A few years back, I attended a presentation by Dan Meyer and he shared a lesson design principle that has influenced much of my work since. Thankfully, he also blogged about it, thanking Alyssa Boike for her keen insight. The post and design principle is, "You can always add. You can't subtract."

In my previous post, you might remember my goal is to bring as many students as possible into math conversations and this principle accomplishes it. To illustrate this point, I will reference the following visual.  

That's it.
I have not included any directions on purpose or stated any facts about the visual. I would display this image to students as is because I want to give students the chance to make sense of it in their own way (see MP1). Yes, I could have removed more from this image and have done that before because once you see it, you can't unsee it. However, I'm using this specific image for reasons that will be revealed in my next two posts.

The main reason I haven't included directions with this visual is because I'm inviting my math students through the next lesson design principle: "Tell me everything you know about this."

 Let me share with you a question that has been going round and round in my head all school year, 

How do we bring as many students as possible into math conversations?

The prerequisite to this post is that we value math conversations in classrooms. This blog post (and those that follow) will mean nothing if you don't value students having conversations about the math they are learning. For the record, let me clarify that math conversations do not include teachers talking at students for the entire class period (or math block). That's not a conversation. A conversation requires give and take, where all included parties have a chance to contribute.

I think of it like this: you're with a group of friends and it's time to go to lunch. If one person says, "we're going to Restaurant A." then there wasn't a conversation that took place about where to go to lunch. None of the friends shared their preference or had the opportunity to provide input or convince the rest of the group of a place to eat lunch. On the other hand, one friend might want Restaurant A, another wants Restaurant B, and a few other friends want Restaurant C. The group of friends begin to have a conversation around which restaurant might be best. Each party provides their reasoning or proposes questions. There's a give and take where everyone has voiced their opinion and/or choice. 
 
In the classroom, a math conversation requires a give and take. It could be student-to-student, student-to-teacher, students-to-students, and even a back and forth between the teacher and whole group. So how do we bring as many students as possible into the math conversation? Here are a few ideas I've been playing around with this year. Some might surprise you, and some might not: 

• When designing a lesson, value the thought, "It's easier to add than subtract."
• Using the prompts, "Tell me everything you know about this." and "Tell a neighbor everything you know about this."
• Use estimation with as many math questions as possible by focusing on a reasonable range.

And now I have three blog posts to type up and share. Stay tuned!

When I first dreamed of Estimation 180, I wanted teachers to have their own "virtual classroom" environment so their students could log in, submit estimates and share their reasoning with each other. Understandably, I didn't (and still don't) have the financial resources to develop and house such a virtual environment. Instead, I settled by capturing student estimates and thinking through Google Forms and Sheets because they're free. One drawback to the Google Sheets is the fact that some students will enter potty language, potentially ruining the experience for their classmates or even other teachers and students elsewhere in the world. Another drawback was the lack of visual representations of the data being collected. Google Forms and Sheets has served Estimation 180 well and I'm thankful for it. At this point it will still be a part of Estimation 180, but it's time for an upgrade. A serious upgrade!
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It's 2017 and many things have happened since that day when Estimation 180 was just an idea in my head. I've learned a great deal about student thinking around estimation, representing estimates on number lines, displaying student estimates in histograms, and more. As most of you can agree, we've also been extremely fortunate to be given access to building Desmos activities for the past few years. Without further ado, I'm pleased to announce the first series of Estimation 180 challenges housed in Desmos Activity Builder. I've combined a new series of Estimation 180 challenges (Ketchup Containers) with the Desmos Activity Builder. Thanks to Lynda Chung, Dan Luevanos, Kristen Bennett, and Hedge for testing these out in your classes and the valuable feedback you gave me.
I'm excited:

• to share with you
• to hear your feedback and classroom experiences
• to build more of these

Before jumping into the activity, the remainder of this post provides tutorial notes and videos for each of the five screens in one challenge. Definitely worth checking out the videos below, my friends.

The 1st screen is important because the student need to enter an estimate that is too low, too high, and just right. If the student fails to enter these three values, they won't be able to participate in the four screens that follow the first screen. 

Notes on the 1st screen:

• use the "Pacing" to restrict students to the first screen
• check your teacher dashboard to:
  • ensure every student has submitted a too low, too high, and estimate
  • check to see if any students used the sketch tool to share their thinking

The student's too low and too high are placed on a number line as red points with labels. I love this new addition to estimation challenges because it presents another opportunity for the student to strengthen their number sense by becoming more familiar with a number line. Using the sketch tool, the student can simply place a point on the number line that best represents their estimate. 

Notes on the 2nd screen:

• Use "Pacing" to include screens the 1st & 2nd screens in case students want to revise their range
• Consider having students calculate the range of their too low and too high before moving to the 3rd screen.

The student will find out where their estimate is actually placed on a number line between their "too low" and "too high". The student will also be told the range between their "too low" and "too high". Additionally, the student will be asked to explain how they came up with their estimate.

Notes on the 3rd screen:

• Use "Pacing" to include the first 3 screens in case students want to revise or revisit the original image
• Look for opportunities to discuss student ranges:
  • what make a brave range?
  • what estimates are not the midpoint of the too low and too high?​

Screen 4 could be one of my new favorite screens and ways to make these estimation challenges even more social in the classroom. Inspired by Graham Fletcher, this screen will capture the "estimate" from every student on the first screen and place them in their respective histogram bin (range). For screen size purposes, I limited it to five bins (ranges). If you're wondering how the bin sizes are determined, here's the short story. 
The histogram will calculate the range between the lowest class estimate and the highest class estimate and pretty much divide it into roughly five equivalent ranges. Pretty slick, right?

On this screen, the student is asked, "How does your estimate compare to your classmates' estimates?"

Notes on the 4th screen:

• Consider using "Pacing" to restrict students to this screen.
  
• Listen to (or look at the dashboard for) student thinking and what they notice about the histogram.

The reveal!  ...but don't go too fast.
PAUSE student screens immediately or pause it back on the fourth screen. Part of the magic of Estimation 180 is watching the reveal video together! Play the video from your dashboard using the "Student" button in the top right.

Let students celebrate or disagree with the reveal and remind them the journey is what matters most. When the dust has settled, resume the activity and restrict students to the fifth screen so they can watch the video. At the end of the video, students are provided with their percent error and asked to explain their percent error.

Notes on the 5th screen:

• PAUSE student screens immediately or on the screen before (4th screen)​
• Play the "reveal" video from your teacher dashboard.
• After the video, allow student to voice/discuss their celebrations or concerns about the reasonableness of the final result.
• Remind students:
  • it IS NOT about "the answer"
  • it IS about their thinking, their plan, their range, their critique of others, and the process
  • consider asking students, "now what do you wonder?"

The first challenge in an Estimation 180 series can be considered a guess for some students because they might lack the reference or information to make a reasonable estimate. That's totally understandable. When we enter the second day of an Estimation 180 series, students have an anchor challenge they can refer to now. Therefore, I believe it's reasonable for us to expect students to consider what they already know from the first day and use that information for making a reasonable estimate on the second day. So when we go to show the video reveal, there's more to it than just watching the video. Let's discuss percent error. Watch tis video to see what I mean. I think you're going to like it.
​
Resume the activity after watching the video reveal as a class:

• Allow students to watch the video on their device
• At the end of the video, students will be asked to explain their percent error

Most fast-food restaurants have been using ketchup dispensers for awhile now. Ketchup packets are still helpful for those on-the-go situations. I've always wondered how many packets would fill those paper containers that restaurants offer at their ketchup dispenser stations. So this wondering turned into a series of Estimation 180 challenges. Before we move forward, and so we can remain friends after this, let's agree that not everyone fills their ketchup packets the same. Personally, when I fill my ketchup containers, I hack it by spreading out the paper folds to increase the container's volume. Secondly, if I can avoid wasting paper, I will. That said, I tend to use one paper container. Lastly, I want to make the fewest trips possible to that ketchup dispenser during my meal so I will jam as much ketchup in that hacked paper container as possible. Take it or leave it, that's how I roll. So hopefully this information will help after you (and your students) have gone through this series. Remember, it's all about estimating and reasoning, not answer-getting. 

The Ketchup Containers series starts on Day 221. Enjoy!

During the past few years, I've created over 70 Desmos activities, mainly for the teachers and students I have supported as an instructional coach in my district. Many of these activities have not been uploaded to the Desmos Bank. I apologize.
*UPDATE: I highly encourage you to visit the Desmos Bank to both look for activities and upload your activities. 

However, I created a Desmos Activities spreadsheet of most of the activities I've made. First and foremost, the purpose of this spreadsheet is for me to be more organized with all of these activities so I can find them quickly. Secondly, it's a useful resource for teachers I work with during workshops. Finally, if you have a lot of desmos activities, I encourage you to create your own spreadsheet so it's easier to find your own activities. Here's how it works.

Sorting:
You'll notice you can sort the spreadsheet by any column you desire. It's currently sorted by Grade Span. My purpose with choosing the grade span is to be as inclusive as possible. Take an activity labeled "6-7" for example. From my experience, this activity could be used to introduce a concept in 6th grade and be used again in 7th grade to continue student development of that concept.

Title:
Some titles are self-explanatory, others are not. This is the result of me trying to be witty. Head over to the "topic" column to decode those mysteries.

Topic:
The topic should help share a little more information, kind of like tags. Still unclear, head over to the "Notes" column for more information.

Type:
Most activities linked are from Desmos Activity Builder. However, there are a few Polygraphs I've made and even fewer Desmos calculator links. If something is marked PD, I have used it with teachers during professional development workshops for various reasons. 

Rating:
The rating system is completely arbitrary and determined by me. Ha! 
If an activity has:
• 4-5 stars; the activity is pretty polished and I've been happy with how it has performed in classrooms with students.
• 3 stars; the activity could use a little more classroom testing and fine tuning.
• 2 or fewer stars; the activity is more of a rough draft and I haven't had a lot of time to fine tune.

FAQs:
There's a Frequently Asked Questions tab at the bottom that provides answers to questions I've already received.
Check there before contacting me about any questions you might have.

I hope this spreadsheet is helpful and inspires you to create your own desmos activities and/or spreadsheet of activities.

Please let me know in the comments if you use this spreadsheet and have feedback for me. 

I recently received an email, requesting a quote in "one or two sentences" explaining the essence of Estimation 180 as a routine. I had two immediate thoughts:
1) I'm honored at this request because I both truly appreciate the request and am flattered that the work I've put into Estimation 180 has inspired so many other students and educators.
2) I enjoyed the challenge to capture the essence of Estimation 180 in one or two sentences. 

Based on your experience, I'm curious how you would best describe the essence of Estimation 180 in one or two sentences. I could be a jerk and have you first leave your description in the comments before I share mine... but I won't do that.
​I would still love to hear your description, so feel free to add it to the comments.

Here's what I submitted:
Estimation 180 provides students with opportunities to strengthen their number sense and mathematical thinking through the use of engaging visuals and rich discourse. 
The visuals at Estimation 180 allow students to engage in mathematical conversations where students are encouraged to support their mathematical claims with evidence and reasoning.

Over at Divisible by 3, I shared a post on using Google Forms and Sheets to create your own form to use with students all year long. I think it's so important we capture, sort, assess, and discuss the rich thinking and data students can give us. Hope you find it useful. Please let me know if you have any questions or suggestions.

Days 201-205 challenge students with fitting small and LARGE marshmallows inside a glass with 8 ounces of hot cocoa. You might ask, "Mr. Stadel, why didn't you do a chubby bunny estimation challenge?" I ran out of marshmallows. Ha!

I'm really curious what conversations might arise in your classrooms as students formulate ideas and reasoning.

In addition to the new Winter challenges, I've also given the Google Forms a crisper appearance and added some constraints/prompts to the fields for students to submit.

What's too LOW?
I've put a boundary and prompt to challenge students to be braver (greater) than zero.

What's too HIGH?
I've put a boundary and prompt to challenge students to be braver (lower) than 1,000,000.

Your estimate.
There's a prompt for students to check if their estimate is within their range.

Your reasoning.
I know we (students and teachers) can do better than simply saying "I guessed."
I'm suggesting a sentence starter for your students, having them type, "I noticed" first and follow it with their reasoning.

I'm open for feedback on these constraints/prompts. Please let me know what you think.

Two years ago, I officially launched Estimation 180. In celebration, T-shirts will ship for free this week! 
Don't forget, you get a free sticker with every shirt. Thanks for your ongoing support!

A few months ago I received a gift in the mail from my favorite professor, who I still have yet to meet. Hopefully NCSM or NCTM, Boston 2015. So Professor Triangleman gifted me NCTM's 1986 yearbook Estimation and Mental Computation by Harold L. Schoen and Marilyn J. Zweng. I just started reading it a few days ago and have already found a few gems. Maybe you saw me tweet them out. I'm about to embark on a section titled "Reasons for Making A Special Effort to Teach Estimation". Here's the introductory paragraph:

Does estimation merit an important role in the curriculum? Perhaps estimation is so easy and so pervasive that students learn the ideas even without formal instruction. Most leaders today disagree with this view; it is generally felt that the amount of instruction in estimation is not what it should be. (Increasing attention to this subject is one reason for the existence of this yearbook!) But why, if estimation is so widely represented in mathematics, must a special effort be made by teachers to work with these concepts? There are many reasons for such an effort, and these reasons for teaching estimation are not the same as the reasons for doing estimation. 

Almost 30 years later, is this worth discussing? 
Would Schoen and Zweng feel differently today?
I'm curious to know where Schoen and Zweng are headed in the following pages of this section. Are you?

I look forward to posting some follow-up notes in the next week. In the meantime, what are your thoughts?

From now until September 1, 2014 (Labor Day), there will be free shipping on all shirts in honor of Back to School! 

As I said in my last post, I'm not selling Estimation 180 gear to make money; it's a hobby to simply spread the number sense and break even. I want to thank all of you who have already bought t-shirts and/or stickers. I truly appreciate the support and I can't tell you how cool it is to see you posting pictures of your gear online. Here are a few of the pictures from my Estimation 180 scrapbook.

Order a gift for your colleague or simply strut your Estimation 180 shirt at a teacher pre-service day. Plus, you still get a free sticker with every t-shirt you buy!

Head on over to the store.