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

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

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

Kahoot (With Embellishments from Desmos)

Screen Shot 2014-11-19 at 3.17.21 PMStudents ask to “Kahoot” practically every day.  They never tire of this incredible (free!) gaming platform.  If you’ve never “Kahooted” before, you can sign up for a free account here.

In a nutshell, Kahoot takes multiple choice formative assessments to a new level of motivation and fun for kids.  You can create a Kahoot by simply typing each question and the possible answer choices into the Kahoot gaming platform.  You can also add an image to each Kahoot question, which can be quite handy in math class.  Additionally, time limits can be adjusted for each question.  Each time limit choice will provide a unique Kahoot song during the classroom game.  For example, if you set the time limit on a question to be 10 seconds, the song Kahoot plays evokes a sense of urgency!  If you set the time limit on a question to be 60 seconds, Kahoot provides a relaxing, zen-like tune.  I like to vary the time limits on questions in my Kahoots so that the music changes for every question.

Once I’ve created a Kahoot, I launch it from my laptop and project it at the front of the classroom on my smart board.  Kahoot generates a class pin number on the spot.  Students join the Kahoot by going to Kahoot.it online where they are prompted to enter the pin.  Having 1:1 devices is ideal, and as students join in, their names appear on the big screen at the front of the class.  If you’d like, you can have Kahoot show a YouTube video as you wait for students to join the game, ha!

Once all students have joined the game, the teacher launches the first question.  Students must look to the screen at the front of the class to read the question and the answer choices, as the screens on their devices only show the answer buttons.  This keeps the game very social, versus having kids absorbed primarily in their own device screens.

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As students answer, those who choose the correct answer the fastest will earn the most “Kahoots” (points).  After every question, a bar graph is immediately generated to show the class responses.  This is a grand opportunity for reteaching!  Then… the leader board shows up, ranking the students who have the most “Kahoots” (points).  This is VERY motivating.

Tradition in my classroom is to have your picture taken at the end of the Kahoot if you’ve “won”.  Here are several champions from recent Kahoots.

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I don’t use Kahoot as often as my students might prefer.  Kahoot rewards students for accuracy and SPEED, and not all math should be speedy.  However, when a lesson relies on vocabulary, quick visuals, or mathematics that can be recognized without doing work, I like to give it a go.

This week, I used Kahoot to assess students mid-lesson on transformations of linear functions.  I created this Kahoot and used Desmos.com to create some graphs as visuals.  Students had just learned about these transformations, and we’d use Desmos to explore them using sliders, so having a few screenshots in Kahoot from Desmos made perfect sense.   Using Kahoot helped me reinforce linear transformations and address misunderstandings right away.

When the fun is done, Kahoot provides a color-coded data report for the teacher (much like Socrative) to examine later.

Teachers have already created hundreds of thousands of Kahoots – when you initiate your free account, you can search them yourself and use them with your students.

Interested in the linear transformations Kahoot I used with students?  Grab it here. 

How are you using Kahoot with students?

What additional middle school math topics make sense for a gaming platform like Kahoot?

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

Twitter Hodge-Podge

Lately, busy days lead to spits and spurts of reflection and PD rather than lengthy blog posts.  I love this time of year – I feel like my students and I know each other well, and expectations are clear all around.  We’re in the groove, and so much is happening at lightning speed that sometimes a quick Tweet is more feasible than hanging out here.

I’m so thankful for folks on Twitter, and all the right-on-time resources and inspiration that happen there seemingly every hour of the day!  Likewise, knowing I can throw an idea out there and receive immediate feedback continues to shape my practice.

Here are a few recent highlights, in no particular order… just the way they happen on Twitter.  If you’re not over there, you should be! :-)

1) A scatterplot intro activity (link to editable file below):


2) Math and ketchup:

3) Math in the bathroom: 

4) A great article:

 5) A Nearpod for exploring volume of cylinders: 

6)  Insight and influence on current apps.  My students went absolutely crazy when Qrafter disabled all timed video ads in their app because they (my students) spoke up and we took the issue straight to Twitter!  Thanks to Qrafter for considering and removing the distraction that long, timed, video ads would be in our classroom!


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

Desmos Function Carnival: Tech & Teacher Take-Aways

IMG_8428When I learned about Function Carnival from Dan Meyer’s blog last school year, I first tried it with students on a wacky-schedule day during a unit that didn’t connect well to the fabulous Desmos lab.  In that first instance, students’ sought to “break” the carnival rather than graph accurately.  I hadn’t anticipated that when I had compliantly walked through the carnival myself to prepare for the lesson.

I learned a lot from my first Function Carnival attempt, and I hope to share several simple strategies that worked well during my second lap through the Carnival with students this past week.  If you haven’t tried this lab with students, please read these detailed notes from Desmos, then consider these additional tips from a classroom that’s been there.

For your reference, my students each have an iPad, I logged in as the teacher from a laptop, I displayed my Function Carnival teacher screen on the Smart Board… and I played carnival music while we worked. :-)

They’re not being bad, they just want to play.

This time, Function Carnival showed up right on time.  Concepts like discrete and continuous graphs, graphs over time, and whether or not a graph is a function were current and relevant.

Also, I knew students would seek to break it.

Any time students try a new tool, we simply have to allow for some play time.  Starting with the Cannon Man graphs, talk about what their scribbles mean.  Showcase one or two gross graphs for the class to see.  Even consider “select all” and play the beautiful mess, talking about how amazing it is to see “not a function” in motion.

Shift your attention to “gamify” the experience.

Then, refuse to give any attention to messes henceforth.  Don’t say, “Okay, no more non-function graphs kiddos.  Stop messing around.” or other responses that might deflate the energy in the room.  Rather, shift your attention very intentionally to the beautiful filter button that says…

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Tell students that Desmos thinks the entire class doesn’t know what to do.  “Desmos thinks every one of you needs help right now.”  At this point, you may have a Golden Child whose graph has been classified by the coveted filter button…



If initially you have some sweet soul who’s already been ranked “very precise”, celebrate that thing.  Select “very precise” and see whose name has the coveted colored check mark in front of it.  Then, shift the focus of the entire class to earn that label of “very precise” too.  I even like to throw in that “Last period, we had 19 students create very precise graphs.  Do you think we can get 20?”

As soon as they see the “very precise” number increasing, they want to get it right.  They cheer.  They celebrate.  They want to know whose name does NOT say “very precise” so they can help them.  Students start yelling, “Show mine!  Show mine!”  and I *only* click on “very precise” when making my choices of whose individual graph to showcase to the entire class.  If a student who asks for their graph to be shown does not have their name listed as “very precise” I simply say, “I can’t show your graph yet.”

I try to move on to Bumper Cars, but if students still have not earned “very precise” they do NOT want to move on just yet.

Got ‘em. :-)

At this point when pacing begins to individualize a bit more, I stop displaying the big screen for a time.  After students have had some time to further adjust Cannon Man, or work through why their squiggly graph does not match the green bumper car :-) I display the class screen and click on “very precise” to see who earned their badge.   The excitement grows as more and more kids have earned this prized label.  I showcase a few graphs, even playing all “very precise” graphs simultaneously… and on we go to the Ferris Wheel.

Thank you Desmos for providing these amazing filters!  Though they appear on the teacher view, I think the students value the feedback just as much.

IMG_8426 IMG_8433

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

Just Playin’

We just wrapped up our first quarter of the year, and I’ve noticed something.

We like to play.

Every class period has it’s own culture… it’s own “thing”.  It’s usually not very math-related, but I’d venture to say this “thing” that unites us in each class helps us learn the math better.  Simply put, we choose fun.

Maybe I should have taken pictures all year and started my own #TodaysDate180 blog (ha!) but every day this year, I’ve created an expression whose solution is (wait for it…) today’s date.  Some days’ expressions are more challenging than others.  It’s a very simple way to continuously review order of operations, exponents, etc.  And in one class, every day, several students take it upon themselves to write a proof of sorts, demonstrating how they know what day it is.  Here’s a not-elaborate-at-all-on-my-part recent date, and a sampling of the daily date-proving ritual:

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Another example of how we play – students started noticing that every day is a holiday.  We start every class by talking about what holidays are listed on a goofy daily holiday website, and if it’s possible, we celebrate it.  High-five day was a recent favorite.  I don’t know how it started, but we do it.  Every day.

We hashtag.  A lot.  When I grade papers, students often hashtag comments to me, and I return the favor.

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When students use language like this to express themselves on a quiz, I take it as a high compliment.  This is how we interact.

Screen Shot 2014-10-22 at 9.58.11 PM

Play is important.  We start every lesson with a smile and make the kind of goofy memories that middle schoolers hold dear for a long time.

Don’t forget to play today.  #justsayin

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

Socrative and Slope-Intercept Form

IMG_8308With new TEKS in tow, my 7th graders taking 8th grade math have been studying proportional and non-proportional linear relationships (wow, right?).  The progression has been a refreshing, concept-based study of LOTS of scenarios featuring “constant rates of change” represented in tables and with graphs, making clear connections to the similar triangles we studied in our last unit (Thank you Desmos for this beautiful contribution!  Twitter can be SO POWERFUL in sharing resources, and I thank Desmos for entertaining my request by sharing this beauty!)  We didn’t even use the word “slope” until about day 3 of our learning when we introduced the traditional subscript-laden formula.  They didn’t flinch once they saw that the formula was simply showing what we’ve been doing all along, and the word “slope” became a lot less scary.

The next step was to add equations to the mix of representations.  Though the text introduces proportional linear first (think direct variation… or y = mx… or y = kx), I mixed things up and started with non-proportional linear (think y = mx + b).  That way, I could emphasize that “b” was just zero in the proportional flavor.

After some scenarios, we talked about how to find an equation if we weren’t given one.  Is it possible to write an equation of a line if all we know about the line is that it passes through two specific points?

Screen Shot 2014-10-11 at 8.13.52 AMI created this “chunking activity” to help students think through the steps.  If we want an equation in slope-intercept form, it would be helpful to have the slope (we can find that) and the y-intercept (we can find that too).  After writing each equation in slope-intercept form, we used Y = on our TI graphing calculators to enter the equation, view the table, and confirm that our line passed through the two points we started with.  After guiding students through the process, they had a few equations to muster up for homework.

Screen Shot 2014-10-11 at 8.56.32 AMThe next day, I used Socrative to review homework.  On the fly, I selected “Quick Question” then “Short Answer” and asked students to enter their first equation.  Using Socrative to type in equations reinforced the keystrokes needed to enter an equation in the TI using the Y = key. Anonymous equations appeared in a list at the front of the class, and conversations about discrepancies began.Screen Shot 2014-10-11 at 8.57.34 AM



Is the slope -7/5 the same as 7/-5?  How about -7/-5?  What do the folks who represented the slope as -5/7 instead need to know?  Sure, Socrative doesn’t have a “pretty” equation editor, but discussions about the meaning of (-7/5)x versus -7/5x versus -7/(5x) might not have happened without the wonky-looking representations.

Graphing lines

y = (-7/5)x

y = -7/5 and

y = -7/(5x)

simultaneously to test parentheses placements added a level of richness to this simple, initially skill-based task.  We entered each equation from the homework, one at a time, using the same process in Socrative, viewing the anonymous list and continuing the conversation.  By the third or fourth equation, we had a nearly unanimous list of slope-intercept form equations, as students had learned and made adjustments to their equations stemming from our discussions along the way.

I can’t overstate the impact that making student thinking visible using simple, free tech tools like Socrative can have on student discourse.

How are you using Socrative in the classroom?



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Functions – Nearpod Learning Check

Looking ahead to our next unit, I was sifting through some ideas about introducing relations and functions to both my algebra students (8th graders) AND my pre-AP Math 8 students (7th graders experiencing new 8th grade TEKS and therefore, experiencing more algebra than in the past).  I created this function vocabulary ThingLink last summer as part of the “ThingLink Teacher Challenge” to help introduce the concept.  I plan to use Function Carnival after a bit more instruction about functions.  Between introductions and Desmos fun, I wanted to give students some sort of “learning check”.

I was exploring Open Middle for ideas (have you not heard of Open Middle?!?  GO!  NOW!) and was inspired by this simple prompt.

Screen Shot 2014-10-05 at 8.40.38 AM

Immediately, I thought of Nearpod’s “Draw” feature and giving students an opportunity to create a table that represents a function, AND a table that does NOT represent a function.  I’ve found that the constant contrasting between what IS and what IS NOT a function helps students understand the concept.  It’s brain-friendly to show contrast!

Why stop there?  Asking students to also create mappings and graphs that ARE and ARE NOT functions would further reveal misconceptions and hopefully solidify understanding in the end.

So, I created a Nearpod “Learning Check” (see below to grab it for your students).  Not every Nearpod needs to be a comprehensive lesson.  This one serves as a brief assessment after instruction has occurred, giving students the opportunity to show what they know by creating relations for themselves.  During the Nearpod session, student work samples can be anonymously shared with all students to further discussion.  There’s a quick 5-question quiz at the end too.

Feel free to use this NPP (Nearpod presentation) with your students.  Clicking on the image below will take you to the Nearpod login screen.  Once you log in, Nearpod will let you know I’ve shared a NPP with you.  Say you’d like to accept it and it’s yours to use.  Feedback welcome!

NOTE: If you’re using iPads, be sure you’re using an updated Nearpod app with iOS 8.  Otherwise, we’ve experienced some issues with the “Draw” slides and students not being able to draw on the far right side of their iPad screens.  A quick fix is for students to not lift their fingers, but draaaaag their fingers to the right side of the slide to continue drawing.  WEIRD! :-)

Screen Shot 2014-10-05 at 8.46.11 AM

Follow-up:  Thanks to Susan Oxnevad for mentioning my “What is a Function?” ThingLink on the ThingLink Blog.  Did you know that Tackk and ThingLink play nicely together?  Click below to check it out!

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Here’s a glimpse of some of my students using the Nearpod learning check.  I wish I could capture the emotion in the room.  They love seeing what their peers are thinking and talking about authentic work samples… even if they’re wrong.  Great discussions always ensue!


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

Math Playdate (from Twitter to Tackk)

It started on Twitter.  My challenge was irresistible to fellow math buddy Kyle.

 Within what seemed like mere minutes, Kyle had a complete task, videos and all, with his own unique spin.  

Fast-forward a few weeks.  Just as Kyle couldn’t let go of the ice bucket, I couldn’t stop thinking about the Big Nickel he posted:

When Andrew Stadel posed this question, I couldn’t walk away.  It awakened within me the “perplexity” Dan Meyer talks about.  I just. needed. to. know.  And I felt responsible to report back.  

After all of my work, I thought using Tackk would be a great medium to share with Tweeps.  This task not only inspired me to explore my own fine-tuned question, but it also encouraged me to create a product to easily share my work with the circle of math friends involved in this conversation, and beyond!  Click the image below to see my Tackk.

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I have not asked students to use Tackk before, but how great could that be?   

There are limitless possibilities here – photos, text, and media can be displayed neatly in a Tackk… and once student Tackk links are shared with the teacher, they could easily be collected and shared in a ThingLink with an entire class, entire school, or the entire world.  Note that Tackk also has settings for conversations to continue within the Tackk itself (feel free to add to mine!  I know my estimate is an over-estimate!  How could we make this estimate more precise?)

Have your students created solutions to math tasks using Tackk or a similar medium?  If so, please share!  I’d love to have more student examples to show my own kiddos before asking them to create their own.

Thank you to all Tweeps involved in this Twitter conversation.  I cherish the amazing PD I receive through our interactions.  You challenge and inspire me!

Ready to take the Big Nickel challenge with your students?  Want to see classroom-ready visuals and resources?  Here’s Kyle’s take on the Big Nickel Twitter Playdate done in classic 3-Act style.

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

iPhones #WCYDWT

With all the (understandable) iPhone hype lately, I couldn’t help but fall for this math-potential-packed image:

#WCYDWT ? (What can you do with this?)

Screen Shot 2014-09-09 at 4.54.13 PM

Attached below is a PDF I made that displays each of these iPhone models to their accurate sizes.  I made the image more transparent to save us all some ink.  Would love to hear back if you use these images with students.  Happy hypotenuse!

iPhones Accurately Sized


Posted in Algebra 1, Pre-Algebra | Tagged , , | 3 Comments

Story Time (Algebraically Speaking)

Algebra students have been solving multi-step equations.  Quite a great, semi-sneaky way to review all sorts of topics students should already be “fluent” in – operations with rational numbers, the concept of “isolating the variable”, properties of equality, and so on.

I presented students with this simple equation:

Screen Shot 2014-09-17 at 5.44.25 PM




Rather than rush to strategies to solve for a, I asked students to tell me the story behind this equation.  “Once upon a time…”

Students’ first inkling was to describe half of something:

EX) “I have half of an apple… no… half of an… armadillo!”

They had “half of” all sorts of appropriate and inappropriate things.  I asked, “Do you have half of just one of those things…?  How many halves do you have?”  Hmmm…

Next, students seemed to notice the other decimal values and opted to talk about money:

EX) “So, something costs five cents each…”  Whoops.  Why does that ALWAYS happen?

We got our place value straightened out pretty quickly:

EX) “No wait, that’s FIFTY cents each…”

I heard a story about Hawaii:

EX) “So I’m going to Hawaii by bike and it costs eight dollars and seventy-five cents…”  Wait… waaah?  Gotta love 8th graders!

I heard a story about underpaid restaurant staff:

EX)  “A waitress makes fifty cents an hour and gets $8.75 in tips.  If she gets $13.25 at the end of the day, how many hours did she work in this awful restaurant?”

I heard a story about gum:

EX) “I buy some packs of gum for fifty cents each, and a container for $8.75.  If I pay $13.25, how many packs of gum did I buy?”

I heard a story about lemonade:

EX) “Some little kids have a lemonade stand.  They charge fifty cents for a glass of lemonade.  A lady feels bad and gives them $8.75 for no lemonade.  How many glasses of lemonade did the kids actually sell if they made $13.25?”

What I can’t capture in a blog post is the energy in the room.  Even for goofy problems, or problems with wrong thinking, students OWNED these stories.  Turning a strategy on its head and ASKING FOR the word problem rather than GIVING the word problem and asking kids to write and solve an equation was a simple, novel, and apparently unexpected strategy.  When we solved the equation (using several different, valid methods), the solution had meanings that students had assigned to it, whether it be gum, lemonade, or hours.

I’d recommend the 5-minute (story) time investment. :-)

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Posted in Algebra 1 | Tagged , , | 2 Comments