basic math - Rocket Math

Help your kid get fast at math facts

Posted on June 18, 2023June 18, 2023 by Dr. Don

Your kid wants to go fast at math.

Having to count out all your math facts is simply painful. There is no need for it. Every child is capable of memorizing math facts so that they can be recalled within less than a second. Like any other facts we know and use daily, math facts, once learned, can be brought to mind instantly. This makes math assignments easy and fast. It enables students to easily recognize many things about numbers that teachers call “number sense.” It gives them confidence. And frankly, they like going fast much better!

The usual kind of practice will not make them fast.

I used to think, as a teacher, that just giving students practice with math facts would help them to get faster. Years of teaching proved me wrong. Students will count and count and count and fill out worksheet after worksheet and never get faster. They hated it and I was discouraged. This is why veteran teachers are most interested in Rocket Math. They’ve learned the hard way that just any old practice sheet won’t work. Then in grad school I learned a simple fact about memorizing.

You can only memorize a handful of math facts at a time.

If a task presents any more than a handful of facts, your brain gives up. Your brain won’t even try to remember, it will just focus on a strategy for figuring it out. However, if you have a small handful of thing to remember, and you get asked right away, you can remember. “Oh, I can remember this. I’m having to come up with this fact again. I should try to remember it.” Rocket Math only presents two facts and their reverse to remember at a time. And that makes all the difference. Well, most of it.

Calling math facts to mind again, before they are forgotten, is key.

Many teachers and parents think that struggling to remember is valuable. Not so much. Instead, just calling to mind the answer, quickly and easily, before it is hard, is all that is necessary. Correctly recalling a fact is what strengthens the neural connections. Forgetting it and having to figure it out again does not help. In fact, it teaches students that the job is figuring it out, rather than remembering it. That’s why the correction in Rocket Math is to simply tell the student the answer. The message is to “just remember it” rather than having to figure it out over and over.

Practicing math facts fast requires recalling them.

Once your brain is focused on calling to mind a small handful of facts, you can recall them quickly. Now, you can go fast and you should be required to go fast. First, requiring you to go fast ensures that you are recalling. Second, it’s more fun. Third, you can get a lot of practice done in a short amount of time. This is why Rocket Math only has students practice for a few minutes at a time. That’s all that’s needed if you are going fast.

Cumulatively adding more facts needs to be done carefully

To get beyond that initial handful of facts, you have to learn more. But we have to be careful not to add too many, too soon. First, make sure everything introduced so far is well mastered without any hesitations. Then and only then are you ready to get another handful. A small handful, lots of practice, so they can be recalled, and then add them into the mix of mastered facts. As the saying goes, “How do you eat an elephant? One bite at a time.”

Practicing fast math facts needs to be daily

There are a lot of math facts to learn. A lot students take four years to learn all four operations. The task should begin early and continue until all are learned, so daily practice is a must. Also, spreading the learning out over time means it is learned more fully. Learning something in a day, it’s forgotten in a week. Learning something over a year, it’s remembered as long as it is still being used. A few minutes a day is all we ask, but it is very important to make math facts practice a daily regimen throughout elementary school.

Sign up for a 30-day free trial of the Rocket Math Online Tutor. It works in ten minute sessions. And kids like it!

Improving math achievement: what’s unique about Rocket Math?

Posted on March 31, 2023May 9, 2023 by Dr. Don

Rocket Math is dedicated to improving math achievement. Long-time educator Dr. Don Crawford founded Rocket Math because of his passion for effective educational tools. He believes all students can succeed in math and dedicated his company to making it happen. Their achievement and success motivate students more than anything else. Rocket Math’s mission is to help students succeed in math.

Motivated by success.

Rocket Math’s Online Game educational app teaches and develops fluency in basic math facts. The app is unique in a couple of respects. First, the game focuses students on their progress in learning math facts rather than distracting them with a cutesy game format. As students fill in their individual Rocket Chart, they become motivated by their progress in learning the facts and developing fluency. Moreover, they also develop confidence and improved self-esteem as a by-product of the process.

Evidence of effectiveness in teaching.

Second, the rocketmath.com website uniquely provides real-time evidence of its effectiveness. Rocket Math charts all its users, showing they are learning and developing fluency with basic math facts. Go to their Evidence of Effectiveness page, and you can see students’ results on fluency tests. The tests are given four times in each learning track (pre-test, 1/3 through, 2/3 through, and post-test). For example, over 55,000 students have completed the Multiplication learning track. The chart shows they began with an average fluency of 11 problems per minute at the pre-test. Those students finished the Multiplication Learning Track with an average of 21 problems per minute. Student scores show they are more fluent at each milestone in all 16 learning tracks, from beginning Addition to Fraction and Decimal Equivalents.

The most powerful thing you can do to improve math achievement.

Helping students develop fluency with basic math facts is the single, most powerful thing school administrators can do to improve student math achievement. There’s no excuse for allowing students to struggle and count on their fingers or rely on multiplication charts while trying to do math. Rocket Math has the mission of fixing that for anyone who uses their app. They even offer a 30-day initial, complimentary subscription so you can see that it works before paying a dime. Rocket Math has a money-back guarantee that using their app will improve student fluency in math facts. Rocket Math continues to grow thanks to the enthusiasm of its customers.

A student counts on his fingers while working through a math problem.

Teaching Math Fact Fluency | 6 Signs Your Class Is Failing

Posted on April 20, 2022May 4, 2022 by Dr. Don

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.

Learn more about teaching math fact fluency

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 don@rocketmath.com.

How to Set Math Fact Fluency IEP Goals (The Easy Way!)

Posted on June 12, 2021March 14, 2023 by Dr. Don

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, but they are also 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.

What are Math fact fluency IEP goals?

Math fact fluency goals are specifically designed to help students master basic math facts so that they can move on to more advanced topics. These goals should be tailored to each individual student’s level of understanding. They should focus on mastering basic operations such as addition/subtraction or multiplication/division, as well as developing problem-solving skills. In addition, these goals should also focus on increasing the speed at which the student can answer questions correctly in order to improve their overall math performance.

Why are math fact fluency IEP goals important?

In addition to targeting academic performance, math fact fluency goals can also help improve overall mathematical fluency, which is defined as being able to solve mathematical problems quickly and accurately without relying too heavily on counting strategies or written algorithms. Mathematical fluency is important because it allows students to think critically about numbers and apply strategies learned from one problem type (i.e., fractions) across different contexts (i.e., decimals). Thus, having an IEP goal related to increasing math fact fluency can help foster overall mathematical fluency by providing students with the necessary building blocks for success in more advanced topics.

How to set math fact fluency IEP goals

When setting math fact fluency IEP goals, it is imperative to consider the student’s current abilities when determining the target goal. Each student should have individualized goals based on their specific needs and abilities. A good starting point for setting these goals would be to identify the number of correct responses per minute (RPM) that the student currently achieves and then set incremental increases from there. For example, if a student achieves five correct responses per minute (RPM), this could be the baseline starting point for setting future IEP goals.

In addition to increasing RPM, other possible goals include mastering certain operations or combinations of operations within a given timeframe or reducing errors in computation tasks. The ultimate goal should be for every student to reach mastery over all four operations by the end of their educational program—which would equate to correctly answering all four operations at 10 RPM without any errors.

Test the student’s present level of performance (PLOP) on math fact fluency

It only takes a minute or two 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 the student can answer in that operation 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.

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 above, the 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.

Set 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 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 will 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 36 boxes on the Writing Speed Test, so his or her goal for 2-minute timings would be 72 for the annual goal for the IEP.

Create a graph with an aimline

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 below.

The student, whose aimline is pictured above, began at 29 problems in 2-minutes. Their present level of performance, or 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 an Annual Goal of answering 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.

Document the short term objectives (STOs)

$short term objectives worksheet$ 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 no more than showing them this graph.

What if the student fails to meet the IEP goals?

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 daily short trip to the Special Education room for a second quick practice 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 Rocket Math 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!

Posted on April 6, 2021June 7, 2021 by Dr. Don

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.

Get the One-Minute Rocket Math Writing Speed Test.

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.

Posted on December 16, 2020June 19, 2023 by Dr. Don

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.

Prove that students using the Rocket Math Online Game are improving in fact fluency!

Posted on September 13, 2020June 19, 2023 by Dr. Don

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.

Here’s what the students experience.

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.

What’s the best order or sequence to do Learning Tracks?

Posted on May 29, 2020January 20, 2023 by Dr. Don

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 (0-9s) 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 (0-9s).

Here’s a link to a printable version of the graphic above.

Kindergarten Students have things to learn before beginning Addition Facts

There are three Learning Tracks in the Universal Level of the Worksheet Program that can help kindergarteners get ready for memorizing Addition Facts in the first grade. These programs are not like the main part of Rocket Math, because they are not set up for peer practice. Instead, the teacher leads instruction, because the little ones don’t really have good skills for working together yet. Using the Beginning Numerals Learning Track, the teacher can teach students how to use their rote counting skill to count objects and identify the numeral that goes with that number of objects. Next the Rocket Writing for Numerals Learning Track will teach students how to correctly, legibly, and efficiently write the numerals 0-9. There are 72 pages in this program, so it will take most of the school year for students to work through it. The third teacher-led learning track is Conceptual Addition. This learning track teaches students what addition is all about by teaching them to count objects to add them together. Most importantly, it teaches student how to “count-on” from a number other than one, so they can add up numbers more than their ten fingers. Click the link to see more information about that.

First-grade Students Should Learn Addition Facts

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 0-9s can move on to the Add to 20 programs for the remainder of the year.

Second-grade Students Must Know Both Addition & Subtraction Facts

Second-grade students must have completed Addition before starting on Subtraction (0-9s). They can also test out of Addition through the Placement Probes which are available within the Addition drawer in the Rocket Math Worksheet program virtual filing cabinet. Addition has priority for second graders who cannot test out of Addition in first grade or didn’t complete it in first grade. Only after getting through Set Z of Addition, should they move into Subtraction. Second-grade students who complete Addition and Subtraction 0-9s can move on to Skip Counting or Conceptual Multiplication, which both do a great job of preparing students to learn Multiplication facts. After that students could do the Subtract from 20 learning track.

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

There is another way to learn facts, through learning fact families. Instead of learning only 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. You must of course, teach the concepts of both addition and subtraction before students can learn in fact families. Students can learn Add-Subtract fact families up to 10 in first grade. Then in second grade they can learn the Addition and Subtraction upper fact families, from 11 to 18 in second grade.

Third-grade Students Must Learn concept of multiplication and then learn the facts

Third graders can begin the year working on addition and subtraction facts or reviewing them in fact families. They should NOT begin memorizing multiplication facts until after they have learned the concept of multiplication in their math curriculum or used the Rocket Math Conceptual Multiplication learning Track. After they have learned the concept of what multiplication is all about, then have them memorize Multiplication facts 0-9s. Once multiplication is mastered, if there’s time, students who need to can go back to master addition and subtraction facts.

As in Addition and Subtraction, students can learn Multiplication and Division by fact families, provided you teach both concepts first. In third grade, just the Multiply-Divide Fact Families through 20 need to be mastered. Once all three of these basic operations are under their belt, I’d recommend the Identifying Fractions learning track next followed by the Equivalent Fractions, followed by the Factors learning track.

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 Multiply-Divide Fact Families to 20 and then Multiply-Divide 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 learning track next followed by the Equivalent Fractions, followed by the Factors learning track. 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

Learn more about Rocket Math: in just 2 minutes! Rocket Math has a fun video for you to learn more about how Rocket Math works. Or check out our website at www.rocketmath.com

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.

Age	Grade	Operation/Skill	Rocket Math Worksheet	Rocket Math Online Game Level
5-6	Kindergarten	Writing Numerals	Beginning Numerals Rocket Writing for Numerals Conceptual Addition	In development
6-7	First	Writing Numerals Addition	Rocket Writing for Numerals Addition 0 through 9s Fact Families 1 to 10 Add and Subtract Add to 20	Addition Fact Families (+, -) to 10 Add to 20
7-8	Second	Addition Subtraction	Addition 0 through 9s Fact Families 1 to 10 Add and Subtract Add to 20 Subtraction 1s through 9s Add-Subtract Fact Families 11 to 18 Skip Counting Subtract from 20	Addition Subtraction Add-Subtract Fact Families to 10 Add-Subtract Fact Families from 11 Add to 20 Subtract from 20
8-9	Third	Multiplication	Multiplication 0 to 9s Multiply-Divide Fact Families to 20 Multiplication 10s, 11s, 12s Identify Fractions Equivalent Fractions	Multiplication Multiply-Divide Fact Families to 20 Multiplication 10s-11s-12s Identify Fractions Equivalent Fractions
9-10	Fourth	Multiplication Division	Multiplication 0 to 9s Division 0 through 9s Multiply-Divide Fact Families to 20 Multiply-Divide fact families from 21 Identify Fractions Equivalent Fractions Factors Multiplication 10s, 11s, 12s Division 10s, 11s, 12s	Multiplication Division Multiply-Divide Fact Families to 20 Fact Families from 21 Identify Fractions Equivalent Fractions Factors & Primes Multiplication 10s-11s-12s Division 10s-11s-12s
10+	Fifth and up	All Basic Operations Fractions Positive/Negative Numbers	Basic Addition, Subtraction, Multiplication, and Division Identify Fractions Equivalent Fractions Factors Learning to Add Integers Learning to Subtract Integers Mixed Integers	Basic Addition, Subtraction, Multiplication and Division Identify Fractions, Equivalent Fractions, Factors & Primes, Fraction & Decimal Equivalents (coming soon)

Use Rocket Math Worksheet Program or Online Tutor or both for math fact fluency?

Posted on July 18, 2019June 27, 2023 by Dr. Don

Rocket Math now has added an Online Tutor to its tried-and-true Worksheet Program. Customers ask, “Which should I use? Should I use both?”

Dr. Don’s answer is “Yes, I do recommend using both. As that opinion may appear self-serving, here’s why.”

1) Online Tutor is an easier route to math fact fluency.

Most students begin passing levels in the Online Tutor right away. They find it quicker and easier and can sometimes pass more than one level in a day. This gives the students a taste of success. The Online Tutor helps them realize they can learn facts and make progress almost from the first day. Students are then more willing to do the Worksheet Program as well. Rarely, there are a few younger students who cannot input answers within 3 seconds. They won’t be able to pass levels and will have to start over many times on the Online Tutor. When monitoring them in the Online Tutor, such students will have difficulty scores over 3. If that’s the case, the Worksheet Program is more flexible, and they may prefer that. But for most students with difficulty scores below 2 in the Online Tutor, they will require a lot less practice to pass levels with the Online Tutor than in the Worksheet Program. That means it will be easier and quicker to learn the facts.

2) The Online Tutor is easier for teachers to implement.

The Online Tutor is easier for teachers to get started using. Teachers don’t have to print out worksheets, maintain files or organize student pairs, or manage their practice. It is, therefore, easier to implement. Less than enthusiastic teachers, who might not start the worksheets, will at least start doing the Online Tutor. After they see the success of the Online Tutor and the students’ enthusiasm, they will be more willing to do the Worksheet Program.

3) The Online Tutor provides consistent quality of practice.

The Worksheet Program is dependent upon the quality of practice in each classroom. Quality of practice is dependent upon the skill of the teacher in teaching routines and getting compliance from the students in following procedures. Therefore, the quality of learning varies, whereas with the Online Tutor the quality of practice is consistent. I have had teachers report that they are seeing, in daily lessons, better fluency in facts than they saw previously with the Worksheet Program. The teachers who say that, are telling me they did not get students to practice well in their classroom. With less skilled teachers the Online Tutor is definitely better. The only variable with the Online Tutor is whether teachers give students the time to practice and if they can effectively assign homework. Both of those are issues with the Worksheet Program as well.

4) The Online Tutor checks every single fact for speed of response.

The Worksheet Program bases individual goals upon writing speed, so we are basically demanding that students write answers to math facts as fast as they can. That’s a high bar and requires a lot of practice. The bar is not as high with the Online Tutor–as everyone has the same 3 second expectation for a one digit answer, and 4 seconds for a two digit answer. If students are using a touch screen and are 8 years old, that’s not as demanding as it could be. That’s why they go through the levels faster. However, every single fact is checked for time, which we can’t do with the Worksheet Program. Because the Online Tutor checks the speed of response to every single fact, it’s more rigorous that way.

5) The Online Tutor is easier for parents to support.

Both Worksheet Program and Online Tutor can (and should!) be done at home. The Worksheet Program’s homework component is for students to bring home the worksheet they tested that day and practice with a parent or sibling, the same way they practiced in school. That takes someone’s time. The Online Tutor only requires access to a device (Rocket Math works well on parents’ phones!), and once the student logs in, the computer does the correcting and rewarding. The Online Tutor is easier for parents to support and gets a foot in the door. Once they see their child’s success and enthusiasm, parents are more willing to do the Worksheet Program. Which will provide more and better learning.

6) Worksheet Program has higher demands for math fact fluency.

Two students participating in one of Rocket Math's math fluency programs

Compared to the Online Tutor, the Worksheet Program is a bit harder to pass a level. By basing individual goals on the Writing Speed Test, we can be sure that students are answering a large number of facts as fast as they can write. This is a high bar. Generally, we see that students have to practice with their partners more time before they pass they pass a level, so students learn facts better with it. They are more solid in their knowledge of facts when they are done with an operation like multiplication in the Worksheet Program than they are if they just run through multiplication in the Online Tutor. This is a reason not to do the Online Tutor only. Of course, students are even stronger in their facts when they practice with both.

7) Saying the facts aloud in the Worksheet Program develops an important learning channel.

The purpose of learning math facts is to make it easier for students to learn and do basic computation. The Worksheet program develops verbal memory for facts. In the Worksheet Program students practice by saying the facts aloud along with the answer, without hesitation. For example, “Nine times seven is sixty-three.” Repeating these over and over day after day, creates a verbal chain in memory. Because of this verbal chain, once the fact is learned, forever after, when saying the fact to oneself, “Nine times seven is….” the answer, “Sixty-three,” pops into mind, unbidden. That’s automaticity and that’s the goal. This is another channel other than what is developed in the Online Tutor.

8) Writing the facts daily in the Worksheet Program will generalize to written computation more readily.

Math work is written, so the Worksheet Program (which is also written) is closer to how math facts will be used. Each day students get into the habit of doing math as quickly as they can. They develop the expectation that they should do math quickly. That means this program will generalize better to computation assignments. It will take longer to pass a Learning Track, but when they are done, you will see a bigger benefit to students doing math assignments when they finish the Worksheet Program than with the Online Tutor. Which is yet another reason to do both programs.

9) The Worksheet Program provides computation practice to maintain fluency.

After students learn the facts, the most important thing is to provide students with practice using the facts in computation. Many of today’s math programs have very little to no computation practice built into the program. The Rocket Math Worksheet Program has learning tracks that provide short 3-minute daily practice assignments in computation. The Learning Computation tracks have assessment so students can be placed at the right level and can gradually improve their computation skills as well as cement in those math facts so they can maintain fluency.

10) Using both the Worksheet Program & Online Tutor develops math fact fluency twice.

Because students are moving through the two programs at different rates, they will get two passes at learning the facts. That means they are getting twice as much learning. The facts will be known better and more readily called to mind during computation when both programs are used.

student counting on their fingers because they do not meet math fact fluency expectations by grade level

The Ultimate Guide to Math Fact Fluency

Posted on July 9, 2019January 11, 2023 by Dr. Don

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 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 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 the 0 through 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 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 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 any fact that isn’t coming to mind instantly.

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

$Students and teacher playing multiplication games with dice sitting in a circle in a classroom$

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.
The games 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.

Every student is engaged in answering math facts—not waiting for a turn.
Students learn only a few new facts at a time so that they can remember them.
The game provides lots of focused practice on each set of facts.
The game requires students to answer quickly, which guarantees the students recall the answer rather than “figuring it out” over and over.
The game gives an immediate correction and extra practice on any facts that students cannot answer quickly and correctly.
The game only introduces new facts once students demonstrate mastery of facts learned so far.
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
Addition: 12 per minute	Addition: 25 per minute	Addition: 25 per minute

Second Grade Math Fact Fluency (problems per minute)
Start of Year	Mid-Year	End of Year
Addition: 25 per minute	Addition: 30 per minute	Addition: 30 per minute
	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
Addition: 30 per minute	Addition: 30 per minute	Addition: 30 per minute
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
Addition: 35 per minute	Addition: 35 per minute	Addition: 35 per minute
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
Addition: 35 per minute	Addition: 40 per minute	Addition: 40 per minute
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:

Weak, needs fact work
Good, but fact work could help
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.