Have you ever wondered how to use subitizing in your classroom? Subitizing is the ability to instantly recognize ‘how many’. Helping our students develop subitizing isn’t just for Pre-K to second grade. Even third through fifth grade kiddos need to develop subitizing. Stay tuned as we delve into how to use subitizing.
We are going to start off with Pre-K to 2nd grade, and then we’re going to talk about how to do subitizing in 3rd through 5th grade. There’s also a download that you can request underneath this video that summarizes the top five ways for Pre-K to 2nd grade, and the top ways to use subitizing in 3rd through 5th grade, that you could jump right into.
Watch the video or read the summary below. **Skip ahead to 15:25 in the video, if you want to just watch the information for 3rd-5th Grade.**
How to Use Subitizing in Pre-K Through 2nd Grade
#1 Quick Images
Example A
The first thing that you should be doing is quick images, or what I like to call, ‘Flash It’. Basically, you just show a quantity for a limited amount of time. So something like this, then you have it disappear.
The amount of time you keep it up is dependent upon how much experience your students have had. For Pre-K kids, I wouldn’t have it disappear in two seconds. In fact I probably wouldn’t even show this image to Pre-K kids because they should be focusing on numbers and quantities of 0-5. So, it depends on the grade level of your students and their experience with subitizing.
If you’re a second grade teacher and your students have not had much experience with subitizing, then this is a great place to start. But you’ll have to leave this image up longer because students have not built the structure. If they’ve never used Ten Frames before, you can’t expect them to instantly know how much is here. So, instead, you might start with familiar patterns like dice patterns (See example B).
Example B
Students who have experience with dice will be able to subitize this quicker than other kids. When you’re first starting out with dice frames, there will be amounts that some of your kids will instantly know. Typically, it’s 1, 2, and 3. The research from Clements and Sarama says above that, kids will start to develop natural patterns like dice patterns and things that they see. As they go into amounts past 5, they’re doing what’s known as conceptual subitizing. Thats where they are combining small amounts to make the bigger amounts. Even as adults, we can’t subitize 8. Instead, we might see 4 and 4.
So you want to start with small amounts and then gradually work your way up to larger amounts. One of the ways to do that is by doing quick images.
#2: Number Talks or Number Strings.
Example C
Let’s take a look at a Number String that you could do with small amounts. You might start off showing an image like this and just kids how many are there.
The hope is that kids would subitize that amount but, depending on the level of your kids, you may have some who are counting. However, you are crafting these Number Strings using images that are subitizable. They are able to subitize in order to tell how many are there.
Then I might move into one like example D and again ask how many is in the image. I wouldn’t ask how many there are now because some kids might say 7.
Example D
One of cool parts of being able to subitize and doing them in a string is being able to pay attention to the relationships.
Once kids are not just paying attention to counting, and they’re able to know ‘that’s 4 and that’s 3’, then we can start having discussions about what do when you notice that changed. This brings in ideas of 1 and 2 more and 1 and 2 less. There is all kinds of relationship building that you can do once kids can subitize and they’re not spending their time counting. We want to be able to focus on what has changed and the relationships that kids can build. So again, I might show an image like example E, and then right after it show an image like example F. Then I could be able to talk about how many there each time. But also, be able to talk about what has changed, what do you notice, and what kind of relationship do these two images have.
Example E
Example F
If you want to do a Number Talk, they are typically around one problem or one image. Then you have the kids talk about all the different ways that they solved that problem. Or, in this case, when it’s an image, how do you know how many are there? How did you figure it out? You’re asking the kids to talk about the various ways that they figured it out.
Example G
Now, here’s my warning.
Example G is really wonderful for subitizing. However, it’s not very good for doing a Number Talk with. Most kids either just know it. They are just able to subitize that and know its a 6. Or you might get kids who will say, “Well, it’s 5 and 1 more.” You might get kids who talk about, “Well, it’s four less than 10.”
With this image, that’s usually not the number one way that kids will see this. You’ll typically get kids who will say, “Five and 1 more.” Then you’ll ask, “Okay, how else did you see it?” and that’s when you’ll get the really off the wall responses from kids. Thats because you’re asking them how else, and theres no other way that they saw it. So they’ll come up with something that really has no relationship to what’s actually in that image.
If you want to do a Number Talk, you probably need to do one that’s not subitizable. So the same amount like in example H. But it’s not instantaneous. Not even for adults.
Example H
If I hadn’t told you that was the same amount and I had just started with that, you would have figured out how many were in that Ten Frame differently than how I did.
Doing a Number Talk needs to have visual images that allow different ways to see it. When we’re focused on subitizing, we usually just see it and we know. Doing Number Strings, you can use subitizable images to help look at relationships. But when you’re doing a Number Talk, you’re not going to have the whole image be subitizable. There are parts of this image that are subitizable. A lot of kids might see 3 somewhere in this image (I’m not pointing it out because how you saw 3 may be different than how I saw 3). It allows for kids to be able to make their own grouping systems, and that is a big idea.
Oftentimes, in our real life, things are not given to us in a nice Ten Frame with the top filled first and then the bottom row. We have to find ways to group it ourselves. So helping kids to find groupable amounts or subitizable amounts is really helpful when you’re doing Number Talks.
#3: Do Kinesthetic & Auditory Subitizing
You need to remove the visuals from subitizing activities. I know that’s kind of counterintuitive because subitizing seems to be all about visuals and helping kids see quantities, which is a big deal. But we don’t want kids to always have to rely on visuals.
There are lots of things in our life where we aren’t subitizing a visual amount but, instead subitizing something kinesthetic. Like movements or something auditory. You might do activities like, “When I clap three times, I want you to line up for PE.” So you might clap once; then four times; then you might clap twice; and then you might clap three times. They have to be able to hear that audio, and they’re subitizing that. The same is true when kids are doing syllables. When we’re asking kids how many syllables are in something, we are basically asking them to hold that amount in their head. If I have to figure out how many syllables are in my name, Chris-tin-a, maybe I can break that into syllables. However, if they’re not able to subitize, they won’t be able to tell you how many syllables there were.
Think about the auditory pieces in our lives that really require kids to subitize and provide opportunities for kids to do those in your classroom.
#4: Show Non-Examples
Oftentimes when it comes to subitizing, we will just show an amount, and ask how many. With the clapping that I just did, I was combining this idea of using auditory but also doing non-examples. The example I gave was that they could go line up for PE if I clapped three times, but I didn’t clap three times to begin with. I was doing non-examples so that they would have to really pay attention and see the amount or in that case hear it.
Example I
You could do the same thing with flashcards or if you make dot pattern plates. A lot of people do paper plates and then use the little yard sale stickers. You might have plates like example I. You’ve got amounts on there, and you’ll say, “When I show 5,” and show 5 dots on a dotted plate, “you can go line up for PE.” So you might get your dot plates out, and you’re flipping through them, and when you land on the one that’s 5, the kids can go line up.
It’s a quick way for them to get lots of practice. Even though I wasn’t asking how many here or how many here, they were thinking about, “Is that 5?” They’re starting to subitize and say, “No, that’s not 5, that’s 8.” “Nope, that wasn’t 5, that was 4.” They’re doing it themselves without you having to ask every single time. It’s a quick way to get through a lot of subitizing images.
#5: Repeated Exposure to the Structures
The structure that we put in place is leading to helping kids with predictability. But sometimes that’s tough for a group of our kids. Now, there’s no research to back me up on this, just my personal experiences. Kids who have unpredictable lives tend to struggle more with subitizing. We are using a built-in structure that seems obvious to us, and we can rely on that structure to help us out. But for a some of our kids, they are not used to relying on predictability. We’re asking them to trust every time the Ten Frame is presented, and the top row is filled in, it’s 5. If they don’t trust it, they’re going to count every single time.
Every time you hold up a full hand of fingers, you probably have kiddos in your classroom who still count every finger because they have not built the trust. They don’t think it’s predictable. If they don’t have predictable home lives, why would it be predictable? How can they rely on the fact, and trust that every time it’s going to be 5? The answer is continued repeated exposure. Help them use that structure all the time. You’re going to have kids who, after just one or two times of seeing images like this, trust that that top is always going to be 5. You’re also going to have kids where it might take a hundred times counting that top row to get to where they trust it.
I just want to be open about the fact that for some kids, subitizing comes more readily, and other kids need extended exposure to trust the structure that we are putting in front of them. It doesn’t come naturally for them. Prepare to keep that in mind as you work to build subitizing for your Pre-K to second grade kiddos
How to Use Subitizing in 3rd Through 5th Grade
#1 Quick Images
Example J
How do we use subitizing in third through fifth grade? I’m going to start off again with quick images or flashing amounts. It’s with whatever number sizes you are working with. So you are probably familiar with images like example J.
We want kids to get those small amounts and be able to quickly tell you how many. Instead of just showing it, we’re doing quick ones where I’m just going and flashing it for a second. As you move into third through fifth grade you should be able to do it a whole lot faster with small amounts. But again, that’s only if they’ve had experience with subitizing before. If they haven’t, you’re going to have to leave it up there until they can trust and they’re able to subitize those amounts. Eespecially large amounts.
As we transition into multiplication, we’re going to use those small amounts to then have groups of those amounts (See Example K). Again, I would leave that up, longer or shorter, depending upon the experience the kids have
Example K
For adults, we could probably do that a whole lot quicker. The idea is you want to take it away sooner than they have the time to count. You want them to try to picture what they just saw and hold the amount in their head. Remember, that only works if they’ve had experience with those small amounts. So this is only a comfortable situation for kids if they’ve had experience with subitizing 5 in that dot pattern format. But also 4, because they have to be able to know that there are 4 groups, but there are 5 in each one of those groups. Then be able to move from there.
Example L
Then even with multi-digit amounts like in example L, we are using base 10 blocks often. We want kids to be able to trust that that stick of the base 10 block will always be 10. Once they get comfortable with that, then we can start doing quick images and don’t have to leave that up there as long as before. Even with fractions, I want kids to be able to instantly recognize how many were just shown there. I want them to be able to instantly tell me that is 1/3. With fractions, the visuals really do help to build their understanding of what a fraction is. It really builds some deep understanding around fractions that kids don’t often get.
#2: Using Subitizing to Develop Addition Strategies
In early grades, we’re using Ten Frames. But Ten Frames can also be really helpful as we start moving into multi-digit amounts. Now, you would want to do activities where they can tell how many this is fairly quickly. You can be doing the quick images like we did before, but I just wanted to show you how example N can then move into helping kids with addition and multi-digit amounts.
Example M
Example N
So here we’re adding 37 + 46.
Now if I just had the digits on an piece of paper, nothing there pulling me towards a certain strategy. But when kids have a visual picture of 37 and 46, they will start to develop strategies on their own. You will get kids who say, “Well, I’m going to put all the 10s together “because I have three 10s and four 10s; that makes seven 10s, that’s 70.” They will do that because the visual is helping them see that. You might get some kids who leave the 37 all as 37 and say, “Man, if I just had three more, I could fill that in and there would be 40.” So they will visually move three of the dots from the 46 over to the 37. Now they have 40 and 43.
Those are strategies that we want kids to develop, and oftentimes, our textbooks try to directly teach these strategies, but the kids don’t have a visual picture to tie it to. Subitizing gives kids those visuals, and once they have them, they start to develop strategies on their own without us having to directly teach them.
#3: Subitizing with Multiplication
As we move into multiplication, the foundational way that we build kids’ understanding of multiplication is this idea of ‘groups of’. It’s not just 5 x 4. It’s 5 groups of 4, and we want kids to have a visual to go with multiplication. However, as they start getting into larger amounts, it becomes hard to hold those amounts in your mind. If I asked you to visualize seven groups of 3 (Example O), you could probably visualize the 3 in each group. But it’s hard, even as adults, to visualize seven groups. So creating visuals that tie with images and structures that they’ve used in the early grades is super important.
Example O
The Ten Frame is a really powerful structure that can help us as we move into multiplication. Being able to put those 3 into a Ten Frame helps kids see seven groups of 3. It also comes with a strategy for figuring that out. Oftentimes when we’re multiplying with 7 it’s helpful to think about it as five groups and two groups. Thats because kids will get quick with their 5s and their 2s, and they can put five groups of 3 and two groups of 3 together to help make seven groups of 3. This is the precursor to distributive property. Having those visuals and being able to subitize 7 x 3 is going to pay off and help kids have a visual when it comes to understanding distributive property.
#4: Subitizing with Fractions
Now, as we move into developing our students’ understanding of fractions, oftentimes there’s not enough time spent in developing understanding, and we move straight into operating. So doing subitizing activities with fractions is really helpful for laying a foundational understanding of fraction sense.
Example P
One of the big things that we need kids to understand when they first start developing an understanding of fractions is that fractional amounts are based in the unit fraction (see above). What that means, is that this is 3/4, but 3/4 is really (3) 1/4 pieces. It is 1/4 + 1/4 + 1/4. Just like when I have a whole amount of 3, it’s 1 + 1 + 1. We want kids to understand fractional amounts as the repetition of the unit fraction. So 3/4 is (3)1/4 pieces. Giving them subitizable amounts can help build that understanding. Showing how 1/4 relates to 2/4 which relates to 3/4 which relates to 4/4, and even into 5/4. What would 5/4 look like? That’s a big deal as they’re starting to develop their fraction sense.
Example Q
One of the ways that textbooks, in particular, have shown visuals of fractions is by using what’s known as the set amount (Example Q). So those individual circles there at the top are showing 3/4. However, that visual build this idea of ‘out of’.
I would say it as ‘out of’, that you have three out of the 4 colored, so you have 3/4. But that image for fractions can lead to some really big misunderstandings later.
Now, when you’re looking at it here, it’s like, who cares? They see 3, 4, it’s 3/4. Let’s say I wanted kids to think about, is 1/2 or 1/3 bigger? Is it, greater than, less than, or equal to, those kinds of activities. Well, if these are the images that they have of 1/3 and 1/2, so many of our kids will say that they’re equal because you get the same amount. The same amount is colored there. You might also get kids who say 1/3 is bigger because there are more pieces there.
Those images portray some misunderstandings that we have to go back and correct versus if we just had it as part of a set or part of a whole instead of part of a set. You can see it’s still 1/3 and 1/2, but now we’re actually working out of the same whole. That is something kids don’t get when we have it as an out of view when it’s part of a set. So using visuals for fractions where it is a whole that’s chopped up and not a set that is colored in, is very beneficial and builds more of a solid foundation for our students when they go to compare amounts and move onto other functions.
Fractions are based on the unit being repeated over and over again. When you have part of a whole, it’s easier to build that understanding for kids. So when you’re doing subitizing activities for fractions, the big thing I want to encourage you to do is have images like example Q, not the left-hand side of example R. Do images that are part of a whole, not part of a set.
Example R
#5: Repeated Exposure to the Structures
For third through fifth grade, the last thing I want to talk about is the same thing I talked about for Pre-K to second. Kids need to be able to trust the structure of the images that we’re using because it leads to being able to predict ideas around those visuals. If they don’t trust the structure, they will never build that trust. Mathematics is all based on patterns and predictability. In example S, If I want kids to figure out how many are there, there is nothing structured here to help me out. So I’m back counting one by one by one.
Example S
As soon as I put it into this structure (Example T), we tend to think that all kids will use that structure. But they don’t. They have to have built the trust in that structure. If our kids have not had repeated exposure to this structure, they will not trust it. They will be back counting to be able to figure out how many.
Example T
As I talked about before, some of our kids have very unpredictable lives. So, in mathematics, when we’re asking them to look at patterns, and use them, they don’t trust those patterns because they don’t have trust built in other areas of their lives. For some of our kids, it’s going to take a whole lot more time and repeated exposure before they will ever be able to use them. For some of our kids, you do it once or twice, and they’re going to take right off and be just fine. Don’t get frustrated if some of your kids don’t use the subitizable amounts that are in these images. They need to be able to do it over and over again before they will trust it.
All right! That was how to use subitizing in each of the grade bands. Now, again, if you want the summary, just download it right below this video. There’s links for a summary of the top five ways to use subitizing for Pre-K to second, and the top five ways to use subitizing for third through fifth grade. I hope that this has helped you build your math mind, so you can go build the math minds of your students.