Ep 36. How to Build Automaticity with Math Facts:
A Practical Guide (solo episode)

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You can listen to the episode here: Chalk & Talk Podcast.

Ep 36. How to Build Automaticity with Math Facts: A Practical Guide (solo episode)

[0:00] Anna Stokke: Welcome to Chalk and Talk, a podcast about education and math. I'm Anna Stokke, a math professor, and your host.

Hi everyone,

If you’ve tuned in before, you know I usually bring in amazing guests to share insights, research, and practical tips for learning math.

But today I’m going to switch it up a little because I want to take some time to summarize something that’s come up a lot in our discussions – mastering math facts. So, today, it’s just going to be me.

This episode is inspired by the overwhelming response to conversations with Dr. Brian Poncy, a psychologist and math facts researcher. After those episodes, Brian and I received a flood of messages from educators worldwide, sharing their concerns about students struggling to recall basic math facts and looking for effective methods to help.

So, I thought it would be helpful to create a practical episode summarizing the best ways to build math fact automaticity, based on my conversations with Brian and other researchers.

My hope is that this episode will be a valuable resource for anyone working with students—whether you’re a teacher, parent, tutor or an older student who wants to strengthen math fact fluency, this episode is for you!

I’ll be walking through some empirically validated techniques adopted by the M.I.N.D. program, which is a free resource Brian co-developed. These techniques have been shown to work with a wide range of students across age, skills and settings.

A huge thank you to Brian Poncy for providing the framework for today’s discussion and for guiding me through the supporting research. I’d also like to thank Amanda VanDerHeyden for her valuable feedback and suggestions for this episode. On the resource page, you’ll find articles authored by both of them along with work by other researchers featured on the podcast, like Robin Codding, Ben Solomon, Matt Burns and Paul Kirschner. Many researchers across fields and research groups have data that converge on high-quality math interventions supporting the instructional hierarchy model, which forms the backbone for today’s episode.

Automaticity with math facts is a foundational skill that is critical for success in math and I’m trying to do my part to tackle what Brian calls a “math fact crisis.” So, on that note, if you know anyone who might benefit from this episode, please do me a favour and share it with them.

Now without further ado, let’s get started.

[03:00] So what is automaticity and why is it important?

Automaticity with math facts means being able to recall facts instantly, without having to stop and think about it. If I ask you, “What’s 6x7?” and you immediately say “42” that’s automaticity. You’re not pausing to count on your fingers or trying to come up with a strategy to figure it out.

As a mathematician who has learned a lot of math and applied a lot of math, I know math is relentlessly hierarchical—it’s like climbing a ladder. Every rung is dependent on the previous one. Mastering math facts is like the bottom rung; everything after that depends on that rung being strong and reliable.

Once math facts are memorized, everything else becomes so much easier. It reduces cognitive load, which frees up space for your brain to concentrate on more complex problems in say algebra or geometry. When students don’t have math facts memorized they get hung up on things like factoring polynomials or solving algebraic equations.

Once math facts become automatic, it’s also easier to learn and gain fluency with mental math strategies so you can do mental calculations with larger numbers.

You may notice that I use the terms math fact automaticity and math fact fluency interchangeably throughout the episode. While these terms originate from different fields, they essentially mean the same thing—responding quickly and accurately.

Can anyone memorize math facts? Well, if a child can memorize things like song lyrics, dinosaur names, or their route home from school, they should also be capable of memorizing math facts. Having said that it may take some people longer, but it’s important to invest that time. With enough practice opportunities and the right approach, they can succeed.

This is an investment in a child’s mathematical future. They'll likely use math facts almost every day for the rest of their lives, not just in the classroom, but in real-life situations like calculating discounts, managing finances or figuring out a tip at a restaurant.

So, this is important. Math fact fluency is the foundation on which future success in math is built.

Methods for Building Automaticity

Now, let’s get into the practical side of things. How do we help students build automaticity? I am going to walk you through some research-backed methods.

But first, an important thing to keep in mind is that the method should meet students where they’re at. This aligns with the instructional hierarchy I mentioned earlier, which tells us that students move through different stages as they learn. (I’ll include a graphic on the resource page, if you’re interested to learn more about it.)

[06:17] Acquisition stage: There are two stages of the instructional hierarchy to consider when building automaticity with math facts: The first is the acquisition stage, which is when students are often inaccurate so they’re still building accuracy.

Think about someone learning to skate who keeps falling down all the time – they’re still building accuracy with that skill. It’s the same with math facts. A student in the acquisition stage with facts still has difficulty getting the fact right – they know that 4 x 3 is 4+4+4, but they still struggle to come up with 12 as the correct answer.

[06:50] Fluency stage: The second stage is the fluency stage.

The fluency stage happens after students can answer math fact questions mostly accurately but are still slow. Back to the skating analogy, someone in this stage can likely stay up on their skates, but they’re wobbly and slow. They’re getting there, but they wouldn't be able to score any goals in a hockey game. With math facts, a student in the fluency stage can figure out the math fact, but it’s not automatic. There’s some thinking going on that slows them down before they can tell you that 4 x 3 is 12.

When students are still working on building accuracy, it’s important to scaffold by practicing a small set of new math facts at a time until they can recall them accurately, rather than overwhelming them with too many facts at once.

When they’re building fluency, we need ways to make sure they become faster so that the skill becomes automatic. Fluency building applies to all behaviors. Just as golfers perfect their swing—or musicians master a musical piece, fluency development enhances performance across many areas.

Also keep in mind that frequent, short sessions are likely most effective. And practicing daily is more effective than practicing every other day or once a week.

So how frequently should students practice math facts? A good goal is 4 minutes daily, ideally twice a day. I’ll add a link on the resource page to a recent study showing that daily practice is essential for achieving the highest success rates.

[08:35] What facts are we talking about?

Basic facts should include addition facts with all single-digit positive integers between 1 and 9 (so up to 9+9) and the related subtraction facts. Multiplication facts should go up to 9x9 (or, if you’re ambitious, up to 12 x 12) and the related division facts.

In terms of fluency, it’s good to aim for 40-60 math facts correct within 1 minute.

[9:06] When should students have math facts mastered? Ideally, aim for automaticity with addition and subtraction by the end of Grade 2 and with multiplication and division by the end of Grade 3. The goal is to get these in place early to help with new learning of more complex problems. Having said that, it’s never too late and it’s always important—work with students at any age to build automaticity using the techniques I’ll outline shortly. I’ll include a few links on the resource page that list grade-level milestones.

Today, I am focusing specifically on committing math facts to memory. By this stage, students have already worked with things like number lines, arrays and manipulatives—they understand that multiplication is repeated addition.

Now, the goal is to help them solidify these facts in memory so that they can recall them automatically.

[09:49] Pairing the stimulus with the response. To commit facts to memory, it's crucial to quickly pair the stimulus with the response—for example, pairing 7x8 with 56. This isn’t the time to use manipulatives, draw arrays or break the problem down using decomposition strategies.

The goal is to minimize the time between seeing the fact (7x8) and recalling the response (56). It’s all about forming a direct connection between the stimulus and the response.

Think of it like training muscle memory in sports. Like shooting a hockey puck or swinging a bat. You don’t want to focus on each part of the movement. To perform well in a game, it needs to be automatic. The process for becoming automatic with math facts is like those repetitive practice shots at the net – it’s like building muscle memory so that recalling the fact 7x8=56 becomes an instant reaction without having to break it down.

So, let’s get into it.

[11:13] A. Flashcards

First up, flashcards! These are fantastic for boosting accuracy, especially in the early stages of learning math facts – that acquisition stage. Flashcards can be used one-on-one with a student or in pairs or small groups during class time.

Here are the best ways to implement flash cards.

Start by assessing the student: Figure out which facts they already know. If they can answer a fact within two seconds, that fact is considered “known” at this stage. Separate the known facts from the unknown facts.
Start with 8 Unknowns: Begin with a manageable number of flash cards from the unknown facts pile – 8 flashcards may be ideal. For younger students or struggling students, you might want to start with 4 unknown flash cards. Use your judgement here.
Model (first time): Begin by modelling the process and saying the facts. Go through each of the 8 cards. First, hold up the cards and say, “6 x 7 is 42.” Then ask the student to repeat it.
Now the challenge. Go through each of the 8 cards. Hold up the card “What’s 6x7?” If they nail it, fantastic! If not, provide the answer and have them repeat it. Go through the set of 8 cards at least five times per session.
Swap out for new facts. After three consecutive days if the student can accurately respond swap out the known facts with new ones and repeat. If they’re still inaccurate, extend the practice with the same facts for a few days. Use your judgment here.

Flashcards are simple to use and effective, and you can adjust the process depending on the student.

Interspersing known with unknown: You could mix in known facts and unknowns, especially for students who get frustrated. For example, you could present 7 knowns and 3 unknowns for that extra encouragement and for some practice of known facts.

[13:25] Incremental rehearsal: Or you could use what’s called “incremental rehearsal”. Think of it like this: say you’re practicing a new piano song and you’re focussing on a new section that you don’t know that well. So you practice the new section and then you add in a familiar part and you keep adding more familiar parts, all the while practicing that new part until it all flows seamlessly. It’s kind of like that.

For math facts, incremental rehearsal works by concentrating on one unknown fact at a time and interspersing it with facts the student already knows, gradually increasing the number of known facts in the practice set.

It goes like this. Say the unknown fact is 6x7. Start by showing the flashcard and asking the student to repeat 6x7 is 42. First set: hold up 6x7, student says 6x7 is 42. Hold up 3x5 from the known pile, student says 15. Second set: hold up 6x7, student says 6x7 is 42, hold up 3x5 they say 15, now hold up another known fact 5x5, student says 25. Repeat this process, adding a known fact every time, until your last set starts with one unknown 6x7 and presents 9 known facts.

In the next set, 6x7 enters as one of the known facts. (I’ll include a video on the resource page, which was provided by Dr. Matt Burns, who I also had on a previous episode.)

[15:13] B. Cover, Copy, Compare

Next up is the Cover, copy, Compare method. This is great for building accuracy –in that acquisition stage. It’s perfect for individual use or class-wide. Plus, it’s not limited to math facts—it’s also effective for things like learning to spell and mastering other foundational skills.

I kind of think of it like this. Say you’re trying to sketch something from memory, like a picture of a dog. A good way to do that might be to examine the picture of the dog, cover it up and try to sketch it, then compare your sketch with the original, fixing it where necessary and then repeating the process until you get it right.

Cover-copy-compare is kind of like that, but for math facts.

A cover copy compare worksheet has a math fact with the answer (like 6x8=48) plus an empty space beside it. There are around 24 per page. I will put an example on the resource page if you’d like to follow along.

Here’s how it works:

Look at the Problem: Start by having the student read the problem and its answer. “6x8= 48.” This could be out loud or in their head, depending on the setting.
Cover It: They cover up the problem with their hand or a piece of paper.
Answer from memory: They try to write down the problem and answer from memory: 6x8=48.
Uncover and Compare: Now they uncover the original to check their answer. If they’re wrong, they cross it out and rewrite the correct one.

This method offers repeated practice, and feedback.

Students can write, say, or think of the answer, depending on your approach. Writing provides a permanent record and may be ideal for classwide instruction, though it takes more time, especially if some students may have handwriting deficits.

Saying the answer aloud or thinking it can increase response rates. However, if a student fails to increase their fact accuracy or fluency you don’t have tangible proof that they engaged in what’s known as a learning trial (i.e., paired the problem 7x6 with the answer 42). So, this can make it harder to measure improvement over time. Use your judgment to choose the best method for your setting.

I’ll link to some free worksheets in the show notes so you can try it out.

[17:49] C. Taped Problems

Now, let’s talk about taped problems. Taped problems can be used in both the acquisition stage and the fluency stage. This is a great method–perfect for use in a classroom or one-on-one. And it’s fun, b/c students try to "beat the computer."

There are two ways you can do this: You can use the audio files and corresponding worksheets that I’ve linked to on the resource page, or the teacher, parent or tutor can act as the computer, by providing the audio cue (the problem 6x7) and feedback (42).

But if you’re recording scores, you will want to download the worksheets.

Here’s How It Works:

Computer reads the problem. A computer reads the problem, say “7 x 8” and pauses for 2 seconds before revealing the answer, “56”. Students try to beat the computer and write down their answer first.
Student Checks Answer: If the student gets it wrong, or runs out of time, they write in the correct answer, recording their overall score at the end.

Taped problems increase both accuracy and fluency. Plus, it’s a fun challenge for students as they try to beat the computer.

[18:57] The role of games in building fluency: Before we move on to the next method, let’s take a moment to discuss games and their role in building fluency with math facts. Taped practice can be considered a game b/c students are trying to beat the computer. Taped practice has been shown to enhance both accuracy and fluency.

You could also create a game like Flashcard War, using the flashcard techniques I discussed earlier. In this game, give students 1 or 2 seconds to answer each question; if they respond correctly, they earn a point, and if not, you get the point. This game can also be integrated with class-wide peer tutoring, focusing on known versus unknown facts and the incorporating appropriate set sizes (like 8 new facts focussed on at a time). Flashcards, when used as I described earlier, have been studied and are known to be effective.

However, many other games may not be effective.

There are a couple of reasons for this: First, any method you use for building automaticity with math facts should allow for targeted practice; this is especially important during the acquisition stage. This means we need to be able to systematically select which math facts to emphasize, and many games do not do that.

Second, the approach should promote high rates of responding, ensuring that students are answering a lot of math facts during the session to maximize learning opportunities and reinforcement. Taped practice is specifically designed to achieve these goals, but if a game doesn’t incorporate designated sets of math facts along with high rates of responding, it’s unlikely to be very effective. Also, the appropriate time to use games is during the fluency stage, when students are already accurate but you’re trying to increase speed – not during the acquisition stage.

[20:52] D. Explicit Timing

Finally, we have explicit timing, which is a powerful and important tool for building fluency. This is introduced at the fluency stage. Timed practice is crucial for students who are accurate, but slow.

Incorporating timed practice is essential so that students become automatic with math facts – remember we are aiming for 40 - 60 math facts correct per minute. Accuracy is an important first step, but it’s not enough.

Why fluency, built through timed practice, is important. Think about the difference between a student who takes twice as long as another student with their math facts and think back to the ladder I talked about at the beginning. Say the first student can answer 25 math facts per minute and the second student can answer 50 math facts per minute.

The first student will struggle more with problems that rely on math fact recall. In topics like fraction addition, they’ll need more time to calculate common denominators, limiting how many problems they can complete in a session. Meanwhile, the faster student gains more practice, now widening the gap on an important math skill – adding fractions. With slower recall, the first student misses out on critical practice and is at risk of falling behind, creating a snowball effect in their learning.

We can get that student to a point where they’re as fast as the second student, but this is where timed practice comes in.

Now, the key with explicit timing is introducing it at the right time; ideally you should introduce timing when students are mostly accurate with their math facts, which means they’re getting them right most of the time (say 90% of the time), but they are slow. Assess students – if they’re at around 20 digits correct per minute, this is a good time to introduce explicit timing. By digits correct per minute – we mean if the student writes 7x6=41, that counts as one digit correct. This is good for assessing to see if students are ready for explicit timing. Students will then track their progress in terms of problems correct per minute – meaning we want to make sure they get 7x6=42, with the aim to reach 40-60 problems correct per minute.

Here’s how explicit timing works:

Give students math facts sheet and time for one minute. Provide students with a full sheet of math facts–each sheet I’ll link to on the resource page contains 72 facts–and have them solve as many as they can in one minute.
Provide instructions. Instruct students to complete the problems in order, working across the rows. This approach prevents them from jumping to the questions they can answer quickly. We want to ensure they practice all math facts and not just the ones they already know well.
Progress monitoring. Progress monitoring is crucial in this process. Students should record their scores (problems correct per minute) on a personal graph each day and aim to improve upon their previous scores.

Students should track their progress over time, trying to beat their previous scores. This builds fluency and fosters a sense of accomplishment. Celebrate their hard work and remind them of how far they’ve come and how it will benefit them when they learn new math concepts.

[24:48] Again, consistent daily practice is important and try to distribute timed practice throughout the day, perhaps once in the morning and once in the afternoon. This approach has been shown to increase learning rates.

Through a combination of timed practice, performance feedback, positive reinforcement and consistent daily effort, students will see measurable progress over time, giving them the confidence and skills they need to tackle harder math concepts, which is ultimately our goal.

[25:01] Conclusion:

I hope you find these strategies useful. Again, the techniques I discussed today have been shown to work with a wide range of students across ages, skills and settings.

Remember, the key to success is frequent, short practice sessions combined with plenty of encouragement. And, daily practice has been shown to be the most effective approach.

Aim to practice math facts every day–not just every other day or once a week–but consistently for at least 4 minutes each day.

Building automaticity with math facts is an essential investment in a student’s future. The time and effort you put in now will pay off, saving them from frustration and challenges down the road.

Once again, a huge thank you to Dr. Brian Poncy for his invaluable contributions to this episode.

Now, we need your help to reach people who could benefit from this information. So, please do me a favour and share this episode with your networks.

Until next time, keep practicing those math facts!

As always, we've included a resource page that has links to articles and books mentioned in the episode.

If you enjoy this podcast, please consider showing your support by leaving a five star review on Spotify or Apple podcasts. Chalk & Talk is produced by me, Anna Stokke. Transcript and resource page by Jazmin Boisclair. Social media images by Nicole Maylem Gutierrez. Subscribe on your favorite podcast app to get new episodes delivered as they become available.

You can follow me on X for notifications or check out my website, www.annastokke.com, for more information. This podcast received funding through a University of Winnipeg Knowledge Mobilization and Community Impact Grant funded through the Anthony Swaity Knowledge Impact Fund.