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.

Posted in Algebra 1 | 2 Comments

Quality Time (not in the lesson plan)

Last week my Math 7 students spent several days exploring ratios and unit rates (including scenarios with complex fractions in the mix). We haven’t used the word “proportion” yet… we’ve just been “playing” with numbers, really. Encouraging students to think flexibly (informally using ratio tables with recipes and other contexts, and just exploring ideas of equivalence in general) was comfortable for some, but made others extremely UNcomfortable.  

Some students viewed having options as “fun”… a game… a puzzle… they found joy in exploring many different, correct ways to represent equivalence…

…others seemed to feel overwhelmed, yearning for ONE WAY to DO the THINGS that would ALWAYS work… but if I give ‘em time, I know they’ll come around!

These flexible-thinking days are an investment into students’ understandings in the future… when we start using vocabulary like proportional, direct variation, and constant of variation, but for now, let’s play a little longer… even if it means taking a bit more time than initially planned.

I experienced the first return-on-investment at the start of class Friday.  Several students told me they’d started considering the date each day, and had begun representing the date as a complex fraction… all on their own. {Note: They’re keeping track of the patterns by hand – I’m using Desmos here so it looks “pretty”.}

Here was how they represented the date on their “Day 1”, which happened to be 10/9/19:

Here’s their “Day 2”:

Before they stacked Friday’s date in similar fashion as a new complex fraction, the students decided to guess whether the date was going to be “better” or “worse” than yesterday’s…

“I think it’s going to get ‘worse’ every day!”

Sure enough…

“We got even WORSE today!  I think we’re going to get worse every day through Halloween!”

“Halloween will probably be the WORST!”

“I wonder how much better we’ll get on November 1!!!”

IT’S HAPPENING…!!!!!!

This exchange and student-driven “game” was the perfect way to end a week for me. Embracing these moments, even when they’re not exactly on topic with *my* lesson plans for the day, is critical and important! As we try to help our students think and understand versus apply tricks and quick-fixes… be patient and persevere.

Enjoy your precious mathematicians as you listen to them and guide them on their journey in the coming weeks and months.

Posted in Algebra 1 | Leave a comment

A Classroom Visit from KLRU – Screens In School: Tech Transformation

My students and I had a unique opportunity recently to host guests from our local PBS station here in Austin, Texas. On the brink of iPad’s 10th anniversary, folks at KLRU came to visit our district, Eanes ISD, to chat with my colleagues and me about how iPad has changed teaching and learning in our schools. The first installment of the “Screens In School” series was released today (credit to KLRU for the classroom photos in this post).

On the day of the classroom visit, my students were starting a unit of study on rational numbers. It also happened to be the first time students were able to use their graphing calculators, so we addressed a few basic features that day, such as turning them on and off, clearing the screen, how to represent negative rational numbers ( in “real life” a negative sign and a minus sign have the same math job, but the calculator has been programmed differently) and how the calculator communicates about repeating decimals (rounding the last digit using traditional rounding rules… five or above, give it a shove). Through this nuts-and-bolts experience using a Nearpod lesson (created in Keynote initially), we began defining things like terminating, repeating, ratio, rational, etc. The proximity of the iPad helped students find the buttons and menus so we could get into the lesson swiftly.

To start the lesson, each student had the opportunity to apply the definition of “rational” using Nearpod’s ‘Draw It‘ feature to “create a rational number you think NO ONE else will think of in this room” (credit to Dan Meyer for that strategy). We examined student creations and compared each number to the definition of “rational” to ensure that it met the criteria. Positive values, negative values, fractions, decimals, both benchmark-y and wacky, provided a variety of student-created examples to talk about.

After scrolling through students’ number creations anonymously at the front of the class, we did a Stand & Talkusing a Venn diagram of subsets of rational numbers as our visual (credit to Sara VanDerWerf for that strategy).

After students shared their ‘noticings’ about how subsets of numbers relate, students completed poll questions and quizzes to check for understanding in Nearpod. To close, students completed a rational numbers Desmos Polygraph, which empowered them to craft meaningful questions using appropriate academic vocabulary in a virtual partner game across the room (credit to Jennifer Vadnais for that resource).

Using Desmos Polygraph to craft questions about rational numbers

I’m so thankful to have had this opportunity with KLRU to share a snippet of the “flow” that can happen in a 1:1 iPad classroom. Instruction and assessment blur and truly become one and the same. Student collaboration and communication are empowered because of the ability to seamlessly share visuals, ask poll and quiz questions, and provide every student with the opportunity to create and share their own unique mathematical thinking.

Check out the video from KLRU below!

Given that the title of this PBS series is “Screens in School”, this thoughtful read might also be of interest.

In Defense of Screen Time ~ Björn Jeffery

My favorite quote from the speech:


“… how can we talk about screen time without knowing what is taking place on the screen?” 

*UPDATE* This “Screens in School” series has four episodes as of 11/6/19!

Check out the final episode here where folks from our district speak to the success of our 1:1 iPad program, how technology is a part of learning in many local districts, and a quick mention of the benefits devices have on the learning cycle from little old me at about 4:45 🙂

Posted in Algebra 1 | 3 Comments

7,300-ish

Roughly 7,300-ish days ago, I began my teaching career in eastern Pennsylvania. I remember my very FIRST first-day-of-school morning… very vividly. I was a newlywed, new to the east side of PA (growing up north of Pittsburgh) and I remember rolling over in bed, thinking it seemed a little brighter outside than it should be.

It was then that I realized… the power had gone out!

Keep in mind, this was the year 1999… before iPhone, iPad, Apple Watch, etc… the available technology for an alarm was an actual alarm clock (which I still use… just me? HA)…

I jolted out of bed, and referenced the analog, battery-powered clock hanging in our apartment kitchen, realizing I had just enough time to shower and make it to school if I started getting ready right away!

I awkwardly attempted applying make-up by candlelight and flashlight-light, and can’t remember if I let my hair simply air-dry, or if I pulled it up in a soaking pony tail or bun, knowing time would surely cure my wet head. The commute is also a complete blur, but I know I made it on time, rattled yet ready. Or so I thought…

It was THEN that I realized that every other staff member had received a “first day of school” paper schedule in their respective “first day of school” folder of information… days before, and that this one sheet of paper had been inadvertently omitted from my folder. Surprise! Classes are out of order and it’s time to think on your feet and be flexible, Yenca! Welcome to teaching! I didn’t know what I didn’t know – there was no Google Doc to reference, or e-mail to check.

I don’t remember what the modified schedule entailed… an assembly perhaps? Shorter classes than I’d anticipated and planned for? That all worked out for the newbie… I had over-planned and was over-prepared right out of the gate due to the omission. But everything I’d meticulously written on the chalk board the day before regarding the bell schedule was suddenly irrelevant.

Time for my first class! As the orange-carpeted classroom (with no windows) filled with my first batch of real students, and the late bell rang, I entered proudly. Before I could speak a syllable, a boy who I learned later was named Peter exclaimed,

“How old ARE YOU?”

I was 22.

But I did not say, “I am 22-years-old, thank you for asking.”

I said,

“Young man, there are 3 things you never ask a woman. You never ask her age, her weight, or if that is her natural hair color. Do you understand, sir?!?”

*Crickets might have chirped at this moment.*

“Yes Ma’am.”

And that’s how it all began.

Today, I woke up before my alarm clock (and iPhone back-up alarm) sounded… I had a peaceful morning of reflection in a quiet house before using my hairdryer and putting on make-up under actual vanity lights… I posed for first-day-of-school photos with my son (a high school freshman) and paused with gratitude that I still get back-to-school jitters about this thing called teaching math. I met my new kiddos… no one asks how old I am anymore… it was a day of fun, and peace, and confirmation that 20 years later, I’m right where I’m supposed to be.

I did find after school that there was a nail lodged in one of my tires, as the sensor in my car alerted me the air was low. Folks at a local garage patched my tire in a jiffy, but I’m truly thankful for that nail. Something about that tiny first-day-of school tire mishap brought all of these 20-ish-year-old memories to the forefront of my mind.

Here’s hoping your first day, full of mishaps or smooth sailing, brings you jitters and gratitude too.

All patched up!
The strangest things can evoke
memories and emotions,
can’t they?
Posted in Algebra 1 | Leave a comment

Ending Another Year {With Desmos}

School’s Out For Summer!

Leaving my classroom after the halls have cleared is a bittersweet moment. I always take a photo of it – and looking at social media the past few days, I can see I’m not the only teacher out there that snaps an empty classroom picture before leaving school. It’s symbolic for me, closing the door on another teaching chapter, and another year of memories with learners who have grown to become a community. Bittersweet.

Farewell Until August!

Year’s end for many of us included state testing. As with the past few years, our Algebra 1 and Math 8 students used the Desmos Test Mode app as well as TI graphing calculators on their STAAR tests… and as in previous school years, I asked students about their calculator preferences after a year of learning with both tools. The kiddos change, but the survey results barely vary. Math 8 students tend to like pressing buttons more for arithmetic calculations… yet ironically do NOT prefer to use their TI graphing calculator for graphing, ha! Desmos always reigns on the graphing front! Algebra is the course where students seem to fall in love with Desmos, appreciating the ease-of-use, dynamic nature, and ease of viewing multiple representations of functions all together on one screen. To read up on our Desmos Test Mode history, check out this post and other posts linked within it.

Here’s progress toward more Texas math students having access to Desmos Test Mode with confidence during STAAR testing in 2019-2020!

Year’s end for many of us also included a final Desmos graphing project! The #MTBoS has been creating and revamping graphing projects for the past few years, and student work floating around out there is so impressive! Check out my Math 8 students’ work from last year, and a new gallery of projects from this year’s Math 8 and Algebra 1 students!

Watch this playlist here!

Year’s end for me also included a unique use of Desmos’ beloved “Polygraph” feature. If you remember playing “GUESS WHO?” as a kid, think of that game… but with a mathy and digital twist. Students ADORE Polygraph, and genuinely don’t often realize how Polygraph promotes the need for rich academic vocabulary to ask proper YES and NO questions. They don’t know they’re learning, but they sure do have fun!

While we’ve certainly had our share of math-content Polygraphs this year, I decided to surprise one of my classes with a one-of-a-kind Desmos Polygraph. Rather than using 16 images related to a MATH concept, the images related to classroom memories, laughs, and inside jokes as we learned math together as a community. While our Polygraph would make literally NO SENSE to anyone on the outside, it made PERFECT sense to my students, whose reaction to the gesture is one I will never forget. 🙂

AHHH, I LOVE TWITTER! Jenee Wilcox is another teacher who has already used this Polygraph idea with her own students!

We’ve had quite the Desmos-y end-of-the-year!

Posted in Algebra 1 | Leave a comment

“Lead & Learn” with “Stand & Talks” Across Content Areas

Several weeks back, our middle school teachers had the opportunity to #BeLikeFred (Rogers) in our #EanesNeighborhood – to either “Lead Like Fred” or “Learn Like Fred” during one of our early release (PD) days. I chose to “Lead Like Fred” and share about my experiences using Sara VanDerWerf’s “Stand & Talks”.

Thanks to all of the resources Sara generously shares, I was able to use her blog post, my own classroom experiences, and the hope that teachers who teach all content areas would see the value in using this strategy with their own students to plan my sessions.

I created a brief promotional video to share on our Lead & Learn FlipGrid. (An aside worth mentioning – I used Apple’s Clips app to create this video. Explore the hashtag #ClassroomClips to find more examples of videos that educators and students are creating using Clips!)

GOAL:

Students will SEE it before I SHOW them.

Students will SAY it before I TELL them.

~Sara VanDerWerf

I shared about Sara’s blog post and powerful “GOAL”, my own classroom stories, and examples and ideas that might help teachers who do not teach math to give their students the opportunity to Stand & Talk too. I gave the teachers in the room several opportunities to “Stand & Talk” with one another during our session.

I’ve heard feedback from math, science, Latin, and history teachers that they’ve already begun using Stand & Talks with their own students with success! YAY!

I’ve included a PDF here with static images of my #Keynote slides from the sessions, my presenter notes, instructions for using Apple Classroom to AirDrop images to students, and a “Getting Started Menu” for the teachers as a take-away. Several slides are shared below as images.

While everyone else is standing and talking… I’m listening! 🙂


Now that I’ve spent this school year dabbling in STAND & TALKS, my lens has changed when I plan lessons. I look at EVERYTHING through a lens of… is there a visual I can provide to my students BEFORE we start “the lesson”? 


Start with the goal, and then find or create a strong visual that will help students talk about the concepts before you teach them.


Using Apple Classroom to AirDrop Stand & Talk images to students is a great way to ensure they have immediate access to the images DURING the Stand & Talk… and after class is over!


A “menu”of ideas to get started!

I’d love to hear how you and your colleagues (mathy or not!) are using Sara’s Stand & Talks with students!

A million THANK YOUS to Sara VanDerWerf!

Posted in Algebra 1 | 3 Comments

Using Kahoot! Challenges and Desmos BREAKOUT to Revisit and Review… and a shout-out to #DesmosInTexas

My Math 8 students took their state STAAR test this past week (SIDE NOTE: This testing season marks lap#5 of my students using the Desmos Test Mode app on iPads as well as a TI graphing calculator while taking the STAAR test… more about that in a plethora of past posts). For a unique test-review twist, this year was my first opportunity to share *ALL* of the Math 8 Kahoots! I created last school year for Math_by_Kahoot with my kiddos en masse.

Using Google Classroom to share with students, I launched an asynchronous “Kahoot! Challenge” link for each and every TEKS-aligned Math 8 Kahoot (SIDE NOTE: These Kahoots! are organized by standard and are available for YOU to also use! Just check out the side bar on the right side of this screen to access Kahoots! for Math 8 and Algebra 1). Next, I compiled all of these links into an announcement post in Google Classroom so that all of my students would have access and the opportunity to play any and all of these Kahoots! on their own time. Additionally, I shared this massive “Kahoot! Fest” of links with my PLC-mates, so their students could play along with my students.

An Asynchronous KAHOOT! FEST!

I was pleased to glance through the reports in Kahoot! and see that students, indeed, chose to use the links to play along with one another, outside of our class time together! Unfortunately, since some students did not use their actual names, I’m not sure how many students participated from my classes or my colleagues’ classes. Bummer!

While glancing through the reports, one Kahoot! in particular seemed to draw more traffic than any other. Why do you think 100 students chose to play? 🙂

SPOILER: Mrs. Yenca played this one, and earned a pretty awesome score. Apparently word got out amongst students, and it became a goal to defeat me! One awesome student beat my score, ha!

In other news, Mr. Jay Chow’s Desmos Linear Breakout! was also a FANTASTIC resource to use to help students take one last stroll through linear lane before their STAAR test. What?!? You didn’t know about Desmos Breakout?! RUN, DO NOT WALK.

Additionally, while many of us were helping to facilitate STAAR testing on our own campuses this past week, we prepared written testimonies to help SB 1453 gain traction. So thankful that Oscar Perales was able to attend and deliver a powerful in-person testimony to help advocate for ALL student mathematicians across Texas! Stay tuned by keeping up with the hashtag #DesmosInTexas.

Want to learn more about Desmos and Testing across the nation? —> https://www.desmos.com/testing

Posted in Algebra 1 | 3 Comments

Using Apple Classroom for “Stand & Talks”

Sara VanDerWerf claims that “Stand & Talks” are “the best thing she ever did to get students talking to one another” and I believe her. For this 2018-19 school year, I’ve implemented “Stand & Talks” intentionally (though, moving forward, I hope to use them even MORE often) and there are SO MANY benefits.

For my middle schoolers, giving them the opportunity to TALK and MOVE early in the lesson provides social, kinesthetic, and math benefits for the rest of the class period. It gives them opportunities to make math observations judgment-free, and to talk to students with whom they might not otherwise interact. We’re moving, talking math, and building community… and it only takes a few minutes! Mere minutes that many of us teachers might use to TELL students things we want them to notice… rather than giving THEM the chance to do so first. This is not “one more thing” to do in our classrooms for which we “don’t have time”… it’s likely a time swap… trading in a LESS EFFECTIVE strategy for a MORE EFFECTIVE one… at least, this is how I see it with my own students! 🙂

Sara provides this AMAZING blog post, detailing her methods and teacher-script for implementing a “Stand & Talk” in her own classroom. Before reading on here, I suggest you check out her post first.

In recent months, I’ve used Apple Classroom to share “Stand & Talk” visuals with my students on their iPads. First, I ask students to ensure that their bluetooth and wifi are ready to go. In the Apple Classroom app on my teacher iPad, I open my current class of students to confirm that most of them have their iPads on and ready to receive a visual from me. I can see icons of students’ faces on my own iPad screen and toggle to see tiny live previews of their individual iPad screens… otherwise their faces show with the label “offline”.

Ahead of time, I’ve prepared a visual to share with students. Sometimes I create the visual myself using Apple’s Keynote. Other times, I use a visual I’ve found online from a fellow #MTBoS-er. I have this visual saved as an image on my teacher iPad camera roll.

Apple Classroom during a Kahoot! Wish I had an image during a “Stand & Talk”! Stay tuned? 🙂

I announce that I have something to share with every student! I select the image from my camera roll. Since I’ve already selected the class of students in Apple Classroom beforehand, the “share square” option for the selected image at hand gives me the option to AirDrop the image to the entire class of students in front of me with one touch of the screen! In a quick moment, I’ve AirDropped the image to my students… like magic! By the way, this process never loses its novelty on middle schoolers! And… even if not EVERY student is ready with a functioning iPad when I AirDrop the image, a “Stand & Talk” still works great. A student who did NOT receive the image from me naturally pairs up with a student who DID receive the image… and that student shares the image with her/his partner so they have it too.

Proceed with Sara’s process here… with iPads in hand, students stand up, walk across the room, partner up, and notice and discuss *insert a big number here* things about the image that’s just been shared. {Bonus – when the “Stand & Talk” is over, students still have access to the image because it’s saved on their OWN camera rolls, thanks to AirDrop within Apple Classroom.} I walk around, listen in, and work VERY HARD to NOT TALK… JUST LISTEN. Once students have noticed and discussed *big number of* things about the image, they start returning to their own seats, which, in my classroom, equates to 8 groups of 3-or-4 students each. Mind you… students have NOT been talking with the people they normally sit with… they moved around and talked with people NOT in their groups.

So… next phase! Now that students are seated back with their groups, I ask them to share their favorite noticings from the “Stand & Talk” with one another. With iPads in hand, students continue to talk and point and share… and I continue to NOT talk and to LISTEN and walk around, likely making all sorts of faces as I try NOT to chime in, ha! 🙂 I ask each group to choose a spokesperson or two to get ready to share out ONE THING they noticed about the visual. Students decide within their own groups about the ONE THING they want to share, and who’s going to share it. We come together as a class, I stand in the middle of all the groups as they WILDLY volunteer to share out first (so no one steals what they want to say before they get to say it… smooth move… I know…) and I point to each group, signaling each spokesperson to share. Sometimes we take ONE lap around the room… ONE sharing from each of EIGHT groups of students… and sometimes I surprise them and take TWO laps… or THREE… Some visuals spark more discussion than others… and sometimes, what ONE group shares helps another group notice something new that THEY want to share.

Having 8 groups of 3-4 students provides lots of room to “Stand & Talk”! Afterwards, I stand in the middle and “take a lap” or two, pointing to each group’s “spokesperson” to share out to the class.

It really is a beautiful process!!!

By the time we, quote, “actually start the lesson”… we’re likely a good way into it, thanks to everything the STUDENTS have noticed and shared ahead of time.

Here are two examples of “Stand & Talk” images I shared this past week with my Math 8 students. This one was shared at the start of class on review day for a unit on 2D transformations in the coordinate plane. I created the slide in Apple’s Keynote and exported it as an image to my iPad camera roll:

Surprise noticing: One student said that Image B was a reflection of Image A over the line y = x because he remembered the extension presented in this Desmos Activity earlier in the unit. MIC DROP!!!! What do you think YOUR students might notice about the coordinates shared here?

Here’s another image I found at MathHooks.com that I used at the very beginning of a scatterplots & data analysis unit, prior to any instruction whatsoever.

The vocabulary I heard was impressive! I heard words like “outlier” and “scatterplot” being used before I said ANYTHING. Students realized that Columns A and B did not match as presented, and swiftly opened this AirDropped image in their own drawing apps of choice, drawing lines to match correct descriptions from Column A to their corresponding scatterplots in Column B as they chatted together. During the share-out phase, students not only CORRECTLY matched the graphs, but ALSO entertained the idea of what the graphs might mean if the descriptions beside each graph DID represent the graph. So silly and fun!

Next, students completed this Desmos Activity... and I waited for THEM to ask more questions about vocabulary after their unsuccessful attempts to sort the cards within their groups on Screen 1. After a brief direct instruction, at students’ request, they were back to sorting cards! As green stacks appeared and student “experts” helped peers obtain green stacks too, we continued with the Desmos Activity to apply what we’d learned about correlation/association, and causation. Later, students had the opportunity to further apply their new-found vocabulary through this Desmos Polygraph Activity.

I have found that using a “Stand & Talk” before a Desmos Activity can be highly effective! “Primes the pump” before diving in! Here’s an example where creating a Keynote slide to “Stand & Talk” about helped students make connections between representations just before sorting cards in a Desmos Card Sort.

Looking ahead to your plans this week, where/when/how might you swap a component of a lesson where *you* had planned to do the telling… for a “Stand & Talk” instead?  

What visual will you use? 

 How will you share this visual with your students?

Posted in Algebra 1 | 2 Comments

#MathResourceRoundup – Pythagorean Theorem

I thought it would be fun (and useful!) to choose upcoming math topics and share resources we love to use with students as we explore these topics. I don’t use everything I find or create every year, but it’s nice to have options at arm’s length when I’m planning and while I’m teaching. Consider this a compilation rather than a comprehensive or cohesive plan. As a matter of fact, I’d love to hear how you use these, or other resources!

A glance at what my Numbers Doc might look like on any given week. I’m always adding to it as folks create and share relevant resources!

{An aside… I like to keep track of such resources using an Apple Numbers document. So many folks share on Twitter using #iteachmath and #MTBoS, and much of what’s shared may not be immediately relevant for my students, but WILL be relevant eventually. It’s been a lifesaver to add these as they come my way to my own Numbers document so I remember them when I’m planning. I literally copy and paste the links to the resources on the specific day(s) I might use them in the future, so they’re ready to consider as I plan each unit/week/day.

Here’s a blank template of the Numbers document.  Each document serves as a place to plan a 9-week quarter. Each week in the quarter has its own tab at the top, and since I teach two courses, each course has its own row of cells for the week at hand. If I didn’t have this template, I’d probably forget about 80% of the goodies you and I have already created! Using this template has helped streamline lesson planning!}


Today’s #MathResourceRoundup Math 8 topic is the Pythagorean Theorem!

STAND & TALK – Squares and triangles visual

I created this using Apple’s Keynote, and I love using Apple Classroom to airdrop the image to every student’s iPad so they can “Stand & Talk” about the things they notice. Just used this today!

  • VIDEO – Visual representation of the Pythagorean Theorem (Kyle Pearce)
  • VIDEO – Visual Pythagorean Theorem demonstration using water
  • VIDEO – Millionaire game show Pythagorean faux pas
  • VIDEO – Wizard of Oz Pythagorean faux pas
  • DESMOS ACTIVITY – Pythagorean Practice (Andrew Stadel)
  • DESMOS ACTIVITY – Pythagorean Triples and Similar Triangles (Michele Torres)
  • DESMOS ACTIVITY – Distance (Andrew Stadel)
  • KAHOOT! – Pythagorean Triples (Cathy Yenca)
  • KAHOOT! – Pythagorean Problem Solving (Cathy Yenca)
  • KAHOOT! – Distance Between Two Points (Cathy Yenca)
  • SOCRATIVEDistance in the Coordinate Plane – import with code SOC-32315155 (Cathy Yenca)
  • iBOOK – Learn Pythagorean Theorem Through Exploration (Kyle Pearce)
  • MATH TASK – Pythagorean Theorem Pile-Up (Michelle Rinehart)

Are there Pythagorean Theorem resources you use every year that I might have missed?

Add your favorites to the comments!

Have a great idea about how you’d use a resource in a unique way?

Share your tips here!

And… I’m curious… how do you keep track of lesson plans and resources?

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Posted in Algebra 1 | 4 Comments