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
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Quick Access to Days 6-10
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Quick Access to Days 11-15
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Quick Access to Days 16-20
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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
Description of 20 Days of Number Sense & Rich Math Talk (K-12)
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.
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.
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.
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?”
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,