Student-Created Visual Patterns and Book Creator

thephotoAfter introducing Visual Patterns to my Math 8 students, I began to see their creative side through various “Draw” work samples from our Nearpod patterns lessons. They did an excellent job generalizing linear patterns!  Though their experiences with nonlinear functions have been slim to none yet, helping students see connections to area and quadratic functions informally helped.  All of this to say, it was time for *ME* to stop being the chief-pattern-creator, and it was time to charge them with the task.

Enter… Book Creator!

I designed a project checklist and permitted students to choose their own groups of ideally 2-3 people.  Each group designed one linear pattern and one nonlinear pattern (I encouraged quadratic patterns at this level, so as to relate to areas of figures), created visuals to show how they saw each pattern growing, and included a table, graph, and equation using Desmos.  All of this student-created media was then organized into a Book Creator mini eBook.

Music Note & Flower.001

The due date is near, and many students have already submitted some fine work!  Want to see students’ completed eBooks? Included in this ThingLink are students’ ePub files (best experienced in iBooks), my sample eBook, and the project checklist.  Want to experience a snapshot of students’ work? Check out a few student pages in the images I’ve included below the ThingLink. Enjoy!

Book Creator YencaVisual Patterns Yenca

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Critter Patterns

Visual Patterns Yenca.002Texas Math 8 standards provide students with a firm foundation of linear concepts and slope-intercept form.  Additionally, my Math 8 kiddos just wrapped up a polynomials enrichment unit.  With this in mind, I felt like they had a solid background to ensure success with generalizing patterns algebraically.  What better way to do this than with “Visual Patterns”!

I’m pretty new to using “Visual Patterns” with students, and in the past, I didn’t feel like I introduced these very well.  Students could draw and describe the pattern, but when it was time to complete a table beyond the first few figures, they had a tough time expressing themselves algebraically.  I think the most popular equation was… y = IDK.

Before I began a few days with “Visual Patterns” this week, I sought expert advice from the #MTBoS and found this video of Jo Boaler sharing various student strategies to be quite helpful in shaping my questioning.  Additionally, Jo’s animations and unconventional (fun) pattern descriptions made me realize that I wanted to truly capture student thinking, ALL students’ thinking, possibly in words AND through visuals.  Could I also provide students with an animated view of pattern growth the way Jo did? (Note: Keynote “Magic Move” and a #SilentSolutions video helped make that happen!)

IMG_4514First, my son and I sat on our patio with graph paper, designing our own “Critter Patterns” to represent some of our favorite animals.  I translated our sketches to Keynote slides that represented Figure 1, Figure 2, and Figure 3 of each pattern.  I purposely created two patterns that were linear, and two that were not.

Next question – pattern delivery to students… Desmos Activity Builder?  Or Nearpod?

I couldn’t choose, so I tried both, in my own little experiment.

I made this Desmos Activity Builder and used it to introduce Critter Patterns to the first of my three Math 8 classes.  I used this Nearpod to introduce the patterns to the second class.

For my third class, I decided I would use either Desmos or Nearpod, depending on which delivery format seemed to go better.

NPPdrawThere was incredible value in giving students the chance to examine the pattern closely, and “Draw” the way they saw it growing using Nearpod.  Asking students to describe the pattern in words right off the bat in the Desmos lesson version proved to be more challenging.  I heard a few grumbles of what-are-we-even-doing-right-now, which told me that the “Draw” had a bit of a lower floor for these Visual Patterns newbies.  Since any URL can be added to a Nearpod lesson, I was able to integrate a prepared Desmos calculator slide at just the right time in the Nearpod lesson (this Desmos-Shows-Up-In-A-Nearpod gig amazes students every. single. time.)

Overall, the Nearpod lesson slowed students down to examine and draw the patterns out, and sharing student drawings at the front of the class was effective and immediately enjoyable.  So many different ways to see the same thing!  That’s not to say that Desmos wasn’t effective – it was just a bit of a bumpier start.  You’d never know it, looking at the activity’s history in my teacher dashboard – having the ability to self-navigate and revise in Desmos Activity Builder clearly had its perks too.

ABSsAfter my Desmos/Nearpod experiment to introduce patterns, I opted to use Nearpod to introduce the rest.  I used Fawn Nguyen’s Visual Patterns as homework each day.  To begin each class following our introduction lesson day, I used blank Nearpod Draw slides to gather student thinking for whole-class discussions of the homework patterns.  Note: Linear patterns went VERY well, and nonlinear patterns varied from students absolutely NAILING IT to the infamous y = IDK.  These students lack experience with quadratics, and some of them sought help from older siblings and parents.  I loved how families got involved in generalizing more challenging patterns!  I was *hoping* students would see some of these in ways that I hadn’t.  I can’t unsee my own way.

Reluctantly, I showed “my way” for each of the quadratic patterns.  They followed along as I got them started, paused short of spilling ALL the beans so that they could take my strategy to the finish line, and as a result, many “got it” when it was time to generalize.  How do you handle it when kids can’t generalize?  Do you show them the way, or just leave it for them to potentially play with?  I dunno.  “You can always add.  You can’t subtract.”  What’s been seen has been seen, this time.

Highlight: Students taking on my here’s-how-I-started-now-run-with-it, ending up with a table, function, and graph in Desmos, and seeing them cheer when a parabola appeared, passing through all of their points.  They don’t even know what a parabola is, but they DO know it’s a good thing when a nonlinear graph passes through their table’s points.  Super fun to watch this!

Critter Patterns Yenca

After several days of this cycle, and exploring both linear and nonlinear patterns, I saw students’ confidence grow mathematically.  Through various Nearpod “Draw” experiences, I saw student creativity as well!

Next up – I’m asking students to create their own “Visual Patterns”.  Student groups will each create one linear and one nonlinear pattern, as well as other components, and showcase their work in a Book Creator eBook.  Stay tuned to see our student-created Visual Patterns mini-eBooks!

For your viewing pleasure, here are more student work samples from this week.  My Nearpod “Reports” are a treasure-trove of student thinking.

NPPHW IMG_4534

 

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

Screen-Shot-2015-04-24-at-9.34.33-AM-300x298For the first time in history… (too strong?)… my Algebra 1 students excitedly embraced the opportunity to use Desmos Test Mode *AND* TI graphing calculators during their End-of-Course STAAR test this past week.

In years prior, TI handheld graphing calculators were permitted, but for Algebra 1 students, having access to BOTH Desmos and a TI calculator was not an option.  Last year, during a Desmos pilot with our Math 8 STAAR test-takers, my Algebra students became very jealous, as we had used both tools equitably during instruction, but only TI was allowed on Algebra STAAR test day.  Since then, the Texas Education Agency has updated their STAAR calculator policy to include secure tablet graphing tools too.

For a time this year, we weren’t exactly clear on TEA’s language in this updated policy – would our Algebra 1 students have to *CHOOSE* between a TI calculator and Desmos?  Or would they be permitted to use both tools?

Had you been in my classroom the day I announced TEA’s clarification that using BOTH tools was INDEED permissible, you may have thought we were watching football.  Yelling, clapping, yahoo-ing, and cheesy grinning filled room 510… because of a graphing calculator, people.  Can you imagine?

Well, if you’re a math educator who uses Desmos in your teaching, then you probably don’t *HAVE* to imagine its educational impact.  You probably see it quite often in your own teaching corner of the world.  Besides being a fluid (and free) graphing calculator, teachers create mathematical experiences for students using tools like Polygraph and Activity Builder.  If I’m not mistaken, Desmos Activity Builder isn’t even a year old, and yet the sheer volume of teacher-created resources here and here is inspiring… and immediately usable!  Shout out to the #MTBoS!

While my Math 8 students have embraced Desmos, my theory in their seemingly not-as-enthusiastic feedback about the graphing tool is rooted in their lack of experience with functions.  y = mx + b is as far as these kiddos go with graphing (though this Activity Builder open-task gave them a taste of graphing ideas beyond our TEKS/standards) and they seem to desire the TI-button-pushing experience over using Desmos to number-crunch in their multi-math sampler-type curriculum.  Algebra 1 includes various forms of linear and quadratic functions, as well as exponential functions, so Desmos has been extremely valuable for Algebra students who favor seeing multiple representations all on one screen.

I’ll let my Algebra students (49 of them who took the survey) speak for themselves here. Check out their anonymous responses to a brief 3-question survey using the link below – one that I’ve also given to Math 8 students the past two years with VERY DIFFERENT results.

I asked three questions:

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

Algebra Calculator Survey Yenca 2015-16

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Note:  These Algebra students WERE the Math 8 students last year who were able to use Desmos on their Math 8 STAAR too, so we’re talking about a generation of kids who have been using Desmos for two years.  I wonder if that also has an impact on their enthusiasm?

*Update* Desmos Test Mode is also available on Chrome here.

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Teamwork and Communication Using Quizlet Live

Screen Shot 2016-04-30 at 8.29.52 AMMy colleague Gary Raygor happened to post a photo online, showing his students having a blast in his classroom, working in teams, arms flailing with… joy or regret…I couldn’t quite tell.  But what anyone could clearly see is that his students were INVESTED in whatever it was that they were doing, so I asked Gary to share more!  I stumbled on Gary’s mention of “Quizlet Live” Thursday evening, then subsequently used it with all of my classes the next day.  Quizlet Live provides a whole new way for students to interact with Quizlet sets in the classroom.  I’m so glad I jumped right in!

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After I logged in to Quizlet as a teacher using my school Google account, I searched for “Algebra 1 EOC” and found existing sets including relevant academic vocabulary, formulas, terms matched to graphs… you name it!  What’s great is once you find a set you like, you can copy it and edit it to make it your own, and it shows up under “Your Study Sets”.  Once you have a set you’d like to use with your class, select the “Live” purple button and project the screen so students can see it.  They simply go online to quizlet.live and enter the 6-digit code to join the game.

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Once all students have signed in, select “Create Game” and Quizlet Live randomly groups students into teams by animal name.  Make no mistake, students LOVE this.  There’s something about naming teams that creates an instant bond!  Students take their devices to sit with their newly-formed teams, and the “game” begins.

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A definition, graph, etc. appears on all teammates’ screens, along with a list of potential matches.  The difference between Quizlet Live and other matching or multiple-choice tools is that each teammate’s screen shows only a subset of possible answers from the Quizlet set.  Only ONE teammate has the correct term on his/her screen, so students have to work together to talk it out.  In every class, I heard great conversations/arguments and comments like “I got it!” or “Oh, I don’t have it!” as students compared their answer choices to the definition etc. at hand.

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Team progress is shown from the teacher dashboard at the front of the class, while all the information students need shows up on their own devices.

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If a mistake is made, the team must go BACK to the beginning and work through the entire  set again.  This was more motivating than it was destructive.  They got right back into the game, and often made an impressive comeback after a fall!

The element of speed is not a timer per se.  The time it takes to complete a round is established by the winning team.  The first team to work together to correctly get through the set “wins” and the game stops at that moment, paying respects to the victors.

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And in EVERY SINGLE CLASS, after the winning team yelled and celebrated, the class begged, “Can we play that AGAIN?”

And so, we did.  Every time we played again, I took advantage of Quizlet Live’s “Shuffle Teams” feature so everyone had to move around.  My favorite thing about this is the instant team bond that seemed to happen with the animal names, and that every student (especially the shy or quiet types) was instantly a valuable part of the group.

I like that Quizlet Live collects stats during each round.  I can display class data for “What We Know” and “What We Learned” that shows common class errors as well as class strengths.  Each team also receives this type of feedback, customized specifically to their own team.

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After doing Algebra EOC reviews with my Algebra students, my Math 8 Pre-AP students practiced multiplying monomials by other polynomials using Quizlet Live.  The practice with properties of exponents and the distributive property was collaborative, and much better than a worksheet would have been!

How will you use Quizlet Live?

 

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The Weeks Keep Flying By…

This time of year, I feel like the days just slip through my fingers.  So many good things are happening, and yet I haven’t stopped to reflect and post about them.  At all!  Forgive my drive-by approach at summarizing a few recent edu-wins that may benefit you and your students too.

(1) After participating in a Global Math Department online meeting with a Desmos theme, I fell in love with an activity featured by Shelley Carranza, inspired by the work of Bob Lochel, entitled “Parabolas and the Number d”.  I edited it ever-so-slightly, and used it with my Algebra students with some skepticism that they’d see the things I wanted them to see regarding the mysterious “d” (discriminant).  To my pleasure, they nailed it.  It’s really effective to feature student work using the “Overlay” feature!  Thanks so much for sharing, Shelley and Bob Lochel! Screen Shot 2016-04-21 at 5.40.32 PM

(2) My PLC-mates and I have been using Socrative on nearly a daily basis.  There really isn’t a simpler tool to create a quick-check on the fly.  The other day, students were practicing simplifying expressions and I had them enter their answers using Socrative so we could examine trends quickly.  I display this matrix for the class to see once all students have entered their responses.  Great questions like, “How are people getting zero for number 6?” become common practice.  Often, the kids find more value in wrong answers than in correct ones.  We try to pick apart the problems students miss (all the while their names aren’t attached to their work) to correct misconceptions. Screen Shot 2016-04-21 at 6.08.37 PM

With Socrative automatically-generated codes, “quizzes” are really easy to share.  Try this one on solutions to inequalities in one variable.  The “quiz” (which I used as a teacher-paced warm-up/discussion starter in class) takes advantage of the feature that allows more than one answer in a multiple-choice prompt to be correct. Go to Socrative.com and import this quiz for ideas, and if you make something awesome, share your quiz code here, and/or on Twitter using the #MTBoS hashtag. Share Quiz: SOC-21965015   Screen Shot 2016-04-21 at 5.56.18 PM

 

(3) When I saw that the original Des-Man activity, inspired by Fawn Nguyen, was down for the count, I whipped up my own.  Then David Petro gave it a linear-only makeover, and I used his version with my Math 8 students.  It’s super fun to see what they came up with.

I’m partial to the turtle. Screen Shot 2016-04-21 at 6.15.27 PM Screen Shot 2016-04-21 at 6.15.04 PM

Screen Shot 2016-04-21 at 6.24.55 PM     IMG_4278

 

(4) Today was polynomial vocabulary day. Kind of a yawn, unless you get students involved in creating various polynomials using Nearpod “Draw”.  Amazingly, they get SO EXCITED to have some say-so in the lesson examples.  They were in hysterics at their own creations, and frankly, so was I.

 

(5) In case you missed it, this was a recent opportunity to share with the folks at MindShift about @Desmos love:

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Using Desmos on iPads… for the Math 8 STAAR Test… Take 2

Screen-Shot-2015-04-24-at-9.34.33-AM-300x298Last year, our district pioneered using the Desmos Test Mode iOS app on STAAR (state) tests.  You can read about that here.

For the 2015-16 school year, we knew that the Texas Education Agency updated its calculator policy to extend the possibility of using a tablet-based calculator not only for the Grade 8 mathematics STAAR test, but also for Algebra I, Algebra II and Biology.

While my Algebra students won’t get to use Desmos Test Mode for their STAAR EOC (end-of-course) exam until May, my Math 8 students completed their math testing yesterday.  Students had the option of using Desmos Test Mode, a TI-graphing calculator… or BOTH tools if they preferred.  Today, I gave my Math 8 students the same survey I gave to my Math 8 students last year.

I asked three questions:

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

Here are the results – while my sample size included more students this year (77 to be exact) the percentages are basically IDENTICAL to last year’s results.

Anonymous student responses can also be seen here —> Math 8 STAAR Calculator Survey 2016 Yenca if you’re curious about the topics they listed (I’m sure they’d appreciate it if I asked you to excuse some of their spelling errors…!)

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I’ll be very curious to ask these questions of my Algebra 1 students post-EOC.  As far as graphing topics in Grade 8 curriculum, we deeply explore concepts of slope/rate of change/unit rate and proportional versus non-proportional linear relationships.  We only utilize slope-intercept form of linear functions, and we only solve linear systems by graphing.  Grade 8 math is still somewhat of a sampler course – we do some number stuff, some geometry stuff, some algebra stuff, some data stuff, and some financial stuff.  There are a LOT more topics in Algebra 1 for which Desmos is an IDEAL tool.  I really think this graph will be quite different for Algebra 1 students… we’ll see!

Check back in May once we’ve conquered the entire Algebra 1 curriculum.

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Curating and Organizing (So You’ll Remember What You Have When You Need It)

Thanks to the #MTBoS and a plethora of digital tools, we have access to a lot of resources. A LOT.  And they’re coming at us at lightning speed thanks to Twitter and blogs… often *not* when we’re teaching the concepts featured in the resources.

How do you keep track of all of the resources you find or create, so you:

(1) Remember that you have them…?

(2) Use them when you’re teaching the concepts they address…?

I have stuff all over the place.  Over the past 4 years in a 1:1 iPad learning environment, I’ve come to the conclusion that there is no one “silver bullet” tool that addresses all classroom needs.  (As a matter of fact, I’m not even looking for ONE tool that can do everything well… because I don’t know that ONE tool can.)  Thus, the content, as well as the information you seek to gain from students, helps determine the appropriate tool(s) along the way.  That’s why it’s inevitable that you may also have stuff all over the place.

My colleagues and I have:

(1) Created Socrative Quizzes

(2) Created and revised ThatQuiz Quizzes

(3) Created Nearpod experiences

(4) Created ThingLinks full of relevant URLs

(5) Created and revised classroom Kahoots!

(6) Created and revised Desmos Activities

(7) Created and found instructional YouTube and Vimeo videos

If you don’t park all of this good stuff somewhere, you literally forget about the work you’ve done and the fine work others have shared with you to use.  That’s why I created an in-detail Google Doc for each course I teach.  With new math TEKS K – 8 last year, and new high school math TEKS this year, I can’t imagine any other way of keeping my sanity and organizing all of the resources and planning we’ve done from scratch the past 2 years.

What’s great about using Google is that it’s with you on every device, wherever you go.  So when that unexpected and awesome resource comes your way, you can simply copy and paste the link in the doc so you’ll remember you have it as an instructional option when it’s time to teach that topic.

Here are several screenshots from my Google Doc – having this ever-present parking-space for good stuff has kept me sane, organized, and has even helped me to reflect upon my lessons, giving me a space to make daily notes about how class went, so I can revise my plans to make them better next time.

How do you keep track of all the good stuff that comes your way?

 

 

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Guest Post – 3-Acts: Using Digital Tools to Give Every Student a Voice

Two things I’m passionate about when it comes to technology integration:

  1. Giving every student an opportunity (and frankly accountability) to weigh-in on mathematics we’re learning about and showcase their thinking… even if it’s incorrect at the start (we value those mistakes as learning opportunities)
  2. Including students in the examination and analysis of their thinking (through digital work samples or other graphical data displays produced by the tech-tool we’re using) to help facilitate rich dialogue, authentic error-analysis, and even determine next-steps in the lesson (versus keeping this information to myself, as the teacher – students benefit from seeing their collective thinking)

Here’s post 4 of 4 in a series at the #NCTM #MTMS Blogarithm Blog.  Don’t miss the chance to snag several ready-to-go lessons, featured in this post, to try with your own students.  While many digital tools can capture student thinking well, this post features ways to use Nearpod in conjunction with tasks inspired by Dan Meyer’s 3-Acts strategies.

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On another note, I was honored to attend the Inaugural Nearpod PioNear Summit here in Austin a month ago.  Highlights from our day are captured in the video here.

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Blogarithm Guest Post – Vertical Value: Part 2

CbWh5fDWEAEkTnXCheck out this @Desmos shout-out on the MTMS Blog, and how I transformed a “worksheet” into a Rectangles Polygraph activity… and when I used it with students, it didn’t go as planned.

If you use this pairs activity, I’m curious about the grade-level of your students, and your favorite student questions.  Does this activity possess “vertical value”?

Yenca Art 2(1)

 

 

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Experiencing Transformations Dynamically With Nearpod and Desmos

My Math 8 students started exploring patterns for various transformations in the coordinate plane this week.  Such a visual and potentially dynamic topic calls for visual and dynamic lesson presentation (ahem… not a static worksheet).  The winning combination this week was to guide students through a Nearpod lesson first, and let them loose on a Desmos self-paced activity to follow.

Nearpod first – why?  Since students had never seen these topics in the context of the coordinate plane, it was extremely beneficial that I could control the pacing initially.  Hear me – this “teacher-paced” format is NOT about the teacher being “in control”.  Rather, it’s about keeping kids from rushing ahead before they should (since, in general, they don’t know what they don’t know). We took our time to discuss student responses to open-ended questions and drawings of the transformations in the coordinate plane along the way.

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I LOVE to run a “Nearpod Cartoon”, clicking quickly through student graphs, using my interactive white board, to show the variations in student work so we can talk about them, and discuss ways to correct them.  We even played the instrumental “chorus” of Bieber’s “Where Are You Now” as I clicked through (if you don’t see the connection, watch his video starting at 1:09 here – that cartoon thing is basically how student work looks, especially if they embellish it a little with color…)

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I like to present the solutions to transformations dynamically as well.  Using Keynote, the “Magic Move” transition, and QuickTime to record a #SILENTSOLUTION screencast helps students see the solutions in motion.  They can watch the solution video (shared within Nearpod) repeatedly to see exactly where those vertices landed.  The silence of these quick videos allows students to provide the narrative for what they’re witnessing.  I wish you could hear students as they watch these silent videos, and how often they’re surprised, and finally say, “OH!  Now I get it!  I see what it did!”

IMG_3822After patterns were generalized and reteaching occurred as needed, I sent students a multi-question “quiz” to end the Nearpod portion of the day.  Individual results from thisNearpod quiz were sent to each student’s iPad screen in the form of a pie graph, where students could revisit the questions and their own responses. Note: when I send this pie graph to student screens, they literally scream, yell, jump out of their seats, and proudly display their completely green (100% correct) pie graphs like a badge of honor!  The room literally ERUPTS!  Except for those with a sliver… or perhaps huge sector… of red on their graphs…  Having this data gave me the chance to intervene with any students who were struggling during the transition from Nearpod to Desmos.

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Once students reviewed their quiz results, and met with me for help as needed, they went to student.desmos.com to work through a related activity.  This time, rather than simply creating sketches in a coordinate plane drawing, students had to accurately complete and correct tables of values to “program” Desmos to graph the desired transformation.

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We’re working on it!

IMG_3804Projecting students’ graphs using the Desmos “Overlay” feature is a great way to check in with the class, often revealing an OOPS or two… or, more than two…  The best part about the Overlay is when students realize they need to correct their graphs, and we can all watch those corrections happening “live” and dynamically! I used my iPhone to capture this time-lapse during one of the Desmos translations tasks.  Check out the video here.

I was very thankful for Andrew Stadel’s impeccable timing in sharing his Chrome tech-tip.  I used it for the exact purpose he shared.  Early in the reflections Desmos activity, I highlighted the word “opposite” and made a big deal out of encouraging those who used academic vocabulary to describe their reflections.  It worked – later in the activity when I looked for the word “opposite” again, many more students had used the term.

I’d love to hear about your experiences using Nearpod or Desmos to teach students about transformations or other dynamic topics!

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