Student Marbleslides 2018-2019

For the past couple years (2016-2017 and 2017-2018) I’ve had students create their own Marbleslides.  Every year it is one of my favorite things I do with my students.  Here’s a few reasons why.

  • I get to see my students explore math.  Whether my students have 2 lines on their slide or 20, they are exploring and learning math!  Sometimes it’s easy for me to get more excited about the crazy graphs, but I try to remind myself that the “simple” graphs can require just as much exploration and thinking.  It’s all awesome!
  • I get to see my students’ creativity!  Every year I’m amazed at how creative my students are as they work on this.  They are creative in where they have the marbles fall from, in the “extra” lines they add to a graph to make it look more visually appealing, and their overall ideas for their Marbleslide challenge.  They amaze me!
  • I get to see my students persevere.  Because the students are the ones to come up with the ideas for their Marbleslides, they are SO persistent and are bound and determined to get it to work out how they want it.  It’s unbelievably fun to watch!
  • I get to see them celebrate over MATH! Because they were so persistent in making their idea come to life, they get SO excited to see “Success!” on their screen!  It’s not uncommon at all to hear screams of excitement or to have multiple students impatiently call me over to see what they just did.  I absolutely love it!

Here is a link to their creations this year!

Note that my students made these on Chromebook, so sometimes some won’t “work” on different size screens.  All of the slides are copied and pasted from my students’ work, titles and all.  I love how you can see students exploring non-linear equations (y=xx).  They hadn’t learned those yet.  We had covered linear equations and that was all.  Any domain and range restrictions were learned from doing other Desmos Marbleslides activities.  In some cases I made notes of where the marbles are dropping from so that you know it might take a while for it to work because you know if middle schoolers are able to have marbles fall from crazy coordinates like (1,1000) they will! 🙂

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Desmos Fellows Weekend

This past weekend I flew out to San Fransisco to the Desmos headquarters for their Desmos Fellowship Cohort 4 weekend.  I had the absolute privilege of learning alongside 40 other Cohort 4 fellows, 10 returning fellows, and several Desmos staff for the weekend.


Imposter Syndrome was definitely a thing for me from the moment I got my acceptance email from Desmos.  I personally know and have met many people who had been accepted in prior cohorts and to now be included in that list with people such as Julie Reulbach, Sara Van Der Werf, Elizabeth Statmore, Jonathan Claydon, Mary Bourassa, and Sam Shah to name a few (and that doesn’t even include those who now work for Desmos) only adds to my Imposter Syndrome feelings.  Not only that, I could name a handful of other amazing educators who have applied and gotten a “not yet” email from Desmos.  Yet, I was selected to be part of this group?  I honestly thought I’d get an email saying, “Sorry, we made a mistake with our previous email.  Please apply again next year.”

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My feelings of Imposter Syndrome increased as we started communicating as a group of  Cohort 4 on Slack before our weekend.  I so appreciated what Stephanie shared with us, “I want to remind everyone. We hand selected each and every one of you. You are enough right where you are today.”  I did my best to go into the weekend with those words in mind.


With that, here’s a recap of the weekend.

I got in early Friday morning and had some time to sightsee before things started at Desmos.  Ashley, Melissa, Chris, and I headed out in the streets of San Fransisco.  We ended up missing a few turns as we spent more time talking and getting to know each other than focusing on the map, but we eventually found our way to the cable cars and rode to Fisherman’s Warf.



After that, we headed back to Desmos HQ for the “official” start of the Fellows weekend.


We started the weekend in our Home Groups -each returning fellow had a group of about 4 current fellows.  The returning fellow touched base with each of us prior to the weekend, and we met in this group for a short period of time each day.  My home group was led by Kathy and included Jamie, Louisa, Vickie, and me.

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Friday night the schedule was really focused on creating a comfortable space for the rest of the weekend.  Shelley talked about the norms for the weekend.

  • Stay strengths-based
  • Stay engaged
  • Embrace our growing edge
  • Attend to self-care throughout

We did introductions (which was somewhat intimidating with such a large group of amazing educators), Mary shared responses from a 20 questions Desmos activity we had completed.  I loved the activity itself and the way she complied the information as another way to get to know our group at the start of the weekend  (much of our group was introverted, reminding us all that calculus is something several of us hadn’t done much with in a while, as well as having us talk to someone next to us and discuss how we answered some questions).  We then had time to talk with different groups of people as we were able to select from a few different options they had set up for the night.  Going into the weekend, I had met a few of the other Cohort 4 fellows, returning fellows, and Desmos staff from TMC or other conferences.  I really tried to be intentional about meeting people I hadn’t met in real life already, but also giving myself time to have conversations and get to know people better that I had already met.

Takeaway:  Here’s what stood out to me Friday night.  Shelley let us know prior to starting that we didn’t need to bring our laptops.  We were at Desmos (an ed tech company), yet the first time we met as a whole group, technology wasn’t needed.

Our hotel was about a mile away from Desmos HQ, and I loved the opportunity to talk with other Fellows as we walked as well as the time to get some exercise and decompress after a day of learning.



Saturday started with Faith and Lisa sharing some of the principles Desmos uses when creating activities.  Lisa led us through Point Collector.  Nico and I worked through this activity together, and I enjoyed starting by using math that my 8th graders would know and then as we progressed we expanded by using other things that we ourselves hadn’t used in a while such as circles.

Takeaway:  I really enjoyed how Lisa made it clear to us while we were working on the activity that we didn’t HAVE to get to all the challenges.  We may try all of them, but maybe we just focused on one and that was ok.

So often in my own classroom I want students to complete everything. Lisa paced the activity in such a way that it wasn’t expected that everybody did everything.  They could have, but it wasn’t expected.  As Lisa used the Snapshot feature to share examples of our work, she focused on the creativity and not the ones that earned the most points.  I also liked how seeing others’ work encouraged me to think of ways that I could apply their strategy to another challenge.

Breakout Session 1 (Lauren and Christelle)

I went to Lauren and Christelle‘s session titled Turning the Diamond on Desmos.  If I’m being honest, I don’t know that I feel “qualified” to write about what I learned and what was discussed at this session as I’m still processing everything.  Please, give me grace here.  We started by talking about why we love Desmos (the tool -rather than Desmos the company) and how those reasons address Access, Achievement, Identity, and Power in our classrooms.  Lauren and Christelle challenged us how to think about how to be more intentional about addressing identity and power in our classrooms.

One of the quotes/questions they shared that stood out to me is, “Do I get to be a better me, or do I have to become you?” in regards to students in our classrooms.

“Do no harm.” is one of Desmos’s principles, and they brought up something I’ve been thinking about following their presentation, “Do anti-harm.”

Takeaway:  Lauren talked about how this work isn’t only for teachers who teach in racially diverse classrooms, but it’s also important for teachers who teach students of the dominant culture as they work to educate those students on these things.

Desmos Design Process (Jenny and Zack)

Jenny and Zack talked about and walked us through part of the process (Crazy 8’s and Storyboarding) Desmos goes through when creating activities.

Takeaway:  I would like to try using both Crazy 8’s and Storyboarding when creating an activity this year.

Keynote (Eli)

Eli talked to us during lunch, and it’s always fun to hear from him, the founder of Desmos.

Takeaway:  I appreciate how Eli is upfront about the fact that he dislikes technology and dislikes ed tech even more.


Then we were given work time to collaborate with others on a project or idea.  I worked with Nicole, Vickie, and Ranesha on a distributive property activity using algebra tiles.



We ended the day with Desmos trivia and then walked to the food trucks for supper.  I’ll admit, I wasn’t really looking forward to trivia, but it was SO fun.  It was also fun to have a few other former Fellows join us as well as other MTBoS friends (Elizabeth and Howie).



Graphing Calculator (Christopher and Michael)

Christopher and Michael did a session on the graphing calculator where Michael led us through his activity Charge!, and Christopher had us think and talk about that activity as a learner, teacher, and leader.

Takeaway:  There is an activity builder for this activity, yet Michael chose not to use it.  How often do I try to make an “activity” out of something where the Desmos calculator might be a better option and lead to more creativity for students?

Breakout Session 2 (Martin)

I went to Martin‘s session titled CPA CL Skills (Copy, Paste, Adjust Computation Layer Skills).  It had been a while since I’d worked with CL, and it was a good refresher.  I would really like to continue working with and learning how to use CL better.


We had time to continue working on the project we started the day before and then shared what we all had started working on.

The Imposter Syndrome started to creep back in as I saw (and continue to see in Slack and on Twitter) all of the amazing things others created.


We had one last opportunity to connect with others as we talked about our takeaways and goals after our weekend together.

In some ways the weekend was everything I expected and more, and in other ways it was so different than what I anticipated.  Other than simply giving a recap of what happened, it’s hard to put into words the entire experience.  It was truly amazing.

I related to so much of what Brett wrote in his reflection in this post, “I’m amazed at how little time I spent in the Desmos environment.  When I applied, I expected to learn all kinds of new things about Desmos, spend time coding in CL, building and critiquing activities builders, but my experience was far more transformative than that.”

I didn’t use my computer charger once all weekend.  Going into the weekend, I anticipated that much of the weekend would be spend being explicitly taught how to do certain things in the Desmos calculator, in CL, or in activity builder.  None of that happened.  Instead, learning in Desmos was organic -when we were working in Point Collector and needed/wanted to do something or when we overheard another group try something new.  Read Jennifer‘s post for more of these.

A huge focus of the weekend was spending time building relationships and connecting with the people there -relationships that will continue online long after our time in San Fransisco.  If this experience parallels other experiences I’ve had with MTBoS (Math Twitter Blog-o-Sphere) friends, I believe that our online communication will be stronger now and more online learning will take place because of the relationships that were strengthened during our time in San Fransisco.

And I am so excited to see that learning that take place!


the whole group


Some of the Desmos staff (top left – Michael Fenton,  top right – Shelley Carranza, bottom left – Eli Luberoff, bottom right – Dan Meyer


Old Friends (clockwise starting in the top left – Lisa Bejarano, Sean Sweeney, Jay Chow, Jennifer Williams and Jennifer White, Mary Bourassa, Joel Bezaire)


New Friends (Clockwise starting in the top left – Mark Kreie, Nicole Madrigal, Larissa Peru and Stephanie Blair, Joce Dagenais)


More New Friends (top – Shira Helft and Ashley Goetz; bottom from left – Lauren Baucom, Melissa Paletta, Kathy Henderson)



Activities for Before Christmas Break

The week before Christmas break is always crazy, and I tend to have plans A, B, and C ready to go because I never know what to expect.  For the most part, I try to keep things as normal as possible for as long as possible, while at the same time knowing things may not pan out as I hope.  I usually leave the last day before break somewhat open so I have some wiggle room if something else comes up and I would need to push a test to that day or if a student was gone and needs to take a test, etc.

Even on that last day, I usually have several different options ready to go that I could use in case something else would fall through.

Here are a couple of my favorite things to do with students the last day before Christmas break.

1. Sara Van Der Werf’s 5×5 Activity.

I have used this activity for the past 3 years, and it is an absolute favorite.  Read all about it here on Sara’s blog.  It’s not super mathy, but there’s addition involved.  In short, as I call out numbers, students place them in a 5×5 grid with the goal of earning the most points.  You earn points by having the same number in adjacent boxes.  Read all the details in Sara’s post.  I am always amazed at how quiet and into the game students get.  I will intentionally pause extra long sometimes before calling out the next number just to see if students will stay quiet -they do.  🙂


2.  Flextangles

I stumbled on this last year, and it is a keeper.  I honestly had no idea how this would go over with my 7th grade boys, but they really seemed to enjoy it.  I had students asking if they could work on this in their free time long after the day we did it in class.

I had some extra time with some of my students in a class this week, and on a whim, I decided to try Function Carnival.  I had never used it with students before, but I thought this would be a good group of students to test it out on.  They loved it!

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It was the perfect activity to use a couple days before break because it was fun and engaging for students, and there was still a ton of great math conversations happening amongst my students.

I’ve already used these Desmos activities in a few of my classes, but may pull them out this week again if needed.  (That’s the one downside to teaching students multiple times -I can’t use all my activities the first time I have them, because I will have them again within the next two years and need to save some of my favorites.)

  • Trees and Tents (one and two)
  • Wolves and Sheep
  • Jay Chow creates awesome Desmos Breakout activities.  This is above where my students are at, but if i taught high school, I would definitely consider using this.

I may also pull out several of the different things I’ve put out on my Play Table, or some of the board games I have in my room (Rush Hour and Blokus are some of my students’ favorites).

I also just found out you can play Otrio online!  I have the game, but I honestly hadn’t had a chance to play it until now.

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Game about Squares is another great one!

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I would love to hear your favorite activities to do with middle schoolers in the day or days leading up to Christmas break!

Marbleslides 2017-2018

Last year (well 2 school years ago now) I shared a Marbleslides project I had my students do.  I realized I never got around to sharing some of the things this past group of students  created.  Again, I was blown away by what they did.  This became one of the tasks students could work on if they had extra time.

For whatever reason, I almost didn’t do this activity with students.  I’m SO glad I changed my mind.  Students got into playing around with the view window to see how long it would take the marbles to show up on the screen or how slowly they could get them to roll.  Some students also got into naming their creations.

It’s so fun for me to see what students figure out just by playing around in Desmos.  They figured out how to restrict the domain and range, make parabolas, circles, and many other things we had not talked about.  I love hearing students ask other students how they did something and seeing them teach each other.

Here is the link to their creations.


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8th Grade Unit 6: Exponents (Part 2 Scientific Notation)

I shared part 1 of our unit on exponents here.

I got most of my notes from Sarah’s blog.  She also has a ton of activities on her blog here.

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As I was writing this, I remembered this image that Heather shared from one of Sara’s presentations.  I think this would be a GREAT way to introduce scientific notation next year.  I’ve got to remember to do that!

The last couple years, I’ve used tables similar to those below to help students notice patterns.

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After we talk about converting between standard form and scientific notation, I’ve used this Desmos activity.  I also like this Desmos activity.

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Then we get into multiplying and dividing numbers in scientific notation.

I made this Desmos activity for practice.

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The biggest thing my students struggle with at this point in the unit is when they multiply or divide and get a number that isn’t in scientific notation.  Something like 64 x 10^6.  They know the exponent will change by one, but many students get mixed up on whether it gets bigger or smaller.  I always, “Don’t try to memorize a “shortcut”.  Think about what 64 x 10^6 is.  Write it out in standard form, and then convert it to scientific notation.  Then you don’t have to try to memorize anything.”  The students that listen and follow my advice, usually have no issues with this, but it’s the students who want to take a “shortcut” that end up not getting these problems correct.  Please tell me I’m not the only one who has this issue!

I’ve got a couple Which One Doesn’t Belong? warm-ups for scientific notation.  I know I pulled the second one from Twitter.  I can’t remember who shared it.  If it’s yours, please let me know so I can give you credit for it.

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I’ve used this scavenger hunt as well.  I like that it gets students up and moving around.

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I created this worksheet for students to practice.  (I think I created it.  I may have modified it from somewhere.  Again, if you recognize it, please let me know so I can give credit to who originally created it.) . You can download it here.  I’ve created a few other worksheets of this format and like that it’s self checking for students.

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I was able to squeeze a few days of transformations in with one of my 6th grade classes.  These are 7th grade standards in my state, but this is the group of students I will have again next year as 7th graders with the end goal of getting to all the 8th grade standards.

I started with this Which One Doesn’t Belong?

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And followed up with this Desmos Polygraph.

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I was able to borrow notes from a colleague for this unit.  Teaching in a small district this doesn’t happen often as none of us teach the same course as anyone else.  For each different type of transformation, I started with a Desmos activity.


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Rotations:  Students made a table of values of the pre-image and new image.  They created different images and looked for patterns to predict how to rotate an image 90 degrees clockwise, 180 degrees, and 90 degrees counterclockwise.

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And we ended with Transformation Golf.  I had so hoped to get to Robert Kaplinsky’s Skytypers or Pac-Man, but there just wasn’t enough time.  There’s always next year.

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I was amazed at how engaged students were with the Transformation Golf.  It was the second to last day of school, and we were doing locker clean outs.  I asked students to sit at the tables in the commons and work on this when they were done cleaning out their lockers, and they did!  They were having so much fun with it, it was great!  Desmos saves the day and prevents chaos at the end of the year!  I shouldn’t be surprised by that at all.


I have a third of my 6th graders again next year as 7th graders.  In those two years, my goal is to teach them the 6th, 7th, and 8th grade standards.  It’s been somewhat of a slow process, but I’m making progress.

This year I was able to get a unit in on similarity at the end of the year with my 6th graders.  I definitely pushed them and challenged them in this unit, and my students rose to the challenge.  I was so proud of them for the challenging proportions they were solving.  Some of my students definitely noticed that I was pushing them a bit more and became frustrated that it wasn’t coming as easy to them, which wasn’t a bad thing.  We worked through that.

It had been a while since we had solved proportions, so I started the first day of our unit with a few review problems.  I knew I wanted to use Marcellus the Giant from Desmos at some point in the unit.  As I was planning, I wasn’t quite sure when I wanted to fit this in.  Should I intro with this and have them try it without telling them anything about similarity or scale?  Do I use it after we have talked a bit about both of these?  I ended up deciding to use it right away at the beginning and was glad I did.  Students may have been confused at some points throughout the activity, but by the end they were able to explain what it meant for a giant to be scale or not scale.

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After a couple days of notes on similar polygons and scale, we did this activity around the room.  I had done another Math Lib activity earlier in the year, and my students love it.  I fully admit that I could have created something, but I was end-of-the-year teacher tired and decided it was worth it to get the activity linked above.

The weather in Minnesota was FINALLY nice, so I decided to do this activity outside with students.


Then I saw this and knew I had to make this happen in my classroom.

Lisa used the game Clue and incorporated scale factors into the activity for students to figure out who was intentionally making math mistakes.  😉  Read Lisa’s post on how she set up the activity with her students.


I ended up doing it slightly different than how Lisa described in her post.  I printed out Clue boards that Lisa shared and the Clue cards.  I wrote different numbers on all of the cards.

Students started by finding the area of each of the rooms on the clue board.  Once they had done that I gave them one Clue card with a scale factor on it and had them pick which room to use that scale factor for.  After they found the new area, I checked their work.

Nearly every group did what I expected them to do.  They took the area and multiplied it by the scale factor, rather than multiplying by the scale factor squared.  That was one of my main reasons for doing this activity -I wanted students to see how scale affected area since prior to this we had just talked about how scale affected length.IMG_7592

I let students struggle with that for a little bit before giving them a hint to help them out.  I put a grid up on the board and we looked at a 1×1 square.  Then I picked an easy scale factor, I think it was 2, and we talked about what the new dimensions of the square would be.  Then I asked students what the new area of the square would be?  I saw the lightbulbs go off for some students, and then I asked how that would apply to the problem they were working on.  It was enough for all groups to eventually figure out what to do in the Clue activity.

In the future when I do this, I would be more intentional about the numbers that I picked for the scale.  I used some pretty small numbers for some of the cards so after applying the scale factor the areas of the rooms were pretty unrealistic.  Overall though, it was a great activity and I am looking forward to using it again next year.

8th Grade Unit 5: Systems of Equations (Part 2 – Elimination & Choosing Method)

I shared here part 1 of our unit on systems of equations -solving by graphing and by substitution.


I started this unit with the following warm-up.

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Then I followed it up with this notice/wonder.

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One of my students this past year noticed that, “These are like the problems we did for warm-up.”  I love when my students notice connections between the warm-up and the lesson for the day and that I’m not just having them do random stuff.

I was really pleased with how this led nicely into the lesson for the day.  Students noticed that in each problem there was a zero.  They were able to tell me why that happened.  When I told them that this is another method for solving systems of equations called elimination, at least someone in each class was able to explain why they thought that elimination was a good name for this method.

It had been a while since we had done Vertical Non-Permanent Surfaces, and these problems work great for that.


Choosing Method

The last part of this unit was having students choose the best/most efficient method for solving a system of equations.

I started with this Desmos Activity.  I didn’t have students solve the systems the first day.  I wanted them to just think through what method they would want to use to solve each.  The next day they actually solved some of the systems.

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I love this Desmos Activity from Paul Jorgens.

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I’ve uploaded some of the worksheets and notes I used from this unit here.

8th Grade Unit 5: Systems of Equations (Part 1 – Graphing & Substitution)


Even though this is Unit 5 in 8th grade, this is the unit I’ve done last the past couple years I’ve taught it.  It just worked out that way my first year teaching 8th grade, and I liked it that way so I did it again this past year.  I like having it at the end of the year because it’s a good way to review graphing lines.

I start the unit by spending a half day or so on just a review of graphing lines.  I almost didn’t do that this year, but was SO glad that I did.

Then we do Desmos Polygraph and this Desmos activity to intro systems of equations.

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Then we spend some more time practicing.  I’ve used this Desmos activity in the past.

After that we get into systems of equations that have no solution or infinite solutions.  I usually start by putting up one of those types of problems without giving students any explanation.

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Students have had a lot of experience solving problems with no solution or infinite solutions by this point in the year, so I usually have some students who come up with the fact that because both equations are the same line, there are infinite solutions.


I blogged here about how I introduce substitution to students.  I’ve used this method 3 years in a row and am still amazed every. time. how smoothly it goes.

Here is the link to download some of the worksheets I use for this portion of our unit.

8th Grade Unit 4: Applications of Lines

We start our unit on applications of lines by discussing independent and dependent variables.  I have a note to myself to remember to use the following language next year because it worked well this year.  Nothing earth shattering, I know.

  • “(independent variable) causes change to (dependent variable)”
  • “(dependent variable) depends on (independent variable)”

I use a lot of Sarah’s resources found here for my notes, and I’m pretty sure that’s where I got the problems for this Desmos activity.

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The next day we do Sarah’s Ghosts in the Graveyard activity with independent and dependent variables.  Every time I use that activity I think to myself, “Why don’t I do this more often?  It’s great!”

After students have a pretty solid understanding of defining the dependent and independent variable, writing linear equations from word problems goes a lot better.

Then we get into parallel and perpendicular lines.  I blogged briefly about what I did last year here.

I start with parallel lines and use this Desmos activity.  One of the downfalls of starting with that activity is that when students are asked to solve problems where they need to write the equation of a line parallel to a given line through a specific point, they want to use Desmos to guess and check.  This is a good strategy, but I also want them to know another method.  I start the next day with a couple problems like these.

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After spending another day or so on parallel lines, we finally get into perpendicular lines.  I start with this Desmos activity.

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We spend another day or so practicing with perpendicular lines.  I’ve used this activity before and like how it brings back different forms of lines.

We also talk a little bit about parallel and perpendicular lines and quadrilaterals using this Desmos activity.

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Then we get into scatter plots.  I start with this Notice/Wonder

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We do Desmos Polygraph next.  Last year I had a student ask if there were two “loners”, and I will forever think of outliers as loners.

After students do that activity, I put the graphs up on the board and ask students to put them in groups.  They end up describing the different correlations to me.

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This Which One Doesn’t Belong? is great around this time in the unit.

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I took a couple tasks from this page and turned them into Desmos activities.  (I know she tweeted out links to the activities at one point, but I couldn’t find them.

Here’s one on correlation.

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And another on lines of best fit.

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Here is the link to download some of the worksheets I use in this unit.