Fact Fluency Part 3: The Power of Subitizing

Have you ever had a student that when you put up 4 fingers and asked them “How many fingers do I have?” they had to count each finger one-by-one?  That happens way too often in early elementary classrooms.  Those children can count, but they are not subitizing and without being able to subitize a child will never move past counting on their fingers to add and subtract.

This last post of my Fact Fluency Series is going to delve heavily into why & how you should be implementing subitizing into your classroom to build students’ number sense, which in turn builds their flexibility and helps them be truly fluent with their facts.

I shared how we should be focusing on building 4 Types of Facts instead of teaching facts as isolated pieces of knowledge kids are supposed to memorize, in the first post in this series,

In the second post I detailed out the three pieces kids really need to be truly fluent plus the 4 Number Relationships that help build the most important piece (flexibility).

I want to start off this third post with a definition of subitizing.  I first learned about subitizing from Doug Clements’ article, but he defines it as “instantly seeing how many.”

Now, I’m going to talk about how subitizing helps build the 4 Number Relationships mentioned in post #2 and activities you can do in your classroom to build your kiddos’ ability to subitize.  BUT, one word of warning….I have no research to back me up on this warning, just my experience….if you work with kids who come from home lives that have no structure, no predictability, no stability, I have found that those kids struggle with subitizing.  It takes them longer to ‘trust’ that every time I have all the fingers up on one hand it is FIVE.  They don’t believe that every time I push over all the red beads on the rekenrek that it is FIVE (you might be trickin’ me, Miss).  When a child has nothing that is reliable in their life, why would they think they can rely on a ten frame to always be five when the top row is filled up?????  Now, this is NOT to say they can’t subitizing…they can, it just takes them longer to trust the tools and images that other kids will quickly be okay with.  Okay, done with my warning….on to the good stuff.

First I’m going to share a couple quotes that I LOVE, but tend to shock some people:

Counting is important, but it does NOT build any relationships about a number.  In fact, it doesn’t even help kids to see how a number relates to a QUANTITY!!!  Think about a kid counting out 6 blocks, they ‘tag’ each block with a number…but what does that kid really know about ‘6’?

Most people respond to that question with “They know it is 6 things.”  But do they???? A quick way to tell is after they count the 6 items, ask the child to show you ‘four.’  A LOT of kids will point to the 4th item, NOT show you four things:

This really hit home to me when I was doing a training for a group of administrators.  I gave them all a Number Path and asked them to circle “six.” Almost everyone in the room did this:

That is the digit ‘6’ but not the quantity of 6.  If all we focus on with our kiddos is that “six” is ‘6’ and looks like this:

then when they start doing 6 + 5, their only strategies are either memorization or using these images of the quantities:

which results in kids counting one-by-one to solve.

Instead, when you take the time to build subitizing in your students using structured images, like ten frames and rekenreks (a.k.a MathRacks), they could count to solve….but they also get the opportunity to build number relationships that will lead into POWERFUL strategies.

Right now, maybe you already see some strategies kids could use when trying to figure out how many are in the ten frames or how many beads are “in play” (for those not familiar with a rekenrek, the beads on the left side are ‘in play’)….but honestly it isn’t for YOU to see.  I want the kids to see those strategies and not have you tell them what to see and how to figure out the total (not that YOU do, but for some it’s easy to just tell the kids to move 4 from the bottom ten frame to fill the top ten frame).

They will only be able to see it for themselves if they have built the 4 Number Relationships.  So, lets take a look at how subitizing can build the 4 Number Relationships (which build number sense) and the by-product of building that number sense is that kids get more flexible with their use of numbers and they come up with those strategies on their own.

#1: Spatial Relationships is recognizing how many without counting by seeing the visual pattern.

My favorite activities include just providing kiddos with lots of visuals.  Create Dot Plates using paper plates with dots on them, create PowerPoints with images that flash in and animate out, create Subitizing Cards using 3×5 cards and dot stickers, do number talks and show an image and let the kids tell you what kinds of groups they see.  The important thing is to make sure kids can see groups…don’t just put dots in a line or randomly placed.  Grouping allows kids to subitizing, otherwise they will go back to counting one-by-one.

#2: One/Two More and Less, this is not the ability to count on two or count back two, but instead knowing which numbers are one more or two less than any given number.

My favorite activities are pretty much the same as the ones I do for Spatial Relationships with one little twist….I will show the kiddos a visual and then ask them to show me “One More Than what I showed” or “Two Less Than what I showed” etc.  This gives them a chance to see the original quantity and then what happens to that amount when we add One More Than or we make it Two Less Than.  I also love doing Number Strings that start with an amount and the next image I show has “one more” and then the next has “one more” and so on.  Here is an image of a completed string of images I have given kids, the goal is talk about how the images relate:

#3: Benchmarks of 5 & 10 are so important because 10 plays such an important role in our number system (and two 5s make up 10), students must know how numbers relate to 5 and 10.

My favorite activities involve the use of ten frames and rekenreks.  Both of these tools/visuals are built upon a 5 & 10 structure.  It allows kids the opportunity to see how a number relates to 5 and to 10.  Do any of the Spatial Relationships activities, but just use ten frames or rekenreks as your visuals instead of dot patterns.  When quantities are arranged in a ten frame in this manner, the structure of the ten frame highlights its relationship to 5 and to 10.

My favorite activities are again all the ones mentioned in the Spatial Relationships, but I like to use visuals that are intentionally highlighting the decomposition of a quantity into different parts OR even starting to use random placements so that the kiddos have to find their own parts.  Take for instance the image below, for a LONG time this type of ten frame placement drove me nuts….but what I’ve come to realize is that this type of placement allows for the KIDS to find their own parts instead of always only seeing six as 5 on the top row and 1 on the bottom.  Try this image out with your kiddos, I bet you get a lot of different ways that they can group the dots to determine the total amount.

I hope throughout this series that I’ve pushed your thinking about the way we teach “the facts” to our young kiddos.  Most of them aren’t ready for the abstract symbols of 5 + 7 on a worksheet, but when you show them a visual of a 5 and 7 in a ten frame it’s amazing how they can determine the total!!!  If you haven’t been doing Subitizing or spending time building your kiddos’ number sense I sure hope you take the time to make it a priority.  Laying the foundation of number sense HAS to happen or else we are just building a mathematical house for kids that with the slightest storm will come crashing down.

If you are still wanting more, I created a 7 minute video in which I describe WHAT subitizing is, WHY it’s so important to do in your classroom, AND HOW you can incorporate it into your daily routine.  Click the button below and I’ll email you a link to a video.