Warm-up Level-up: Estimation 180

I’ve been working on improving my warm-ups and want to blog about them so that I keep doing beneficial things!

Previous Warm-up Level-ups:

In the Beginning

When I first found out about Andrew Stadel’s Estimation 180 activity, I thought it was a great idea and wanted to implement it in my weekly warm-ups. I had two estimations each Friday (so not 180 of them) and this has always been the most popular warm-up ever since I started a weekly routine of these warm-ups. I tried to make the second one related to the first so that students had some ability to make a more educated estimation.

I used to call on students or asked them to shout out their guesses, and proceeded to write all the guesses down on the whiteboard. As many teachers have pointed out, getting the students to say or write down their guess gets them to have “skin in the game” so they’re more invested in the answer. But this was time consuming and every student didn’t always feel comfortable shouting out an estimation. The bigger problem was that people tended to follow the first estimation, reducing the amount of thinking they were doing.


Now I have students go to a link (bit.ly/WHSestimate1 and bit.ly/WHS estimate2) on their Chromebooks and this takes them to a Google Form.


Then I look at the spreadsheet and sort by their estimation so we can quickly see the smallest, largest, and get an idea for the range of the guesses.


I then hide their name by scrolling to the right (I do this before sorting so they don’t see each other’s names). The anonymity helps shy students have the courage to submit an answer knowing they’re not going to be ridiculed for whatever answer, even if they have no clue.


I also try to emphasize and read some of the better “reasoning”, though I give the students 1 minute (via a timer) to make the estimation and explain, so that’s not always the highlight.

After looking at the estimations, I reveal the answer (often by waiting excruciatingly long!). I go back and show the winner(s). The winner gets to have the “rolling chair” for the day and the upcoming week until the next Friday. If there is more than one, I paste their names here and randomly choose one.

In the Future

The thing I would like to do is better emphasize the “explain your reasoning” part, which makes the students think critically. One way I’ve done that is highlighting a few of the reasonings (before revealing the answer) and then after revealing the winner of the chair, I’ll reward those who had good reasoning with candy. Or sometimes I’ve said “the winner must have decent reasoning” so all the “idk” entries couldn’t win. But then there’s the gray area of “What makes good reasoning?”, which is, I suppose, a good discussion that I need to be willing to embrace, even though it makes me a little nervous to have if only because there’s no clear “right answer” to that question as there is in most of math.

I do like how this warm-up moves quickly (if I set a timer, the students know they should open up their Chromebooks before the bell rings to not miss the 1 minute deadline!) and how students are highly motivated to participate. What’s fascinating to me is that in classes where there are one or two students who “don’t care about any of this math” they are very eager and excited to try the estimation.

The other way I want to improve this warm-up is to make it more personal for the students. Andrew Stadel’s stuff is great, but one of the top questions I get is “did you make this video?” and I’m forced to answer “no, one of my math teacher friends[1] made it.” Some of the best warm-ups are ones that connect to the students lives[2] and I’m slowing replacing Andrew’s warm-ups with my own photos and videos. The more I can make it about them and/or me, the better our relationship and the better they’ll learn in the class. These types of warm-ups just beg to be made more personable and this is such a good opportunity for just that!


[1] I’ve met Andrew in person once, so that counts, right?

[2] One of my favorites is taking a photo of a combine harvester at the county fair during the week of the fair as many of our students are highly involved in the county fair.  There was a sign for the price of the harvester and many students exclaim “hey, I saw that sign!” but then struggle to remember the value of the harvester!

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Warm-up Level-up: Which One Doesn’t Belong?

I’ve been working on improving my warm-ups and want to blog about them so that I keep doing the good stuff!

Previous Warm-up Level-up: Visual Patterns


I’ve been using Which One Doesn’t Belong in a pretty standard way: on the first day that we do this routine I ask students to identify which one doesn’t belong.


The students each pick one and once we’ve shared at least one way, I point out that there are other “right answers”. In fact everyone should find at least four (one for each panel) and probably find even more! I try to reward out-of-the-box thinking, even if it’s not mathematical, such as “25 is the only one without a hole” (think about it) [1].

Every warm-up after that students spend 1 minute coming up with their own reasoning, trying to get at least one for each one, then they share with their seat partner or table-mates for 1 minute, and then we share in the class. I would call on students randomly at first, then take volunteers towards the end. I type the students’ observations for everyone to then type down on their own computer.

The Problem

This warm-up always encouraged out-of-the-box thinking, and often we brought in vocabulary in a non-threatening way (e.g. “Oh by the way, we call that ‘prime’, when you can’t divide any number into 43 other than 1 and itself.”) but I noticed that students would not necessarily listen to what each other was sharing–they would just wait for me to type up at the screen and then they would copy that.

The Level-up

I wanted students to be engaged with one another, even as they were sharing with the class, so I added one simple, yet beautiful twist. I asked the student to share what they noticed, but not which it applied to. Then I called on a second student to see if they could tell which panel the first student was referring to. Then, once the second student guessed, I try to always return to the first student and make them the authority on their observation “Is this other student correct?” I ask.

This (1) forces the students to listen to each other, (2) think critically about all of the panels with every students’ comments, and (3) be the authority on their comment (so they must listen even after they’ve given the comment).

I was hoping that it would also encourage the students to find very interesting and difficult-to-tell facts to make it more difficult for the second student to identify which one. Perhaps I’ll have to issue a challenge such as “See if you can come up with a fact that isn’t obvious, and makes the rest of the class think!”


As an aside, I shared “Which One Doesn’t Belong” with a group of new teachers and a Social Studies teacher really liked the idea, so he started the next day with a WODB (obviously with Social Studies items instead). He found me the following day and shared that “his students talked more, shared more, and thought more deeply about the content than they had all year in his class!”


[1] Still stumped? Look at the shapes of the actual numbers.

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Warm-up Level-up: Visual Patterns

Recently I’ve been working to improve my warm-up routines.  This is how I’ve improved one of my warm-up routines recently and want to blog about it so I remember to keep doing this!


I think it was Fawn Nguyen who pointed out that warm-ups do not need to be related to what you’re teaching for the day. So the warm-up routines is where I am able to do the math practices with students: routines that sometimes touch on what we’re doing, but from a very different perspective.

I have 5 routines:

I create a Google Doc for the week with all of the warm-ups and share it with the students (used to use Google Classroom, now our school uses Schoology). Students know that the first thing to do in class is open their Chromebook[1] and pull up the warm-up.

Visual Patterns

I used to show a visual pattern on the board and I would ask students for the numbers.


We would make a table, talk about patterns we saw in the numbers (not from the pictures), and try to figure out an equation from the numbers. I realized that I didn’t need to have a visual pattern for this, so I included a section titled “observations”. I would encourage students to make as many observations as possible before we moved on to filling out the table or the equation. But we still filled out a table prior to making an equation. Looking back, it was an okay warm-up. It got students noticing and thinking some.

But then I attended a webinar led by Fawn.


Fawn showed a way of talking about the patterns and finding equations by skipping the table. She pointed out that the table, with the numbers, gets in the way of the students seeing the math directly in the pattern. I always thought it was a stepping stone, but it’s more of a stone wall.

She asked the students to find two simple ideas in the pattern: “What is changing?” and “What is staying the same?”. Later you can ask a third idea: “Where are the rectangles?”.

At first I didn’t understand what she meant, but having tried it with my students several times now (every Thursday!), both my students and I are getting the hang of it! I’m trying to think of wording that works better for me and my students because they often will mark the “new stuff” on each image. This leads well to a recursive formula, which we do need to talk about, but it doesn’t give an explicit formula. I might try to ask “What is growing?” rather than “What is changing?”

At first I tried walking around, using my slate to imitate students’ work that I saw. This was better than calling on students to explain their drawings, but it still did not involve me showing off student work, and so students were one step removed from the drawing that was on the board.

Then I realized that, using Schoology (or using Google Drive), I could jump into students’ documents and copy and paste what they sketched at the start of class! I believe that Fawn uses paper for this reason: she can put the students work directly under the document camera. The students responded with excitement: “Hey, that’s my drawing!” and I immediately felt that the task had become more authentic to them. I can still walk around with the slate and mark it up further, primarily labeling their diagram with numbers[2].

Now we check the formulas by substituting in a step number because function notation is so important in Algebra 1, but only after we already have an equation. So I’ve revamped the look of the warm-up.


Another piece of advice from Fawn that I really appreciated is “never move on from a student who can’t answer a question.” Now I keep working with the student, changing my question until the student is able to answer something. This does 2 things: (1) it lets students know that they never get “off the hook” by saying “I don’t know” and (2) it tells my class that every student is capable and every student has something to share.


[1] Don’t have that many computers at your school? I used to print off a paper with all of the warm-ups that would work just as well (better for some warm-ups, in fact!).

[2] I just realized that this is the next thing I need to have students do! I’m really building this airplane while it’s flying–next semester I’ll have new classes and can start the Visual Patterns routine more robustly, as Fawn shared in her webinar.


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Planning a Blended Learning Class

I reached a threshold in my Blended Learning experience this past weekend. This was one of the first times that, while planning, I chose a model because of my students, rather than choosing a model because of me.

The Background

Students took several quizzes on Friday on the following topics: 5.0 Simplifying Radicals, 5.1 Solving Quadratics by Taking the Square Root, 5.2 Solving Quadratics by Completing the Square, 5.3 Solving Quadratics with the Quadratic Formula, and 5.5 Labelling parts of a Quadratic Graph. [1] Students clearly needed to revisit the topics, but not all students needed all of the topics.

In the past (earlier this year) I’ve used sessions, and that’s a great tool to have and use: students teaching students, correcting each other’s misconceptions. I was ready to use this awesome tool, but looking at the quizzes, there simply weren’t enough students in the class to merit that many “session leaders” (students that did well across the quizzes).

So instead, I transitioned to a station rotation model where one station was teacher-led and I was going over the quiz and fixing misconceptions, followed by some practice focused on those misconceptions. The station rotation model was selected because roughly 1/3 of the class needed work on 5.1 and roughly 1/3 of the class needed work on 5.3, while the remaining third consisted of students that aced the quizzes or students that needed help on another topic.

So What?

None of these models are new–I’ve done each of these before this year! The difference is that I had several different plans and intentionally chose which model to use based on how many students needed help on which topics. It was me stepping away from “let’s do this plan because I like this” and stepping towards “let’s do this plan because the students need this”. In many ways I prefer sessions over a teacher-led station because it feels more student-centered [2], but if students need the teacher-led station, I’m willing to sacrifice my own theoretical ideal of “what makes a good classroom” for student needs.

Students responded and seemed to do very well with going back over the quiz, which I appreciate. Last time they needed review, we did stations and they responded well to that, too. I guess that just means I have awesome students!


[1] The numbers are my naming convention to help me organize while using standards based grading. It also helps the students know which notes and which practices go with which topics.

[2] In the teacher-led station I sometimes started with this line: “We all made mistakes on this topic. You’re going to get to retake this quiz and you won’t make the same mistakes, but you might make a different mistake! So, in the interest of hearing what other kinds of mistakes you might make, let’s share our mistakes and listen to each other’s mistakes so that you don’t make any of the mistakes that are made here around this circle.” Students were eager to share “their” mistake on the quiz!

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Blended Learning [Mindset]

Not necessary, but…

I’ve been jumping into blended learning this year as a part of the FCPS Vanguard program and I’m leaning heavily into station rotations as a model for making my class “smaller”. This week I’ve turned my attention to my seating arrangement.

I must say that I appreciated one tweet a few years back with the caption “Seating doesn’t create a cooperative classroom, students do” and it had a picture of a classroom where the seats were in traditional rows, but the students were sitting in a group–some in seats, others on the floor. The students were clearly working in a group despite the seating arrangement and I admired that teacher for developing such a sense of group work in his/her students that I didn’t see the need for rearranging my desks that were also in rows (actually pairs, but essentially rows). I have been using VNPS. However, I have had the luxury of a teacher intern (student teacher) for the past three weeks and I’ve gotten a new perspective on my classroom and really want to try a new seating arrangement.

I moved the desks around and I’m now super excited for my students to arrive on Monday!


Yes, that’s a trombone and a music teacher in my math classroom


Cool panorama of how lame my seating was

Screenshot from 2019-11-08 21-45-06.png

Early this year I went with the color-coding to quickly assign students to stations and rotate them through the stations.

After attending a workshop by Catlin Tucker, I realized that I need to focus more on my teacher-led station being conducive to, well, being led by a teacher. So I changed one station.

Screenshot from 2019-11-08 21-47-45.png

And it helped the flow of my class and I started to like the teacher-led station more. Then I realized “hey, I could use the seating to help the blended learning”.


Screenshot from 2019-11-08 21-54-36.png

It’s amazing how much more space I have[1] and I like that the students are now already organized in groups. Before I had to put them into groups every time they got to the “groups” station, which took me away from the teacher-led station, which took time out of my class, which delayed their starting their work, etc.

Here are some pictures of my new classroom setup.

The brown table now is where students quickly pick up supplies and any papers based on their current station. The table was between me and the students at the front, but now there’s nothing in the way!

The teacher-led station is also around the projector rather than a random whiteboard, so I don’t have to go back to the 19th century[2] and draw all of the graphs by hand.

The Question Wall

Another little addition around the room are a few “question walls” (sometimes called a “question parking lot”) for each station. This was suggested originally to me by my Vanguard Coach, Kent Wetzel, and later reinforced by Catlin Tucker’s workshop.

The idea is that I don’t want to divert my attention away from the teacher-led station (even if it’s student-centered, as I hope it most often is!). But I still need to do a “lap” to ensure students are focused and working around the room at the other stations. However, the danger is that students, who were perfectly independent a moment ago, suddenly become helpless and hopelessly stuck when a teacher walks by. But if I get bogged down in answering “proximity questions” as they’re called, I will never return to the teacher led station in a timely manner. So students write specific questions in that space and then I only address written questions on my lap around the room (which is done on my time, not at the insistence of a student). Students have other resources that they need to get better at using: their notes, their classmates, their brain.

[1] Yes, I shrunk the desks in the diagram, but there really is more space!

[2] Well, a 19th century that had whiteboards…

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Vanguard Program, Day 2

We started off the day by doing this great ice-breaking activity designed to quickly ask deeper questions. The cards came from We and Me and I really liked the questions. Each card had a question, we asked our question of a random other person in the room, then we traded cards, so we had a new question to go find a new person in the room. After the activity, the creator of the cards encouraged us to focus on the person we’re talking to and “going for the Win” rather than just turning the conversation onto ourselves. This is exactly what the Bible tells us to do: “Each of you look not only to your own interests, but also to the interests of others.” (Philippians 2:4) This is something I’ve been trying to practice to become a better teacher and colleague.

Eric Hanes discussed Micro-credentials, which are the ways that we show that we’ve been growing in the Vanguard program in the 4 areas: Mindset, Instructional Technology Skills, Teaching Practices, and Professional Learning & Networking.

We participated in a fun BreakoutEdu activity, which our group won!

For “lunch”, we had a learning marathon, where we walked around Downtown Frederick and looked at various businesses and how they personalize the experience for their customers.

In the afternoon the most helpful thing we did was to review scenarios in which students, parents, or colleagues struggled to understand Blended learning, and gave push-back on the practice. It was helpful to share even some of my struggles with students responding negatively to the flipped classroom. I believe that many of those cases were actually a failure on my part to “onboard” students, or teach and train the students how to be effective in a flipped classroom environment. I am planning on doing much more practice of classroom routines this year.

That’s the next step for me: planning out the first few weeks and how I will train students to be effective in a Blended learning environment. I will need to teach each of the items that I listed in my day 1 post, assess their comprehension of those methods, and follow-up with students who didn’t grasp the methods in the first place. This will be a lot of non-math teaching, but the more I teach, the more I realize that a master teacher is a teacher of everything, not just a teacher of <insert subject area>.

I’m excited to begin the process of teaching students so they can best learn!

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Vanguard Program, Day 1

Today is the first of a 2 day “summer camp” for all of the 3rd Cohort Vanguard teachers of FCPS. I’m excited to be joining this group of educators and am excited to bounce ideas for how to improve my classroom off of other expert teachers.

We started with a “speed dating” activity to meet other teachers in the program. Afterwards, we met with our “Mentor Groups” which is where I met with other HS teachers. This was beneficial for me as I got to put a face to the other HS teachers and see how many of us there are (about a dozen).

Other memorable activities include the “station rotation” where we got to investigate the difference between Personalized, Differentiated, and Individualized learning; Eric Hanes explained a handful of models we could use in the classroom for Blended Learning; we investigated and did a little big-pictures planning for our classes next year. The challenging thing about planning long-term is that the Blended Model is supposed to be personalized and respond to the class’s needs and specific students’ needs. That means that although I have a good “feel” for how a 9th grade class at my school may interact with my flipped classroom, I don’t know how that class will interact and so I will need to adjust as the school year starts.

So I came away with the idea that I need to do a better job of “onboarding”. That’s the idea that I must teach students how to move around the room, as elementary as it sounds. Here’s a short list of things that I’ll need to teach students to do because it’s different in my class:

  • How to learn math by watching a video[1]
  • Station Rotations
  • Playlist with limited options
  • Playlist with lots of options (menu)
  • Help students figure out their own learning strengths and weaknesses

This is of course in addition to the normal things that I have to train students, especially 9th graders: warm-ups, bathroom procedures, cell phone policy, reassessment policy, etc.

[1] I create my videos for my class, specifically where they are, give students a guided notes outline to fill out as they’re watching, and put it into PlayPosit which asks questions throughout the video. So no, they’re not “just learning from a video”. But I need to be flexible for students who struggle with this medium.

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