Desmos Multiplying Integers Investigation

While looking for a way to introduce multiplying and dividing integers to my students, I found this Desmos activity.  I really liked the progression of the activity.  I liked how the activity asks students to notice things, emphasizes patterns, and has students work to figure out these patterns and rules on their own, rather than telling them these things.  These are all things I am trying to do more of this year.  However, I wanted something for multiplication rather than addition and subtraction.

I created this activity by modifying the above activity.  Overall I was happy with how things went.  I would love to hear any feedback on how to improve it or advice/tips on how facilitate these types of activities.  This was one of the first times I’ve used the Activity Builder in Desmos, and I found that I’ve got some learning to do on how to best implement things like this in my classroom.  How often do you pause and have large group discussions?  I like that students can work at their own pace and struggle to know if/when to stop for discussion as students are at different places within the activity.


(Note that I’ve since changed the numbers in the above slide to be consistent with the numbers in later screens to try to emphasize the pattern better.)

I was happy to see many groups of students applying the patterns they were noticing throughout the activity and to see them figure out the “rules” on their own.


Not all groups had answers like these.  There were some groups that missed the mark on parts of the activity.   I think if I had been better at setting things up for students and reminding them of certain things along the way, those groups would have done better.  However, I also wanted to see what these students would do on their own with this. This group of students looks to me for answers quite often, and they start to get uncomfortable when I don’t rescue the class by answering my own questions.


Mathematics is the study of patterns.

This summer I was crazy fortunate to spend several days learning from Sara Van Der Werf. If you’ve ever heard her speak or even been around her for more than 30 seconds, you know what a huge blessing that was!  SO much of what I’ve done these first few days and things in my classroom are either from her or a result of something I’ve learned from her this summer or her blog.

One of the things that Sara continued to bring up in her sessions was that math is the study of patterns, and that mathematicians notice patterns, describe patterns, and generalize patterns.  In my notes from one of her sessions I have written down that one of the things she tells her students related to this is that powerful people notice patterns, describe them, and generalize them.


This idea kept coming up over the summer, and I knew I wanted to make a poster for my classroom with that on it to remind myself of this so that I can stress this idea to students.

Sara said she’s got a blog post on this topic, so let’s hold her to it and make sure she blogs about it soon!

Update 7/21/17 –  Read Sara’s post on this here.  She’s got some ideas I will DEFINITELY be using the first week of school this year!

The files for the poster are here.  The poster is 24″ x 18″.  I printed it from Vistaprint.  If you use the Publisher file, you will need the fonts KG Life is Messy, KG Dancing on the Rooftop, and KG When Oceans Rise.


A Teacher’s Noticings and Wonderings from Day 1

These past few days have been somewhat of a blur with changing to a 7 period day, teaching all middle school for the first time ever, and even teaching in a new classroom where I’m not used to the set up yet.  I’d forgotten how exhausting teaching is with all of the decisions we make in a day!

But I am LOVING the changes!  I don’t know if it’s the fact that I’m teaching all middle schoolers now, that half of my classes are students I’ve taught before, or that I’ve been trying quite a few new things in my classroom, but it’s been a great start to the year!

I know I’m probably super late on Annie Fetter’s Notice/Wonder video, but it was new to me over the summer.  I’ve been asking students to notice and wonder quite a bit already this year and also ask students “What else? What else? What else?” thanks to Sara Van Der Werf.

During the first day of “Notice/Wonder” and “What else?”, I noticed and wondered things as the teacher.

The first happened when students were noticing and wondering things about Fawn Nguyen’s Noah’s Ark problem.


At one point, I was sort of hiding out in the back of the room so students could focus on the picture on the board.  It didn’t take long for me to notice that a few students had turned around and looked to me.  I exclaimed, “You guys!  You aren’t noticing and wondering things about my face!  Look at the board!  You’re noticing and wondering things about the picture up there!”  Maybe not the best reaction I could have had, but that’s what happened.

Now, I’m wondering what I can do to change the culture in my classroom so that students don’t always look to me for the answers and trust themselves to be able to come up with their own mathematical ideas about problems.


The second instance occurred when we were talking about group work norms after using Sara Van Der Werf’s 100 numbers task.


After seeing pictures of themselves doing the task, students were answering the question, “What does good group work in math class look like?”  As they were giving me responses, I kept saying “What else?”.  At one point a student said, “Can you give us a hint?  What does it start with?”  Another instance of a student assuming that I had a specific answer I was looking for.  The student was surprised when I said that there wasn’t anything particular I was looking for and that I wanted them to come up with responses.  Again, I wondered how I can change that culture in my classroom this year.


At first I was sort of hard on myself regarding both of these situations because they both happened in classes of students I’d had before.  However, when I taught them before, I didn’t know what I know now.  Now I know, and I’m glad I have the opportunity to work with these students again and teach them the things I now know.

Also, I shouldn’t jump over the fact that I noticed those two situations in my classroom and that they stood out to me.  I don’t know that I would have done that in the past.  I may have noticed them in the past and found them funny, but now I notice them and realize that they are examples of something I need to work on with students in my classroom.

New Classroom

I FINALLY get to start school tomorrow!  I.  Cannot.  Wait.

I’m beyond excited for my new classroom, but I’m even more excited to see it full of students tomorrow and for all of the great math that will happen here this year!!

If you see something you’re interested in, and I haven’t included the file, comment and I’ll add it.  The link to the download the posters I’ve made is at the end of this post.

Here’s the outside of my door.  The welcome sign is from Sarah and can be found here.  After going to training this summer from Sara Van Der Werf, I was inspired to make one for my own school.  Here’s her post on the math badges.



This is on the other side of my door.  I saw this on Twitter I think and ended up changing some of the fonts.  I also read this post, and again changed up the font for the quote.  You can find the files for these here, along with other posters found in this post that I’ve made or edited from others in the #MTBoS community.



When you walk in the door, this is what you see.  🙂  I just love it!  I already joke that I live at school, but now I’m really not going to want to leave.



View from the front.  The posters above the cupboards are these from the same blog post from Rock Star Math Teacher as the Yet posters.  The cupboards, shelves, and storage behind my desk are a work in progress.  I’m waiting until I start using things during the year to decide where the best places for things are.



When I finished this today, I felt like I was ready to start school.  I don’t know why, but setting up a weekly calendar for homework was one of the first things both times I’ve set up a classroom.  These are the road sign posters above the calendar.  (Red posters on the right: This is the top poster, and this is the bottom one from Sarah Carter.)



In the back corner of the room, I’ve got a version Sarah Carter’s perfect Square and Cubes posters.  I had seen this post before Sarah blogged about the ones she made, and that font with the dots stood out to me.  I ended up finding a similar font and added it to the Publisher file from Sarah’s post.  I also liked what Math by the Mountain added, so I added my version of that.  The #mathfail sign and my version of the perfect squares and perfect cubes posters are also found here.



I’ve also got my #mathfail bulletin board thanks to Sara Van Der Werf.  You can find lots of pictures on her blog.  Here’s part 1, and part 2.



Sarah Carter’s place value posters.

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Here’s a view from that back corner.



Here’s a view from my desk in the back.  I haven’t done clothesline math before, but I’m envisioning it between those two things that jut out by the windows.  And those windows!!  Love them!  The blue and yellow posters back there are my version of Sarah Carter’s “Mistakes are” posters.  You can find my version here.



And here’s another view from my desk.  I LOVE all of the whiteboards they put in for us!!  I’m excited to try some #VNPS with them!


Here is the link to download the posters I’ve made.