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.


“One Incorrect” Worksheets

One of the things that’s a constant struggle for me every year is giving students access to answer keys for homework problems.  I want homework to be useful to students.  I want them to be able to check their work to know if they’re doing it right, but I go back on forth with whether I should just give students answers or worked out solutions.  I am also terrible at remembering to upload answer keys to Google Drive for students.  If anyone has a system that works for them, please share!

Last week in two of my classes, I assigned a worksheet like this:

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I was introduced to this type of a worksheet this summer by Sara Van Der Werf.  She had us do the one below at one of her PD sessions this summer.  It was this activity from Don Steward.  All but one of the expressions simplifies to 5n + 3, and you need to find the expression that doesn’t and show that all the others do.  I like it because students know that 7 of the answers will be the expression in the middle.  I don’t have to worry about remembering an answer key for students!


I created similar versions for evaluating expressions and order of operations with integers that I used last week in two different classes.  It was easier to make 7 problems that all evaluated or simplified to the same answer than I anticipated.  For the problem that doesn’t work, I tried to create a problem that if students make a common error, the expression still equals what’s in the middle.  For example a problem might have -62 and if students say it is 36 the final answer will equal what’s in the center.

So far, I am really liking how well students have been working together on them.  For whatever reason, it seems that students are more engaged and are more willing to go back and find their own mistakes rather than asking me for help right away when they know that 7 of the answers are the same.  I’m not really sure how this is any different than having the answers in the back of the book, but I’ll take it!


I’m using this one this week for simplifying expressions because I was looking for slightly different types of problems than what I found on Don’s website.


You can find pdf files for the worksheets here.  I don’t know that the Publisher files would be of any use to anyone since I created the equations in Word and copied them to Publisher and used a random font for the other text, but if you want them let me know.  I can upload those too.

Update 2019:  Here’s an order of operations one that I made without integers.

Screen Shot 2019-03-15 at 7.00.42 PM

If anyone has created something similar to this or ends up creating similar things, I would love to share resources!


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.