## Teaching Math Fact Fluency | 6 Signs Your Class Is Failing

High-stakes state tests do not directly test fluency on math facts, although they should.  Your students can become bogged down in deriving basic facts during state testing.  When that happens they will be unable to demonstrate the higher-level math skills they have been learning.  You may have a math fact fluency problem, depressing your math achievement scores, but not even know it.  Here are six things to look for–to evaluate for yourself.

## 1) Finger counting during math testing shows a fact fluency problem

Students who are counting on their fingers (see above) during math testing are a definitive sign of a math fact fluency problem.  Finger counting is a bad sign in grades 3 and above, where they should have mastered math facts.  Students who don’t know the facts, need to use crutches to derive the answers to math facts.  Crutches make doing simple calculations take a long time to complete anything.  Your students may perform poorly on state tests just because they won’t complete the test for lack of time.

## 2) Students who lack math fact fluency need times tables available

When students in grades 3 or 4 and up have to do multiplication, they either have to know their facts or have a crutch.  If you see times tables on student desks that shows that the students need these crutches, and therefore do not know the basic multiplication facts.  Student folders sometimes come with these on the inside.  Some teachers put up a large poster of the multiplication facts–even though students find it nearly impossible to use from their seats.  Others provide laminated cards to the students which appear suddenly when students are set to do their “math work.”  When you see those times tables being used by more than a couple of students during math, you can tell you have a fluency problem.

## 3) Students who lack math fact fluency don’t participate in math lessons

Good teachers work to engage the class.  One good way, while working a problem for the class, is to ask the class for the answers to math facts.  Watching a lesson you may be able to spot a class that lacks fact fluency.  For example, imagine you watch the teacher demonstrating this problem.

Class, we begin this problem by multiplying nine times four.  What’s nine times four, everybody?”  [Only a couple of students answer.]  Yes, 36.  Now we write down the six and carry the 3 tens up to the tens place.  Next, we multiply nine times six.  What’s nine times six, everybody?”  [After a long silence, one student answers.] Yes, 54.  And we add the three to the 54, what do we get?  [Several students call out the answer.] Yes, 57.  That’s what we write down.

That interchange tells you there’s a math facts problem in this class.  When the problem is very easy, like 54+3 you get a good response.  When the fact is a “hard” one, you get silence and then one student answering.  Medium facts get minimal response.  This is a class that does not know their math facts.

## 4) Over-reliance on calculators signals a lack of math fact fluency

There are two kinds of over-reliance on calculators you may see in classrooms.  In the first kind, you see students who do not know facts using calculators to tell them the answer to single-digit facts they should have memorized.  Using calculators for single-digit facts is terribly slow and inefficient–and not what they are designed to do.  You can see this over-reliance on calculators when observing in a classroom.

The second kind of problem is harder to spot. Using calculators without knowing math facts instantly can be dangerous.  It is easy to make a data entry error, AKA a typo.  When a user does that, they’re assumed to know math facts well enough to know when the answer is wrong, as in the example pictured here.  A student who doesn’t know that 5 times 8 is 40 and therefore knows that 521 times 8 has to be more than 4,000 will accept the answer displayed on the calculator.  Accepting incorrect answers from the calculator is a sign that students do not have an adequate mastery of facts.

## 5) Avoidance behaviors in math signal a lack of math fact fluency

Having to count out facts or look each fact up in a table is very slow and onerous.  Students come to hate slogging through math computation that is so hard for them.  Conversely, students who know facts instantly, hop right into assignments to get them done.  Students like going fast doing math problems, just like they run for the joy of it on the playground.  How do you know there is a fluency problem in the classroom?  Students who lack fluency start avoiding getting started on computation work by getting water or sharpening pencils or just taking a break first.

## 6) Really slow computation during math lessons is due to a lack of math fact fluency

Good math teachers assign, within their lessons, a few math computation problems to do independently and then be checked as a group.  If students know math facts they can do a few problems in a minute or two.  Students who do not know math facts may take ten minutes or more to do the same mini-assignment.  Students who are done and waiting with nothing to do, begin talking and distracting the others.  When there’s that big of a discrepancy between the first and the last student to do a few problems, there is a fact fluency problem in the class.

## To be sure–give school-wide 1-minute tests of math fact fluency

If you see hints that your school may have a math fact fluency problem, it isn’t hard to know for sure.  It only takes a couple of minutes.  You can have everyone in the school take written 1-minute tests of math facts pretty easily.  However, you’ll also need to evaluate how fast students can write.  Students can’t answer math fact problems any faster than they write.  You cannot expect a student who can write only 25 answers in a minute to answer 40 problems in a minute. Conversely, a student who can write 40 answers in a minute is not fluent with math facts if he answers only 30 problems in a minute.

You need a test of writing speed as well as a chart to evaluate their performance and the tests for the four main operations of addition, subtraction, multiplication, and division.  Print these out for free at this link.  But basically, a student who cannot answer math facts at 75% of the rate at which they can write, needs intervention.

Teaching math fact fluency is necessary, of course, for fluent computation. Math fact fluency is also required for understanding and manipulating fractions. Find out more ways of successfully teaching math fact fluency to your students and why this skill is essential.

If you would like the free use of use the Rocket Math Online Game to assess for fluency, please contact Dr. Don at [email protected]

## How to set math fact fluency goals and objectives for IEPs

Setting IEP goals and short term objectives is a snap when you measure growth in fluency.  Not only are fluency growth goals easy to write and set, they are easy to measure and monitor.  You can adjust the intensity of the intervention ensuring the student can achieve the goals and objectives.   Finally, you’ll be able to demonstrate growth and improve student achievement.

## Fluency with math facts ensures success in math

Math facts are a “tool skill” of mathematics.  Students need to be able to call math facts to mind instantly.  Students should not have to hesitate or stop to “figure out” single digit math facts.  This is a tool they need in order to do math assignments quickly and easily. Knowing math facts instantly enables students to concentrate better and learn math more easily than students who are distracted by figuring out facts.  Once students are fluent in math facts they can keep up successfully in regular math classes.

## Test the student’s present level of performance (PLOP) on facts

It only takes a minute to have students take a timed test in an operation to see how well they know their facts. You want to know how many facts in that operation the student can answer in one minute.  Test first-grade students in addition and second-graders on subtraction. Starting in 3rd grade and up, multiplication has priority, so test and focus on multiplication facts for your IEP.  You can move on to other operations once multiplication facts are fluent.  Here is a link to a page with Rocket Math’s one-minute pre-tests in all four basic operations.  However, you can’t evaluate whether a given student is fluent until you know how fast they can write. Students who are fluent with facts can answer them about as fast as they can write.  But they cannot answer them any faster than they can write.

## You must also test the student’s writing speed

You cannot set achievable goals of how many facts a student should answer in a minute without first knowing how fast they can write.  That sets the upper limit.  So test their writing speed by having them write a mix of one and two digit numbers for one minute.  See to the left, Rocket Math’s one-minute Writing Speed Test From the link you can print it out for free.  Once you know how fast your student can write you can evaluate their performance on the one-minute fluency tests.

## Is math fact fluency an area of need?

Now that you know the student’s writing speed you can evaluate their present level of performance.  Rocket Math has a handy evaluation sheet you can use to determine if there’s a need.  Or you can do the math yourself.  If students answer math facts at a rate less than 75% of their writing speed, they are weak and math facts is an area of need. Putting math fact fluency on the IEP and working on it as a goal would be very helpful.  If the student can answer math facts at a rate that is 90% of their writing speed, they are strong and this is not an area of need.  Between 75 and 90% of their writing speed they are good, but could benefit from some more work.

## Get a starting point on the progress monitoring measure

If you’re going to test every week with 1-minute timings and you have a bunch of those available, you already have a 1-minute timing starting point.  If you’re using the Rocket Math Worksheet Program as your intervention, it uses 2-minute timings to measure progress weekly, so you’ll want to use one of those for your starting point.  (You can’t just double the 1-minute score because students don’t usually keep up at the same rate for two minutes.)  So give one of the 2-minute timings, in the operation you’re going to focus on, to set a starting point.

## Set the math fact fluency goal based on writing speed

Students who have successfully developed math fact fluency in an operation can write answers to math facts almost as fast as they can write. As fast as their fingers can carry them is the most you could expect.  You could set a goal at 80% of their writing speed. It would still be rigorous enough.  If they met that goal the student would be fluent in math facts.

You can do the math yourself from their writing speed test. The Rocket Math Worksheet Program has weekly progress monitoring 2-minute timings.  In that case, your student’s goal for the 2-minute timing is on the handy goal sheet ** that you put into each student’s folder.  You can see the student shown here filled in 24 boxes on the Writing Speed Test, so his or her goal for 2-minute timings would be 38 for the annual goal for the IEP.

## Create a graph and draw an aimline from starting point to goal

Now the coolest thing about progress-monitoring a fluency goal is that it is easy to graphically see on a weekly basis if the student is on track to meet the goal.  You simply create a graph, with enough spots at the bottom for all the weeks in the year.  Next you put in the starting point performance in the first week of the graph (or whenever you tested).  Then put in your goal performance at the end of the year.  Then draw a line between those two points.  That line is called the aimline and is shown in the example at the top of this article.

The pictured student began at 29 problems in 2-minutes.  Their PLOP was 29 problems correct in 2 minutes.  The student had a writing speed of 40 problems in a minute.  Therefore 80% of that is 32 problems in a minute or 64 problems in two minutes by the end of the year.  The aimline is simply a straight line between those two.  You can see that the first couple of two-minute tests did not meet the aimline, but by the third test the student was right on track for meeting the goal by the end of the year.

## Short term objectives (STOs) are set by the aimline

Once the aimline is drawn, the STOs are found by reading up from the date of the quarterly STO reporting date.  Wherever the aimline is on that date, that’s the STO.  In the example above the quarter 1 objective looks to be about 38 problems in two minutes.  The second quarter looks to be 45 problems in two minutes with the 3rd quarter at 53.  Very simple and easy to set and to read and report.  Since every student in Rocket Math should have a graph like this reporting to parents on a quarterly basis would be more more than showing them this graph.

## What if they aren’t meeting the aimline?

In all the struggle with writing and evaluating IEPs many times we forget the purpose.  IEPs are designed to evaluate whether our intervention is adequate to meet the student’s needs.  So if the student is falling below the aimline or doesn’t make the STOs what are we supposed to do?  Wringing our hands or shaking our heads sadly at the IEP meeting at the end of the year is not what is supposed to happen.  Instead we are supposed to be using these goals as a way to determine if we need to intensify our intervention.

## How do you intensify your intervention?

So if a student is not meeting the aimline when we monitor their progress we should re-double our efforts.  With Rocket Math that’s quite doable.  If the student is falling below the aimline for three weeks in a row, add another practice session each day.  The standard ten minutes a day for Rocket Math may not be enough for this student. So you need to arrange for them to get in another practice session each day.  Often a short trip to the Special Education room for a second quick session with the teacher or an aide will do the trick.  If two a day at school aren’t enough, maybe you can add one each evening at home.  Some students do need more practice to meet these goals.  The good news is that you can find out quickly with your graph and get going soon.

**The Goal Sheet was updated in 2021 to reflect the 80% expectation for IEP goals.  The update shows that students who can fill in 15 boxes in a minute can go ahead and do Rocket Math, while those who can only fill in 14 boxes are candidates for help with writing numerals in the Rocket Writing for Numerals Learning Track.

## Instant assessment for basic math fact fluency: Ask ’em!

Teachers and parents often ask, “How do I know if my children need to study math facts?” Here’s an instant math assessment you can do to test them for math fact fluency. Ask a student a “hard one” such as, “What’s 9 times 7?” or if they are in first or second grade, “What’s 8 plus 9?” If they start counting on their fingers or hesitate while puzzling it out, they do not have “math fact fluency.” They need a program of systematic math facts practice until they know them all “by memory,” as the Common Core State Standards (CCSS) say.

## Math fact fluency means instant recall

Some teachers and schools teach “tricks” for remembering facts that are supposed to help children. However, they should at most be a temporary crutch. Such techniques need to be replaced with instant recall. The student shown here is using the commonly-taught “doubles plus one” trick for figuring out the answer to, “What’s 8 plus 9?” This is not fluency. He needs practice in math facts so they become “automatic” in recall. If he is still having to do this in fourth or fifth grade, he’ll find math work slow-going and drudgery. He’ll also find it hard to follow a math lesson when he has to stop and puzzle out simple facts like this.

## Math fact fluency makes math easy

Students who know the math facts instantly can fly through their math assignments. They enjoy the exercise and feel good about their math abilities. On the other hand, students who have to count on their fingers, or use a number line or a times tables chart to do their math assignments come to hate math. It is so-o-o-o-o slow. I’m sad to say that when I taught elementary and middle school remedial students I knew they hated math because they had to puzzle out most of the facts. What else could I do but assign lots of math fact practice that they hated?

In graduate school, I learned how to design a math facts practice program in a way that every student can succeed in memorizing the facts. I put a paper-and-pencil program together back in the ‘90s and have been sharing it with people ever since. I called it Mastering Math facts, but everyone else just called it Rocket Math. That became its official name in 2007.

Teachers have been successfully using my nearly secret curriculum with wild success for decades. Oddly enough, students actually enjoy the Rocket Math Worksheet program. They enjoy the paired practice with a partner, and can actually see themselves learning and getting better.

## How to assess students in math

Before you start Rocket Math’s Online Game or Worksheet Program, it’s a good idea to find out which operations your student needs to practice most. Rocket Math offers a few tests to identify where your student should start their Rocket Math journey.

### Writing Speed Test

Many students aren’t able to write the answers to 40 problems in one minute, which is normal and doesn’t affect their math fact knowledge. Before administering the Operation Pretests, evaluate your student’s writing speed to make sure the results reflect your student’s true proficiency, and that they are not held back by their writing speed.

### Operation Pretests

Once your student has completed the Writing Speed Test, give them a pretest in one or more of the four basic operations.

### Evaluate Results

For students in 3rd grade and above, test multiplication first and then division. If students struggle with either of those two operations, they should start learning those operations. For 3rd graders and above who don’t struggle with multiplication and division, test addition and subtraction to assess any weakness. For students in 1st and 2nd grade, test addition first and then subtraction.

Evaluate your student’s results based on their individual writing speed with the Evaluation Chart for Pretests. Use their writing speed to determine if their performance on the Pretest is weak and shows a real need for work on math facts, or is good but could use some help, or strong and no practice is needed.

## Free Online Game subscription as long as you need to decide

There is no reason for students to be bogged down and discouraged by math, especially by lack of math fact fluency. This doesn’t need to happen to children. Every student is capable of memorizing basic math facts with a little effort and a carefully sequenced curriculum, like the Rocket Math Worksheet Program.

Or if a paper-and-pencil curriculum like the Rocket Math Worksheet Program involves standing at the copy machine, is not what you are looking for, Rocket Math is now online. The Online Game app starts with a complimentary initial subscription of 14 days. You can learn more about it at that link. Or you can just go ahead and register an account and start it on this link

Send an email to me at don at rocketmath.com and I’ll extend the complimentary subscription as long as you need to decide.** If you need one to ten seats it is a whopping \$4.50 a seat for a year. Twenty or more seats are \$2.50 each for the year and per-seat prices go down from there. Really there’s no reason to leave kids counting on their fingers.

## The Online Game never teaches anything wrong.

Are your students complaining that the Online Game said they were wrong, when they were right?  This is similar to a problem we found with students and their checkers in the Worksheet Program. Bear with me a second while I explain.

In the Worksheet Program students often complain to their teacher that their checker made them do the problem over, even though they weren’t wrong.  Trying to adjudicate such a dispute is nearly impossible, as veteran teachers have learned the hard way.  The extra practice didn’t hurt the students and you’re going to be inundated with complaints if you try to adjudicate them. In workshops we always counseled teachers to respond to such complaints with, “The checker is always right.  Just do the problem over again.”

The extra practice that the Online Game) makes a student do is never harmful.  The problem and the answer that Mission Control gives is never wrong.  When students complain to you about the game telling them a right answer was wrong, just tell the student, “The game is always right. Just do the problem over again.

## The Online Game only says right answers, so it’s not wrong.

The correction procedure says both the problem and the correct answer.   Students may say, “But, that’s what I put!” They are not confused. They are just complaining that they were “unjustly” corrected.  An unjust correction is relatively unimportant compared to an actual error.

The program never says a student’s answer is “wrong.”  The game does a correction whenever it does not process the correct answer within the time limit.  The student may hit the correct answer just a fraction of a second too late to be processed by the game. Even though correct, the game will say “Time’s Up” and do a correction.

Sometimes a student misses the button they mean to hit, they make a “typo,” and the game buzzes and the screen shakes “no.” Sometimes, a glitch occurs and it skips ahead to the next problem and processes the last answer as incorrect. However, the game can only say a problem and its correct answer as those are the only words that are recorded.  There are no recorded errors.  For example the game will say, “Six plus two equals eight. Go again.”  After that the game waits for the student to enter the correct answer AND waits for the student to hit the checkmark. No amount of arguing, “But that is what I put!” or “But that wasn’t the problem I was answering” will change it.

## The extra practice caused by an “unjust correction” is not harmful.

Students should listen to Mission Control while it is displaying and saying a problem and the correct answer.  Then the game will show the problem just stated without the answer.  Students will know what they should do. They should just enter the answer and hit the checkmark.  Students should just do the problem over again regardless of whether or not they think they entered the right answer.  The game never says anything incorrect and the extra practice won’t hurt them. While an unjust red “X” for an error seems terrible to students, it will not do anything other than give them more practice, which is good for them.

We  offer a \$50 gift certificate to the store of your choice if you can capture an error by the game on video, as we have never seen the game make an error and can’t replicate the problem.

## Document improved fluency by assigning a 1-minute RACE.

We have a feature that will allow you to assign a fluency test to all or some of your students. We call it a “1-minute RACE.”

### To Assign a Fluency Test 1-Minute RACE:

1) Select the students to whom you want to assign the test RACE, or Select All.

2) Click on the orange Bulk Action button.

3) Pull down to “Assign 1-min RACE on next login.”

After doing that, in your dashboard you will see that the 1-minute race has been assigned on the next login.
The next time those students login, they will be given the mission of doing a 1-minute race with ALL the facts in the Learning Track they are studying. They can skip facts they don’t know, by hitting the checkmark.

## A 1-minute test RACE is also automatically SCHEDULED after Sets A, i, R, and Z. See their latest results in Review Progress!

### Assign a 1-minute RACE individually also–at any time you wish.

You can assign a 1-minute RACE at any time for specific individuals as well, using the green Individual Action button at the end of their row.

• ## Export the test RACE results in spreadsheets.

• Separate exports for results from RACEs you Assign from the RACEs that are Scheduled after working through some levels in the Online Game (After sets A, i, R, and Z).

• ### See averages across your class or school.

• Each spreadsheet will show the average for your class as a teacher or for the school in the account of the Subscription Manager or owner.  There are separate averages for each Learning Track.
• ### See trends over time.

• You’ll see the improvement each student makes from the beginning after Set A to each of the subsequent tests RACES.

## Learn the Basics (add, subtract, multiply, divide) first.

Basic, optional, and alternative—there are a lot of different Rocket Math programs to help students learn math facts. A common question teachers ask is in what sequence should they teach the various Rocket Math programs? The basic programs of Addition, Subtraction, Multiplication, and Division (1s-9s) have priority and must be mastered by all students. Addition in the first grade. Addition and Subtraction in the second grade. Multiplication (as well as Addition and Subtraction) by the third grade. Then, all four, including Division by fourth grade. If a student is on track, those basics have first priority.

## Optional programs if the basics are already on track

The rest of the programs are optional and should be offered to students once the basics have been mastered and only then. The only exception would be in a school where Kindergarteners did not get a chance to learn how to quickly and easily write numerals, through using the Rocket Writing for Numerals program. In that case, you might take the first two months of the first grade year to run students through Rocket Writing for Numerals before beginning Addition (1s-9s).

If first-grade students are taking all year to get through sets A-Z in Addition, they need some extra help. You should intervene to help students who take more than a week to pass a level. Often they need to practice better or with a better partner, and some may need to practice a second time during the day or at home in the evening.

Another intervention would be to use Rocket Math Online Game for Addition facts, as students seem to progress much more quickly in the online game.  The Online Game has an adjustable game speed for first-grade students who are having trouble (their difficulty score is over 3) moving their fingers fast enough. First-grade students who finish the 1s-9s can move on to the Add to 20 programs for the remainder of the year.

## Fact Families is Another Way to Learn Addition & Subtraction Math Facts

There is another way to learn facts, which is called Fact Families. Instead of learning all Addition facts, students can learn Addition and Subtraction facts at the same time. A fact family consists of four related facts, for example: 3+2 = 5, 2 + 3 = 5, 5 – 3 = 2, 5 – 2 = 3.

It is challenging for students to switch between Addition and  Subtraction. But it does drive home the reciprocal nature of the two. There is no evidence that it is better to learn in fact families than it is to separate the operations. That’s why we offer both alternatives. Students can learn fact families up to 10 in first grade. Then the upper fact families, from 11 in second grade.

## Third-grade Students Must Learn Multiplication Facts

In third grade, Multiplication has priority, even if students have not mastered Addition and Subtraction. Multiplication facts are so integral to the rest of higher math that students are even more crippled without Multiplication facts than they are having to count Addition and Subtraction problems on their fingers. So do Multiplication first, then if there’s time, students who need to can go back to master Addition and Subtraction.

As in Addition and Subtraction, students can learn Multiplication and Division by fact families. In third grade, just the fact families through 20 need to be mastered. Once all three of these basic operations are under their belt students can go on to 10s, 11s, 12s in Multiplication. If that is done and there is still some school year left I’d recommend the Identifying Fractions program next followed by Factors.

## Fourth-grade Students Should Know Both Multiplication and Division Facts

Fourth-grade students need to have completed Multiplication before going on to Division.  They can also do Fact Families for Multiplication and Division, starting with facts to 20 and then part two is fact families from 21 on. If they complete Multiplication and Division, they should go back and do Addition and Subtraction. If those are not mastered, either straight up by operation or in families. Then students can go on to Identifying Fractions, then Factors, then Equivalent Fractions. They can go on to 10s, 11s, 12s Division, but it is less valuable than the pre-algebra skills of factors and fractions.

## Fifth-grade Students & Up Need to Know All Basic Operations First, Then Branch Out

Fifth-grade students should have completed all four basic operations (1s-9s). If students have not completed these basics (and cannot test out of them with the Placement Probes), then the sequence they should follow is Multiplication, followed by Division, then go back and complete Addition followed by Subtraction. Again, as an alternative, students can learn the basic facts in families. The same recommendations hold for students in any grade after fifth.

Once students have mastered the basics (1s-9s add, subtract, multiply, divide) the supplemental pre-algebra programs are recommended. These will help more than learning the 10s, 11s, 12s facts. I would recommend this order: Identifying Fractions, then Factors, followed by Equivalent Fractions, followed by Learning to Add Integers, Learning to Subtract Integers, then Mixed Integers.

## Rocket Math Worksheet & Online Game

Here is a quick and easy chart to help understand which operation/skill students need to learn in which grade level and which Rocket Math Worksheet and Rocket Math Online Game Level they should be at.

## The Ultimate Guide to Math Fact Fluency

Students counting on their fingers is a sure-tell sign that they didn’t acquire math fact fluency. It is sad to see students, ashamed of the only thing they know, counting on their fingers under their desks. Our elementary educational mission is failing students who haven’t developed math fact fluency, which  is the foundation to more advanced math skills.

Developing math fact fluency takes structure, organization, and work on the part of both teachers and students. In this article, I will share everything you need to know about developing math fact fluency.

## What is Math Fact Fluency

Math facts are single-digit problems such as 7+9 or 6×8 or 14-5, and so on. A common name for all the multiplication math facts is the “multiplication table.” Math fact fluency is the ability to answer all math fact questions instantly from recall without having to think through the problem.

Students should be able to recall math facts instantly without having to count on their fingers or  hesitate to think about the answer. This may seem like a high bar, but our brains are great at recalling an unbelievable amount of information daily, and with practice, math facts can be recalled the same way.

## Three Reasons Why Math Fact Fluency is Important

Math fact fluency is critical because it is a “tool skill.” Meaning, it is a tool that is used in the process of doing other math problems. Developing this tool skill makes learning math easier as concepts get more complicated. This tool skill needs to be automatic in the student’s brain, in order to save precious short-term memory resources.

Math fact fluency can be compared to reading. Students must recognize words automatically to comprehend the author’s meaning. Otherwise, they will spend too much time decoding individual words.

When students are fluent in math facts, they are focused on the math process as a whole, rather than stopping to puzzle out the facts. This is important for three reasons:

### 1. Students with math fact fluency make fewer errors

Students who lack math fact fluency often make careless errors doing arithmetic computations . If they devote too much energy to deriving math facts, they lose sight of the problem at hand and make mistakes that would otherwise be obvious. Those who can effortlessly recall math facts can concentrate on what they are doing, and ultimately make fewer errors.

### 2. Math fact fluency makes learning math easier

When a new math procedure is introduced, students who have math fact fluency can easily follow the thread of instruction. Without this fluency, students fall behind instruction or demonstrations as they try working out math facts. This distraction takes away from a student absorbing all of the details necessary to successfully learn new math processes.

The first teacher to use Rocket Math to teach subtraction facts to her second graders realized the benefit first hand. She told me that with Rocket Math, she was able to teach regrouping in subtraction in just three days.

Her students mastered the math facts, and the outcome was extraordinary. The teacher shared that since these students had developed fluency in subtraction facts, they were able to learn other procedures easily.

### 3. Students who have developed math fact fluency enjoy math and always complete their work

Having to count on your fingers or look up facts on a timetable is slow and onerous. When students can’t work quickly, math problems become a dreaded drudgery. Students are motivated by mastering new skills, which will help them work faster and build confidence . Those who can quickly recall math facts will complete their work with ease , and enjoy the feeling of accomplishment.

## How to Build and Improve Math Fact Fluency

Building and improving math fact fluency requires a systematic effort over the elementary years. It is a long climb to achieve mastery and there are no short-cuts.

Consistent daily practice throughout elementary school is important for retention. Slow and steady wins the race when building math fact fluency.

Math fact practice should be structured in such a way that students are learning a small number of facts at a time. These small groups of facts  should be practiced daily until students have reached mastery. As time goes on, more groups of math facts are introduced systematically in small amounts for students to master.

Learning 1s to 9s facts in the four basic operations will take elementary students months to master. Worksheets and game applications are two of the best ways to teach math fact fluency over time. Combining structured math fact learning, practice, and evaluation with fun math fact games helps students develop number sense and understand complex numerical relationships.

## Teaching Math Fact Fluency with Worksheets

Worksheets are popular tools that teachers reach for when teaching math facts, but sadly, they often fall short for the majority of students. A few select students will begin memorizing the facts on their own accord in order to make the worksheets easier, but most students will continue to slowly work out the facts either on their fingers or in their heads. These students may never develop a strong recall of the facts and become flustered when asked to answer problems on the spot.

Fortunately, there are specific worksheets that are effective in building math fact fluency. The key is having worksheets that are structured, systematic, and sequenced. Each worksheet should only have two to four facts to be learned.

By working on only two to four facts, these worksheets help teach memorization for a strong recall, rather than reinforcing working out problems slowly. Students  will then be able to remember these small groups of facts easier, and by the end of the worksheet will be writing answers from memory.

## Teaching Math Fact Fluency with The Rocket Math Worksheet Program

The Rocket Math Worksheet Program improves upon this concept by using paired practice and saying facts aloud. Students partner up and practice quickly recalling facts together. One student asks the questions and watches for when their partner hesitates to answer. He or she then gives his or her partner more opportunities to practice the harder facts.

The students switch roles, and after both have answered questions, they then take a one minute test on the facts that they have learned so far. If students are answering as fast as their fingers will carry them, then they pass the level and move on to the next worksheet in the sequence.

Ten minutes of practice  every day gets the job done, especially when paired with using these facts in higher level math problems.

## Teaching Math Fact Fluency with Games

In addition to worksheets, schools of education tell teachers to use games to “teach” math facts. Unfortunately, most games and fun activities do not actually help individual students learning math facts to the level of fluency. These games, such as bingo or dice, have several fallouts:

• Students spend most of their time waiting for their turn rather than practicing facts.
• They do not focus on teaching a small group of facts in a manner that helps students commit them to memory.
• The games do not adjust to an individual student’s level of fluency.
• Students can pace the game slowly enough to have time to figure out facts rather than requiring recall.
• It is difficult to keep every student engaged, as those who are behind are less likely to participate.

## Using the Rocket Math Online Game as an Effective Way to Teach Math Fact Fluency

There are games that are very effective at building math fact fluency. Games such as the Rocket Math Online Game have several important features that make a big difference.

1. Every student is engaged in answering math facts—not waiting for a turn.
2. Students learn only a few new facts at a time so that they can remember them.
3. The game provides lots of focused practice on each set of facts.
4. The game requires students to answer quickly, which guarantees the students recall the answer rather than “figuring it out” over and over.
5. The game gives an immediate correction and extra practice on any facts that students cannot answer quickly and correctly.
6. The game only introduces new facts once students demonstrate mastery of facts learned so far.
7. The game gives students explicit feedback so they have a sense of accomplishment as they work their way through an operation.

## Math Fact Fluency Benchmarks

The following benchmarks are reasonable expectations for a school that has an effective math fluency program in place. Of course, a student cannot write math facts any faster than they can normally write, so take that into account when looking at fluency benchmarks. Adjust the benchmarks for students who do not write quickly.

### Kindergarten Numeral Writing Fluency Benchmarks (digits)

Start of Year Mid-Year End of Year
20 digits per minute 40 digits per minute

### First Grade Numeral Writing Fluency Benchmarks (digits)

Start of Year Mid-Year End of Year
40 digits per minute 60 digits per minute 60 digits per minute

### First Grade Math Fact Fluency Benchmarks (problems per minute)

Start of Year Mid-Year End of Year

### Second Grade Math Fact Fluency (problems per minute)

Start of Year Mid-Year End of Year
Subtraction: 12 per minute Subtraction: 25 per minute

Third Grade Math Fact Fluency Benchmarks (problems per minute)
Start of Year Mid-Year End of Year
Subtraction: 30 per minute Subtraction: 30 per minute Subtraction: 30 per minute
Multiplication: 30 per minute Multiplication: 30 per minute

Fourth Grade Math Fact Fluency Benchmarks (problems per minute)
Start of Year Mid-Year End of Year
Subtraction: 35 per minute Subtraction: 35 per minute Subtraction: 35 per minute
Multiplication: 35 per minute Multiplication: 35 per minute Multiplication: 35 per minute
Division: 20 per minute Division: 35 per minute

Fifth Grade Math Fact Fluency Benchmarks (problems per minute)
Start of Year Mid-Year End of Year
Subtraction: 35 per minute Subtraction: 40 per minute Subtraction: 40 per minute
Multiplication: 35 per minute Multiplication: 40 per minute Multiplication: 40 per minute
Division: 35 per minute Division: 40 per minute Division: 40 per minute

Math Fact Fluency Assessment

Use this printable packet of free math fact fluency assessments to test your students’ skill levels relative to  the above benchmarks. This will give you a clear idea of your students’ fluency and where there is room for opportunity.

Rocket Math’s assessment packet includes a writing speed test, which helps create realistic expectations for individual students. Using the goal sheet ensures you will evaluate the individual student math fact fluency in light of their writing speed.

Rate students as:

1. Weak, needs fact work
2. Good, but fact work could help
3. Strong, fact work not needed

Special triage priority: if you have fourth-grade students and above, start with multiplication facts. Multiplication facts are essential to future success in math above fourth grade. Even if fourth graders are counting on their fingers for addition and subtraction, teach multiplication mastery first. If fourth graders move to the next grade without strong multiplication fact fluency, they will have a hard time successfully progressing through math.

## The Best Tools for Developing Math Fact Fluency

With the right tools, any student can develop math fact fluency and have fun while doing it! Students use Rocket Math’s Subscription Worksheet Program to practice with partners, then take timed tests. Rocket Math also offers math facts practice online through the Rocket Math Online Game. Students can log in and play from any device, anywhere, any time of day! Start a free trial today.

Both the worksheet program and the online game help students master addition, subtraction, multiplication, and division math facts for a lifetime of success in math.

## Beginning Numerals and Counting

Dr. Don has created another math program and put it into the Universal level virtual filing cabinet at Rocket Math. This is a beginning program for kindergarten students and is to help them learn counting and numerals. That means they can’t learn on their own, the teacher must provide instruction. Teachers can use the counting objects kindergarten worksheets to effectively teach students to count objects aloud and then match the word with the numeral. You can see the top half of Worksheet A above.

If you’re already a Rocket Math Universal Level subscriber, you can find the worksheet in your virtual filing cabinet. Not a subscriber yet? Get the counting worksheets.

## I Do: Demonstration of Counting

Each worksheet begins with a demonstration of counting objects and circling the numeral that matches. On Worksheet A, there are only the numerals two and three to learn. The teacher demonstrates (best with a document camera so all students can see) how she counts the objects and then points out that the answer is circled. Suggested teaching language is something like this,

“I can do these. Watch me count the frogs. One, two, three.. There are three frogs in this box. So they circled the three. Everybody, touch here where the three is circled. Good.

How many frogs were in this box, everybody? Yes, three.

Now watch me do the next box.”

## We Do: Counting Together

In the “We Do” portion of the worksheet, the teacher counts the stars first as a demo and then with the students. Worksheet A you all just count three stars. Suggested teaching language is something like this:

“Our ‘We Do’ says to touch and count. Start at zero and count each star.

We are going to touch and count the stars. Put your counting finger on zero,

everybody. We are going to start at zero and count each star. Let’s count.

One, two, three. We counted three stars. That was great!

Let’s do it again! Fingers on zero, everybody. Let’s count. One…”

By Worksheet S the teacher and the students are counting 12 stars together.

The program has a page of teacher directions with suggested language for teaching the worksheets.

## You Do: Independent Counting

In the “You do” portion of the worksheet (after learning the numerals with the teacher), the students are asked to count the items in each box and circle the correct number. They are not asked to form the numerals–that’s numeral writing skill. They just identify the numeral and circle it. Besides cute items, there are also dice to count, fingers to count, and hash marks to count–so students can learn multiple ways of keeping track of numbers.

Passing a level requires 100% accuracy. Students who make any errors should be worked with until they can complete the worksheet independently and get all the items correct.

## Rocket Math’s Counting objects worksheets for Kindergarten

This Beginning numerals program will build strong beginning math skills for kindergarten students learning the meaning of numerals. Combined with Rocket Writing for Numerals it will set students up for success in elementary math.

If you’re already a Rocket Math Universal Level subscriber, you can find the worksheet in your virtual filing cabinet [use your link]. Not a subscriber yet? Get the counting worksheets.

## In What Order Should Students Learn Fast Math Facts?

Basic, Optional, and Alternative—there are a lot of different Rocket Math programs. But which program should you use first? And in what order should you teach fast math facts? Well, it all depends on the grade you teach and the fast math facts your students have already memorized.

## An overview of Rocket Math’s fast math fact programs

Rocket Math offers multiple programs because their are several ways to teach fast math facts. Here’s a link to a printable version of the different Rocket Math programs shown here.

### The Basic Program

Rocket Math’s basic program includes Addition, Subtraction, Multiplication, and Division (1s-9s). The basic program must be mastered by all students.

### The Alternative Program: Fact Families

There is another way to learn facts, which is called Fact Family math.  Instead of learning all Addition facts, students can learn Addition and Subtraction facts at the same time.  A fact family consists of four related facts, for example: 3+2 = 5, 2 + 3 = 5, 5 – 3 = 2, 5 – 2 = 3.  As an alternative to using the Basic Program, students can learn fact families up to 10 in first grade.  Then students can move on to the upper fact families 11 to 18 in second grade.  There is no clear evidence that this way is better or the separate operations way is better.  That’s why we offer both options.

### Optional Programs

The rest of the fast math facts programs like Rocket Writing for Numerals or Skip Counting are optional. You should only offer these programs to students once they have memorized the fast math facts through the Basic Program or the Alternative Program.

The only exception would be in a school where Kindergarten students did not get a chance to learn how to quickly and easily write numerals. In that case, you might take the first two months of the first grade year to run students through Rocket Writing for Numerals before beginning Addition (1s-9s).

Let’s take a closer look at how to implement each program in different grade levels.

Rocket Math fast math facts programs for first graders include:

• The Basic Program
• The Alternative Program
• Fact Families (1-10) Add & Subtract
• Optional Programs
• Rocket Writing for Numerals

If first grade students are taking all year to get through sets A-Z in Addition in the Basic Program, they need some extra help.  You should intervene to help students who take more than a week to pass a level.  Often they need to practice better or practice with a better partner.  Some may need to practice a second time during the day or at home in the evening.  First grade students who finish the 1s-9s can move on to the Add to 20 Optional Program for the remainder of the year.

Likewise, if you choose to teach Fact Families (1-10) Add & Subtract from the Alternative Program instead of using the Basic Program, your students can use the Optional Programs for supplemental learning purposes.

Rocket Math fast math facts programs for second graders include:

• The Basic Program
• (1s-9s) Subtraction
• The Alternative Program
• Fact Families (1-10) Add & Subtract
• Fact Families Part Two (11-18) Add & Subtract
• Optional Programs
• Subtract from 20
• Skip Counting

Second grade students must have completed Addition before starting on Subtraction (1s-9s).  They can also test out of Addition through the Placement Probes.  Second graders who cannot test out of Addition in first grade or didn’t complete it in first grade must focus on Addition.  Only after getting through Set Z of Addition should they move into Subtraction.

You can substitute the Basic Program’s (1s-9s) Addition and (1s-9s) Subtraction for the Alternative Program’s Fact Families (1-10) Add & Subtract and Fact Families Part Two (11-18) Add & Subtract.

Second grade students who complete Addition and Subtraction 1s-9s (or the Alternative Program) can move on to Subtract from 20.  Students who finish Subtract from 20 can do Skip Counting, which does a great job of preparing students to learn Multiplication facts.

## Third grade math facts: Learn Multiplication

There aren’t any Alternative Programs available for third graders from Rocket Math. There are only Basic and Optional Programs. These include:

• The Basic Program
• (1s-9s) Multiplication (priority)
• (1s-9s) Subtraction
• Optional Programs
• 10s, 11s, 12s Multiplication
• Factors

In third grade, Multiplication has priority—even if students have not mastered Addition and Subtraction.  Multiplication facts are so integral to the rest of higher math that students are even more crippled without Multiplication facts than they are having to count Addition and Subtraction problems on their fingers.  So do Multiplication first. Then, if there’s time, students who need to do so can go back and master Addition and Subtraction.  Once all three of these basic operations are under their belts, students can go on to 10s, 11s, 12s in Multiplication (one of the Optional Programs).  If students successfully progress through each program and there is enough time left in the school year, introduce the Factors program next.

## Fourth grade math facts: Learn Multiplication and Division

Like the programs for third graders, there aren’t any Alternative Programs available for fourth graders. There are only Basic and Optional Programs, which include:

• The Basic Program
• (1s-9s) Multiplication (priority)
• (1s-9s) Division (second priority)
• Optional Programs
• 10s, 11s, 12s Multiplication
• Factors

In fourth grade, students need to have completed Multiplication before going on to Division. If they complete Division, they can go on to 10s, 11s, 12s Division, followed by Factors, and then equivalent fractions (shown in the fifth grade section below).

## Fifth grade math facts: Learn all basic operations first, then they can branch out

By fifth grade, students should have completed all four basic operations (1s-9s) within the Basic Program (or the Alternative Program for grades one and two).  If students have not completed these basics (and cannot test out of them with the Placement Probes) then the sequence they should follow is Multiplication, followed by Division, then go back and complete Addition followed by Subtraction.  The same recommendations hold for students in any grade after fifth.

Once students have mastered the basics (1s-9s add, subtract, multiply, divide), the supplemental pre-algebra programs are recommended.  These will help more than learning the 10s, 11s, 12s facts.  I would recommend this order:

1. Factors
2. Equivalent Fractions
4. Learning to Subtract Integers or Mixed Integers

## Math Fluency Programs should be part of on-going elementary school routines

Most elementary teachers do some activities to promote math fluency.  Yet many elementary children are not fluent with math facts by the time they hit upper elementary or middle school.  A hit-or-miss approach allows too many students, especially the most vulnerable, to slip through the cracks.   Math fluency programs, like Rocket Math’s Worksheet Program, need to be part of your elementary school’s routine.  Effective math fluency programs should be properly structured and every math teacher should be on board, every year.

## Math fact fluency enables students to develop number sense

Many teachers learn in their training programs about the importance of “number sense.”  Students who have “number sense” can easily and flexibly understand relations between numbers.  They can recombine numbers in various ways and see the components of numbers.  Students with number sense can intuit the fact that addition and subtraction are different ways of looking at the same relations.

What is not taught in most schools of education is that developing fluency with the basic math facts ENABLES the development of number sense much better than anything else.  Once students memorize facts, they are available for students to call upon to understand alternate configurations of numbers. Students find it much easier to see the various combinations when they when they can easily recall math facts.  Once students master the basic facts, math games that give flexibility to thinking about numbers become much easier.

It may be hard for new teachers, straight from indoctrination in the schools of education, to imagine this is true.  However, if they land in an elementary school with a strong math fact fluency program they will see the beneficial effect of memorization.

## Why is math fact fluency important

In the primary grades, students who have not developed fluency in math facts will have a harder time learning basic computation.

Students who are not fluent with math facts find the worksheets in the primary grades to be laborious work.  They finish fewer of them and may begin to dislike math for this reason.

By the time students reach upper elementary, if they have not memorized the math facts, they find it very difficult to complete math assignments at their grade level.  They find themselves unable to estimate or do mental math for problem-solving.  The need to figure out math facts will continue to distract non-fluent students while they are learning new math procedures like algorithms.

In the upper grades, their inability to figure out multiplication facts becomes a huge stumbling block.  Manipulations of fractions, decimals, and percentages will not make intuitive sense to students because they haven’t memorized those facts.  Without math fact fluency, students rarely succeed in pre-algebra and may be prevented from learning algebra and college-level math entirely.

## Math fact fluency must be assured through regular monitoring

Some students will need up to ten times more practice to develop math fluency than other students.  Therefore, monitoring student success in memorizing the facts is critical. Teachers can assume that what is “enough practice” for some students is NOT going to be enough practice for all students.  Effective math fluency programs must have a progress monitoring component built in.  Progress monitoring gives comparable timed tests of all the facts at intervals during the year.  Teachers look at the results of these timed tests to check on two things:

### 1. Are students gradually improving their fluency with all the facts gradually over the year?

In other words, are students able to answer more facts in the same amount of time?  If they aren’t improving, then the instructional procedures aren’t working and need to be modified or replaced.  Math fluency programs like Rocket Math’s Worksheet Program have two minute timings of all the facts in each operation that can be given and the results graphed to see if there is steady improvement.

### 2. Are all students reaching expected levels of performance at each grade level each year?

Proper math fluency programs identify students who are not meeting expectations and give them more intensive interventions.  Ultimately, by the end of fourth grade all students should be able to fluently answer basic 1s – 9s fact problems from memory in the four operations of add, subtract, multiply and divide. Fluent performance is generally assumed to be 40 problems per minute, unless students cannot write that quickly.

Expectations vary by grade level and the sequence with which schools teach facts can vary.  While it is great to achieve all that the Common Core suggests, it is critical only to assure that students master and gain fluency in 1s through 9s facts.  Some schools in some neighborhoods may find that waiting until second grade to begin math facts may not provide enough time for all students to achieve fluency.  When to begin fact fluency and how much to expect each year should be based on experience rather than some outside dictates.

## Successful math fluency programs must have these 3 features

1. ### Sequences of small sets

No one can memorize ten similar things, like the 2s facts, all at once. Students easily master math facts when they can learn and memorize small amounts of facts at one time. Effective math fluency programs define math fact sequences, which students memorize at their pace before moving onto new math facts. Rocket Math’s fluency program uses only two facts and their reverses in each set from A through Z.

2. ### Self-paced progress

Even if you only introduce small sets of math facts, some students need more time to memorize than others.  If you introduce the facts too fast, students will begin to jumble them together and progress will be lost. The pace of introducing facts must be based on mastery—not some pre-defined pace.  This is why doing all the multiplication facts as a class in the first six weeks of third grade does not work.  It is just too fast for some students.  Once they fall behind it all becomes a blur.

3. ### Effective practice and corrections

When students are practicing facts, they will come to ones they have forgotten or can’t recall immediately.  Those are the facts on which they need more practice.  Allowing students to stop and figure out the facts they don’t know while practicing, does not help the student commit them to memory.  Instead, students need to IMMEDIATELY receive the fact and the answer, repeat it and try to remember it.  Then they need to attempt that fact again in a few seconds, after doing another couple of problems.  If they have remembered the fact and can recall it, then they are on their way to fluency.  But students must practice the next day to cement in that learning.

Math fluency programs like Rocket Math’s Worksheet Program teach students math facts in small sets, allow students to progress at their own pace, and support effective practice and error correction. Each Rocket Math Worksheet program has 26 (A to Z) worksheets specially designed to help kids gradually (and successfully) master math skills. Gain access to all of them with a Universal Subscription or just the four basics (add, subtract, multiply, divide–1s to 9s) with a Basic Subscription.