Movement: Incorporating Math Concepts into Movement Activities

(I’ve written several other posts on movement:  Post 1 • Post 2 • Post 3)

Movement has been a huge part of my classroom since attending Sara Van Der Werf’s session at a conference my first year teaching.  When I first started being more intentional about incorporating movement into my classroom, I would often have students do 10 jumping jacks, 5 push ups, or skip around the room, etc.  Every once in a while I have an epiphany about a way to incorporate the concepts I’m teaching students into these movement activities and think to myself, “Why did it take me so long to come up with this?!”

Here’s the list of what I’ve found to work best so far, more for my future reference than anything.

  • Perimeter/Area – I have students skip around the perimeter of the room or hop through the area of the room.  (I will also often add clockwise or counterclockwise to the directions.  I’m always shocked at the number of students who don’t know these words!)
  • Exponents – When doing something like jumping jacks, I started giving students an exponent to evaluate, rather than just a number.  This way I can sneak in exponents all year long.  “Do 3 to the second power jumping jacks.”
  • Prime/Composite – I’m all about finding ways to expose students to vocab words all year long.  I sneak these vocab words in by having students “Do a prime number of push-ups.” or “a composite number of sit-ups.”
  • To get back to their desks when we’re doing with a movement activity, I will sometimes have students count the number of “hops” to get to their desk and then do something with that number such as find the prime factorization of the number or we’ll talk about who hopped a prime number of times or whose number is divisible by 3, etc.
  • Ratios – I pick 2 activities and have students do them at a specific ratio.  For example, “Do jumping Jacks and sit-ups at a ratio of 3:2.”  (This was my “Why haven’t you thought of this before now?” moment of this year.  6th grade is ALL about ratios.  Seriously, why did this one take me so long to do?!)

I would love to hear how you incorporate the skills you’re teaching into movement activities in your classroom!

One Problem Lesson Plans

I’ve heard of people who spend an entire class period on one problem.  One problem!  With middle schoolers!  Most days, getting middle schoolers to focus on anything for 40 minutes, let alone a math problem, is an insurmountable task.  (Side note:  I’ve been working on a grad paper recently aka trying to make myself sound formal by using big words like insurmountable that you would likely never hear come out of my mouth if I were to ever have a conversation with you in person.)

I couldn’t wrap my head around finding a problem that would engage middle schoolers for 40+ minutes.   I didn’t have a clue what that type of problem would look like.  I didn’t know where to begin with a lesson like that.

I worried that my students wouldn’t “learn” as much by spending so much time on one problem compared to multiple problems on a worksheet or some other form of practice.

Enter this problem:

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I learned I was wrong.  So very wrong.

Several weeks ago, I gave my students the Open Middle problem above.

Oh. my. goodness.

I was not prepared for the awesomeness that took place that day.  I still smile thinking about it.  I anticipated the problem taking 5-10 minutes, maybe.  Some students worked on it for the entire 40 minutes!

The concept of the problem was simple.  Students knew how to write equivalent ratios.  They understood they needed the digits 1-9 and knew they could only use each digit once.  But the answer?  That wasn’t quite as easy to find.  They were hooked.

And so was I.  I wanted to find other problems to re-create that atmosphere in my classroom.  I completely underestimated the rich conversation that could take place from what I considered a simple task.

By the end of that class period, I knew I needed to do more of this in my class, but what sealed the deal for me was listening as students tried to figure out how to continue working together on the task as a group after class.  They asked me if they could do a group chat with each other that night so they could keep working on it.  Then I overheard, “If I figured it out, I’ll email you! And if you figure it out, email me!”

They were excited over solving a problem in a way that I hadn’t seen from them before.

This week I used the problem below in the same class.

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From Chris Smith‘s newsletter via Jo Morgan’s blog.

I was actually nervous for this lesson after how well the lesson with the Open Middle problem went.  I tried not to hope for the same results I got the first time but was worried it would flop.  It didn’t, and again, I was amazed at the conversation that resulted from this one task.

This week I used the problem below from 1to9 Puzzle with my other two sections of 6th graders.  I thought it would take about 5 minutes.


I quickly realized it would likely take longer than I anticipated and saw the opportunity for those students to experience what my other class had.  While it didn’t relate to the content we were covering like the other two problems, I decided to deviate from the lesson plan and give students more time on this.  It was well worth it.

In the few times I’ve done problems like this, a couple things stand out to me.

  1. I am amazed at how many students don’t know how to guess, check, and adjust their answers on problems like these.   Some students could not wrap their head around the idea of just picking numbers as a starting point and going from there.  It was an eye opener for me, and I realized I need to continue to incorporate more situations where students need to do this.
  2. My doubts about whether students would “learn” as much from doing one problem like this rather than another practice activity were erased.  The conversations amongst students while doing problems of this nature still amaze me.
  3. One of my absolute favorite parts of doing these are watching students’ reactions when they finally find a solution.  They are SO proud of themselves.  This past summer I had the privilege of spending a lot of time learning from Sara Van Der Werf.  One of the things I heard from her over and over again was how one of her goals in her classroom is to get kids addicted to the cycle of being puzzled and becoming unpuzzled.  I was able to physically see this in my students more while doing these types of problems than possibly anything else I’ve done so far this year.

Do I have the “one problem lesson plan” down pat?  Absolutely not.  Is it even close to great?  No.  So far it’s really been pretty unintentional.  I’ve pretty much just been lucky and stumbled upon problems that have turned into great lessons.  I need to get better at bringing everyone back together to close the lesson after doing a task like this.  I’ve added finding more tasks like these to my summer to-do list.

UPDATES:  I’ll add more of “one problem lesson plans” below as I try them in my classroom.

This problem found here was another winner with students.  After students found a solution, they continued to work to find other solutions with me telling them to.  Sigh.  I needed that little reminder that week that we were in fact making progress.


Parallel and Perpendicular Lines

One of the main focuses during my first year of grad school was the idea of constructivist teaching.   If you’re unfamiliar with the idea of constructivism, in short, it’s teaching in a way that gets the students to discover (construct) on their own what you want them to learn.  At first, I really struggled to wrap my head around how that would work in a math class.  My goal my first couple years teaching was to explain the math so well that students  didn’t have any questions.  My goals are now very different than those first few years! The more I started using constructivist activities in my teaching, the easier I found it was to implement more of those types of activities into my classroom.

When I started implementing more activities that led students to discover the math last year, I was not very familiar with Desmos activity builder.  I’m slowly becoming more familiar with how to use it and am loving how it makes these discovery-type activities run much smoother for both me and my students.  There was little to no direct instruction when my 8th graders were learning about parallel and perpendicular lines.  For the most part, students discovered it all through a few Desmos activities I created (with the help of some Twitter friends).  🙂


Here are the links to the Desmos activities.

Parallel Lines

Perpendicular Lines (Thanks to Ilona for the help with this one!)

Equations of Polygon Sides (Thanks to @GrainBrowth for the help with this one!)


As I think back on how the lessons went, a few things stand out to me.

1.  I probably shouldn’t have been, but I was surprised that nearly every student used “guess and check” to find the answer to the question below.  That meant that we had to spend some time talking about ways that students could come up with a solution without using Desmos since I have yet to have students use Desmos for tests.  However, I think because of this I had far fewer students write “y = 4x + 10) for their answer because they saw what happened in Desmos when they tried that.

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2.  When I give an exit ticket at the end of class after doing one of these activities, I’m still somewhat amazed at how well students do.  It’s encouraging to see that this type of instruction works.

3.  In the past when I’ve taught this concept, my lessons looked something like this:

  • Get students to understand parallel lines have the same slope
  • Get students to understand perpendicular lines have opposite reciprocal slopes
  • Spend time using those ideas to solve problems

This year I decided to spend about 2 days on just parallel lines and solving problems with parallel lines.  Then about 2 days just on perpendicular lines and solving problems with that.  Then, I combined the two before having students look into the equations of polygon sides.  This seemed to go better for students.  The biggest mistake I saw students make was when they were asked to write a line perpendicular to another line through a specific point.  Many students who made a mistake on this type of problem, knew to change the slope because the lines are perpendicular.  However, when they would find the y-intercept, they would leave the slope the same, and then at the end when they wrote their final equation, they changed the slope.  However, in the past when I’ve taught this, students have made the same mistake.  I don’t have the data to back this up, but it seemed that fewer students made this mistake this year, and I taught this concept to more students this year than in the past.

4.  As students were working through the activities, I wish I had a better way to quickly check which students were on the right track.  The Desmos teacher dashboard is awesome, I’m just not that great at using it efficiently yet.  I mentioned to my co-teacher that I wish I had a better way to know if students were on track or not, but that I also had the same problem when students were doing this types of activities without Desmos activity builder -it’s actually worse without it.


Student Marbleslides

Last summer at Twitter Math Camp, someone mentioned that they have their students to to to create activities.  Genius.  Pure genius I tell you.

This is what my students came up with.

Next year, I hope to be more intentional about how I use this with students because this year it just sort of happened without any sort of plan whatsoever.  What happened was awesome.  With a little more planning, maybe it could have been even better.  (Those were my thoughts when I started this post.  As I wrote it, I wondered if this ended up being so awesome because students didn’t feel restricted by the guidelines I gave them.  There were no rules.  They could do whatever they wanted.  If I had planned, would my planning have narrowed students’ thinking too much, stopping their creativity?)

The idea came out of desperation more than anything.  I had two 7th graders finish all their assignments super early.  My thoughts were something along the lines of, “What?!  You’re finished?  Already?  With how much time left of class?!?  And you finished the Marbleslides activity from yesterday?  Umm…I guess go to  Yeah.  Good idea.  Do that!”

I was amazed by what they came up with.  The first couple were basic -what I expected to see.  Then I overheard one ask the other, “How do you make the line stop like they did in the other one?”  The other girl responded, “Oh, I think they used those curly bracket things…” and in a couple of seconds they figured out how to restrict the domain -they didn’t know it was called that though as we had never talked about it.

In what seemed like no time at all, they came up with something like this.


After the test that week, they asked if they could work on it more.  Their excitement over it got me thinking, “What if I had the entire class do this?”  “What if I gave those girls more time to work on this?  What would they come up with?”

I had to find out.  We ended up spending 2 days where most all of my students worked on creating Marbleslides.  Part of me felt guilty for “wasting” 2 days on this, but as I walked around, I was in awe of the conversations students were having and the questions they were asking each other.  I didn’t feel that this was really “wasting” 2 days and wished I had done this before the test instead of after.

The first day, I let students go with minimal direction other than to create their own Marbleslides.  If a student raised their hand, my response was typically, “I’ll listen to your question, but I can’t promise I’ll answer it yet.  I want you to work to figure it out.”  When students asked how to “cut off the lines”.  I directed them back to the Marbleslide activity they had done a few days prior to look at those graphs to try to figure it out, and they did.

When I wanted to push students’ creativity a bit, I pulled up an example from one of the girls who had been working on it for a few days.  They had figured out how to restrict the domain, so naturally all students wanted to know how to do that.  Students really took off after that!

The two girls who were the first to start, ended the day figuring out how to make the marbles go in two different directions!  I don’t know that I ever would have come up with that on my own.  I told them their homework assignment was to figure out how to make the marbles shoot back up.*

I was pretty much giddy going through what students had made after the first day, and it only got better after that!  I can’t count the number of times I’ve clicked “launch” on students’ work.

Some students created Marbleslides like they had done in the Desmos activity, where the person playing would need to change the graph to be successful.  However, as students’ graphs became more complex, more students just played around with creating the graphs and leaving them so they would see “Success!” when they clicked launch.  I loved seeing students come up with an idea and figure out how to make it happen.

I also love what Sean does here.  What are other ways you use Marbleslides with students?

Here is the link again to their creations.  I’m just so darn proud of them!

Below I’ve commented on a few of the Marbleslides my students came up with.

This is one from a student who isn’t always confident in what he is doing.  Partway through the second day he goes, “I’m the master at this!”  He had a star WAY down the line on the bottom right and was timing to see how long it would take to see “Success!”  He gave me thoughts for other ways to use Marbleslides.

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This student also intentionally put a star way off to the right so the marbles barely make it.  Again, she’s not always the most confident.  It was fun watching her teach other students how to do things.

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This student had fun getting the orange line just right so the marbles would bounce off the end.


*Those two girls did their homework.

One of the other math teachers I teach with is the dad of one of the girls.  He showed her how to make a parabola, and the things she came up with after that still amaze me.

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Her dad helped with the orange parabola, and she came up with the rest.

The next day she showed the other girl how to make parabolas.  The other girl was working on this one.  You can’t really see the line on the graph, but it’s the 3rd equation.  She figured out that she needed that little line there because without it, the marbles wouldn’t go to the right when they fell through the two parabolas there.

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Differentiated Review Stations

At Twitter Math Camp last summer, I attended Michelle’s morning session on differentiation.  In the session she talked about how the teachers she works with have “slowed down to speed up”.  In a nutshell, leading up to a unit students take a pre-assessment on skills they should already know that are necessary to know for the new content they will be learning.  The students then work through various stations on the skills they showed they have not yet mastered from the pre-assessment.  Michelle talked about how by slowing down and getting students to master those skills necessary for the new content, the teaching of the new material was much better and more efficient.

Up to that point, here’s what pre-assessment looked like in my classroom.

  • Pre-assess at the start of the year everything I will be teaching so that I can give the same test at the end of the year to show growth.
    • This was pure torture for everyone involved.  I was frustrated wasting time with this because I already knew students didn’t know the material.  They hadn’t been taught it yet.  I hated watching students suffer through this test.  There’s nothing like raising anxiety at the start of the year with something like this! Plus, I didn’t want to grade them.
  • Pre-assess the day before I teach something to see where students are at with a concept.
    • Really, what was I thinking with this??  The day before?  How did I think that would give me time to do anything with the data let alone create lessons in response to what I learned from it?

In Michelle’s sessions, she helped me see that while I wasn’t using pre-assessment effectively, many of my thoughts on pre-assessment were on track.  She helped me see how to better use pre-assessment with students.  Here are some of my notes from last summer.

  • Don’t test what you WILL be teaching them.  Test what they SHOULD know from last year.
  • Pre-test far enough in advance so you can do something with the results.
  • One skill per question.  That way you know where their mistakes are.
  • Short:  one page double sided with lots of white space
    • What do they actually NEED to know for the end goal?  What do we need them to know in order to UNDERSTAND the new lesson?
  • As little language as possible:  Is the barrier the language or the math?

This wasn’t the first time I had heard about the idea of stations and students working where they needed to work.  The idea absolutely intrigued me; however, I wasn’t quite sure how I could see it working for me.  I’m pretty type-A and the thought of giving 6th graders that much freedom scared me.  A lot.

BUT fast forward partway through the school year when I start getting into fractions with my 6th graders.  Every year this is a struggle.  They should know so much coming in from 5th grade, but they don’t.  In the past I have spent WAY too much time re-teaching stuff they should already know.

One of my 6th grade classes is ahead of the other two, so I decided to use them as my guinea pigs with something like this.  And it. was. awesome.  I loved it.  They loved it.  It’s been a while since I’ve done something this big in my classroom that I’ve been this excited about.

I was definitely glad I sort of piloted this idea with that one class to start because it helped me work out a few things before doing it with all my classes.  That first hour class recently finished their second round of stations, and my other two classes have just started the second round.  (I loved the first round so much that I created a 2nd set of stations for the new material they were learning.)


Here’s how this process has worked for me so far:


  • When I first created a set of stations, I gave the pre-test well in advance.  That way if there was a certain skill only a couple students missed, I didn’t spend time creating a station for that one, instead I pulled those students aside and worked with them on the skill rather spending a bunch of time creating a station for a couple students.
  • Once I had most of the front end work done of creating the stations, I didn’t give the pre-test as far in advance with my other 2 classes.  I just needed enough time to be able to grade the pre-tests and get the student progress sheets made.
  • From the pre-tests, I made a spreadsheet for each class so I could mark of which skills students have mastered.  Students also receive a half-sheet with the skills.  They get a sticker when they have mastered it.


Stations:  This is by far the most time consuming piece of this entire thing.

  • I grouped the skills from the pre-assessment into stations.  Typically, one skill per station; however, there are a few that I grouped together.  For each skill, I found one or two relatively short videos explaining the concepts.  In the future, I think I would like to create these videos myself, but right now I didn’t have the time to do that on top of everything else.  Then I found a variety of ways students could practice that skill.
  • Michelle uses trifold boards for her stations.  For my first go-round with this, I just had the stuff piled on my shelf and pulled them out every day.  What was I thinking?! I quickly realized I needed another way to organize this.  I decided to use 12×12 storage bins, which have worked well for me.  These are what I’m currently using.  I love that I’m able to put everything for one station (task cards, dice, folders, etc.) in one bin.


  • For the worksheets, I printed off smaller versions and taped them to the front of the folder so that students (and I) know what’s in the folder.
  • Each bin is labeled with a number, and I have numbers hanging on the wall in my room so students know where each station is.  These number also correspond to the numbers on their sticker sheets.
  • I tried to include a variety of ways for students to practice the skills:  games, Desmos activities, Quizlet, QR Cards, tarsia puzzles, IXL, create your own problems, worksheets, etc.   I know everything I’m currently using isn’t awesome, but again, I did the best I could with the time I had without completely killing myself getting this set up.
  • Once students have mastered all the skills, they get to work at the enrichment station.  At this station students can choose to create a stop motion video, work on quarter the cross, open middle problems, and other logic puzzle type activities.  I’m still working in expanding what students can work on at this station.


Implementation:  Once everything is set up, this is the fun part!  The first time I did this I was so nervous about how this would go.  I worried I spent all those hours at school preparing it only to have it completely flop after day one, but it didn’t!


  • Having the numbers on the walls match the numbers on the bins as well as their half sheets really helped with this.  I didn’t do this at first, but it has helped streamline the process.  The stations are in the same place every day, and I don’t have to remember where that is. Students know where each bin goes at the start of class and can set them up themselves.


  • The first day or so I spend time walking around the room answering student questions mostly on how an activity at a station works and monitoring students trying to keep them on task.  After a couple days I started pull a group of students to work with me.  Some days I would choose which students were going to work with me based on their progress or behavior the previous day, and other times I would announce which skill I was going to work on and let students choose whether or not they wanted to work with me.
  • The picture below has saved me so much time through all of this.  The first time, I tried to put whiteboard sleeves at each station, and it was a pain.  Having one central location for whiteboard sleeves, markers, and erasers has worked much better.  Also, the tray on the bottom is where students put folders so that I know I need to make more copies.  It’s great!  Rather than me going through each bin everyday, I can just look there and know what I need to make more copies of.



  • The first time I did this with students I allowed them to take quizzes to test out of skills every day.  Some days I would let them quiz in the middle of class and some days at the end.  It was really just sort of random.  When my other 2 classes started doing stations, I used the last 10 minutes or so of class for this and every student would return to their seats for this.  My first class to try stations told me they wanted more opportunities to take quizzes; however, as I thought about this after doing the first set of stations with my other classes, this seemed to be too often.  The second round, I’m going to try quizzing ever other day to see how that goes.  I’m still working to figure out a good system for having students quiz out of skills.
  • I created several different versions of each quiz, and starting with the second round I also added the corresponding station number to the top of each quiz along with the skill.



This has truly been one of my favorite things I’ve done in my classroom all year.  It’s so awesome to look around my room and see 10+ groups of students working on different things and know that everyone is working on what they need.  It was definitely a stretch for my type-A personality.  My classroom is typically very structured, but I think that’s part of the reason why this worked as well as it did.  By this point of the year, students know my expectations so they were able to handle the freedom that I gave them.

Did all of my students master everything?  No.  But I believe more did than would have had I done this in large group instruction.  Were some of the students who mastered all the skills quickly bored at the enrichment station?  Probably.  But these are the same students who would have been bored sitting in large group instruction.  I had more students engaged during this than ever before.  One of my students who is a challenge to get to participate and engage in anything was engaged every single day during the stations.  Every day!


Movement: Slope Dude

I’ve been in search of a movement activity/game that I thought I could get my 8th graders to buy into.  I’ve written here and here about things I do with 6th graders, but I haven’t been brave enough to try those with my older kids yet.  I use stand and talks frequently, but I was looking for something that was more like a game.

Insert slope dude.

I had first read about Slope Dude on Sarah’s blog a while back.  I loved it, but at the time I wasn’t teaching classes where this was relevant (in hindsight, that probably wouldn’t have mattered, I should have done it anyway).  Now that I’m teaching 8th grade, I was excited to use it in a place the fit into what I was teaching.

The day before I showed students the video, I pumped them up about the video we were going to watch that would change their lives forever and how it was a SUPER high budget video.  😉  I love giving them an excuse to roll their eyes at their crazy math teacher!

In class the next day, we watched the video.  They had a love/hate relationship with the video, and it was fantastic.

I put this slide up on the board completely taken from Sarah and told them to stand up.  They groaned and complained, but not for long!


I played exactly how Sarah did.  We first went through the motions together before playing.  It’s just like Simon Says.   Here’s her post on Slope Dude Says, and you can download her posters here.

These are comments from my students in the past couple weeks:

“We were going to play Slope Dude Says in English, but then the teacher came back.”

“I feel bad for Z.  He’s missing out on slope dude.”

“Can we play again??”

“Are we going to play Slope Dude Says today?”

During work time, I saw numerous students move their arms to help them determine the sign of the slope before finding the actual slope.

“I’m pretty sure L wasn’t here for slope dude at all, can we play it today?”

“Even when we’re done with this stuff, can we still play Slope Dude Says?”


I call that a win.


Relations, Functions, and Function Notation

I’m teaching 8th grade for the first time this year.  I feel like there are so many huge, important things introduced in 8th grade, and I find myself way overanalyzing how to go about presenting the information to students in a way that they will truly understand what’s going on rather than memorize and follow a set of procedures.  I’m also learning how far I can push students to figure things out on their own without leaving them feeling completely lost and frustrated.

Relations and functions was one of those things that I was somewhat dreading having to teach because I wasn’t quite sure how to go about it, but I’m really happy with how much of those lessons have gone.

Day one of the unit started with Which One Doesn’t Belong to get students thinking about graphs on the coordinate plane.


Then students did notice/wonder with the following image.  One student noticed that it looks like it came from a textbook.  Ha!  That may have been the first time all year they had seen anything from a textbook.  Whether it’s a good thing or not, I rarely, if ever, use a textbook with students.  When I use it, it’s for my own reference and isn’t shared with students.


As students noticed other things about the image, they were able to tell me the similarities and differences among the different representations of a relation.  I didn’t have to teach it!  They taught it to each other.

Day two started with the following problem.  Two days in a row with images from the textbook.  That was definitely a first for the year!  I wasn’t anticipating liking how this would go as much as I did, but I loved how some students were stuck at first because the graphs have no numbers and eventually figured it out.


Then I used Sarah Carter’s telephone activity.  I liked how this went, but next year I want to change it up so that students are participating more often.  If I put students in groups of 4, I may give each of them a sheet and have each person start by writing down ordered pairs. Then I would have everyone pass the paper around so that all students have a sheet at all times.  They would also get practice with each of the different ways of representing relations this way.

I also realized that at times I need some work on giving directions…  In my first class I had one student whispering the ordered pairs to their partner rather than using the piece of paper to pass the “message” along!  Oops!


The next thing was magic I tell you.  Magic.  I put the following image up and had students notice/wonder about it.  Things had been going really well up to this point, and I worried adding the next thing would completely throw some students for a loop.


I looked up some students’ actual birthdays through our school’s grade book website.  They were immediately engaged.  Thank you Hannah for this!!

Again, they were the ones to tell me “you can’t have two birthdays”, which lead into a conversation on functions and the similarities and differences between relations and functions where I helped fill in the correct vocab.  I honestly expected this to be a stumbling block for some students, but it really was a non-issue.

This was one of my slides from day three.  Students all had mini-whiteboards with coordinate grids on the back.  I started by picking 3 inputs and outputs and had students plot them on the coordinate plane and decide whether it was a function or not.  Then I had students create their own examples of functions and non-functions and had some write their answers on the SMART Board.


Then I had students do a stand and talk and discuss the two sides of the chart they had just made.  At this point in the lesson, the green vertical lines weren’t up there yet, but in every class while students were working in their groups, I had someone come up to the board and point out the vertical line to their partner!  It was awesome!  Again, the students came up with the vertical line test on their own and taught it to each other.  I didn’t have to!

Day four started with a review of the vertical line test and this Desmos activity from Cathy Yenca.

All of my students have iPads, and when students were working in pairs on this, we had to revisit what it looks like to be working in pairs when both students have devices.  I told them how sometimes they look like toddlers playing.  Some gave me confused looks at first, but I explained how if you ever watch toddlers play together, they don’t actually play together.  They play next to each other and don’t interact.  They laughed, but I told them that’s what they look like sometimes.  They got the point and things improved after that.

I used another Desmos activity on day five from Rockstar MathTeacher followed by the introduction to function notation.

I started by putting a couple problems like y = 3x + 8 up and asked students what y equals when x = 5, etc.  Then I put the picture below on the board and had students try to figure out what the “stuff” on the right meant.  (And yet another image from a textbook!  I’m almost positive this unit more than doubled the textbook pictures students had seen all year in my class.)


Students were frustrated at first.  They thought I was crazy for asking them to do this, but they got it.  You could see the lightbulbs go off and how proud they were of themselves.  During the stand and talk, I again had students coming up to the board to point things out to their partners.  I don’t ever remember that happening before this unit.  It was fun to see.

Then this went up on the board next, and I asked students to figure out the pattern and to use it to complete the bottom two rows.


Once again, students were the ones to figure this out and teach it to each other, and I just helped fill in the vocab words here and there or nudge them to use the correct vocab words.

Day six was a quiz and more practice with function notation.

Day seven started with Set.


My last class was struggling to find the last set.  I asked if they were ready to call it good and move on.  And one students immediately said, “No!  We’re not stuck on the escalator!”   There was no way I was going to let them quit after that.

Then students worked on a Tarsia puzzle.  Most students were familiar with this puzzle from when they had me as sixth graders. The responses I got when I took them out were, “Yes!  I love these things!”  and “Oh yeah, I remember these.  These are fun.”


Honestly, the plan was for students to work on this half the hour and then move on to linear function.   However, I decided to let students continue working for two reasons.  One, they were working!  In my first class, it was a little bit louder than usual, but as I looked around every group was on task talking about math!  In my other class, students were quietly working and focused during last hour of the day on a Friday!

The bigger reason I decided to let students keep working was because when we do activities like this I tend to underestimate how long it will take students to finish and as a result, maybe a couple groups will finish and the rest won’t, never getting that feeling of accomplishment and of having completed the puzzle.  I wanted as many students as possible to end the week feeling that way, and most did.

I wish I could remember where I got the file for that puzzle.  It was likely on Mr. Barton Maths website.  If anyone knows for sure, please let me know.  Here are the files I used.  Note:  the card that has a 12 on it has a typo.  The function is missing the equal sign.  It should read f(x) = -5x² – 3x + 14; f(-3)

It was a good week and a half or so!  I also had graphing stories ready to go when I had a few extra minutes in a class.