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In this episode, we explore how the ability to instantly recognize quantities without counting supports deep mathematical understanding. This foundation matters not just in the moment, but across a child’s development. From early number sense to part-whole relationships and fluency with operations, subitizing lays critical groundwork.
We take a closer look at how these ideas unfold over time, how to support them intentionally, and how to spot what your students’ strategies reveal about their understanding and fluency development.
Understanding Subitizing and Its Role in Early Math Development
Hello, Meaning-Makers! I’m so happy you’re here for part one of this two-part series about subitizing. Subitizing is an important skill that helps lay the foundation of understanding wholes and parts, which evolves into addition, subtraction, and later multiplication and division. So today, we’re going to talk about the two types of subitizing, dig into ways we can encourage subitizing, and a great natural progression of skills to follow with your students. Sound good? Okay, let’s go!
What Is Subitizing and Why Does It Matter?
Now, before we just jump right in, let’s make sure we have some of the basics down, like what exactly is subitizing? Subitizing is when we instantly recognize the number of objects without actually counting them. So if I roll two dice, I might instantly recognize that one dice reads three and the other reads five without having to count the individual dots.
Want to hear something that shocked me? Research has shown that even infants can differentiate between quantities without any formal understanding of numbers. Now, I know we are not working with infants, but it’s important for us to know that these skills are beginning to develop even in very, very young children.
Our role as teachers is to support the development of those skills because we know that children who can subitize have a stronger math foundation. They are better able to identify amounts of objects in collections. They’re also better able to represent numbers and later add and subtract numbers.
Subitizing plays a huge role in students’ math growth so much so that many state standards, including New Jersey, Maryland, and Illinois, even include subitizing in their pre-k standards!
The Two Stages of Subitizing: Perceptual and Conceptual
What Is Perceptual Subitizing?
There are two different stages of subitizing. The first is perceptual subitizing. Perceptual subitizing is the ability to just know how many objects without needing to count. Most people can subitize this way with up to five objects.
For example, when most of us see the four dots on a typical die, we automatically recognize it as four. No counting was needed. This is because of our ability to subitize. However, it’s very important that we give children exposure to multiple configurations.
Many children may be able to instantly identify common dot arrangements, like those found on dice and dominoes. However, those same children may struggle to identify other arrangements with automaticity. This means that while they can recognize common configurations and recall their value, they have not yet mastered the ability to subitize that number. This is a BIG difference!
We want children to be able to recognize four in multiple configurations. Think about the game Tetris. Consider all of the different arrangements of those four blocks. We want students to be able to see any of those configurations AND MORE and be able to simply know that it’s four without counting.
Children need to be able to subitize numbers through 5 in order to see the parts that make up larger numbers. So how do we do this? Utilizing Number Talks is a great way to support students in developing perceptual subitizing skills. Allowing them to explore different dot arrangements while participating in discussions with their peers provides so much room for growth and meaning-making.
What Is Conceptual Subitizing?
So what happens when children start to approach quantities beyond five? I want you to picture this dot image, are you ready? Imagine 3 dots stacked vertically. Then, to the right, there are four more dots configured in a square, like on a die. Do you have that visual in your mind? Okay, let’s consider how some children might approach this representation:
Some children will see this representation as seven individual dots. These children see the dots in isolation and are not yet ready to start considering parts and wholes. They first need experiences that will help them identify small quantities with automaticity before being expected to find those same small numbers within a larger group.
There will also be children who see groups of two’s and one’s. These children are making progress, but counting by twos is more of a counting strategy. We want to see children counting by groups greater than two to ensure that they are moving on from counting to seeing parts of numbers.
Before, I mentioned two types of subitizing. We’ve discussed perceptual subitizing, where we just know how many objects without needing to count, and we can perceptually subitize through the number 5. The second type of subitizing is conceptual subitizing, which involves seeing an amount in parts and then adding them.
A child who can perceptually subitize is ready to begin conceptually subitizing. If we go back to the configuration of seven dots, do you have it ready in your mind? A child who is ready to see parts of numbers may recognize a group of three and a group of four. Another might see a group of five and a group of two.
From Counting All to More Efficient Strategies
Now, many students who are ready for conceptual subitizing will still be working within the “counting all” stage. As the name states, this is where students literally count every number to find the answer. They are unable to count on from either part because they can’t hold a number in their mind and count on from it. So the student might have seen a group of three and a group of four, but they could not hold onto the three and count 4, 5, 6, 7. Despite knowing the parts, they still needed to count one at a time to arrive at 7.
This strategy represents an entire phase of fluency development. And it’s important to honor where our students are, by accepting the strategies they use. So if right now they are “counting all”, that’s great! Let’s recognize this strategy and how it allowed students to find a way to solve the problem and arrive at an answer. Simultaneously, we need to foster a desire for those students to find a more fitting, efficient way to discover “how many” so that the need for a better strategy comes from them, not you.
The Seven Stages of Subitizing Development
Why Knowing the Subitizing Progression Helps Teachers
Before I share a few engaging ways to build subitizing skills, I want to talk about how these skills develop. You know we love digging into the progression of skills, (hence why we have an entire video of more than 60 videos breaking down conceptual development), so I’m going to briefly share the seven stages that students go through when learning to subitize.
This is important for teachers to know because students NEED to be able to find success with each stage before progressing to the next. When we have students working at stage five at a math center and they haven’t mastered stages 1-4, it’s hard for them to feel successful. But if we know the stages, we can be a better guide for our students and create engaging experiences that meet them where they are.
Perceptual Subitizing Stages
The first four stages all focus on perceptual subitizing, and progress as follows:
First, students will begin to subitize amounts within three using common configurations. This can include dice arrangements, dominoes, or common finger patterns, like holding up your index, middle, and ring finger to show three.
Second, students will begin to subitize quantities within three with less familiar configurations. Perhaps holding up your thumb, index and pinky finger, or having three dots in a triangle pattern. This stage helps move students from simple recognition of arrangements to actually subitizing.
The third and fourth stages mirror the first and second, but now we’re working with quantities through five. So the third stage is recognizing common configurations through five, like having all five fingers raised, or recognizing four dots in a square formation.
The fourth stage is recognizing amounts through five using uncommon configurations and patterns, so think back to Tetris and the many ways to represent four. We want our students to be able to identify any representation of quantities through five.
Conceptual Subitizing Stages
The fifth, sixth and seventh stages all focus on conceptual subitizing. The fifth stage is still working with quantities through five, but when those quantities are clearly decomposed into two separate groups. For example, when we show two dice, one with two dots and one with three dots. Here, students will subitize these amounts separately and then compose them into a single amount.
The sixth stage is similar to the fifth, but now we are working with quantities through ten that have been decomposed into two or three parts. This could mean two dice showing six and four, or three dice showing four, four and two. In either case, if students can quickly recognize that amount as ten, they are able to conceptually subitize!
The seventh goes back to our understanding of unitizing. This final stage asks students to subitize unitized groups, such as place value blocks or objects sorted into equal groups. For example, a student can instantly recognize 6 rods, AND understand that while it is six, it is also six groups of ten, so the value is actually 60.
Classroom Strategies for Building Subitizing Skills
Using Number Talks to Reinforce Subitizing
Do you see how each stage slowly builds on the success of the previous stages? How does this look in the classroom? How can we actively encourage subitizing skills with our students?
Earlier, I discussed the use of Number Talks! Offering Number Talks that slowly follow the progression of these skills is a great way for students to learn from one another, latch onto strategies, and gain exposure to configurations outside of typical dice, domino, and ten-frame patterns.
Engaging Math Centers and Games for Subitizing Practice
I also love using dot cards instead of standard playing cards. If your students work at centers and play games with cards, consider using dot representations instead (either in typical or atypical patterns depending on where students are in their understanding).
There are engaging partner games that can practice these skills too. A student favorite is a game called SWAT. The way you play: Put dot cards out on a table or up on a whiteboard. Give the student a fly swatter and then you or their partner call out a number on the board. Students then have to quickly swat the image that matches the number you called out. You can play this game competitively or not, and I usually let students decide – it’s super fun either way!
I hope this episode helped you build a better understanding of subitizing and how it develops, and offered some actionable ways you can support it in the classroom. In our next episode, we’ll be discussing how we can use subitizing to support multiplication fluency in second and third grade, so stay tuned! Make sure you’ve subscribed to this podcast so you don’t miss it! And if you have a moment, would you be willing to leave a review so we can support even more teachers like you?
Thank you, Until next time, Meaning-Makers, have a great one!
