Estimation 180 + Desmos

Last year I used Estimation 180 almost weekly in my middle school classes.  Students had access to this file on their iPads and filled it in each week.  This worked ok, but I wanted to find another way of doing this that students publicly committed to an answer.  I think I’ve seen other teachers who have their students use Post-it notes and put their answers on the board, but this just wasn’t something I could envision working in my classroom on a regular basis.  For one, I covet my Post-it notes way too much to have students use them regularly for this.  😉

I missed doing these activities with students and knew my students could use practice with their estimation skills.  After becoming more familiar with Desmos activity builder this summer, I thought that seemed like a much more realistic option for my classroom than something like Post-its.

I’m sure I’m not the first person to combine Estimation 180 and Desmos.  When I was looking for what else was out there, I struggled to find something to steal from someone else.  I saw this tweet from Andrew Stadel, which is awesome.  However, I was looking for something quick I could use as a warm-up activity.  My goal was to combine Desmos with Estimation 180 into an activity that could be done in 5-10 minutes with students.  I wanted to be able to put the class code up for students as they walked in the room and let them go so that I could take care of attendance, passing back papers, etc.

This is what I came up with and used on 3 consecutive days in one of my classes this week.


Overall, I liked how this went compared to how I did this last year, and I realized how much my students really need practice with this!  I think I will continue to use this structure, but I know this could be made better.  What would you do to improve this?


Update:  Since the original post, I’ve done a few more of these with students.  I’ll add the links to all the activities I’ve done below.




The warm-up problem that changed me, my students, and my classroom

Every once in a while a lesson goes nothing like what was planned, and it turns out to be the best. thing. ever.

The lesson plan was simple:

  •  A 10 minute warm-up to review simplifying expressions (Students had just been tested on it, but many could still use more practice to continue to gain confidence with it.)
  • About 15 minutes of notes and examples of solving equations with square roots
  • 25 minutes of work time

That simple lesson plan turned into one of the best things that has ever happened in my classroom.

If you’re looking for some great, new, exciting warm-up, you’re looking in the wrong place.  You won’t find it here. What you will find is how a basic, boring warm-up problem, changed my classroom, my students, and me as a teacher.

The warm-up for the day was My Favorite No.  Students seemed a bit sluggish that day, so after picking “My Favorite No” and putting that incorrect solution on the board, I paired it with a couple Stand and Talks.  (You can read about what that looks in my classroom here.)


THE warm-up problem.

After the Stand and Talks, I had more students willing to volunteer than prior to the Stand and Talks, but I was tired of having “more” students willing to participate.  I wanted all students to participate.

What happened next was so completely unplanned.  I wish I could say I was intentional about planning a lesson so that something like this would happen, but I didn’t.  It was a complete accident.  Sometimes I just hate that some of my best teaching moments are those spur of the moment things that just happen.  It almost makes me want to try winging it all the time just to see what happens.  Almost.  😉

I pointed out to students that they had just spent several minutes talking with two different people about mistakes in the problem, and that I heard them talking about the problem and knew that everyone should have something to say.  As I was saying this, the teacher I team teach with, went around pulling the students’ hands in the air.  Many of the students grinned sheepishly because they knew they were just choosing to not engage in what we were doing.

I called on a student and the response I got was, “I don’t know.  She raised my hand.” (as he pointed to the teacher).   I told the student I would come back to him.  I wasn’t going to let him off the hook.  We finished going over the mistakes in the problem.  I went over to my computer, hit the undo button until the problem was back to how it was at the start with the mistakes still in it.  I went back to the first student and asked again for a mistake in the problem.  Again, the student still didn’t have an answer for me.  Again,  I told him I would come back to him.  As we were going over the problem the second time, I called on another student who also did not know where a mistake in the problem was.

I think we went through that same problem 4 or 5 times.  I hadn’t planned on that, but if a student didn’t have an answer or could name a mistake but couldn’t explain why it was a mistake they heard, “Ok, I’ll come back to you.”  We did the problem until every single student in the class could explain a mistake in the problem to me.  In that moment, I decided that participating and engaging in class was no longer an option for students.

Then I put another problem up on the board and told them to try it.  We went over it on the board, and while the participation was higher than an average day, it still wasn’t where it should be.


I said, “Ok, now try this one.”  As I said it, I still didn’t know if I was going to put the same problem up again, but I decided I wanted to drive my point home with students, so the same problem it was.

When we went over the problem the second time, nearly every student in the class was willing to raise their hand.

When I said, “Ok, now try this one.”  I heard, “Oh no, not again!”  🙂   I put a problem similar to this up.


I walked around to see that every. single. one. of my students wrote the problem down on their paper, and most students had done at least the first step.  This was HUGE.  By this point in the lesson, I could feel that what was happening was special, and I was excited.

We hadn’t done any problems yet where the square root of x was being multiplied by anything.  Some students got stuck with what to do once they added 8 to both sides of the equation, but I expected that to happen.

However, what my students were stuck on was not worthy of my attention at that point. I stopped the class and made a big deal out of the fact that every single student wrote down the problem.  I asked them what they would have done a couple days ago if they had seen a problem like that where we hadn’t gone over anything like it before on the board?  Many admitted they wouldn’t have even written it down, and a student in my other class said, “We would have been stuck on the escalator.”  It couldn’t have been a more perfect response!  (Scroll through this post from Sara Van Der Werf to read about the escalator and beagle video she shows her students.  I highly recommend using them in your classroom!)

I let them know how proud I was of them for engaging in the problem and getting started with it even though it looked different than anything they had done before.

I put up a third problem on the board.  When it was time to go over it together, I told the class to look around and asked, “When have we ever had this many people willing to answer?”  They all responded with, “Never!”  And then I asked, “And have we already gone through this problem together today?”  Their response, “No!”

I could see in their faces that they were getting it.  Not the math, but they were getting it.  They were getting what I wanted them to see and know and believe about themselves as math students.

They may not admit it, but I could tell they felt good about themselves.  I told them that this shows them that if they engage themselves and participate they can do it.  In my other class we talked about how some of them walk into my room and because it’s a math class they feel they can’t be successful.  However, I just showed them in less than 30 minutes that if they participate, they can do it.

I don’t know that I have ever been more nervous to teach a lesson than I was my second 8th grade class that day.  My first class had gone SO well, and it was so un-planned.  Part of what made it so great was that it just happened.  I feared that I would try to force something with that second class, and it would flop.

By the end of that class, I had a student literally jumping out of her seat wanting to tell us what to do next in the problem.  This was a student who never participated in class. ever.

I had goosebumps.

And that is how a simple, boring warm-up problem has had such an impact on me, my students, and my classroom.


Find the Flub with Stand and Talks

At Twitter Math Camp, I went to a session led by Jessica and Lisa on warm-ups they use.  (Here’s the link to the TMC Wiki page with the stuff from their presentation.)  One of the warm-ups they mentioned that stood out to me is what they call “Find the Flub”.  A worked out problem is put on the board, and students need to find the mistake or the “flub”.  I have not done this part, but Jessica and Lisa then have students classify the mistake that was made -similar to what Sarah Carter talks about in this post.

I knew I wanted to incorporate some version of this into my warm-ups this year because I’m really trying to focus on the role mistakes play in learning this year with my students.  Here’s how it has played out in my classroom these first few weeks of school.

So far, all the problems I’ve used are problems I work out and take pictures of to put up on the Smartboard.  Students are directed to find the mistake, explain it, and then correct it.


an example of a Find the Flub problem

One of the first times I did this with students, I walked around the room while they were working and saw they had answers written down.  When I asked for a volunteer to explain the mistake, silence.  I KNEW students had answers, but no one was willing to share.


Then, I remembered Sara’s Stand and Talks.  (Read about them hereScroll down to #4.)  I instructed students to stand and once everyone was standing I said something along the lines of this, “Find a partner and talk about a mistake you found in the problem and why it is a mistake.  If neither you nor your partner found a mistake, work together to find one.”

Instantly, nearly everyone in the room was discussing the problem and debating about whether something they thought was a mistake was actually a mistake.

When conversation started to die out, I then gave the following instructions, “Find a new partner and discuss a mistake in the problem.  It might be something you just learned from your partner or it could be something you already had written down on your paper.”

All of that probably took less than 3 minutes, and after students returned to their seats, I asked again for someone to explain a mistake in the problem to me.  Nearly every hand in the room was up and students were eager to share.

I don’t always have students find a second partner, especially when I know there’s only one mistake in the problem, but I need to.  Writing this post reminded me of why I had students get with a second partner the first time I did this.  It was my attempt to give students who didn’t have something to talk about with their first partner an opportunity to talk about a mistake, as well as to get students listening to each other and practice explaining each other’s thinking.

I LOVE when I unintentionally do something that turns out to be something I use over and over again in my classroom.  I think this is one of those things.  Now every time I do Find the Flub for a warm-up problem, I pair it with a Stand and Talk and so far I’ve gotten great responses from students.


Number Muncher: An Order of Operations Game

One of my favorite activities/games I started using my first year teaching is something my students named “Number Muncher”.  It’s an old Discovery Toys game I had from when I was younger.  (Thanks mom for instilling my love of mathy games young!)  I couldn’t remember what it was called but knew it needed a name, so I decided to have my students name it.  I made a list of several of their ideas and had them vote from that list.  Number Muncher it was.  I’ve since learned that it’s actually called Number Jumbler.

I don’t think I fully recognized the value of activity my first year teaching because since then I’ve used it less and less each year, and I don’t know why because it’s SO good.  It’s low floor/high ceiling.  It’s a great way to review order of operations, exponents, properties of multiplication and division, and even fractions.  It allows students of all levels to be successful but also challenges all students.  I’ve mentioned before that I’m working to be more intentional about the tasks I have students do in my classroom, and this one makes the cut.  It will be making a comeback this year!

The goal of the game is to write expressions equal to the middle number using the numbers around the outside.  You don’t have to use all of the numbers, but you can only use the numbers on the outside and can’t use them more than once unless there are duplicates.  (For example, in the picture below, you can only use one 3 but you could use three 6’s.)

Because the numbers are random, some sets of numbers are  much more challenging than others.  I want students to feel success with this game at first, so I try to make sure that the numbers are nicer to work with the first few times we play (i.e. when I write the numbers on the board I change some without students knowing -particularly the middle number.  I think the numbers on that cube are 10, 20, 30, 40, 50, and 60.  I like to keep that one smaller at first.)

I vary how long I give students to work depending on the numbers, but it’s usually around 3-5 minutes.  I usually make it a competition, and whoever comes up with the most correct expressions wins.  Each expression is worth a point, and depending on what math concept I want to encourage students to use, I may give students bonus points for certain expressions.  For example, I may tell them they get 2 points for every expression they come up with using an exponent.

After time is up, we go over several of their answers on the board.  In nearly every one of those conversations, addition and multiplication properties naturally come up as well as whether the parenthesis a student used in an expression were necessary or not and why.

I’ve used this as a warm-up.  Other times I pull it out when we’ve got an extra few minutes at the end of class, or when I’ve got some early finishers.   How else do you think I could use this with students? As I’ve been writing this post, I’ve thought of the following ideas:

  • After students have had individual work time, put them in pairs or groups and give them a few more minutes to work as a group to come up with a collective list.  Then we could have a group winner.
  • Rather than going over students’ solutions on the board as a class, pair students up and have them check each other’s work.  Then maybe as a class we would highlight some of student’s favorite solutions.
  • Play sort of like Scategories and only give points for unique answers.

I know this is similar to some of the other order of operation activities out there, but students love to be the one to roll the purple thing to come up with the numbers.  They think it’s so cool.  I couldn’t find it sold on the Discovery Toy’s website or on Amazon, but I did find a few on eBay if you’re interested in one for your own classroom.  You could also use 7 regular dice and pick one to be the “middle number”.