Raise your hand if you have students in your upper elementary classroom who still count on their fingers or draw circles, or draw tally marks to find the product of 6×8?
I’m guessing if you have been in an upper elementary math classroom for pretty much any length of time, then you have seen students who count on their fingers, who draw circles, or tally marks to calculate sums, differences, and products.
Multiplication Fact Fluency is the biggest roadblock for students who struggle in math. How can upper elementary teachers navigate this challenge?
I’m going to throw some big words with definitions at you and then I will break it down further.
✅The first one is automaticity, and this is the ability to automatically process and recall information resulting from long-term memory commitment.
✅Next is math fact fluency, and this is the automatic recall of basic math facts without conscious effort.
✅And the last one is computational fluency and this is the ability to efficiently and accurately calculate any math expression.
So I’m sure you know that the reason your students are counting on their fingers, and drawing circles and tally marks is because they don’t know their math facts.
But it is more than that.
They have the ability to reach a solution by using these remedial strategies, but they are just not efficient strategies, and certainly not feasible to use as the math skills get more and more challenging in the upper elementary grades and moving into middle and high school.
The fact that they haven’t committed these basic math facts to memory is the roadblock to the automaticity that they are searching for when they are trying to solve higher level math problems….and because they lack automaticity, they are struggling with accuracy and efficiency in the computational fluency.
So How Should Teachers Build Multiplication Fact Fluency?
It all comes back to math fact memorization.
But how do we get students to memorize basic math facts when they have no desire, or motivation, or reason to put in the effort, because quite frankly most kids are pretty lazy when it comes to doing tasks that don’t come naturally to them or that they don’t find enjoyable.
As you may know I taught 5th grade when I was in the classroom, and from my very first year, I was shocked at how many students would come to me in 5th grade without knowing their basic multiplication facts. Sadly, I would see those same kids struggle with the higher level math that I was trying to teach them.
How can they be expected to solve 4,852 x 86 if they don’t know 6×8? Or 8×8?
Sure they can use counting strategies to find the product, but while they are using those strategies, they are also getting distracted by where they were at in the process of the algorithm. This leads to frustration, inaccuracy, and inefficiency….which all leads to hating math!
The solution to this problem of students struggling with higher level math, is that they need to commit all of the basic multiplication facts to memory.
When I was an elementary student, it was just a normal part of the learning process…multiplication fact memorization, and somewhere along the way this crucial element of our education system just disappeared.
So, I am on a mission to encourage teachers to bring back the emphasis on multiplication fact fluency because it is such a critical missing piece in math education.
I want to invite you to sign up for my free masterclass so that you can start building multiplication fact fluency in your classroom and get your students on a path towards a better relationship with math.
It’s free to sign up, and once you do sign up you will get instant access to the 25 minute pre-recorded workshop that will give you the tools you need to start a multiplication fact fluency program in your own classroom. Sign up >HERE<!
How Multiplication Fact Fluency is Like Baking a Cake
Imagine reading a sentence that says:
“Elevated abecedarian pupils toil amidst computative certitude eloquence credentials instigating extensive thwarting.”
Are you able to comprehend the meaning of the sentence?
Maybe you can comprehend but it takes you just a little bit longer because you aren’t familiar with the meaning of all of the words.
Now imagine that you are baking a cake.
You have mixed your butter, oil, and sugar and you are heading over to the fridge to grab some eggs when you realize you are out of eggs. So you hop in your car to go to Wal-Mart and get a carton of eggs.
When you get home you look at the bowl of mixed ingredients and think to yourself “did I already add the oil to that mixture?”
You decide you better add just a little bit of oil just in case you forgot.
Then you start to crack eggs when your phone rings. You quickly run your hands under the water with a little bit of soap before you answer your phone. It’s the doctor’s office calling to remind you of your appointment tomorrow.
When you hang up the phone you go back to your cake batter and you have to look at your broken egg shells to remember how many eggs you have already added, and then you wonder “did I already add in the vanilla?”
You finally get the cake batter mixed, poured into your baking pans and placed in the oven.
You set your timer for 25 minutes and then you head to start some laundry and take care of some other chores…when suddenly the power goes out.
You are frustrated, but then you remember the cake in the oven. The power clicks back on…but what was the timer on when the power went out?
Is that cake going to be the best it could’ve been if you hadn’t had so many distractions?
Think back to the sentence you read a few minutes ago…if you don’t know the meaning of the words in context, or worse, if you can’t decode the words to even begin to know the meaning of the words…then how are you going to comprehend anything that you are reading?
Multiplication fact fluency is the same concept.
We have to recognize words to comprehend a text and we also have to recall basic multiplication facts to comprehend higher math.
With our sentence analogy, we must break down the sentence word by word, to first figure out the meaning of each word, and then put it all together to make sense of the words together, and comprehend the meaning of the sentence.
“Elevated abecedarian pupils toil amidst computative certitude eloquence credentials instigating extensive thwarting.”
- Elevated means upper
- abecedarian means elementary
- pupils is another word for students
- toil means struggle
- amidst is another word for with
- computative is another word for math
- certitude means fact
- eloquence is another word for fluency
- credentials means skills
- instigating means causing
- extensive is another word for major
- thwarting is another word for frustration
So that complicated sentence simply means:
Upper elementary students struggle with math fact fluency skills causing major frustration.
All of these steps that we are taking to comprehend this one sentence can be compared to a student who is trying to solve 4,389 x 78.
If this student has to stop and count on his fingers to find the product of 8×9, and then again with 8×8, and again with 7×8, it is going to be much more difficult for him to solve, not only because it is going to take so much longer this way than if he could pull those products out of his memory, but also he is going to get distracted and lose his place in the algorithm.
He will figure out that 8×8=64 but then he might forget which numbers he needs to multiply next or he might forget to record his placeholder zero, or he might forget to add the numbers he has regrouped.
And he most certainly is not going to be able to make sense of the process of why he is recording a placeholder zero or adding those numbers he regrouped.
The point I am trying to make here, and that I am so passionate about, is that if students would first commit basic multiplication facts to memory, then all other higher level math would be so much simpler for them because they are not getting distracted by having to stop and use remedial counting strategies in the middle of an algorithm, which means they are not frustrated when it takes them 10 minutes to solve one problem.
But What Exactly is Multiplication Fact Fluency?
Mastery refers to having great skill at something or total dominance over something. If you are fluent in a language, you have a mastery of the language.
There are 3 characteristics that I believe must be present in order for a student to have reached a level of mastery with a single multiplication fact.
The first characteristic of mastery is that students can accurately recall the product within 3-5 seconds.
What this means is that when they see 6×7, or hear 6×7, they reply with 42 in less than 5 seconds.
If they reply with 40 in 2 seconds, this is not mastery, obviously, but even if they reply with 42 within 7-10 seconds, this still isn’t mastery.
The reason for this is that for it to be considered mastery, it must be AUTOMATIC recall.
This doesn’t mean that the student doesn’t know 6×7 is 42, it just means that the student should spend time practicing 6×7=42 so that he or she becomes fluent and can recall the product in less than 5 seconds.
The second characteristic of mastery is that the product is recalled from MEMORY without the use of counting strategies.
This means no drawing circles or tally marks, no nines tricks or any other strategies that don’t involve the strict memorization of the fact.
The third characteristic of mastery is that the product of EVERY math fact 1 through 12 is recalled within 5 seconds from memory.
This means that the student not only knows that 6×7=42, but also that 7×6=42.
This is one of the unique features of Math Facts Simplified (my comprehensive multiplication fact fluency program) in that all of the math facts 1 through 12 are assessed, including reciprocals like 6×7 and 7×6, because sometimes students view 6×7 differently than they see 7×6.
What is “Incomplete Fluency”?
If you have been teaching math for any period of time, I am sure you have seen some of the computer “fluency” programs out there.
I am not going to mention any by name, but my frustration with these “fluency” programs began when I was teaching 5th grade math several years ago, and I created a reward system for fact mastery.
Students were assessed through this computer fluency program, and when the computer said they had mastered all their facts, that meant they had mastered all their facts.
However, what I noticed is that what the computer considered mastery was in fact not mastery..it was more like “This student knows a lot of the basic math facts, but not all of them.”
I remember distinctly sitting with a student who was struggling to solve an expression. I don’t remember the expression or even what type of expression it was…all I know is that he was NOT fluent with his math facts, and his name was up on the “Mastery Wall” because the computer said he had mastered his facts.
Hmmm. This intrigued me.
And this is what I call incomplete fluency.
Incomplete fluency is a problem because these programs are giving a false assessment that the student has committed every math fact to memory and is able to recall every math fact within 5 seconds, without the use of counting strategies.
So I set out to create a solution to this very large problem.
That’s how my multiplication fact fluency program, Math Facts Simplified was born.
The idea behind the system is
✅assess
✅practice & memorize and
✅track for fluency
But it’s more than that, which you can learn more about in my free workshop.
Why Memorization is Essential for Multiplication Fact Fluency
The solution to this problem of students struggling with higher level math, is multiplication fact memorization.
There it is. I have said it. The one thing that will change math forever is for students to memorize basic math facts.
I am going to give you 3 reasons that I think students should memorize their basic multiplication facts.
1️⃣ When a student has to stop in the middle of an algorithm to find the product of 4×9 or 7×8, he will get distracted, which creates frustration.
So that is the first reason…to relieve the frustration that is sure to build if they don’t have these facts memorized.
Think about the student who takes so long trying to draw circles and figure out 7×8 and 4×9 that by the time he gets the product he has forgotten where he was in the process!
2️⃣ The second reason is to help them be more efficient in solving higher level math expressions.
They aren’t having to spend several minutes using counting strategies to figure out the product of 4×9. Instead they can quickly recall these products so that they can move on in the algorithm.
3️⃣ And the third reason students should memorize their basic multiplication facts is to help them be more accurate in the calculations.
As I mentioned before when students have to stop in the middle of the algorithm when they are solving a higher level math expression, they are more likely to get distracted and miss a step in the process leading to an incorrect solution.
So what can you do about this growing problem? I want to invite you to sign up for my free masterclass so that you can get your students on a path towards a better relationship with math.
It’s free to sign up, and once you do sign up you will get instant access to the 25 minute pre-recorded workshop that will give you the tools you need to start a fact fluency building system in your own classroom. Find it >HERE<!
I hope that you have enjoyed this article about multiplication fact fluency. If you are looking for engaging ways to help your students practice their math facts, you should grab a sample of my multiplication fact games by clicking the image below.
And when you are ready to implement a program for building multiplication fact fluency in your upper elementary classroom I hope that you will check out my programs. Click on each image below for more information.
If you have questions, you can email Danna@TeacherTechStudio.com