Math Fact Fluency: The Ultimate Guide for Teachers
What is math fact fluency, and why should you care as an upper elementary teacher?
Well, math fact fluency is actually foundational for helping 3rd grade, 4th grade and 5th grade students understand on level math.
Essentially, math fact fluency (especially with multiplication facts in the intermediate years), is truly fundamental. It’s the equivalent to phonemic awareness in reading.
In this article, we’ll take a deep dive into what is considered math fact fluency, and how we know when a student has it.
We’ll discuss the following: what is math fact fluency, why should we care as an upper elementary teacher and how you know if a student has it.
Consider this your ULTIMATE GUIDE to math fact fluency. There’s a lot here!!
So if you can’t read it all now, pin it for later, or save it as a bookmark. 🙂
How Important is Math Fact Fluency?
Table of Contents
It turns out, math fact fluency is pretty important to have as a student.
If we don’t have phonemic awareness for reading, then we can’t decode simple words and sounds – which means we can’t read.
If we don’t know our math facts, then we are completely unprepared and ill-equipped to do on-level math.
I go more into why we should care as teachers in this short YouTube video.
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Free Math Fact Games and Activities
When you were searching for math fact fluency, I totally get that you might have just been searching for games and activities, and not a whole eBook on the topic of math fact fluency itself.
If this is the case, here are all of my free resources related to times table and multiplication facts practice.
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I mean like, let’s be real – we can often learn more from binging an hour of TikTok than sitting in an all-day training!
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I’m always sharing teaching tips and math fact fluency teaching hacks on there.
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It’s a whole free COMMUNITY of teachers who have committed to becoming better at differentiating their math instruction.
I’m also a BIG fan of the Math Teaching Mastermind group on Facebook, which I co-run with several other teachers, math coaches and TpT sellers.
Free Google Jamboard Templates to Foster Math Fact Fluency
Looking for ways to help students foster math fact fluency online?
Jamboards are fantastic for that.
You can use them as checks for understanding, digital math centers, in-person center activities for a “tech,” “tablet,” or “laptop station, and/or formative assessments.
If you don’t have time to read another article, and you just wanna “get to the good stuff,” click here to get your free Google Jamboard templates by opting into my Mini Math PD emails.
Free Multiplication Chart Printable PDF to Help Your Students
If your students are working towards math fact fluency, then they’ll definitely need a multiplication chart!
Especially if your students are in 3rd grade, 4th grade or 5th grade.
Too Busy to Learn About Math Fact Fluency?
That’s OK, just pin this post for later!
You can pin this article to any of your favorite math teaching boards.
What is Considered Math Fact Fluency?
Let’s get to the basics of math fact fluency.
At its core, math fact fluency is the ability to quickly and accurately recall addition facts, subtraction facts, multiplication facts and division facts.
When looking at depths of knowledge based on Bloom’s Taxonomy, we can see that recall is the lowest (or, you could consider it the first) level considering depth of knowledge.
It’s the “shallow part of the pool.”
Many teachers and administrators take this to mean that math fact fluency isn’t really important though, and that we shouldn’t prioritize it.
This couldn’t be further from the truth!!
If you still need to be convinced, read this article.
Your students definitely need to memorize their math facts!
What is Math Fact Fluency?
If you’d rather watch a video about this topic instead of read this epic guide, I totally understand!
Check out this video I recently posted in the Mini Math Minute series on my YouTube Channel.
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If you want to learn more about math fact fluency, or just about other topics taught in upper elementary math in general, definitely subscribe to my YouTube channel!
Basically, math fact fluency is where comprehension meets automaticity.
Math fact fluency is someone’s ability to quickly and accurately recall the answers to simple one digit by one digit problems.
When working with students in primary grades (Kindergarten, 1st grade or 2nd grade – otherwise known as K-2), we usually mean addition and subtraction when it coems to math facts.
However, once we get into the upper elementary grades (3rd grade, 4th grade and 5th grade), math fact fluency usually refers to multiplication fact fluency (one digit by one digit multiplication facts, like 5×6=30), or division facts (one digit by one digit division, like 77/7=11).
Other Posts You Might Like
Math is one of those topics where different skills and concepts build on each other. So it’s totally worth your while to take a few minutes and read more articles!
- 20 Super Fun Ways to Motivate Your 3rd Graders to Learn Their Times Tables
- What Should I Sell on TeachersPayTeachers?
- What is Math Anxiety? And Why Should Every Teacher Know About It?
- Math Fact Fluency: The Ultimate Guide for Teachers
- What True Authentic Learning Is and Why Your Students Need It
What Are The Four Components of Math Fact Fluency?
There are four components of math fact fluency.
These four components are efficiency, accuracy, flexibility, and the ability to choose and apply the right strategy that’s appropriate for the problem.
Let’s break each of these down a bit further.
Accuracy
Simply put, accuracy means whether or not a particular student is getting the correct answer to a given expression.
Kindergarten students should be able to decompose 5 into 2+3, for example. So they should also understand that 3+2=5, 5=2+3, and 5=3+2.
Flexibility
Though at first glance it might seem that they’re all exactly the same, different situations may call for flexibility in the way a student sees or thinks about a problem.
For example, if you’re trying to figure out how many slices of pizza one has altogether, then combining 2+3 would make sense.
However, if a student has five slices and they’re trying to figure out how many slices each person gets (technically, early division), then decomposing 5 makes more sense.
By the time we’re adults, these thoughts are so quick and automatic that we don’t even think about them. But while we’re young children learning, these skills can be quite difficult to learn!
Efficiency
The easiest way to explain efficiency in relation to math fact fluency, is a student’s ability to stay on track throughout the process of problem solving.
Let’s say, for example, a student is looking to solve 8×11.
They may not know the answer to 8×11, but they DO know the answer to 8×10.
8×10=80.
They realize that, if they just add one more group of 8, they can solve 80+8 – which equals 88.
Therefore, 8×11=88.
Those steps are simple and streamlined for adults who have mastered their math facts.
For but a student still working on achieving math fact fluency, that can be an arduous and drawn out process.
This is why efficiency is considered one of the four components of math fact fluency.
If this example is helpful to you, I delivered a video training about using Math Workshop to foster math fact fluency in students.
You can grab that training for $17, along with my Guided Math Groups Lesson Planning Guide (usually $9 on its own!) here in my TeachersPayTeachers store.
Grab your seat for my Math Workshop Webinar here! Just $17.
Appropriate Choice of Strategy
Before I go on, I should say that “strategy” actually isn’t the most accurate word to use here.
When we think of the different methods students can use to think about and solve problems, it’s actually more correct to say students are trying different “tactics.”
Often, the overall strategy itself is similar, if not exactly the same.
Generally, the strategy is:
- Students observe the problem
- Students think about the knowns, unknowns, and known unknowns of the problem
- Students choose a tactic (which could be an algorithm, trick, formula, etc) to solve said problem
- Student goes about using chosen tactic to solve the problem
- Student collaborates if, when, and as needed throughout the problem-solving process
For the sake of learning and reading, when I discuss learning and teaching strategies here, know that I generally mean “tactics,” since the strategy is pretty much the same for every student.
Recalling and Applying Known Properties for Math Facts
When students truly learn the properties associated to the operations, they can start to use the knowledge of those properties for problem solving.
For example, if a student is figuring out the answer to 5×0, they may remember the Multiplication Identity Property of Zero – which states that the answer to any number multiplied by zero, will be zero – because one cannot have zero times of anything, without having nothing.
Though the student may not use that specific verbiage every time, they’ll eventually know and remember that “anything times 0 is 0.”
Modeling and Applying With Manipulatives
Creating 2D and 3D models often helps students gain a more concrete understanding of various concepts in math.
The same can be said when students are developing their math fact fluency.
A student might be asked to model 4×6, then 6×4.
This can be a very difficult and confusing question for a student who hasn’t had the time to think about the differences between those two expressions.
Once a student does an array, it’s easier to start seeing the differences, and how these differences may come up depending on the particular context of the problem.
Why I’m So Obsessed With Math Fact Fluency
Since my focus is on upper elementary math, you’ll usually find me talking about multiplication facts – as that’s the focus in 3rd grade, 4th grade, and 5th grades in regards to math facts.
But division facts are major for that age group too, so you’ll also hear me talk about those.
The main reason is, we wouldn’t expect for students to pick up and cold read a grade-level text, if they still couldn’t identify letters or decode basic letter sounds.
I think a small part of me also loves talking about math fact fluency because I just love an underdog.
Throughout the early 2000’s (wow, even just typing that feels weird!! If you’re a millennial, then I bet it feels even weirder reading it lol), there’s been this huge push to put away anything dealing with “rote memorization.”
…but what if that rote memorization is absolutely key to helping students build conceptual understanding and other skills in math?
Memorization is just one step in learning.
What Are the Stages of Math Fact Fluency?
So many think that it’s all about memorization.
That’s just one stage.
Here are the four stages of math fact fluency:
- Applying
It may or may not surprise you to hear (or shall I say, read?) that I actually have students apply their learning first.
More about “how” I do this in a minute – keep reading! - Conceptualizing
This is when we start actually “getting” what it is we’re learning. - Learning
This is the step where things start to get a bit fuzzy, especially when it comes to learning multiplication facts. This is where I see most teachers go wrong!
Definitely don’t skip this step in the learning and teaching process. - Memorization
This is actually the last stage in learning.
Prefer to Listen to The Stages of Math Fact Fluency?
Listen to this episode of the Learning to Love Math Podcast here!
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The First Stage of Math Fact Fluency: Applying
There’s a lot of evidence out there to suggest that engaging students with the material, and that getting them “doing” right away, actually leads to better learning. I welcome and encourage you to read it all!
But for now, just know that this usually looks like a warm-up problem, a “solve-and-share,” or something similar.
It’s not always solving expressions, though! Sometimes, when building understanding of math fact fluency, I’m having students use manipulatives or do some other kind of active work to help them better understand addition, subtraction, multiplication, and/or division.
This doesn’t just go for math facts, by the way; this is the key to success for learning anything!
Get them applying the concept first before they even know what it is.
This builds the schema in their brains, and it allows you to scaffold past and future learning.
The Second Stage of Math Fact Fluency: Conceptualizing
When application is done first, it actually gives students some background experience to draw from if they didn’t already have some going into the lesson.
This is especially helpful with math fact fluency – because, it’s one thing to know what 8×7 “equals.” It’s another to be able to draw a mental picture (or a physical model!) of what that looks like.
This is when students are using the vocabulary, making models, drawing math pictures, and talking about what they’re seeing and doing.
Having this step after application is awesome – because it allows them to go back to what they were just doing, and assign meaning to it with their newfound understanding!
This makes for some really rich discussions and number talks.
The Third Stage of Math Fact Fluency: Learning
This stage is where many teachers unknowingly make mistakes.
Usually, teachers will put their students on a game like Fastt Math, Math Facts Pro, Reflex, or something similar so “students can learn their math facts.”
The problem with this, as you can imagine, is that the students haven’t learned them yet.
Now, I want to be clear in saying sites like those are fanstastic I personally use Math Facts Pro and highly recommend it since the kids think it’s fun, and since the data is really top-notch.
But these apps and games are for reinforcing math facts fluency; not for teaching the actual math facts (multiplication facts or otherwise).
The Fourth Stage of Math Fact Fluency: Memorizing
You can see that, I actually do things quite differently in my classroom.
I have students engage with higher DOK level activities first. I truly believe that doing things “backwards” is the reason my students have had so much success (because, I assure you – it’s nothing special about me!! I am secretly lazy, so I have learned to be as efficient as possible 😂😂).
Once your students have truly learned their math facts, it’s time to start focusing on memorization.
You can do this by times table (6 times table, 7 times table, 8 times table, so on), or you can have students set their own milestones.
I am a HUGE fan of having students set, track and reach their owl goals – so if this is something you want to work on this year, get your students this math fact fluency tracker!
Buy a math fact fluency tracker for your students here! Just $3 in my TeachersPayTeachers store.
How to Tell if a Student Has Achieved Math Fact Fluency
This might be the hardest part of it all: how can we tell once (or if!) a student has achieved math fact fluency?
And, what’s the difference between math fact fluency and math fact mastery?
Stay tuned for the next blog post, where I’ll be diving into how you can assess math fact fluency (I’ll give you a hint – it’s actually really simple, and you can assess in ways that don’t stress your students out!). 😉
Learn More About Math Fact Fluency
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