- Episode Highlights
- Transcript
Traditional approaches to math fact fluency often emphasize speed and memorization, but there are more meaningful ways to support student learning. This episode explores how subitizing, a visual strategy commonly used in the early grades, can be extended to build multiplication fluency through pattern recognition and numerical reasoning.
Learn how intentional visual routines can strengthen number sense and help students internalize multiplication facts through understanding, not rote recall. This discussion offers practical insights for teachers looking to make fluency work more engaging and effective across the elementary grades.
Building Multiplication Fact Fluency with Subitizing
Hello, Meaning-Makers! Welcome back for part two of our mini-series on subitizing! I’m so happy you’re here.
One of the most common questions we get asked by teachers is, “How can I best support my students with math fact fluency?”
In a perfect world, all of our students would come to us at the beginning of the school year having mastered the fluency standards from the previous year. But, unfortunately, it’s not a perfect world, so as teachers, we’re always looking for ways to help our students build fact fluency.
But problems can arise when we turn to “fast fact” programs that rely more on memorization and quickness than making meaning or noticing number relationships.
Today, we’re going to explore a strategy that not only supports multiplication fluency, but is also a lot of fun for our students.
What Is Subitizing?
Before I get into specifics, I want to share a funny story that happened not too long ago…
A friend of mine was driving her daughter home from school and asked about her day. Her daughter responded, “I learned how to subitize today!” My friend replied, “Oh! You mean you learned how to summarize?” Her daughter insisted, “No! I learned to subitize!”
After going back and forth a little bit, she decided to call me, her teacher friend, to find out what in the world her kid was even talking about. I explained to my friend that yes, subitizing is an actual thing, and that I was actually quite happy to hear that subitizing was being implemented in her daughter’s classroom.
Like many of us, my friend was unfamiliar with the concept and was certainly tickled by the fact that her six year old already knew something she didn’t.
Even though the term, “subitizing” was coined in 1949, it has just recently started to make its way into the elementary math classroom. Subitizing simply refers to the ability to quickly perceive a quantity without counting.
Research has shown that infants, and even non-human animals like crows, have the ability to subitize!
Tips for Leading Subitizing Activities
Although subitizing is usually thought to be implemented in the primary grades, it can certainly be used to support number sense and fluency in the upper-elementary grades as well. And conceptual subitizing just so happens to be one of my favorite strategies to build multiplication fluency.
The important thing to understand about subitizing is that the images must be shown only for a brief moment to encourage students to subitize and to discourage counting.
I usually use dot images that resemble counters, but any image can be used: ladybugs, mustaches, emojis… feel free to get creative!
After the image is shown briefly and then removed, I will ask, “How many did you see?” and “How did you see it?” This is where the students begin to conceptualize quantities and in this particular case, make important connections to multiplication. Throughout the subitizing activity, you may even encourage your students to name a multiplication equation that represents the dot images.
Using Subitizing to Model Multiplication Concepts
So let’s dive in and explore a few ways subitizing can be used to support multiplication fluency. I will warn you though, these ideas require a lot of visualization, so this episode lends itself best to listening in a space where you are able to mentally picture the images I’m about to describe.
Modeling the Identity and Zero Properties of Multiplication
Subitizing can be a great way for students to conceptualize the zero property of multiplication and the identity property of multiplication. As straightforward as those rules may seem, it is not uncommon for even fourth and fifth graders to have the misconception that any number times one is one, or that any number times zero is itself.
Luckily, subitizing can clear up these misconceptions pretty quickly. For example, you might start by showing an image of three groups with one dot in each group. Your students will quickly see a quantity of three and connect the image to the equation, 3 x 1 = 3.
The next image would show one group with three dots inside the group. The students still see 3, but now represented as 1 x 3 = 3, instead of 3 x 1 = 3. Can you visualize the difference?
Continuing to show the image that represents either groups of one or one group, and connecting the images to multiplication provides an opportunity for students to conceptualize why any number times one has a value that is equal to itself.
Subitizing to represent zero is so simple. Each image would show different numbers of groups, but always with nothing in each group. Although this may seem silly, it can actually be pretty meaningful for students who need more support conceptualizing the rule of zero that may have previously just been “told” to them and expected to remember.
Ok, now let’s move on to a different fact!
Using Subitizing to Build Fluency
Subitizing and 2s Facts
The most efficient way for students to recall 2’s facts is to double the factor being multiplied by two (rather than skip counting by 2’s). So this is the exact approach that I take when subitizing two’s facts.
The first quick image I show will be of a particular quantity, like 3 dots for instance, and the image that immediately comes after that will be that same image doubled. If students can make the connection to doubling, or “timesing” by 2 with addition, many students will quickly realize that they already know these facts!
Subitizing and 4s Facts
Moving on from 2’s facts to 4’s facts is a very natural progression. This is because when we multiply a number by four, we are simply doubling that number (sound familiar?) and then doubling it again! Subitizing fours looks very similar to subitizing doubles, but in this case, the quick image of doubles will be shown to students first, and then that same image repeated will come after.
So back to the 3 dots: we might show two groups of 3 dots first, and then next we show those six dots with another six dots (that same arrangement) next to it.
Students will begin to notice, for example, that two fours is eight, so four fours is equal to two eights. Or that two sixes is twelve, so four sixes is equal to two twelves. This language and the “aha!” moments that authentically come out of subitizing discussions are exactly what we’re aiming for.
Subitizing and 3s Facts
Subitizing 3’s facts also feels like a natural progression following the conceptualization of twos facts. This is because threes facts can be recalled by doubling that number and then just adding that number one more time. If a student can quickly recall 2 x 8, then 3 times 8 is just one more eight!
To visualize this strategy, I would first show two groups of the same quantity: and then the same image but with one more set added: for instance, I might show my students an image with two groups of 6 dots. Students will say they saw twelve dots because two sixes, or 2 x 6 is 12.
The quick image that would follow is the same image as before, but with one more group of six added to the image. I guarantee at least one student will say something to the effect of, “I know 3 x 6 is 18 because 2 x 6 is 12, plus one more six is 18!”
I’m telling you, the conversations that are brought about by subitizing are so powerful!
Visualizing 9s Facts with Ten Frames
When it comes to subitizing quantities greater than six, ten frames are an especially useful tool. They are helpful because most people are only able to perceptually subitize up to quantities of six, meaning, most humans can “just see” no more than six of something. So that means any quantity more than six must be organized somehow to be subitized conceptually. Which leads me to the next set of facts… nines!
Subitizing nines is my all-time favorite set of facts to subitize! This is the perfect way for students to visualize that groups of nine are really just groups of ten, minus one from each group.
I rely on ten frames to subitize nines. I begin by showing my students a full ten frame. I want to first establish that when they see a full ten frame, they are subitizing the quantity of ten.
And then I show my students an almost full ten frame with one missing: Now they see nine! This is the foundation for what follows…
Next, I might show four full ten frames, and ask, “How many do you see?” “Forty!”
The very next slide will look almost exactly the same as the last slide, but now one counter will be missing from each ten frame:
Some students will say that they saw four nines (9 + 9 + 9 + 9), but others will explain that they saw four tens minus four (40 – 1 – 1 – 1 -1) .
After a few examples, I will ask students to start attaching multiplication sentences to the images. For instance, 3 full ten frames can be represented as 3 x 10, and 3 ten frames with only one missing from each is 3 x 9 which is equal to (3 x 10) – 3. It never fails, my students are mind-blown when they begin to see the (oh, so dreaded) nines facts this way!
Subitizing is a powerful way to build multiplication fluency with your students because it gives them an opportunity to visualize strategies that can help them quickly recall unknown facts. For many students, subitizing feels a lot less scary and a lot more fun than flashcards, or other more traditional forms of fluency practice.
So what do you think, Meaning-Makers? What other multiplication facts can be explored using subitizing? What would it look like? I hope you’ve enjoyed our two-part series on subitizing! If you haven’t yet, be sure to hit subscribe, and if you have a moment, please consider leaving us a review so we can reach and support more teachers.
Until next time, Meaning-Makers, have a great one!
