. They were looking at patterns, relationships, and equal ratios to “create”… YES! Since they weren’t limited to a typical 10-by-10 coordinate plane on paper, they were able to be more flexible in their thinking.

After sharing graphs and talking about several student creations, I used Teacher Pacing to navigate everyone to Screen 2, where students were prompted to fill an empty table of values to create a line that is non proportional. Again, with students creating, we had a wide variety of examples, and a few non-examples we could help students revise.

To close, I think having students experience ALL of these tasks was valuable. My “Three Bears” comparison here is more about how *I* was feeling at various points in the lesson, using various resources that accomplished different goals. Any one of these resources in isolation wouldn’t have been as powerful for students as using all three.

A message I want to share to encourage you is a friendly reminder that not every activity we do in Desmos or other tools has to be this huge, comprehensive entire-class-period or entire-lesson thing. Sometimes small creations used intentionally can make an impact! More about that here.

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Posted in Algebra 1 | 2 Comments