Number Sense Routines have become my passion. Over the past couple of years, I’ve been exposed to more and more websites with so many free resources. Now, I am obsessed! There is so much variety. I love how these routines and puzzles teach students so many skills. Most of these could be used in an online environment, so no matter how you’re teaching this year, these will work for you! I used all but a couple of these with my sixth graders; most of them will work for a wide range of grade levels from Kindergarten shapes and weight cards from Clothesline Math to percent comparisons for credit cards from Would You Rather Math.
Before I list all of these amazing resources, I want to share one thing I’ve done in person (that I think could be adapted online). I set up stations one day when I had a sub where I taped up different number sense routines all around the classroom. Students then filled out this sheet as they walked around to the labeled activities and justified their thinking. This might give you an idea of what I expected out loud in class. Since students had exposure to all of these routines, it was easy for them to do independently and they freely talked and shared ideas afterwards.
From Steve Wyborney. The concept of Splat is that you’re subtracting the little dots from the total listed in the upper right. So for this image, you can see the total is 19. There are 7 blue dots visible. The number of dots hidden by the “splats” – the black blobs – is 12. This often involves subitizing, being able to visually count as opposed to counting one by one. He has simpler ones as well as ones with fractions! Here are his Powerpoint templates and Google Slides templates.
Have you ever made a guess for one of those puzzles at the fair that asks, “How many m&m’s are in the jar?” My dad is crazy amazing at these. These pictures from Steve Wyborney are like those games. You’re given an image, and students make an initial estimate. Then, you slowly give them more clues so that they can adjust their estimate. The clues often involve more math vocabulary, and there are even fun tricks (for instance, in this one, the dice is a relevant clue). So many people loved these that Steve actually made more after his initial round. You can find them here and here.
If you like Esti-Mysteries, you might also like Estimation Clipboard by Steve here. It consists of having 4 similar images so that students need to compare between the images. His blog is amazing. Other fun resources are Cubed Conversations and Tiled Area Questions. If you haven’t looked at his resources yet, you should.
3. Would You Rather Math
I am pretty sure almost everyone has answered a Would You Rather question at this point. What’s great about WYR questions is that there is not a “right” answer. If you’re passionate about your choice, you might think others are wrong, but there is reasoning for choosing either option. The same is true for these math related questions. The site Would You Rather Math is amazing because it has such a variety of difficulty. It compares credit cards or paths you should take when driving, but it also compares how many grapes are in a bowl cut in half vs. whole or how many pencils you’d prefer to have of different lengths. The reasoning behind a choice can be varied, so it’s quite low floor, high ceiling – my favorite kind of task! When I use this in class, I have students write “I choose (A/B) because ____.” Then, they can share aloud their reasoning. I find this helps all students, especially ELLs.
4. Clothesline Math
There are a few sources of these; I particularly like Daniel Kaufmann and Kristen Acosta. The idea of clothesline math is that you are ordering numbers from least to greatest or objects from lightest to heaviest. The descriptors are not all equally spaced as “normal” number line would be. There also are often numbers that are equal but represented in different ways. I love that there are situations, images, and more on the cards so that students have the real world connection. The fraction set from Kristen Acosta includes fraction bars, fraction circles, and numerical fractions; the integer set has elevation, checks where you’re paying money, bills, etc. In addition, you can also make your own pretty easily. While the ones provided are intended to be printed, cut up, and hung on a clothesline in the classroom, this could be done digitally through Jamboard, Google Slides (see Theresa Wills Continuum slide under Math Routines for some templates for this or you can have different images on different slides and literally move the whole slide around), Kahoot premium (you can order items), etc. This would be a great activity in small groups where they can discuss more.
5. Number Lines
Similarly to the idea of comparing and ordering with the clotheslines, you might also enjoy thinking about organic number lines and open number lines. Organic Number Lines can be built upon as a class which could make for a great display. Another really fun question I love to ask students is, “How many ways can you show the number ___?” I’ll give them 5-10 minutes to come up with as many ideas as they can with their group. I often do this on paper, but it could just as easily be done on a digital whiteboard, Jamboard, or Google Slide.
Open Number Lines are also fantastic for number sense discussions. For example, looking at the first line, A student might say A = – 3 only because it is 3 spaces from 0 in the negative direction. If they look closely, though, they can tell that each marker is counting by 2s. For the third line, C could be a variety of numbers. It would not be -12 or less nor would it be a positive number, but there are a few numbers that would be reasonable. I created and used these number lines as an assessment tool, so I wanted to be able to “grade” an answer, but you could also have number lines that are completely open on one end or the other which allows for some open-minded thinking.
6. Algebra Picture Puzzles
You might have seen one of those tricky puzzle questions on social media that’s intended to trip you up. These puzzles are like that, but with less sneakiness and more logic. They are a great introduction to equations. The idea of a variable staying constant within one equation is a useful concept to build. These often are naturally engaging and entertaining. I’ve seen some pretty math-resistant kids do these for homework and proudly show it off the next day. Mash Up Math has a million of these images on the website and on Pinterest. I also have curated those free images into Google Slides, so if you’d like that, contact me.
7. Array Chat
This was new to me this year! Arrays are a visual for multiplication. It’s a way of seeing patterns. Many of the array chat images I’ve seen also include some subitizing where you are figuring out how many are left based off of the fact you “see” 3 missing and don’t have to count those 3 spots. Those array chats also can then include 2 operations – multiplying then subtracting. For example, a cupcake tin of 3×4 is 12. If 2 are missing, there are 10 cupcakes. This could lead to a great discussion about order of operations. It would not make sense to subtract the 2 from 4 then multiply 2×3 to get 6. There are 10! Here is a Google slides presentation of images I’ve collected from Twitter and social media. I apologize I do not attribute tags to these; I’d like to go back and change that. The image above is from me @aestohs.
8. Which One Doesn’t Belong?
This might be one of the more popular number sense routines out there now, and I’m so glad! The idea of WODB is that you’re looking for connections and exceptions between numbers and/or mathematical items or images. In the example above center, 16 is the only even number. 9 is the only number whose digits to not add up to 7 (1+6=7 and 2+5=7 and 4+3=7). 43 is the only one where the tens place is larger than the digit in the ones place. 43 is also the only one that is not a square number (3×3=9, 4×4=16, 5×5=25). There are so many examples on this site. I use one with clocks in this video at minute 30:00.
Same But Different
This is similar to Which One Doesn’t belong but it focuses on a comparison of only two things. There’s a curated list of resources on this website.
9. Estimation 180
The website Estimation 180 has so many different images that can be used to build estimation skills. Measurement and volume are often ambiguous to students, and this resource is so supportive of translating it to the real world. Some of the answers even have videos! I love the idea of pausing the answer video halfway and having students revise an estimate. I do that for Day 207 (pictured above) in this video at minute 40:00.
10. 101 Questions
This website is really interesting. There are tons of images, and the goal is to ask math questions. This encourages divergent thinking and could be a great introduction into a math task. You can search by topic or grade level, so you can get lots of ideas. One of my favorites is a short video of Girl Scout Cookies filling in a trunk. This particular image has more guidance than many of them. There are so many different images and directions you can go. It’s incredibly open ended.
11. Dot Images
I’ve mentioned subitizing a few times in this post already. The idea of subitizing is that you can count visually. Looking at the dot images on the right, I do not have to count one-by-one. I might say that I see 3 in the upper left and 3 in the bottom right so 3+3=6. I might also say I see 2 in the upper left, 2 connecting in the middle going in a diagonal line, and then 2 on the other side so 2+2+2=6. Strong visuals of grouping numbers is important to number sense; it helps us visualize numeric problems without as much work. It also helps us as we navigate the world. You can read about subitizing here. There are Subitizing and Challenge Problems on Steve Wyborney’s blog here. Dot Image resouces can also be found here and here.
Like I said, these resources will be valuable no matter how you are teaching. They are easily used whole group or small group or even 1-1. They foster mathematical discussions. On top of all that, most of these are just fun! I hope you enjoy using them as much as I have!
Bonus!! 3 More for Independent/Small Group Work
Number Mobiles/Solve Me
The website, Solve Me, has these mobile puzzles. The number at the top in the cirlce is the total, and then sometimes you’re given the value of a shape. I love this for thinking about equations, dividing numbers equally, etc. I played this by myself and legitimately had fun.
Maze Hundreds Chart
Yes, it’s another Steve Wyborney resource. I think this would be fun to put on Pear Deck for kids to insert numbers or to set up as independent work. This helps students see patterns in hundreds chart. If you are a primary teacher, you know what a great skill this is!
Greg Tang Math
There are a ton of games on this website. I did not know about so many of them. This one, Expresso, in particular utilizes order of operations practice. While many of these would make for great whole class discussion, this one might make for better independent practice or small group work.