The debate rages on. Do students need to master math facts?

Drum roll please 🥁. . . yes, students do need to master math facts.

Research has identified that when students master math facts leading to

early fluency, later on they will experience success in math.

Before I share the 11 Easy Activities, I will elaborate on why it is important to master math facts.

But, for those who want the TL:DR tidbits, scroll straight to the end. 😉

## Why do students need to master math facts?

Math facts fluency helps students to figure out more complex math work like multi-step word problems, model solutions, or play around with systems of equations by freeing up brainpower or working memory.

Without math fact fluency students can forget the initial problem as they focus their attention on basic arithmetic.

Determining the answer to 4×6 by repeated addition, (6+6+6+6) is possible, but it becomes cumbersome and time consuming over time.

Students who need to continue to resort to this option will take more time to get less done, and eventually they will become increasingly disengaged with math.

Student engagement is vital to both learning and effective classroom management.

Constantly being behind their peers will leave them frustrated, and may lead to math anxiety.

Because of the availability of math tools (abacus, calculator, Google, number lines etc.) people debate whether or not it is important for students to master math facts.

Although it is true that these tools need to be available for students with a true math disability such as dyscalculia , it is equally true that whenever possible students also need to master math facts for math fact fluency.

## Why math fact fluency is important

Although I no longer spend much time (or any time for that matter) adding or multiplying fractions, I do recall that both processes involve being able to multiply.

Multiplication fluency is linked to success with fractions.

Consider this equation. : 3/6 + 4/9 = __

To find the solutionI must find a common denominator: 18/36+16/36 which involves multiplication.

Then I want to reduce the fraction: 34/36 = 17/18 which involves division or even knowledge of fact families.

3/6 + 4/9 = 17/18 . . . Wow! I have not done anything like that for years that I recall.

However, I could easily problem solve the answer because of my math fact fluency literally made the common denominator appear in my brain with very little thought on my part.

## Math facts addition and subtraction to 20

Addition facts are foundational to the rest of elementary arithmetic.

As students master math facts to 20 for addition, students will have more confidence as they tackle:

- subtraction.
- word problems.
- multi-digit addition and subtraction.

Students typically master math facts addition and subtraction to 20 simultaneously, and through this they will learn to master math facts families; a concept they will hopefully recognize more quickly when they are learning multiplication and division.

That will make multiplication and division so much easier to master.

Consider this, if students know that 6+7=13, it is so easy to make the leap to 26+47=73 once they are able to fluently do that regrouping in their head.

Once they know that 13 – 6 = 7, it is possible to see that 73 – 47= something that ends with a 6 (or at least that is far as I get easily). From there it isn’t a huge challenge to sort out the tens column.

However, if these calculations don’t come easily then math anxiety might set in, and all too often people believe that they “can’t do math.”

Although math anxiety may mimic a math disability such as dyscalculia, they are, in fact, two different things.

One of the differences is that math anxiety uses a lot of the working memory, and that may create lower achievement in math, which leads to more anxiety.

A vicious circle. 😞

## Creating a Math facts program: How to teach math facts fluency

To master math facts for fluency means that the student can quickly recall their math facts in addition, subtraction, multiplication, and division.

The steps to master math facts are:

### 1) Conceptual understanding

To begin with they will need a conceptual understanding of what they are doing.

This means that when they are adding 2+3, they are able to show with blocks, or other manipulatives, or with a drawing what the numbers and plus sign mean.

### 2) Understanding their math strategies

There are a few widely taught math strategies:

- Counting on and back by one
- Counting on and back by two
- Make ten and parts of ten
- Adding and subtracting doubles
- Adding and subtracting near doubles
- Ten more ten less

And there are some other less widely taught math strategies:

- Adding and subtracting 8
- Adding and subtracting 9
- Adding and subtracting 11

Students need to understand the relationship between these strategies, and when best to apply each one.

They also need lots of opportunities to practice drawing and modeling these strategies to give them a deeper conceptual understanding.

When students master math facts they are able to easily move between these math strategies applying what is necessary to problem solve for the correct answer.

### 3) The importance of memory to master math facts

Throughout the process of learning and understanding their strategies they are making connections and developing their number sense.

We will jump into ways to memorize math facts a bit further along.

However, they still need repetitive opportunities to memorize them.

I don’t remember the process for mastering my addition facts, but I do remember standing beside my desk with my class calling out the times table day in day out. 🥴

## Determining math facts mastery

A student is considered to have achieve math facts mastery if they have achieved these key components:

1) Flexibility – Can they easily apply different strategies to determine the correct one?

2) Appropriate strategy use – do they end up selecting the best strategy for the problem?

3) Efficiency – Are they able to quickly weed out the strategies that are obviously not appropriate?

4) Accuracy – do they solve the problem accurately?

A strong number sense is also important. Knowing that 7×8 is 56 is fantastic.

However, when your memory fails (as mine does on the daily) to know that 7×7 is 49, and that 7 more gives you 56 provides. This is a part of the essential flexibility that I mentioned in #1 above.

It is easy to see how the students that achieve math facts mastery will be more engaged, effective and successful math students.

## The down side to math facts sheets like mad minutes

Mad minutes have been around for a long time. Far too long in my opinion.

They can be fun for strong and competitive students. But if they are the primary method of practice for students to master math facts, they are not good enough.

For far too many students, mad minutes are anxiety producing. Even if students do not feel anxious they may be more focused on beating their peers or the timer than actually remembering the math facts.

There are better ways to master math facts than to complete boring row after row of math facts sheets.

## How to practice math facts

### Students need different types of opportunities every single day to practice.

The 11 Best Easy Steps to Master Math Facts are:

- Send home games and resources for students to practice with their families about math fact fluency.
- Listen to and sing songs. Some examples: Doubles, Doubles Plus One.
- Celebrate every time you see a strategy applied.
- Have a growth mindset and model it to the students.
- Incorporate individual activities like color-by-number or digital resources.
- Include partner games like board games.
- Plan small group games like card games.
- Enjoy whole class activities like write the room or number talks.
- Use online programs like Splashlearn
- Invite students to track their own progress with some kind of progress tracker. Copy a free tracker here.
- Create a system so students can independently work through them sequentially. I share mine a bit further on.

Students will need you to provide a variety of opportunities to master math facts on a daily basis. And they should continue to practice until they are able to recall a fact within 2 seconds.

### Juggling, and incorporating, all these great 😉 ideas to master math facts

Some activities we did as a whole class, like write the room activities as a part of a math warm up or to practice a skill.

Activities like board games the children enjoyed with partnerse, but the game might have been adapted to their level to support differentiation.

Computer activities were done as individual activities as a part of math centers, typically on Friday when they were pretty done for the week.

But worksheets, like color-by-number, would be kept in my filing system. I could easily direct students there during math warm ups, for early finishers, or even a no-prep sub-activity.

### Organizing worksheets to keep your sanity

Students did not always finish the activity in the time I gave them, and they stored it in their binder until the next time with their math tracker.

The found these independent activities in my numbered filing system.

Each strategy, starting with Counting on 1, had a series of worksheets that a student needed to complete before they could go on to the next strategy.

Once they completed, marked and corrected a worksheet they received a sticker for it on a worksheet tracker that had the right number of spaces for each strategy. I spot checked their worksheets to help maintain the honour system, but the children were pretty good about it.

Sometimes they were confident they had been able to master math facts for a particular strategy before completing all of the worksheets. Then they got a simple assessment.

Depending upon the day it may have been as simple as a one on one verbal quiz. Then I just needed to initial their math fact tracker. Very simple record keeping done on the spot.

Once they have mastered the math facts from one math strategy, they can go on to the next strategy. But you will want them to revisit each strategy during spiral review.

## How to set each child up for success to master math facts

Last but not least, it is best if you can differentiate math strategies when student work to master math facts.

Differentiation in math is essential for your students to successfully master math facts as determined by

Lev Vygotsky’s theory on the Zone of Proximal Development or (ZPD) identifies what a student may not be able to do on their own, but may be able to do with appropriate support and guidance from adults or peers.

Think of the ZPD as a bullseye target. In the center is what they can do independently, any work that you give them here is just practicing what they already know and may, over time, lead to boredom and disengagement.

The next circle out is what they can stretch themselves a little bit to do with appropriate instruction, any work you give them to do here can be energizing and engaging for them. This is their ZPD.

Finally, the outer layer is work which is beyond the student’s grasp, and it will be frustrating.

The possibility that all of your students are in the same ZPD at the same time in all subjects is nil.

So, yeah. Differentiation is important.

## Coming soon to a blog near you

My next blog post, “7 Fun Ways To Learn Math Facts And Offer Differentiation” will cover how the activities I have shared here are already differentiated (hence the “Easy” in the title of this blog post), or can be easily differentiated.

Until then, if you haven’t started providing regular opportunities for your students to master math facts, just take it one step at a time. What appeals to you the most?

Excellent! Try that. I would love to hear how that went in the comments!

Blog posts I referenced in this post:

What is Student Engagement? Why is it Important?

What is classroom management? Why is it Important?

How to Unlock the Mystery of Differentiation in Math

TL;DR

The Best Easy Steps to Master Math Facts are:

- Send home games and resources for students to practice math fact fluency with their family.
- Listen to and sing songs. Some examples: Doubles, Doubles Plus One.
- Celebrate every time you see a strategy applied
- Have a growth mindset and model it to the students
- individual activities like color-by-number or digital resources
- partner games like board games
- small group games like card games
- whole class activities like write the room
- Use online programs like Splashlearn
- Invite students to track their own progress with some kind of progress tracker.
- Create a system so students can independently work through them sequentially.