math fact fluency Archives

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.

Math Fact Benchmarks: Guarantee To Meet Them With Student Effort & Rocket Math Online Game

Posted on May 11, 2022June 8, 2022 by Dr. Don

Not meeting benchmarks: what should it mean?

When it comes to learning math facts, most students have had no opportunity to learn them in a systematic way. Unless they have had an extraordinary school or an unusual teacher they have not received structured, systematic learning opportunities to memorize math facts. After three decades working in schools across the country, I know this to be the case. Without systematic practice and effort, students will not meet math fact benchmarks. They won’t meet the Common Core expectation that students will “know [math facts] by memory.” Whose fault is that? It is not the student’s fault, nor the parent’s fault. So “not meeting benchmark” should mean that here is an area where the school needs to provide some intervention to build fluency.

Are you certain your fluency intervention is effective?

The teacher and the school have an obligation to provide an intervention that is effective. Some so-called “interventions” do not reliably produce increased fluency. An essential part of using an intervention is to measure its effectiveness. [That’s why IEP goals are supposed to have measurable short-term objectives!] The best way to measure the effectiveness of a fluency intervention is with timed, curriculum-based fluency assessments.

If you measure the same way for the same amount of time, you can see if fluency is increasing. You can see that the student’s fluency is increasing if the student can complete more items during the timed test each time you measure. If the vast majority of all of the students improve in fluency, then you can be certain that the intervention is effective. The graph above shows that for Multiplication, 23,540 students have increased in fluency as they worked through the Rocket Math Online Game. See evidence from all 16 Learning Tracks here.

Rocket Math Online Game is effective

As students work through the levels in each Learning Track in the Rocket Math Online Game, they are tested after completing the first level (A), then after completing 33% at level I, and then after completing 66% at level R, and then after they finish at level Z. Each test is a 1-minute fluency test of a random selection of facts taught in that Learning Track. Therefore, the scores are comparable. When the number goes up at each point in the curriculum, you can be sure that students are increasing in fluency. The chart to the right shows site-wide data. You can see students improve on average as they work through the Learning Tracks in the Online Game. You would not expect students to meet benchmarks until they have completed Set Z in the Learning Track.

Math fact fluency benchmarks in the Online Game: 16/minute in addition and subtraction.

The 1-minute RACEs in the Rocket Math Online Game are a good way to measure math fact fluency. On average students exceed 16 per minute correct at Set Z and the average at the beginning is much less. So a reasonable benchmark is 16 correct problems per minute.

The teacher can assign a 1-minute RACE at any time and the student will need to do it upon their next login. The results will be available in the Review Progress screen as well as be exported from the button that gives “Results from Assigned races.” However, the best measure of whether a student can meet the benchmark is after Set Z, when they have completed the Learning Track. You can see the score by clicking on the pink button for exporting “Results from Scheduled Races.”

You can see the screenshot of an example of the results from scheduled races for all 16 Learning Tracks across our website. You can see the Account Average shows improvement at each level. Those scores after Set Z show that nearly all students are proficient by the end of the Learning Track. So we know that the Online Game is an effective intervention. But there’s a catch. At the Level Z test data there are no scores for students who had not completed Set Z in Multiplication. Students have to actually play the game in order to learn.

Students must participate to learn: monitor and recognize effort

Assigning an effective intervention will not help unless students are engaged and participate. Instead of reporting on benchmarks of academic achievement, why not report on benchmarks of effort? Each time students login and complete a session (five, ten or fifteen minutes in length) on the Online Game their session is recorded towards their effort score for the last 14 days. Students should complete a session every day in school and some at home for homework. In the effort rating system every four sessions completed earns a star, so 15 completed sessions over the last 14 days earned the student to the left 3 and 1/2 stars.

If you monitor the effort scores and recognize students who are putting forth great effort, you’ll get more students participating. Completing 12 sessions in the last two weeks is good effort and earns 3 stars. 16 sessions over the last two weeks would earn 4 stars!

You might consider giving out Star Effort Awards (available in the teacher section of the site) once a month for students who are putting forth super-star effort. If you reward effort, we guarantee you’ll get achievement. Soon after doing that, you’ll probably have to start awarding Learning Track certificates for students who are completing Learning Tracks. All awards are available on the admin page on Tab (K) in the main rainbow navigation bar.

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.

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.

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.

How School Math Fluency Programs Work

Posted on March 27, 2019March 10, 2019 by Dr. Don

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

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.
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.
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.

Math Fact Apps: Do they help – Or Waste Time?

Posted on March 25, 2019February 20, 2023 by Dr. Don

Just doing math is not enough to develop math fact fluency.

If you want to help your kid succeed in golf, you must first help them develop a good drive. Before they can successfully go out and play a game of golf, they will have to spend some time on the driving range. Right? The same thing goes for math. To help your kid succeed in math, you must first help them develop math fact fluency. Math facts are single-digit problems like 5 +9 or 6 x 8. The times tables are math facts in multiplication. Math facts are the fundamental units of all math problems. They are the drivers, if you will, of doing math. Children who struggle to remember basic math facts will find learning math and doing math difficult. We know what that looks like, right? On the other hand, students who can easily answer all math facts, who can answer math facts with fluency, find math a breeze and are successful and confident in math. Math fact apps can be a great way to help with learning math facts and improving math fact fluency.

Not all math apps build math fact fluency.

There are a lot of apps out there that look like they would help your child learn math fact fluency. If they have to answer math facts, won’t that work? Not really. Just playing a game that asks you to answer facts won’t help you learn new facts. In fact, most apps for practicing facts discourage students who don’t know their facts well. Why? Because most of the people designing the app don’t have any experience teaching or knowledge of instructional design. A teacher with expertise in instructional design, like the Rocket Math Online Game App creator, knows how to effectively teach a student new math facts (or any facts) and knows an effective math app from an ineffective one.

Three essential features of an effective math fact app.

There are plenty of ineffective math apps. Some apps don’t give the answers when a student doesn’t know them. Some apps just fill in the answer for the student and then move on. When the student doesn’t know the answer, the app has to teach it. To teach a math fact that the student doesn’t know, the app has to do these three things:

Tell the problem and the answer to the student, if needed.
Ask the student to give the correct answer to the problem from memory.
After a short delay, ask the problem again a couple of times, to be sure the student can remember the answer.

The key job in developing math fact fluency is learning new facts. By doing these three things, the app will be able to teach the student new facts, and the student will develop fluency beyond what they already have.

An effective math app will only teach a few math facts at a time.

Math facts are all very similar, which is what makes them hard to remember. No one can learn a bunch of new and similar things all at the same time. A person can only learn two, three, or four facts at a time, and you cannot expect to learn more at one time. That’s enough for one session. The student has to practice those facts a lot of times to commit them to memory. Once or twice is not enough. It also won’t help to practice the same fact over and over. Proper math fact fluency practice intermingles new math facts along with facts the learner has already memorized. No more than two to four facts should be introduced at a time. If a student has to answer a lot of random untaught math facts, you will have a very frustrated learner.

How to build math fact fluency by practicing

Some students learn to solve addition problems by counting on their fingers. That’s a good beginner strategy, but students need to get past that stage. They need to be able to simply and quickly recall the answers to math facts. An app is good for developing recall. But the app has to ask students to answer the facts quickly, faster than they can count on their fingers. The app has to distinguish when a student recalls the fact (which is quick) from figuring out the fact (which is slow). Second, the app must repeatedly ask the learned facts in a random order, so students recall them. But the app should only throw in new facts once all the facts are mastered and can be answered quickly.

Introduce new facts only when old facts are mastered!

The trick to effectively teaching math facts is to introduce new math facts at an appropriate pace. If you wait too long to introduce math facts, it gets boring and wastes time. If you go too fast, students become confused. Before introducing new facts, students need to master everything you’ve given them. An effective app will test whether students have mastered the current batch of math facts before introducing more facts. And it will also introduce math facts at a pace based on student mastery. That’s the final piece of the puzzle to ensure students learn math facts from an app.

Rocket Math Online Game App–try it for 30 days for free

You probably guessed that we know of an app that meets all these criteria, the Rocket Math Online Game. It is like a driving range for math–it will develop math fact fluency. But don’t take our word for it. Try it for free for 30 days. If your child or students use it daily for 30 days, you’ll know they are learning and becoming more fluent with math facts. Keep it going, and they will become confident and successful in math. And that’s the point, isn’t it?

*The Rocket Math Online Game App focuses on two facts and their reverses at a time, such as 3+4=7, 4+3=7, 3+5=8 and 5+3=8.

How to Grade 1-Minute Math Fluency Practice Tests

Posted on February 7, 2019May 8, 2019 by Dr. Don

Katy L from Wilson Elementary asks: How can I keep up with everyday Rocket Math grading? Do you teach students to grade their own 1-minute math fluency practice tests?

Dr. Don answers:

Only grade 1-minute math fluency practice tests if students pass

An integral part of the Rocket Math Worksheet Program is the 1-minute math fluency practice test. One-minute fluency practice tests are administered every day, to the whole class, and only after students practice in pairs for two to three minutes each. Check out the FAQs page to learn more about conducting 1-minute math fluency practice tests in class.

Teachers do NOT need to grade, score, or check daily Rocket Math 1-minute math fluency practice tests unless the student has met their goal. Students do NOT need to grade their own daily Rocket Math fact fluency tests either.

Why grading each math test is not important

The important part of math fluency practice is the oral practice with the partner before the test–what’s going on in this picture. Because the students are orally practicing every day and getting corrections from their partners, there should be VERY FEW errors on the 1-minute math fluency written tests.

Correcting written tests doesn’t help students learn anyway. Corrections are only helpful if they are immediate, the student has to acknowledge the correct answer, and remember it for a few seconds–all of which is part of the oral correction procedure. “Correcting” what’s on the paper takes a lot of time and does not help students learn more, so it shouldn’t be done. But you have to check them before declaring that the student has passed a level.

How do you know if a student passes?

Students should have a packet of 6 sheets math fact fluency sheets at their level. Each Rocket Math student has an individual goal. For example, if a student has a goal of 32 (based on their Writing Speed Test) and they only do 31, they know they did not pass. If the student does 32 or more, they pass!

What to do when a student beats their goal (passes)

If a student meets or beats their goal, then have them stand up, take a bow, and then turn their folder into a place where you check to see that all problems were answered correctly. When YOU check (after school?), make sure all of the completed problems were correct and the student met their goal. If so, then you put the unused sheets in that packet back into the filing crate and re-fill the student’s folder with a packet of 6 worksheets at the next level and hand the folder back the next day.

When students receive the new packet of worksheets, they know to color in another letter on the Rocket Chart (and maybe put a star on the Wall Chart).

What to do if a student doesn’t pass?

Students who don’t meet their goals, don’t pass. These students should put the non-passing sheet into their backpacks and take the sheet home for more practice.

The next day they will use the next sheet in their packet of 6. If you want to give them points, do that the next day after they bring back their worksheet where they did a session at home (signature of helper should be there) and all items on the test are completed. If that’s done, they get full points.

Sometimes you’ll catch errors on sheets that students turn in as “passes.” If you see an error, the student doesn’t pass. As a result, the student keeps the old packet and has to continue with that same level worksheet.

For more information about conducting 1-minute math fluency practice tests in class and how to implement the Rocket Math worksheet program, visit the FAQs page.