So whether you are educating at home with your own kids or you have a classroom full of kids, a common concern is how to help kids learn their math facts. 

I’m Christina Tondevold, The Recovering Traditionalist and today, we’re going to take a look at helping kids learn math facts in our quest to build our math minds so we can build the math minds of our students or our kids.

Watch the video or read the transcript below:

Watch all the videos in this Fluency Series:
Video 1: Fast Does Not Mean Fluent
Video 2: Helping Kids Learn Their Math Facts (This Video)
Video 3: Math Experiences That Build Fluency, Not Memorization 
Video 4: Students with Math Fluency
Video 5: The Importance of Visuals in Math
Video 6: The Root of Math Fluency 

Now, for those of you who don’t know me, I was definitely the kid who learned through memorizing and when I went to school, that’s the way that math was taught. We were taught it as a series of facts and rules and procedures that were to be memorized and followed.

But that’s not the way that math is being taught right now. Teachers are really trying to help kids build in understanding of the math and sometimes, it can seem from the outside that the focus is only on helping kids build an understanding and not so much on making sure that kids are fluent or get correct answers.  

But really great math learning is actually a balance of both.  So, before we get into what that looks like for math facts, I just want to tell you real quick that I have a free download that helps both parents and teachers build a better understanding of this idea of how we actually build fluency for our students. It’s called the Building Math Fluency Starter Kit. There is one that’s for teachers and what to do when you’ve got a classroom full of kids, whether in-person or you’re doing it virtually with kids, but there’s also one for parents and don’t worry, if you are both a teacher and a parent, just grab the teacher version because we will also send you the parent version just in case you want to pass it along to the parents of your students.

Well, this kit was designed to help you really prioritize the important mathematical understandings that we really need to ensure our students have because whether you’re able to actually work with your students right now or you’re looking at being able to plan for when you have them back in your classroom, this kit will help you build an understanding of math fluency for elementary kids but let’s start off this video with how to build fluency with math facts. 

What is fact fluency

Now, the first thing I want to start off with is what is in fact fluency? Now, the teachers use the term fluency a lot but as parents, we tend to like look at our kids and say, “are they fast or not?” In a prior video, I talked about the difference between these two terms and how we really shouldn’t use them interchangeably. Now, that video is linked up inside of the Building Math Fluency Kit and I also go into a lot more detail about what is fluency, and how we build it inside of that kit. If you want more detail about it, go to the kit. 

For this one, I just want to do a quick little overview, that fluency is not just fast. So if your child seems like they are fast with their math facts, that doesn’t necessarily mean that they’re fluent and the other way, even if they’re not fast, they can still be on their way to building fluency. Fluency actually has three parts. We do want kids to be accurate, get the correct answer, efficient, which means are they fast? Do they get there fairly quickly? But also a third part which is are they flexible and this is often a piece that is missing for students to be truly fluent. Just because they’re fast and they get the right answer doesn’t mean that they are fluent in math, they also need to have some flexibility.

Build Connections for Easier Recall

 What does that actually look like? Here’s a little image that I want to share with you that if we are just focused on getting kids the correct answer, this is really the only connection that we are building for kids. 

If we are focusing on 6 + 7 = 13 and we are just trying to drill it into them, 6 + 7 is 13, they only have this one connection point that is built. This idea of building flexibility in our students means helping them to see it in lots of different ways and the way that first starts out, which is not where we want them to end, but the place that they first start out is with counting. 

They do a lot of counting and counting on. A lot of kids might tend to start to see that 7 + 6 is related to 6 + 7 and it eventually gives you that same answer of 13 but we don’t want kids to always be falling back to counting and unfortunately, that’s what happens. If you have a kiddo who doesn’t instantly know that 6 + 7 is 13, the only other connection point they have is to go back to counting, which is what you may see students or your own personal kids do and it makes you feel like they aren’t fluent and they aren’t yet but how do we get them there besides just learn it, memorize it, know it? 

So, one of the first things that I encourage all of us to do is to use lots of visuals and put the problem into context, but we will go into that in more detail in the Building Math Fluency Starter Kit. 

So, the other piece comes in when we start to look at these different strategies, that 6 + 7 is related to 6 + 6 because it’s just one more or it’s also similar to 7 + 7 and you just subtract one or there’s kids who like to make 10. So, they’ll find a way to break apart the numbers and turn one of the numbers into a 10. 

All of these pieces, we don’t want them to have to relearn them all but oftentimes, they are kind of taught in isolation.  Learn your doubles and your doubles + 1, your doubles + 2, but the way that they really build this flexibility is by building in connection points. 

Did you see that? Did you notice the difference?

The more connections that we can help our students, or our own personal children, build the easier it is for them to recall information. Being able to recall information is different than memorizing. I can memorize something for a short period of time but to truly be able to recall information, the more connections we have built, the easier it is to recall information of any kind but especially in mathematics, where we have all of these isolated facts. 

If you think about just the addition facts, that’s 121 different facts that kids are supposed to memorize and if your child is not a great memorizer, it becomes very difficult and that’s just addition and if you throw on subtraction on top of that and then as they move into multiplication and division, that’s a lot of facts to be memorizing.

Instead, I want to give you an alternative about helping your child, or your students, be able to see types of facts and how they connect together. So, this is true for addition, subtraction, multiplication, division.  We’re going to take a look at addition and multiplication because those are where it tends to be a sticking point for kids. So, even like the image of all the connection points for addition, the same holds true for multiplication facts. We don’t just want a single connection point, we want to build lots of connection points so that they can recall the facts easier and faster.

Addition Facts

Okay, so how do we help build those connection points? What are the types of facts? So for addition, there are really 4 types of facts and this chart is a color chart to help emphasize what those are to make it a little bit easier to see them.

Now, there’s not a specific order that kids need to learn these in. It’s just the fact that I want you to be able to see these different types of facts. The orange ones, the bright orange ones are what’s known as the doubles, 2 + 2, 4 + 4, 3 + 3 and then the lighter orange ones are the ones that are related to that. If your child or kids in your classroom know 3 + 3, how can we use that to help them learn 3 + 4, right? I want you to be able to use this chart to see those connections. The green ones are the ones that make 10. Kids will gravitate to things that make 10 and then we can use their understanding of things that make 10 to help them understand the lighter green ones, which are just + or – 1 or 2 of those. And then the blue ones are the teen numbers, I call it the 10 plus somethings. Like kids really do kind of struggle with what 10 + 3 is, 10 + 4. So if we can help them build those, then it helps with those lighter blue ones. And then the purple ones, I tend to save for a little bit later because adding nothing, adding a zero is just a strange thing for young kids but we do need them to understand what happens when they add zero and then what happens when they’re just adding 1 or 2 more. 

So, the dark colored facts are the ones that kids will naturally gravitate towards and they are what I kind of call those power facts. If kids know those, then we can use those to help them understand the ones that are connected to that. Now, there’s also a chart like this for multiplication.

Multiplication Facts

So here’s the one for multiplication and again, it’s not the order that you do this in, it’s the fact that we want you to really focus in on the types of facts and then helping your students, your kids be able to see the connections between them.

Personally, I like to start with x2, because it connects to the doubles addition facts. So, 2 x 3 really means 2 groups of 3, which they should know from addition facts, it’s 3 + 3. Then you can work with the lighter green ones, which are multiplying by 3 and multiplying by 4 and how they connect to multiplying by 2. I also like to go up to times 10 and helping kids understand what happens when you multiply by 10 and then we go to multiplying by 5 and then the purple ones, which are the x 0 and x 1 and those are really just properties of multiplication, all right? But helping them really understand, like when I learned it, it was just anything x 0 was 0. It was just something I learned and I memorized, but I didn’t really understand it. So we want kids to be able to know that anything x 0 is 0 but understand why.  Why does that work? 

That’s what really helps make the math facts stick, is not just memorization. Kids can memorize things for a short period of time and it may seem like they know it. I have a friend, Mike Flynn, who likes to call this the “illusion of understanding.”  That kids can show that they’re getting a right answer and it seems like they are fluent, but they just have it memorized and they don’t really understand the underlying mathematics that’s happening. So, we really want to build that for our students and my final thing that I want to leave you with is the way to build this with your students. 

Discuss don’t Drill

Now, I’ve mentioned the Building Math Fluency Kit. So if you want a lot more, go to the kit for this but my first tip I want to give you in this video and there’s going to be more to come in future videos but for this video, the only thing I want you to focus in on is doing more discussion with kids than drills, right?

When we’re doing flashcards and worksheets, it feels like we’re being productive, like they’re getting through a lot of problems, but it isn’t really helping them build connections, right? Especially for the ones that they don’t know. If they get stuck on a problem on a worksheet or they get stuck on a flashcard, do they have a way that they think about it? 

So, it’s okay if you’re doing some flashcards but instead of just asking for the answer, ask for them to tell you how they know and if the kid can just say, “Well, I just know it,” then you might want to mark that down. There are certain ones that kids will just know but they shouldn’t have that for all of them even as adults, some of us still have those ways that we think about it, it’s not all just memorization. 

So instead of drill, do discussions. Here’s another way that I do it, not just with a worksheet, when I do have worksheets that come home, we sit down and we have some discussion about what they’re noticing within the problems but another thing that I personally do with my own kids is what’s kind of called a string of problems. It’s purposeful practice. 

So, when I sit down with my 3rd grader who’s working on multiplication facts, I like to give things in ways that help build connections. So here’s an example. I might give him 2 x 5 and then 4 x 5 and then 2 x 7 and then 4 x 7 then 2 x 8 and then 4 x 8.

He may not notice it while we’re doing it but the point is afterwards, if he doesn’t notice it, to have a discussion, what did you notice about 4 x 5 versus 2 x 5 and we’ll have a discussion about hopefully how he’s seeing it and if he’s not, then I might have to explicitly bring it out. Do you notice how 4 x 5 was just double what the 2 x 5 was? And then looking at that pattern throughout the problems that I gave him. And then I can even extend it to things like, I might ask him 2 x 12 and then 4 x 12 and I’m not thinking that I want him to sit down and you know, calculate out 4 x 12. I want him to be able to use that connection that we just discussed about, if you know 2 x something that can help you with 4 x something because it’s just double and that idea of doubling and halving becomes super important as kids get into their work with fractions. 

So, it’s not just about their math facts, building all of these connections just builds a solid foundational understanding of mathematics for your kids that’s going to extend beyond just their math facts. So, again, for more in depth understanding of all this stuff about how to build fluency, why it’s important, how it connects to other learnings that they’re going to be doing in elementary math, go ahead and download your Building Math Fluency Kit. There’s links below this video or in the description of the video that you can go and get your download. All right, I hope that this video helped you build your math mind so you can go build the math minds of your kids.

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