**Back to the game. Here’s how we play.**

The game board is simply a grid with integers and an “x” to mark the starting position. Choose the integers you like. Next, we need two teams. A spokesperson who can handle the pressure of making a team decision in spite of potential disagreements is essential to classroom sanity. One team can only make horizontal moves, and the other team, vertical moves.

Let’s say horizontal movers arbitrarily go first. Starting at the “x”, the team gets to decide which number *in that row only* they’d like to have. That number represents the points earned by their team. *(Note: Sometimes students realize in this moment that we need to establish how a team wins this game. Most points? Least points? Closest to zero at the end? They come up with a lot of creative ways to win.)*

For this example, let’s say the teams establish that the MOST points at the end wins the game. So, team horizontal chooses the 7, and earns 7 points. Now, that 7 is used up. Done. Circle it and keep a running total of points earned.

Now it’s team vertical’s move. Since the other team chose the 7, team vertical must choose an available number in that column only, and they’ll receive that number of points.

Being new to this game, that 9 is probably pretty tempting. So, team vertical chooses the 9 and earns 9 points. Back to team horizontal we go… and either BEFORE team vertical chooses that 9, or just AFTER they do… everyone is realizing that there’s a bit more strategy to this thing than they realized at first glance. *(Remember when I said each team needs a spokesperson for classroom sanity? That’s to preserve YOUR sanity, teacher! That spokesperson has to make each choice based on team feedback, so you know who to listen to for the final decision on each move. Let’s just say this gets passionate. FAST.)*

Eventually, either every number is used up, or a dead-end occurs and the game ends. I like to play at least ONCE as a whole-class activity with a spokesperson for each team, and then have students play in pairs.

**Fun Things That Often Happen**

Sometimes, it doesn’t occur to either team to establish how we win. This can get very interesting when it comes to strategy. One team starts aiming for the biggest numbers, and the other team aims for the smallest numbers… with every turn, students confuse their opposing teammates with their point choices, and mid-game, someone finally says, “Why are you choosing those numbers? Wait, does the SMALLEST score win?”

“Does it?” say I *(and Dennis would be SO proud of that response).*

It’s also really cool when teams make up unusual rules for how to win. The other day we played, and several students had an idea. They thought we should find the mean of the two final team scores at the end. Then, look at how close each final team score was to this mean value. The team whose score is closest to the mean score, wins…

… and so we follow this victory rule… and the teams TIE! Not with a nice value, but each team is exactly the same convoluted decimal distance from the mean! It’s a miracle! How did this happen?!? The class goes BONKERS and wants to play again, under these same circumstances.

And I am biting my tongue and practicing my best poker-face.

We play again, and AGAIN, a perfect tie! This time, the distance each team’s score is from the mean is less obscure, but it’s the SAME! Again! Are we amazing, or what?

*Wait for it…*

**“… wait, Mrs. Yenca. Will this happen EVERY time?!?”**

*What do *YOU* think? *

*How do you know?*

School’s out for summer for me… but is it for YOU? Give this integer game a try, and share any new strategies you or your students come up with!

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Hey #MTBoS #iteachmath There are so many amazing examples of @desmos graphing projects floating around! Has anyone designed a rubric or checklist you really like to use? Hoping to have Ss work on this (in part at least) in my absence, so a resource would help! Thx for all you do!

— Cathy Yenca (@mathycathy) May 3, 2018

Math 8 students set a firm algebraic foundation for linear concepts. Included in Math 8 Texas TEKS are the following Readiness Standards:

*8.4(B) Graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship**8.4(C) Use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems**8.5(I) Write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations*

To prepare Math 8 students for future linear studies in Algebra 1, Desmos *Pet House*, a math-meets-art-meets-coding project, began as a seemingly simplistic graph paper sketch. However, the open task proved to be a “low floor, high ceiling” experience that whisked students into the world of linear functions, linear inequalities, restrictions on the domain and range, and even animations! Desmos provides a platform for instant visual feedback for the algebraic “code” students wrote.

*The Project in a Nutshell:*

*Students sketch a “pet house” rough draft using graph paper, labeling the slopes of all line segments on the sketch.**After draft approval, students gain access to a Desmos activity where brief tutorials help them explore new graphing skills.**Students recreate the draft “pet house” using linear function “code” in Desmos.*

As my Math 8 students explored and discovered how the mathematics they wrote impacted the math-art they created, their hunger for more math extended the due date for the final project repeatedly. They didn’t want to stop! Thanks to the teacher dashboard in the Desmos “Activity Builder” platform, students could view one another’s projects in progress as they worked during class, creating a constant collaborative atmosphere of, *“How’d you DO that?”*

After exploring restrictions on the domain and range of linear functions using Desmos, students met the linear expectations of the “pet house” quite quickly. However, the project didn’t end when students met the minimum requirements. Rather, students wanted to include nonlinear elements in their houses, shade various regions with color, and even animate their pets! **Essentially, students had created their own “problems” when they designed their houses, and through research and experimentation, they solved the problems that they, themselves, had created. Ownership win!**

To access the project description, rubric, and Desmos Activity where students will ultimately create a “pet house”, visit this link.

To see project showcases for each class, check out the videos below! Each video showcase was created exclusively on my iPad using Apple’s Clips app. I took screenshots and screen recordings of student work from teacher.desmos.com, right on my iPad, and used this media to create the #ClassroomClips.

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…until RECENTLY when I learned about Jay Chow (@mrchowmath) and the way he connects the idea of “breakouts” with math content using the Desmos platform. Already made. Ready to go. Boom.

First, I worked through his linear and quadratic escape tasks, filling pages of notebook paper with work I’d anticipate my students might do. I love how Jay addresses paths in his activities for those who might make a mistake along the way, as well as the variety in the tasks themselves. SO FUN. I decided to use the quadratic activity with my Algebra 1 students, and the linear activity with my Math 8 students.

I created student groups, and generated several Desmos activity codes so each group in each course had a different code. I didn’t want student groups to know that they were all doing the same task… at least initially… I also didn’t TELL them what the code was for. To add a bit to the “drama” of introducing these “Escape Room” tasks, I stuffed envelopes with old, one-sided worksheets (to be used for scrap paper, not to do the worksheets… would students actually just start working on random worksheets that didn’t even align with any math we’d been learning?). Also in each envelope was an index card with student group members’ names, and that mysterious “code”. I wrote the name of one group member on the outside of each envelope as well as **#BREAKOUT**.

Thx @mrchowmath! PUMPED to use your Quadratics Breakout tomorrow! I stuffed envelopes w/ index cards containing S group member names, a mysterious code (to the @Desmos activity) old 1-sided worksheets (for scrap paper… and also to make them wonder what they’re for… ) #MTBoS pic.twitter.com/r6ox1PDKKt

— Cathy Yenca (@mathycathy) April 11, 2018

On launch day, I started class by standing at the front of the room, announcing that some students “got mail”. I called the students to the front to receive the stuffed envelopes, and the buzz was immediate. What is Mrs. Yenca up to? What is this “mail” she’s giving to us? Is she going to call my name? *They know me*, and started grinning and hypothesizing.

Students with envelopes were instructed to wait until I gave the word, and they were to open them simultaneously. They found the index card with student names on them, and realized that #BREAKOUT was a huge clue about what we were about to do… 🙂

Then, just like that, student groups got together, started typing the mysterious code into various apps, eventually trying it in student.desmos.com with success. And… some groups just started doing the math worksheets! I didn’t let this linger long… I stopped by their groups and said, “Some groups found a code in their envelopes… did you get one too?” “NO WONDER! I WAS WONDERING WHY YOU’D PUT WORKSHEETS IN HERE THAT HAVE MATH ON THEM FROM YEARS AGO!!!” I let them know to use the back of the worksheets to do any figuring and they chuckled and got right to work!

Can I capture the energy in the room and convey it accurately to you here? Nope. I wish I could. It was REALLY SOMETHING! All I can do is encourage you to work through these awesome tasks yourself, launch them with your kiddos, and get ready for high energy, determination, and JOY!!!

P.S.

How does Mr. Jay Chow create this Desmos magic? I think it may have something to do with this… and boy, do I have a LOT to learn!

NEW FEATURE FRIDAY

Computation Layer, the private scripting language that powers all of our hottest activities, is now available free for anyone to use. https://t.co/11JDBo9tkg pic.twitter.com/LL9WLkHNoP— Desmos.com (@Desmos) April 27, 2018

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*Students making a fast choice without reading the choices at all**Students getting caught up in the leaderboard MORE than the MATH**Students feeling unnecessary pressure because the clock is ticking*

However… I’d be willing to bet you may have ALSO experienced the following:

*Students communicating mathematics, arguing and justifying their choices**Students realizing and fixing math misconceptions in real time**Students engaged and having a whole lot of fun*

**For me, the positives outweigh the negatives here if we’re intentional and strategic… as we should be for every tool, high-tech or no-tech, eh?** Lisa and Eric’s clever work-arounds make Kahoot! an effective platform in math class, and I’d love to piggy-back on their ideas with a few more, including Kahoots! that you can use or tweak for your own students.

I like to pose more in-depth math questions by using TWO questions in the Kahoot! platform.

QUESTION 1: Consider giving students the maximum time allotted (120 seconds) and creating answer choices that aren’t ANSWERS, but are reflection statements about confidence in one’s solution, or method choices for solving the problem. Make this initial question worth zero points.

Then, in QUESTION 2, provide a shorter timeframe for students to choose an answer for the VERY SAME QUESTION. Since the teacher ultimately controls the pacing, even when students need more than 120 seconds, delay advancing to the next question as long as needed. Consider having discussions before providing students with the opportunity to see the answer choices.

Example: **Algebra: Write a Linear Function**

Example: **Algebra: Solve Linear Equations in One Variable**

Visual math ideas work BEAUTIFULLY within the Kahoot! platform.

Asking students to identify and interpret attributes of graphs can serve as a great pre-assessment, mid-lesson check-for-understanding, exit-ticket… you name it! Students feel confident that they can complete visual tasks in a shorter timeframe, so they work well within the platform.

Example: **Algebra: Graphing Linear Systems**

Example: **Algebra: Attributes of Quadratic Functions**

Rather than use Kahoot! as a “quiz” or “assessment”, consider using it as a platform for *posing questions* that guide students to understand concepts incrementally.

Here’s an example that helps students visualize the difference of two squares by asking strategic questions, combining the questions with meaningful visuals, and scaffolding concepts along the way. Teach by asking questions that include EVERY student, and have discussions before advancing to the next question.

Example – **Algebra: Difference of Two Squares**

Rather than ask students to cut-to-the chase and solve a problem within the Kahoot! platform, ask about one concept at a time, making each question a building-block toward a greater goal.

Example – **Algebra: Systems of Linear Inequalities**

Example – **Algebra: Solve Quadratic Equations**

Do you use Kahoot! in math class?

What are some additional tips you have to use Kahoot! more effectively?

Please share in the comments!

Check out other creative strategies for effectively using Kahoot in math class shared by Laura Wheeler here.

**AND… Scroll up to check out TEKS-aligned math Kahoots in the sidebar for both Algebra 1 and Math 8! —>**

**8.7(D) Determine the distance between two points on a coordinate plane using the Pythagorean theorem.**

“The book”, being a static resource, included diagrams where a diagonal line segment already had perpendicular reference segments… and the step-by-step work… which, of course, had the Pythagorean Theorem as the first step. *Static resources can inevitably provide static lesson spoilers too.*

I wanted to create a journey for students, providing information incrementally, asking questions along the way, while giving EVERY student a chance to weigh in at each step.

Socrative was my tool of choice here. The super-clean interface for asking questions and eliciting responses is often my go-to. ** I love their Teacher-Paced option**, so that I can pose and display one question at a time from the front of the class, and I can hide responses until everyone has weighed in. If I want to know the specifics about who-answered-what, I have a detailed report for that later. In the moment, I’m often less interested in knowing who said what, and more interested in seeing the variety of responses, and overall progress AKA class percentages. *Sometimes too much detail in the moment makes the lesson experience feel clunky.*

So, students entered class, joined our Socrative “classroom” and began by answering two “low floor” questions (graphs created using Desmos.com). Piece of cake… except some students DID count incorrectly, and commented on how, next time, they’ll consider coordinates and/or look at a nearby axis to confirm their counting abilities. THEY came up with these little tips. Sweet!

I could hardly wait to send out the next question. I anticipated the looks on their faces ahead of time… but their reactions are generally even better than I anticipate. Furrowed eyebrows, various thinking sounds like, “Huh…” “Wait… what?” and a handful of students who transitioned to… “I think I know what to do here…” and “OH! I totally know what’s going on!” Scanning the classroom and just watching and listening… I mean… SO FUN.

Some students simply estimated, others guessed correctly, others tried relating this experience to finding the slope of a line, and others knew EXACTLY why the distance was 5. We’d also experienced Pythagorean Triples in class (as well as THIS particularly emotional YouTube video) and I strategically chose the most familiar triple so that the students who made the connection could do so mentally. The big idea here wasn’t necessarily about showing WORK or needing to grab a CALCULATOR, but seeing RELATIONSHIPS. Simple dimensions were important for that.

Students who had made the connection celebrated quietly – they knew a secret that others didn’t yet. Rather than encourage a class discussion at this point, I quickly moved to the next question.

At this point, some students were about to burst with excitement, and others were super curious… what did these confident students know that they *didn’t* know *yet*?

Next question…

My typical “curse of knowledge” surprised me a bit here. In every class, the correct answer choice percentage ranged from 79% to 85%. I thought I’d nearly spoiled the lesson at this point, but in every class, some students were still working through why I’d provided this additional visual information…

During this mushy spot in the lesson/warm-up/whatever you want to call this 15-minute Socrative experience, I heard a lot of what I call “The Sound of Learning.” Lots of grunts and a-ha’s… all happening at DIFFERENT MOMENTS. I get the privilege of actually seeing and hearing each student go from *not knowing* to *making connections*. Such a JOY!

To be sure I didn’t miss anybody, I provided another experience just like this one, using 5-12-13. Question 1: What’s the distance? Question 2: How confident are you about your answer? Question 3: Right triangle time. SWEET. Check out THAT percentage.

And just for good measure, I asked once more. No Pythagorean Triple this time. No guiding questions. Just find the distance.

Much more meaningful than a lesson spoiler! If you would like to use this Socrative resource, here’s the link:

**https://b.socrative.com/teacher/#import-quiz/32367596**

*What other math concepts do you think lend themselves to Socratic Questioning rather than spoiling-by-telling?*

And by now, it’s almost cliche to say “it’s NOT about the tool, it’s how you USE the tool that matters”. As with all tools, using Kahoot when appropriate can be very effective, and kids might not realize they’re *learning*! **In math class, use Kahoot carefully. **We don’t want to make kids feel unnecessary anxiety or reinforce that *fast* math = you’re *good* at math. So, before we poo poo the fact that much of Kahoot! relies on timed-tasks and a little friendly competition… please… don’t throw out the baby with the bathwater. Let’s not dismiss a tool that KIDS LOVE that can be used strategically and effectively.

I had the pleasure of attending a session at an Apple Institute this summer that presented brain research regarding the concept of “retrieval practice” or the “testing effect” – namely… instead of being a teacher who’s always trying to put information INTO students’ brains… provide plenty of opportunities for them to pull information back OUT of their brains as a means of LEARNING and RETAINING concepts. The “testing effect” is not about “tests” or “grades” in the traditional sense; rather, students are “testing” their own ability to understand, apply, and retain concepts.

Tools like Socrative and Kahoot! serve students well in this purpose. Teach by asking questions, one at a time, and display the class results for each question so we can talk about them, correcting misconceptions in a low-stakes no-grades-here retrieval practice environment that’s also fun!

*Note: It’s easy to get swept up in the Kahoot “leader board” and classroom energy without pausing to consider and discuss student responses between questions. Don’t miss the opportunity for some valuable classroom dialogue here. Putting on the breaks before advancing to the next question is a great way to reteach and have conversations with students about the content at hand! *

I’ve had the pleasure of partnering with Kahoot! Studio the past few months – “a new offering of original, ready-to-play games from Kahoot! content creators and our partners within education, publishing, entertainment and other industries”. These standards-aligned and curated Kahoot! experiences might serve your students well in retrieval & distributed practice.

My favorite part about this creation opportunity has been using the Kahoots! with my OWN students, and seeing their excitement and success. GHOST MODE is a favorite feature, as well as using the Kahoot! app to share CHALLENGES that can be done asynchronously.

A comprehensive collection of Kahoot! Studio math resources can be found here.

I’ve also created this Google Sheet to organize the Kahoots! I’ve been working on, aligned to Texas Algebra 1 TEKS. This document will change as new Kahoots! are created and released!

Distributed practice?

Review?

**There are so many ways a Kahoot! can be used with students!**

**How are YOU using Kahoot! in math class?**

So I’ve been away from the classroom for two-and-a-half weeks. I’ve celebrated the holidays with a house full of guests and friends, and braved Disney World at this most wonderful time of the year (in unseasonably cold temps) so forgive me if I’ve forgotten just a little that… oh yeah, I teach math. A rest is necessary for those of us who eat, sleep, and breathe what we do, so I’m thankful to have had this time to refresh and pursue other hobbies and interests.

Anyone who knows me can speak to my second passion – interior design and home improvement projects! We bought a fixer-upper several years ago, and the to-do list never ends… and I’m okay with that! Just as with teaching, there’s always room for improvement, implementing fresh ideas, and learning from mistakes!

Most recently, I couldn’t resist a smokin’ Black Friday deal to buy a box of peel-and-stick reclaimed wood to give my 1980s kitchen peninsula a facelift. I didn’t anticipate that all of the pieces of wood would vary in size so much, so this little project quickly became mathy. I was NOT about to run out of wood OR have to make unnecessary cuts, so I took inventory of the wood that was shipped and turned to Apple’s Keynote to make a plan.

First, I created a custom slide size that would represent the area of the two cabinet faces I wanted to cover with wood. Using pixels as my units, I created color-coded rectangular shapes to represent the piles of wood, moving the shapes like puzzle pieces to fill the faces. I was short two small lengths and became immediately thankful that I’d requested free wood samples a year ago – those two pieces saved the project!

A dry run on the floor before peeling-and-sticking…

…and VOILA! Mission accomplished! I seriously don’t know how anyone could complete such a project successfully without a color-coded Keynote plan!

I also made the impulsive decision to sell my former counter-height dining room table and chairs on Craigslist (we NEVER sat in those tall chairs…) several short weeks before Christmas, knowing the aforementioned house full of family and friends would be coming over… what was I thinking?

I needed a new dining set pronto, and had to make a plan. Again, scale models on a Keynote slide and some research regarding recommended clearances between dining chairs, walls, table sizes, etc. helped me plan what to buy.

VOILA! After a bad shipment of broken chairs, tracking our table down and retrieving it from a local warehouse that was too booked up to deliver it before Christmas… we DIDN’T have Christmas dinner on my dining room floor after all!

And, I got to share a little ed-tech fun with family by designing a Kahoot for us all to play together after dinner!

A highlight of our family gathering – playing Kahoot Family Trivia… complete with fun facts and family photos in the questions! @GetKahoot pic.twitter.com/dkMI0NcSrI

— Cathy Yenca (@mathycathy) December 27, 2017

Speaking of Christmas, I received an unexpected gift in the mail from one of my kind students in NCTM’s “Seeking Students Who Hide” online course this past fall. A beautiful card and set of magnets from Taiwan greeted me in my teacher mailbox before break. This kind blog post is a gift I will forever cherish.

From a Cart pusher to a math teacher! https://t.co/Fja3ei5OYv Reflections on NCTM-Math Forum Fall course: Seeking Students who hide. Many thanks to @mathycathy and @MikeFlynn55 #MTBoS #iteachmath

— Joanne Ward (@JoannecWard) January 4, 2018

I am so thankful for my students – the adolescents and the grown-ups alike. Thank you for helping me grow, and for your kindness!

Best wishes as we embark on 2018 together!

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As students grabbed rulers and worked alone while I took attendance, I walked around, and gave them several minutes of individual work time. To transition, I grabbed a clean warm-up sheet, plopped at the document camera, and asked for volunteers to explain to me, step-by-step, how to graph each function.

Except, I told them I would be a 6-year-old and that I would be doing EXACTLY what they told me to do. Literally.

Whelp, I can’t express through a post all of the silly things I did, and all of the laughs we had. I took their instructions very literally, and they howled, eventually leading me to graph each line correctly. When I transitioned back to “myself” they begged me to be “the baby” again as they explained various problems to me in extreme detail.

There was no lack of volunteers here. As a matter of fact, they were BEGGING me to call on them.

*Could “the baby” help develop precise language with a math concept you’re working on? *

*Note: Sense of humor required!*

Reminded me of this “Exact Instructions Challenge” and all of this could be extended to this week’s Hour of Code.

]]>*~ You’re solving proportions and a kiddo with stars in her eyes exclaims, “The BUTTERFLY METHOD!”*

*~ You’re isolating a variable while solving equations, and when you ask what’s next, a student offers, “Well, those cancel out, so you have x = -3…”*

*~ You’re solving inequalities in one variable, and as you graph the solutions on a number line, an excited student exclaims, “ I know a shortcut! The way the symbol is pointing tells you which way to point the arrow when you graph it!”*

Some of these “a-ha” moments might happen * as* we’re teaching (the inequality idea above, for example). I have no data to back this up, but my guess is that more often than not, these ideas have been

My students when I ask them to do a problem slightly different from the one we just did #iteachmath pic.twitter.com/Z7JPE4LkYe

— Jonathan Osters (@callmejosters) November 20, 2017

**When these moments inevitably happen in your classroom, literally, what is your next move? What’s the expression on your face looking like? What are the words that you say? What’s next?**

I have handled these moments across the gamut – with grace, all the way down to (sporting my best pouty face), “I never use the word * cancel*… except when I tell students that I never use the word

How do we respect those who are trying to help students by teaching them “tricks”, yet steer things toward learning mathematics for understanding (especially when students LOVE and ADORE a good trick)? Simply asking and pursuing, * “Why does that work?”* can help – some students’ reactions are PRICELESS as I watch them UNDERSTAND the mathematics right before my eyes. Other students look a bit like Osters’ aforementioned tweet, preferring the “trick” that “works” instead.

I’ve gotten lots of ideas for exploring alternatives that promote understanding from Nix the Tricks. If they’re already pre-programmed to “FOIL” I’ve found the conversation about why that acronym is so silly *(because it only helps when multiplying two binomials)* can bring clarity.

Another approach I’ve tried is to create “proactive problems” and ask strategic questions as we work them. I see huge potential in creating some sort of problems-resource as a community that might help us be more proactive in the moments *before* a student is just about to utter the “trick”.

~ *Instead of cross-products right out of the gate, ask students, “How can we isolate the variable in this equation?” (What? Proportions are equations?!? I can multiply both sides of the equation by 40 first? I can DO that?)*

~ *Instead of saying “cancel” during instruction, verbally describe what’s happening every time using visuals and concepts of identities. Reinforce this language as students begin to use it when they explain their thinking.*

**What are your favorite ways of handling “tricky” instructional moments of opportunity?**

And, I’d be naive to think there aren’t things that *I* am explicitly teaching my students, with the best of intentions, that might drive my students’ future math teachers nuts.

*What topics and methods am *I* teaching right now that will make my students’ future math teachers roll their eyes?*

*What sort of “proactive problems” handed down from my students’ future math teachers could also help ME know why I might consider changing the way I present certain topics now?*

*How can we get better at this?*

*Follow-up:* Check out Dan Meyer’s living document of ideas from folks all over to help create “Mathematical Headaches”

Might we create a similar resource along the lines of… “Rethinking Tricks with Proactive Problems” Directory? or “Instructional Language to Overcome Tricks” Directory?

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At the top of the sheet was the simple question… **“Is It a Rock?”**

At our seats (probably alone first, then in groups) we had to analyze the information provided in each of the 9 blocks and decide, did that piece of information describe a rock? Yes or No? Take a stand. I loved the simplicity of the question, and the depth of the information provided in each square on the handout.

**Why not for math?**

I started thinking of questions we could ask students… Is It Linear? Is It Parallel? Is It Perpendicular? Is it a Direct Variation?

Maybe you’re thinking of some **“Is It ________?”** questions that are coming up in your own mathematics curriculum. Though the question is simple, and the answer will be “Yes” or “No”, the beautiful part of this strategy is choosing what you’d like to put in those (9 is an arbitrary number of) blocks.

**So, I made this.**

I created a few different versions using a Pages template I whipped up, asking students various “Is It ________?” questions.

This week, I assigned one of these for homework. At the start of class the following day, students discussed their stances on each of the 9 blocks.

I walked around and listened to their conversations and arguments. In the past, my next move would have been to place my own sample key on display for students to check their work, and have a little Q & A as needed, and that would have been it.

**But I’m glad it didn’t end there.**

This time, rather than show “my” key, I asked students to show their final stances on each of the 9 blocks by completing a Desmos Card Sort that contained the same 9 equations as the handout. In theory, students had plenty of time to do the work they needed to do for the 9 blocks independently as homework, and had a chance to talk it out with a friend and possibly make revisions, but no “answer key” had been provided this time.

As students started to sort their cards to match the thinking on their papers, we started to see some red stacks. The polarizing feedback of a Desmos Card Sort can be harsh sometimes… a stack turns red if *EVEN ONE card is out of place*, so this was eye-opening.

When students were surprised by red stacks, there was a new level of engagement in the room. They started talking more, asking more questions of one another, and darn it… they wanted GREEN STACKS!

They asked better questions too. “Wait, can a line be parallel to ITSELF?” Or, understanding NOW that (2*x*)/3 and (2/3)*x* are equivalent, and WHY 2/(3*x*) is not the same. Catching errors through showing more work than they initially had… and, to be fair, some didn’t show ANY work at all at the start, as my handout’s directions didn’t seem to require it… all that was “required” was a checkmark, no?

**The question, “WHY IS MY STACK RED?” was a lot more intriguing than, in the past, “Why doesn’t my paper match Mrs. Yenca’s answer key?”**

You see, I don’t think they ever really wanted MY answer key anyway. Once Card Sort became part of the experience, they wanted to create their OWN key.

**And that’s what they did.**

Below is a PDF file of this “Is It Parallel?” task, as well as a link to a Desmos Activity. The Desmos Activity can be used independently, or “chunked” as I’ve described here.

**I’d love to hear about some “Is It ________?” questions you’re thinking about!**

**What are some “Is It __________?” math questions you could ask your students, using this “blocks” format?**

*How could a Desmos Card Sort follow-up bring engagement and encourage more **dialogue and **deeper understanding to the task?*

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