# 20 Days of Number Sense & Rich Math Talk (K-12)

20 Days of Number Sense & Rich Math Talk – for all grades from K-12. That is the goal of this series. Entirely new, exclusive content fills this post in a ready-to-use format that will allow you to deeply explore 4 rich math routines.

By downloading each day, you can have a clear pathway to presenting rich number sense and math discourse opportunities to your students.

Additionally, each day contains multiple levels, so that a 2nd grade teacher, a 5th grade teacher, and a high school teacher can all be using the same file – and can all have access to other grade levels. The opportunities to differentiate across levels abound in this series as well as the opportunities to see into other grade levels from K-12.

Update: If you would like to read about Kathy Iwanicki’s journey into 20 Days of Number Sense & Rich Math Talk, you can find her blog post here. Thank you for sharing your story, Kathy!

After reading this blog post, take a look at **THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG**.

**Quick Access to Days 1-5**

*Simply click on the blue link to download the file. *

Day 1 – The Estimation Clipboard

Day 2 – The Estimation Clipboard

Day 3 – The Estimation Clipboard

Day 4 – The Estimation Clipboard

Day 5 – The Estimation Clipboard

**Quick Access to Days 6-10**

*Simply click on the blue link to download the file. *

Day 6 – Exclusive Splat Sequences

Day 7 – Exclusive Splat Sequences

Day 8 – Exclusive Splat Sequences

Day 9 – Exclusive Splat Sequences

Day 10 – Exclusive Splat Sequences

**Quick Access to Days 11-15**

*Simply click on the blue link to download the file. *

Day 11 – Exclusive Esti-Mysteries

Day 12 – Exclusive Esti-Mysteries

Day 13 – Exclusive Esti-Mysteries

Day 14 – Exclusive Esti-Mysteries

Day 15 – Exclusive Esti-Mysteries

**Quick Access to Days 16-20**

*Simply click on the blue link to download the file. *

Day 16 – Exclusive Cube Conversations

Day 17 – Exclusive Cube Conversations

Day 18 – Exclusive Cube Conversations

Day 19 – Exclusive Cube Conversations

Day 20 – Exclusive Cube Conversations

**Quick Access to the solutions for the Advanced Cube Conversations**

The Answers to the Advanced Cube Conversations Tasks (Days 16-20)

**Quick Access to the Cube Conversations Book**

The Cube Conversations Printable PDF

**Description of 20 Days of Number Sense & Rich Math Talk (K-12)**

__Days 1-5__

I’ve opened the series with a brand new set of Estimation Clipboards. The Estimation Clipboard strategy is a very invitational way to draw students into rich number sense discussions as it layers in more and more context and continues to provide students with estimation opportunities. The Estimation Clipboard strategy is also where a very important math instructional reality becomes abundantly clear: Writing is a powerful springboard into math discourse. As students WRITE their estimates (particularly for images 3 & 4) the math talk in your classroom will become very rich. You’ll find the power in the pattern of (1) students estimating (2) writing their estimate (3) explaining what their estimate is, and why they chose it. Then right before each reveal, your classroom will become very quite in anticipation of the reveal. Don’t be surprised if there is a lot cheering as the answers are revealed.

Days 1-5 have set the stage with The Estimation Clipboard. Not only have the 20 Days of Number Sense and Rich Math Talk begun, but both students and teachers have detected the power of invitations, estimation, writing, sharing their ideas aloud, and experiencing the joy and wonder of math.

Day 1 – The Estimation Clipboard

Day 2 – The Estimation Clipboard

Day 3 – The Estimation Clipboard

Day 4 – The Estimation Clipboard

Day 5 – The Estimation Clipboard

__Days 6-10__

After the highly invitational nature of the Estimation Clipboard, opportunities to richly explore numbers continue in the Splat! images which are all brand new – and are all designed to work in both PowerPoint and Google Slides (just like everything else in this series – so feel free to use either one).

Ranging from Splats through 10 through Fraction Splats! and now including 10 of the most challenging Splats! that I have ever publicly released, your students will have very rich opportunities to lean into number sense and richly discuss their mathematical thinking while also hearing from other students. They will be able to see and explore multiple strategies for decomposing numbers, adding, subtracting, multiplying, dividing, and connecting many concepts together.

Since every day includes materials across a wide range of grade levels, there is also a really good opportunity to take a look at content from other grade levels and offer even more challenges to your students.

Let’s take a closer look at each of the Splat! levels include in 20 Days of Number Sense and Rich Math Talk.

Splat! Level A includes numbers through 10 and is ideal for grades K-1. In these sequences the dots appear so that students can count them. Then, when you click, the total number appears in the corner. On the next click, the SPLAT appears and covers some of the dots. The immediate question is, “How many dots are under the Splat?” You will be amazed at how many different ways students see this, solve this, and even how they mentally move the dots around to decompose and make sense of the numbers. If you look at the images below, you’ll see that some of the Splats separate the visible numbers and create a Part-Part-Part-Whole scenario. Splat Level A appears in all 5 days.

Splat! Level B includes numbers through 10 and is ideal for grades 1-2. It also provides the first example of a grade level (kindergarten) that may recognize the opportunity to venture to higher levels. Just like in Level A, the first click introduces the dots, the next click brings in the Splat and the question, and then the Number Sense and Rich Math Talk begins. When I use numbers through 20 in the classroom, I sometimes quickly move through the counting step by saying, “Here are some dots. There are 19 of them. This is the Splat!” I find that counting so many dots can slow down the opportunities that the Splat introduces. Of course, counting is critical, and so is finding many different ways to count, so at other times I spend more time on a variety of grouping and counting methods. The reality is that there are so many opportunities in these slides that you have many opportunities to focus on a wide range of concepts.

The images in Splat! Level C are some of the most wide-ranging images I have ever worked with. It offers opportunities across so many grade levels. I’ve labeled it as primarily matching grades 2-5, but I’ve seen it used very effectively in many grade levels. Level C is where multiplication and division begin to play a much stronger role. While students in younger grades may access the image above (the one that shows 14) by adding, subtracting, grouping, counting on, repeatedly adding 3 to 5, or repeatedly subtracting 5 from 14, I’ve seen other strategies across grade levels. For example, fourth grade students sometimes view it as 14 ÷ 3 with a remainder of 5. Likewise, high school students have viewed is as 3x + 5 = 14. Imagine the power of the conversation among the students across those grade levels!

A very interesting option opens up in Splat! Level D. In the images above you are seeing the first of the reveal clicks. In the moment before this – when all of the Splats are opaque, and none of the dots beneath the can be seen – students approach a new question, which is “What could the total be?” In the first image above, before it is revealed that each Splat is covering 3 dots, students find themselves working with the concepts that the total must be 3 more than a multiple of 3, so the total must be a multiple of 3. However, in the second picture above (again before the first Splat is revealed like you see in the picture) students can see that the total is unknown, that there are 4 visible dots, and that there are 7 splats. By rule, each splat is covering the same number. So students can work with the concepts such as that total must be 4 more than a multiple of 7. As the identify possible totals, they can see that it could be 4, 11, 18, 25, … Then when you choose to reveal the value of a Splat by clicking, you’ll see a single Splat turn transparent (which is what you see in the images above) and the students can determine what the total number of dots is. You may expect the students to use multiplication to do so, and many will, but they will also surprise you with a wide number of strategies that you may never have expected. They are showcasing both Number Sense & Rich Math Talk!

Level E is a favorite of many teachers. In this level, all of the whole dots and all of the fractional parts of a dot can be seen. Then when you click, the Splat appears, and covers some of the whole dots and fractional parts. The immediate question becomes, “What is the value beneath the Splat?” I am amazed at how students approach these questions.

Level F is similar to the previous level with one exception. While, Level E allow the students to see all of the images before the Splat appeared, Level F simply presents the total, the Splat, and the visible parts of the total all at the same time. Students once again bring very impressive insights into the conversation. It’s Number Sense and Rich Math Talk and the way that students contribute to one another’s insights is eye-opening.

Level G allows the students to see the all of the whole numbers and all of the fractions on the screen and gives the students the opportunity to determine the total. When you click the total will appear. Then, with the next click, multiple Splats will appear on the screen. By rule, each of the Splats is covering the same number (the same value), although those numbers may be represented in different ways. The students task is to determine the value of the Splats (not the specific pieces) under each Splat.

Level H is similar Level G, accept in Level H the Splats all appear at the very beginning, so the first image the students see are just line the ones that are showing above. The question is, “What is the value of each Splat?” Within Level, H (on days 9 & 10), I have included 10 of the most challenging Splat questions I have ever publicly released.

Remember that I’ve written slides for ALL levels on EVERY day. Download the day you are on, find the level you want to work with, and let your students exercise their Number Sense and engage in Rich Math Talk.

Also, consider challenging your students by trying out 2-3 slides from another level.

Day 6 – Exclusive Splat Sequences

Day 7 – Exclusive Splat Sequences

Day 8 – Exclusive Splat Sequences

Day 9 – Exclusive Splat Sequences

Day 10 – Exclusive Splat Sequences

__Days 11-15__

Exclusive Esti-Mysteries

15 brand new Esti-Mysteries fill these 5 days, and each day includes 3 different levels, ranging from kindergarten to advanced math concepts. As a bonus, the first 3 Esti-Mysteries include appearing charts on the screen. Additionally, 2 of the Esti-Mysteries include multiple perspectives and hidden clues that can be found in the 2nd image.

Esti-Mysteries strongly call upon number sense and promote rich math talk while also giving students rich opportunities to COMBINE estimation with a range of math concepts in the context of rich math talk. Students will be discussing their estimates – much like in the first 5 days when the work with the Estimation Clipboard – but will also be looking carefully at math concepts and seeing how those concepts are interrelated.

Day 11 – Exclusive Esti-Mysteries

Day 12 – Exclusive Esti-Mysteries

Day 13 – Exclusive Esti-Mysteries

Day 14 – Exclusive Esti-Mysteries

Day 15 – Exclusive Esti-Mysteries

__Days 16-20__

Exclusive Cube Conversations

The highly visual cube conversations strategy is used in the final 5 days to promote number sense and rich math talk. In addition to brand new Cube Conversations Images, the downloadable set of matching pages will give students clear opportunities to annotate and describe their insights to one another.

As with all other days in this series, there is a very good opportunity to see into other grade level bands, and this can be use to differentiate content, challenge students, and promote even deeper number sense and rich math talk.

At the end of each day there is also a challenging task, which is placed in the highest grade band. The printable PDF includes 2 different versions of each task. One version includes 4 copies so that students will have an opportunity to try out 4 different entry points into the task, while the other page simply offers a larger, easier-to-use version of the image.

The beginning level of Cube Conversations provides very good opportunities to visualize and decompose small numbers in a wide variety of ways. The middle image shown above is animated to showcase 3 different ways that students may see how to decompose the shape. Likely, they will find many more than the 3 examples, but the animated examples typically provide a nice momentum and a clear invitation to seek out many different ways to decompose the number. Then another image appears (like the third one shown above) with 4 additional copies below it so that ideas can be shared with the entire class. As with all levels, every image is also available on the downloadable PDF so that each student can decompose the images on their own and then share their ideas with one another.

Deepening Cube Conversations (grades 2-5) introduce some layers of complexity that allow students to work with additional concepts, such as visualizing sets in multiple ways, visualizing shapes that overlap (so the overlapping cubes may need to be subtracted), and shapes that appear to have holes in them.

The 2nd image above shows layers that will appear when you click (although on the slide you download the images will all be in a single location on the slide). If you look at the middle image closely, you will see how the image has been decomposed into 9 + 3 groups of 3, then 2 groups of 5 and a group of 3 and 5 groups of 1. Still focusing on the blue and yellow shape in the middle image above, you can see why students describe it many ways. For example, a student might say, “I see 3 groups of 5 in the blue and yellow image.” If you look carefully, you’ll also see 3 groups of 5.

Then moving the the last image in the center picture above (the image which is red, yellow, and blue in the bottom right corner) you can see how a student might say, “I see three groups of five plus three more – but I see it in a different way.” Remember, that is just the example page and it is followed by the wide open opportunity presented on the next slide. When you look at the third picture above you can see how a student might describe two groups of 9, two groups of 8, or even 2 groups of 7 while other students describe groups of 2, 3, or 5. You may also hear that a student sees a 25 minus two groups of 4 and 2 groups of 1. The possibilities go on and on as your provide students with rich opportunities to explore Number Sense and to explore and describe their insights together.

The routine continues – but at a deeper level – in Textured Cube Conversations. Remember, every level is available on every day in this blog post, and all content in 20 Days of Number Sense and Rich Math Talk is exclusive to this post.

The first image will present a structure, several examples of how the structure can be visually decomposed, and will finally reveal the number of unit cubes. Then a new image will appear with 4 opportunities on the bottom of the screen for students to show their thinking to each other.

All of the Cube Conversations images are available in PDF format so that you can provide each student with their own copy to annotate – and then to share their ideas with one another.

Advanced Cube Conversations will feel very much like a rich task. Two of the Advanced Cube Conversations are illustrated in the pictures above.

The thinking that comes from these tasks is tremendous!

On the downloadable PDF you will find a page with a large image of the structure an an additional page that provides 4 smaller versions of that picture so that students will have multiple opportunities to try out a variety of entry points.

In each case the question is, “This structure is composed of how many unit cubes?”

Day 16 – Exclusive Cube Conversations

Day 17 – Exclusive Cube Conversations

Day 18 – Exclusive Cube Conversations

Day 19 – Exclusive Cube Conversations

Day 20 – Exclusive Cube Conversations

I hope you enjoy 20 Days of Number Sense & Rich Math Talk. If you do, please leave a comment. You can even share who is using it. Perhaps we’ll see some classrooms from around the world leaving comments like, **“We are using #20DaysNS in Hunters, Washington!”**

As always, you can find me on Twitter @stevewyborney

I’ll be keeping an eye on #20DaysNS on Twitter.

I wish you well as you work with your students and give them opportunities to develop their numbers sense and engage in rich math talk.

All my best,

Steve

Thank you ! Your work is so helphful to try and improve math conversation. I’m a french teacher and we are not used to work like that. So it’s a way to innove. I’m grateful.

Hi, Mireille. I’m glad that you are enjoying the experience of math conversation. It is such a powerful way to learn. Great work!

Thank you so much for your wonderful math activities. My first graders really enjoy them. Now that I am fully remote for the time being, it’s nice to have something I don’t need to convert to digital that the kids enjoy interacting with. Great practice for my lower leveled kids and challenging for my more advanced kids.

I’m glad you shared this, Kathleen. I’ll keep sharing the materials. It’s great to know that they are helping so many learners.

Hi, I really appreciate all the powerful opportunties you create for students to deepen their thinking. Thank you. I am relatively new to technology, and I have a few basic questions about your work for DL for my 4th graders this fall. Can I integrate your 20 days of number sense or estimysteries into a google slide deck or Pear Deck? I’m wondering if it’s possible for me to add a slide where the kids write/draw their thinking? Thanks so much. -Amanda in Berkeley

Hi, Amanda. Catching up on comments… Yes, you can save 20 Days of Number Sense into your google drive, open the files with google slides (which actually creates a Slides version copy of them) and then you will be ready to go. I haven’t used Pear Deck for a little while, but I believe you can easily use the same files (from within slides) to easily use Pear Deck as well.

Hi Steve,

Quick question: In esti-mysteries 11 – the apples- I like how you included the number chart and blacked out numbers after the clues as a support for students. I am trying to add that to the esti-mysteries 12 with the paper being measured. I am animating it in with each clue clue like you did, but I am not sure how to do the “see-through” black you used over the numbers on the chart. Can you tell me what you used to do that effect? I think it will be helpful for our students to have that feature.

Steve,

Thank you so much for offering all of these great number sense activities. During this COVID time, I made videos for all of these activities and then shared them with our students grade K-6. I received lots of positive comments from the parents and students. Thank you again!

Steve, this has been so fun! My kids (most of them…=) have loved doing these!! Each day we start math with these and one day we missed it and they were disappointed later when they realized we hadn’t done one that day!! Any chance of another set of 20 to come? ?? =)

Thanks for all of your work in putting this together. As a veteran teacher of 30 years I appreciated having something that I could pick up and run with and that I didn’t have to spend time putting together, but could jump straight to the ‘how does this work’ stage of the game.

Thank you again so much!!

Chris

Hi, Chris. Thanks for the note. I haven’t planned another 20 days, but now you have my wheels turning about possibly posting another set. I appreciate the kind comments! Wishing you a great week!

Thanks, Steve! I’ll keep my eyes out in case you decide to do another one! =)

Hi Steve, With us being limited to online zoom teaching, this website has been a gold mine. Thank you for sharing and thank you for putting together this 20 day regiment. It makes the implementation super simple!

WOW nearly end of year but I’m going to try out some of these next week…ty so much for sharing!!

Steve, thank you for the 20 days. It took a longer than 20 days but my students enjoyed the whole process. I teach first and second graders. Splat and the cube conversation were both big hits.

Hi, Cathy. I’m so happy the hear that. Cube Conversations is such a powerful resources and I’m glad to hear it is being used by your students. Nice going!

I watched your video during a math pd summit. My students have loved the google slideshows with the clipboards and the estimation jars! In fact they cheer when the first slide pops up. I found your site and was excited to download the powerpoint estimysteries. However, I am unable to get them to play. I’m wondering how I can download them as a google slide. It doesn’t give me the option of a slide only the ppt.

Hi, Lana. If you are using Google Slides, there is a really simply solution. Just save the PPTs in your google drive, then open them with Slides. After that be sure to click present so that the slide show will be playing. When it’s playing it will reveal all of the parts of the presentation correctly.

I figured out how to make it work. Just had to save it as google slides. Thanks for offering this great number sense opportunity!

Has anyone used these with google sheets? I am using a chrome book and the REVEALs are not working. Is it just because I’m not using powerpoint? We are simply dragging the word away at this point, but not sure how we can quickly/smoothly use the splats!

I figured it out! Thanks!

I’m so glad it worked!

Hi, I’m beyond excited to try this with my students. However, I think I’m either misunderstanding the estimation clipboard activity, or I don’t know how to use the PP. I don’t know how to show the slides one section at a time. I get the first slide with the question, but then all 4 of the other pictures show up on one slide at the same time. Help please!

Great question. It sounds like the slide show is not playing. When it is playing, the animations are set up to show just one of the pictures at a time. If you are using PPT, just go to slide show… view show. Let me know if that takes care of it.

Hi Steve,

I love this! But when I click on the link, there is no blue D01 20 Days….so nothing to click on. After the first link, I can’t get anywhere. Can you help me figure it out?

Thanks so much.

Beth

Hi, Beth. I’ve recently updated the website. Can you try it now and let me know if it works for you?

Great presentation! Just watched the 20 Days at the Build Math Minds summit. Question: How long does each day take? Would you use these as a warm up?

Hi, Kasi. I recommend about about 10 minutes for each one, sometimes reaching up to 15 minutes depending on the grade level. As you get into days 16-20, there are some cube conversations that could be allotted much more time, but use about 10 min. as a rule of thumb and adapt from there.

This is amazing, thanks so much for sharing! I can’t wait to use this to introduce my 2nd graders next year. Thanks for this work!

Hi, Rachel. It’s my pleasure to share the resources. Thanks for the comment!

I just watched your presentation on Virtual Math Summit and am so excited to share these with my students. We are a Google-only school and I can only see that I access your resources as Powerpoints, but you state that they are also Google Slides. Where can I find the Google friendly version?

Hi, Amanda. While they are PowerPoint files, they will work in Google. Simply save them into your google drive and open them using googles slides. I’ve used only animations that will work in both slides and in PowerPoint.

I love all of this! I am moving back into the classroom and transitioning from all science to 7/8 math. I want to create experiences and a math classroom like students have never had before to reignite an enjoyment in math or continue the fire. This is going to be great for the first 20 days of school and then revisit each topic throughout the year in rotation stations! Thanks so much for sharing!

I’m glad it will be helpful. Have a wonderful year!

I am on Day 6 with my small group of third graders who come for math support. They absolutely love these. We just started the fraction unit and I used the fraction splats with them today. We had not talked about fractions greater than one and how they are written. I gave them fraction circles to model and figure out. The discussions were so rich and my students want to keep going longer. I can’t wait to share with the other teachers. Thank you Steve!

Thank you so much! This is exactly the kind of story that motivates me to keep posting more of the materials that are sitting on my computer desktop. I’m very grateful that you took the time to share this with me.

I did. Thank you!

Thanks, Alexa. I’m finally catching up on blog comments and wanted to be certain. Have a great week!

I can’t thank you enough for providing these resources to us free of charge. I have an advanced group of fifth-grade students who THRIVE on solving math challenges and they are loving the cube conversation activities. Thanks so much!

Hi, Janet! I’m so happy to provide these resources, and you are very welcome. I’m glad to hear that is is providing a challenge that your students are thriving on. I really appreciate the comment!

My students love these! We are currently on Day 16/20. Is there any chance that you can either post or send me the answers for the advanced cube conversations? My students are very eager to know the correct answers after our conversations!

Hi, Alexa. I’m just doubling back to this. Did you receive the answers to the advanced cube conversations, or possibly download them from the site now that they are posted?

I have Math right after recess in the afternoon. When my 2nd graders come in the room and one of your slides is up, word spreads like wildfire and they excitedly grab whiteboards and come to the carpet. We all LOVE how you stretch our thinking and give us such great discussions! Thank you for making all of these resources available!

I’m so happy to hear this, Sharon! Have a wonderful week!

Congratulations for your wonderful material. I have a problem since in my school they don´t have PowerPoint as our computers are linux based. When I import them to google presentations they don´t work, any advise?

Thanks

Hi, Jose! When in your google drive, open the file with google slides, and then be sure to click present. I hope that will take care of it for you.

Steve! I absolutely love all the resources you have created and are sharing! My students love your activities and are so engaged when I use them! You have greatly enhanced my Math programming. Thank you so very much! I am a teacher from British Columbia, Canada and I love your Esti-Mysteries in particular. Your new series now includes the measurement estimations which are, of course, in inches. Are you planning to release a version for us Canadian followers with metric measures? I have been able to go in and change some of the units myself, but the mysteries with clues are not so easy to change. I would be a follower for life is this is something you would consider doing!!! (Actually, I will stay a follower even if you don’t!) Thanks again for sharing your rich programming!

Hi, Madelaine. So far, Days 2 and 5 of 20 Days of Number Sense are based on metric units. I’ll try to keep adding more as I go forward. I certainly appreciate your kinds words! Thank you for the comment.

Steve,

Thank you so much for posting this. Our school site is working on collaborative math lessons and these will be perfect to share!

Brenda, I’m glad that these will help in the collaboration process. Thank you for taking time to leave this comment!

Hi Steve,

I love the new material. I have been using the Esti-Mysteries in many classes K-3 in the Huntington School District in New York. The students love them! Some of our students have created some Esti-Mysteries. They are currently in the “publishing” stage. I am hopeful that they will be completed soon. We are creating some in spanish too. Our dual language 3rd graders are working on creating them. The students have been so enthusiastic and have really enjoyed creating clues!

Christine Lofaro

Math Coach K-3 HUFSD

Christine, I am so excited to hear about all of this. When students create their own Esti-Mysteries they learn so much throughout the process. It gives them a chance to find and think through so many key decision points all wrapped up in rich math concepts that they can select. I’d love to see some of the final products.

Wow, these are fabulous! My pupils always want to count the objects as they like to get it correct, they just won’t estimate but these real object pictures are great. Like you said many won’t join in the discussion for fear of being wrong but your slides seem to engage them all. Thank you!

Lynn, thank you for the kinds words here. I’m glad the slides are engaging them in the math thinking. I hope you have a wonderful journey in 20 Days of Number Sense!

Wow. The estimate clipboard is amazing! The kids were cheering when they got close to the correct reveal answer! Great resource!

Kelly, thank you for sharing this with me. The moment of the reveal is so filled with enthusiasm. I also notice that moment right before the reveal when the room goes quiet in anticipation of the reveal. I’m glad to hear about your experience with The Estimation Clipboard.

Am I doing something wrong? When I try to download the Day 1 – The Estimation Clipboard, I am being directed to install several different pdf converters. I have Adobe Reader.

Hi Diane,

Download Questions – The blue blink on the main blog page leads to a download page where there is another link. This second link is the one that downloads the materials.

The blue link on the download page simply says…

D01 20 Days

When you click that link, it will download the materials.

Let me know if that takes care of the question.

Steve, another home run! It’s winter break for me and my Brooklyn, NY 6th graders. We have hit a soft spot in our classes, trying to get engagement on the rise, and increase a level of numeracy.

This looks like it will do it.

A personal comment: I tend to not be too close on my first guess, but then I try to calibrate and re-adjust my guesses on the 2nd, 3rd and 4th photos, and I’m often satisfyingly close. If others (my students included) experience this way-off-the-mark first guess too, they can feel better by their next guesses.

Looking forward to trying this in class!

Frank, I have had many similar experiences with my first estimate. I noticed with my own estimates, and then with the estimates of others that the first estimate someone makes is often about 2/3 of the actual total. Ever since I first noticed that, I’ve observed it again and again. I’m learning a lot from this process. Thank you for the comment!

My favourite blog just keeps getting better! Thank you Stevie Wy!

My pleasure, Donna!