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 Assignfrom 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.

You want your middle-grade students to complete the pre-algebra math topics so they are ready to begin to study algebra in 8th or 9th grade. A disheartening number of middle-grade students have not memorized basic multiplication facts (times tables). Students must know multiplication facts to follow, absorb, and implement pre-algebra topics. How to teach multiplication facts to struggling students? How can a teacher help their struggling students learn multiplication facts when a lot of their students do not need to do that work?

Rocket Math Online Game includes learning tracks for pre-algebra skills as well as basic multiplication and division facts. Within the Rocket Math Online Game, teachers assign students the learning tracks that they most need.

Math Strategies for Struggling Students

Students who do not know their multiplication facts are constantly distracted from learning math strategies by having to stop and “figure out” basic facts. Every time they are asked to provide the answer to a multiplication fact, they have to turn their attention to working it out or looking it up. By the time they have gone through their process, they have lost the thread of the strategy they are supposed to be learning. The most important thing a math teacher can do for struggling math students is to help them bring math facts to automaticity. Then answering math fact questions no longer interferes with learning multi-step strategies for solving math problems.

Why Multiplication facts are Important to Learn Before Middle School Math

Many pre-algebra math topics assume students have a ready knowledge of multiplication facts to even understand. When I was a middle-grade teacher, my remedial students were unable to follow or understand topics such as Finding factor pairs, reducing fractions, equivalent fractions, converting fractions, unlike fractions, and so on. I realized that it was because they did not know basic multiplication facts. When I reduced 8/24 to ⅓ it was like magic because they did not quickly recognize the multiplication facts involved. They didn’t understand the concepts we were trying to learn because they did not see the relationships they were supposed to know. When I asked them to think of the factor pairs of 36 they were unable to find them all, no matter how much time I gave them. While students can do multi-digit multiplication problems using a times table chart, it does them no good in pre-algebra topics because it takes too long, even if they know what to look up. Now let’s look at how to teach multiplication to struggling students using Rocket Math Worksheets or Rocket Math Online Game.

How to Teach Multiplication to Struggling Students Using Rocket Math

Students who have not yet mastered multiplication facts are going to require a very effective teaching methodology to learn them. The haphazard, leave-it-up-to-the-student methods have already failed them. By now, these students lack confidence in their ability to learn the facts, so you need a sure-fire system.

Rocket Math is just such a system. Both the Worksheet Program and the Online Game systematically introduce students to the facts in a careful sequence that they can do. The Worksheet Program and Online Game ask students to memorize only two facts and their reverses at a time.

Students demonstrate mastery of those facts by answering them without hesitation. Then Rocket Math will add two more facts and their reverses. Small steps at a time, systematically the students can memorize the facts and answer them instantly from memory. If students practice every day, within a few weeks you’ll see a dramatic improvement in their recall of multiplication facts.

But what about the students who already know their multiplication facts? Rocket Math has something for them as well.

Rocket Math Programs for Advanced Students

Teachers can assign Rocket Math as a 10-minute warm-up or cool down for all their students whether they are behind or advanced. Rocket Math has several pre-algebra topics for those students who already know their multiplication facts. Each of these topics will help them do pre-algebra processes more fluently and to quickly recognize relationships that they have memorized.

When students initially learn about fractions they are often only shown proper fractions. As a result, they have a limited understanding of fractions and can be confused by improper fractions or mixed numbers. The Rocket Math programs (both Worksheet and Online) prevent this problem. From the start, we teach students using examples of both proper and improper fractions as well as whole numbers and mixed numbers. Students learn to identify over 90 different fractions quickly and easily by getting lots of practice. Their understanding of fractions will deepen and become more flexible as they learn to recognize many examples of fractions.

Students will memorize the most common equivalent fractions with this Rocket Math Learning Track. They will also learn to identify a number of fractions, such as 2/9, that do not “reduce” or for which there are no equivalent fractions in lower terms. Students also learn to recognize a fraction equal to 1 whole in its various forms. When students don’t instantly know the answer they are told the equivalent fraction and given practice on it. The computer gives help in the Online Game. Their partner gives that help in the Worksheet Program. By the end of the program, students will learn over 90 equivalent fractions. This gives students an excellent start on being able to manipulate fractions quickly and easily.

Students are required to “find the factors” when dealing with unlike fractions and reducing fractions. Rocket Math Worksheet and Online Game teach students how to find factor pairs. Students learn how to find all the factor pairs and what they all are for many common numbers. They also learn to identify prime numbers and their characteristic of having only one and themselves as factors. Students learn the factor pairs in order and know the “last” factor pair when they see it. When the game asks “What’s next?” students can provide the next pair of factors or click the checkmark to indicate there are no more factors. When students go through this Learning Track they will no longer hesitate when asked for the factors of common numbers.

Learning Track 16: Fraction & Decimal Equivalents

Common fraction and decimal equivalents should not require a laborious process to “figure out.” Students should just know these, so this Learning Track in the Online Game allows them to memorize a bunch of common decimal and fraction equivalents. Having a facility with a lot of fraction and decimal equivalents means faster computation as well as a way to check their process when manipulating fractions and decimals. Students also learn another essential pre-algebra skill that often confuses them. They learn to correctly and fluently translate a fraction into a division problem and vice-versa.

Developing math fact fluency requires memorization and enables success in math

In case you have any doubt, every set of official recommendations about elementary math recognizes that children need to “know facts from memory,” which is to say recall. Memorization is required to develop math fact fluency or easy, automatic recall. Teaching math fact fluency is necessary, of course, for fluent computation. Math fact fluency is also required for understanding and manipulating fractions. Instant recall of math facts is required to be able to recognize when the calculator is not showing the right answer. How students should learn facts, and when they should begin the process is not as well understood.

What Students must know before beginning to memorize math facts

Students need to understand the operation, whether it is addition, subtraction, multiplication, or division, before they begin to memorize the math facts in that operation. What does it mean to say a student “understands” an operation? It means that given some time, they can figure out the answer to a math fact problem in that operation. A student who can add 8 and 7 and get the answer of 15 by drawing lines or counting on their fingers understands the operation. A student who can add 6 five times to get 30 understands multiplication well enough to begin learning answers. Really if you think about math facts, there are only two things to know: how to figure it out and what the answer is. Once students can “figure it out,” then all that’s left is memorizing the answer, so they don’t have to keep figuring it out over and over!

What students do NOT need to know before beginning memorization

There is a very widespread belief that students must play around with math facts before they begin memorization. That they need to experience a variety of ways of figuring out facts. Or that they need to first learn relationships among facts, like the doubles or doubles plus one. It is believed they need to do these before they begin memorization. Yes, done poorly, timed tests of ALL the facts without a program of instruction, is bad for students. Timed tests without learning results in students reconfirming their worst fears, that they are “bad at math.” That is counter-productive. We want students to develop confidence in their ability to learn and do the math. But do they need to play a lot of games or spend a lot of time figuring out math facts? Maybe not.

Experimental Research has NEVER Shown the Necessity of Games.

Some advocates suggest that students must learn how to figure out facts “efficiently” before beginning memorization. But there is no cognitive difference between being able to figure out a fact efficiently or inefficiently. John A. Van de Walle, an author of “developmental” and “student-centered” math textbooks, is quite emphatic. He says,”Do not subject any student to fact drills unless the student has developed an efficient strategy for the facts included in the drill. … Drill prior to development of efficient methods is simply a waste of precious instructional time,” (Van de Walle, John A. Elementary and Middle School Math).

It is a bold claim, but not one that is backed up by any experimental evidence. Proponents like Van de Walle often cite “research” to “prove” that students must explore and play with numbers before memorization can begin. The “research” citations are not experimental studies with control groups. They are simply recommendations or observations of what students do when they try to memorize on their own.

It is true that if there is no systematic instruction, students will start finding ways to remember facts on their own. These little techniques are not bad in themselves but are abandoned when students finally learn the facts. When you can instantly recall the answer to a fact, you know it without going through any intervening thought. In fact, there’s no time for that. If you know that 8 plus 9 is 17 in a straight recall, instantly, you don’t need anything else. You no longer benefit from thinking through that “8 plus 8 is 16 and since 8 plus 9 is one more, the answer is one more than 16 or 17.”

Real research into teaching math fact fluency is desperately needed.

An interesting experiment, that has never been done, would be to put randomly selected students into two groups after they had learned how to figure out an operation. One group could do these various non-rote, playing with numbers activities. That play-time would be followed with a program of memorization of math facts. The second group would go ahead with the program of memorization without bothering with all exploratory activities. Rocket Math would gladly fund such a research study and provide the math facts practice materials to do it. Seriously, which group do you think would have learned the facts soonest?

Common Non-Rote Activities that Just Waste Time

Dice.

The various types of activities that have students roll dice and add numbers together are usually a waste of time. Generally, most of the students are not doing math at all; they are just watching. The ones who are doing math, are just practicing figuring out the facts–but that’s something they already knew.

Cards.

Some recommendations include having children play cards–hoping they will learn more about numbers by doing that. If you don’t know math facts, you will find playing most card games that involve combinations to be difficult. You might start trying to remember some common combinations on your own. That does not help you memorize facts any faster, however.

Combinations.

One popular idea is having students make up combinations of numbers that add up to ten. Here’s an example of one version. Use a large dice and a whiteboard with a blank number bond drawn on it. Put the number 10 in the middle circle, and tell the students that you are going to make a number bond that equals 10. Roll the dice, and whatever number comes up, it goes into the top circle. The students then have to decide what number goes in the bottom circle to complete the bond.

Here is another variation of the same thing. Set up three hula hoops in the yard. Take ten students at a time and roll the dice. Four of them moved into one hula hoop and the other six crowded into the other. Then have them get back together as a group of ten. Roll the dice again, and then have them split into two pairs again. It may take several rounds of this moving in variations of 10 before the students “get it.”

No time left to teach math fact fluency.

These activities take up a lot of valuable instructional time, to no clear end. The real result of these recommended activities is that teachers NEVER get enough time to work on memorization of facts. In the United States, a huge percentage of our children are not fluent in math facts or computation or the prerequisite skills for algebra. These games and activities waste the time needed to actually develop math fact fluency.

How to Improve Math Fact Fluency with Rote Learning

Students can only memorize a few facts at a time. Almost no one can memorize ten similar facts at the same time. Instruction must introduce a careful sequence of a few facts at a time, followed by plenty of practice. Well-designed instruction makes memorization easy. Students can instantly recall the answers to facts they have committed to long-term memory. Facts introduced too quickly can overwhelm a student’s memory capacity. The task requires a steady process of accumulating these facts over several weeks. Students learn at a pace based on their ability. Everyone can memorize the facts, but just not all at the same speed. Everyone can do rote learning, but it takes time and patient practice.

How to Get Kids to Memorize Math Facts (And Love Doing It!)

There isn’t anything less intrinsically interesting than learning math facts. However, students and teachers commonly tell me that “doing Rocket Math” is their favorite time of the day. Why is that? Both the Rocket Math worksheets and the new Online Game are designed to carefully introduce facts at a rate based on student learning. Students are continuously successful and are not overwhelmed.

A second reason students love Rocket Math are its built-in milestones. As they achieve them, students can recognize the progress they are making. Students love feeling themselves achieving mastery–it is fun. They know they are in school to learn, and they love it when they can tell that they are learning. Far from being harmful, learning math facts can help build the self-esteem of all students. Not to mention making math easier in the long run. Don’t let anyone tell you that you have to postpone this important aspect of your students’ education.

**Nor do the proponents of these various math activities and games say which grades should do these and which ones should stop playing games and get to memorizing. Consequently, many teachers keep doing these games all the way through elementary school and never do get around to the memorization part.

20 years of Rocket Math shows that going straight to memorization works fine

Teachers have been using, and students have been learning from Rocket Math for over 20 years, without first doing these games, and not having any problems. You can too. Try it for yourself and see. We have a 60-day free trial of Rocket Math Online Game. Call us if you need an extension.

Math drills are used to help students learn their basic single-digit math facts. The goal is to help students answer basic math facts from recall and develop automaticity. The only way to tell if a student is recalling the answer rather than figuring it out is by using timed math drills as benchmarks. But students cannot learn how to recall a full page of math facts by drilling on them. The drills will likely cause anxiety and frustration for students. Here are some common pitfalls that are wise to avoid when teaching students basic single-digit facts.

Common Problems With Math Benchmarks

Schools typically set “benchmarks” to evaluate whether students have achieved their educational goals. When it comes to math fact memorization, schools will set benchmarks to distinguish between knowing the answers by a quick recall from the slow process of figuring out the facts. There are two main problems with these benchmarks.

Learned one at a time.

The first problem is that math facts are learned individually and students meet the benchmark one problem at a time. The benchmark should be to answer a problem in less than a second. If they can, then it would be clear which math facts a student has memorized and which ones they don’t. It is more common for schools to give tests on all the facts in an operation and these tests can’t tell the schools which facts are memorized. A more meaningful report would be which facts in an operation can a student answer instantly.

Time to write the answer.

The second main problem is that no matter how well students know facts, they cannot write answers to facts any faster than they can write. Elementary students vary in speed and can write answers anywhere from 10 answers in a minute to 50 in a minute. If a student can answer 40 problems in a minute, they have achieved mastery of math facts. But if they can’t write answers that quickly, they can not meet their school’s benchmark. In order to set a reasonable standard, teachers need to know how fast students can write and a writing speed test will help determine this.

Common Core Math Fact Fluency Need Not Cause Anguish

The Common Core Idea says that students must have a quick recall of math facts to progress successfully in math. For some reason, almost all children have memorized 2+2=4 and can answer this problem from recall. It is not stressful or hard and will not cause math phobia. So, we know that learning how to answer a math problem instantly from recall is doable and can be done without being stressful. The challenge is that there are a lot of facts to learn, but taken a few at a time, they can all be learned equally easily.

To do this though, it takes a systematic effort, daily practice, and careful monitoring. Teachers need a facts program of some kind to help their students commit a large number of facts to memory. Before developing the design principles behind Rocket Math, I had thought this was a nearly impossible task. But in the last 20 years, I have seen how Rocket Math has been used successfully to teach math facts to students. With plenty of time, patience, and encouragement, students can learn to recall math facts from memory and with Rocket Math they can do this while having fun.

Rocket Math Writing Speed Test

The writing speed test for Rocket Math

Here is a simple easy-to-use Writing Speed Test to help figure out how fast a student is able to answer when they have all the facts in an operation memorized. The test is a mix of one and two-digit numbers so it works with addition and multiplication.

Simply give the test to your students and have them write the numbers they see in each box for one minute. You will be able to find out how many boxes they can complete in one minute. That number is the upper limit of math fact problems you can expect them to be able to answer–if they are answering from recall rather than by figuring them out.

Writing speed is number of boxes completed.

When the student has finished the test, you will have the number of boxes they can complete in a minute. You can expect the student to be able to finish at least 80% of that number if they can recall the facts instantly. If the student can answer 90%, they don’t need any fact work. If they are between 80 and 90% of that number, they are good, but more facts work would help them. Anything below 80% and they are having to stop to figure out some of the facts and need more work.

If you’re not interested in doing the math over and over, here is agoal sheet for pre-tests, where the numbers are worked out for you. You can print it from this link.

Benchmarks must be based on writing speed.

Benchmarks that don’t take into account the speed at which children can write, leave a lot of children with an impossible expectation. Asking children to do something they are physically incapable of doing will cause a lot of unnecessary anguish.

Kindergarten Math Benchmarks

Students should be taught how to write numerals correctly and efficiently in kindergarten. The methods of drawing numerals that children invent on their own can be slow, cumbersome, and inefficient – causing them to have a slow writing speed later. Rocket Math Writing for Numerals is a systematic method that will help students learn how to form their numerals. Benchmarks for kindergarteners should focus on the speed of writing numerals, which takes a good amount of practice and instruction.

First-grade students need to be fluent in writing numerals. Not every kindergarten does this, so teachers should test and give some kind ofnumeral writing program to students who do not meet these writing standards.

First Grade Numeral Writing Fluency Benchmarks (digits)

Start of year

40 digits per minute

Mid-year

60 digits per minute

End of year

60 digits per minute

We also want first-graders to learn addition facts to the level of instant recall. The student’s writing speed is the number of boxes they can complete in one minute.

First Grade Math Fact Fluency Benchmarks (problems)

Start of year

Addition 20% of writing speed

Mid-year

Addition 40% of writing speed

End of year

Addition 80% of writing speed

Subtraction 20% of writing speed

Second-grade Math Benchmarks

In second-grade we want students to master subtraction facts as well as addition.

Start of year

Addition 80% of writing speed

Mid-year

Addition 80% of writing speed

Subtraction 40% of writing speed

End of Year

Addition 80% of writing speed

Subtraction 80% of writing speed

Third-grade Math Benchmarks

In third-grade it is important that students master subtraction and begin working on multiplication.

Start of year

Addition 80% of writing speed

Subtraction 80% of writing speed

Mid-year

Addition 80% of writing speed

Subtraction 80% of writing speed

Multiplication 40% of writing speed

End of year

Addition 80% of writing speed

Subtraction 80% of writing speed

Multiplication 80% of writing speed

Fourth-grade Math Benchmarks

In fourth-grade it is important for the students to have multiplication mastered and begin division.

Start of the Year

Addition 80% of writing speed

Subtraction 80% of writing speed

Multiplication 80% of writing speed

Mid-year

Addition 80% of writing speed

Subtraction 80% of writing speed

Multiplication 80% of writing speed

Division 40% of writing speed

End of year

Addition 80% of writing speed

Subtraction 80% of writing speed

Multiplication 80% of writing speed

Division 80% of writing speed

Fifth-grade (and up) math fact benchmarks

In fifth-grade it is important for the students to have mastered their basic math facts in addition, subtraction, multiplication, and division.

Start of year

Addition 80% of writing speed

Subtraction 80% of writing speed

Multiplication 80% of writing speed

Division 80% of writing speed

Mid-year

Addition 80% of writing speed

Subtraction 80% of writing speed

Multiplication 80% of writing speed

Division 80% of writing speed

End of year

Addition 80% of writing speed

Subtraction 80% of writing speed

Multiplication 80% of writing speed

Division 80% of writing speed

All the 1-minute pre-tests and the writing speed tests and the goal sheet can be found on this page https://rocketmath.com/pre-tests/.

Rocket Math Is A Fun Way For Students To Learn

Rocket Math has a systematic approach to teaching students how to become fluent in basic math facts and still have fun learning math. Math can seem daunting to learn and if not taught properly, using a good math program, students can build a math phobia. Teachers have been using Rocket Math for over 20 years now and believe it to be an invaluable tool to help their students learn math.

Searching for a program to practice math facts online that will help your learner power through their math facts and have fun?

Rocket Math Online Game offers effective addition, subtraction, multiplication, and division practice, and students have a blast doing it! Why do they love the game? The game helps students quickly and methodically memorize math facts, which means less frustration and more fun! The game also shows students their progress with exciting, rocket ship-themed graphics and audio to keep them motivated to learn more. It turns out that students learn better and are more motivated to continue when they can clearly see their progress. Who knew?

How Rocket Math’s online math game works

Too many children still count on their fingers to figure out basic addition facts. If a child continues to spend hours counting on their fingers, it is a sure way to make them hate math. Professors of education frequently teach that “all rote learning is bad for children.” This is not true when it comes to math facts. Memorizing basic facts is a necessary step (to free up working memory) on the path to higher-order thinking in math, and by skipping math fact memorization, teachers are handicapping their students. As a result of the dogma against memorization, few new teachers have any idea how to effectively help their students memorize.

For example, giving students a worksheet full of problems that they haven’t been able to memorize isn’t going to help. Nor will a computer practice game that randomly gives problems for students to solve. A good math program will provide students with a few math facts at a time to work through before adding more.

Rocket Math Online Game does just this. Starting with two math facts and their reverse, the game won’t let the student move on until they can answer these math problems instantly. Rocket Math Online Game will then gradually, carefully, and systematically add new facts to those already learned. Students have to answer in 3 seconds or less, or they have to do that part over until they can answer the math fact immediately. They will work through set A to set Z with 26 levels in three phases; Take-Off, Orbit, and Universe. Each time they complete a set, the tile for that set explodes and falls away. As students progress through the levels, they can fill out the Rocket Chart to see their progress and stay motivated.

Addition Math Facts Practice in Rocket Math Online Game

First-grade students should begin working on the first Learning Track: Addition 1s through 9s math facts and have all those facts memorized first. With Rocket Math Online Game, there are three Learning Tracks to choose from for your first-grade class.

The Basic Learning Track

1. Addition 1s through 9s

The Alternative Learning Track: learning addition and subtraction facts in families

5. Fact Families (+, -) to 10

Optional Learning Track

7. Add to 20

If you notice a student is taking more than a week to pass a level in sets A-Z of Addition 1s through 9s, that’s a sign for you to intervene. Often this means that the child is struggling and needs to practice more. They need to logon and practice at home in addition to their practice in school. The first graders who can finish the Learning Track for Addition 1s though 9s, can move on to the Optional Learning Track, Add to 20. Advanced first graders who are very quickly mastering facts can certainly move into the Learning Tracks recommended below for 2nd grade.

There is an alternative sequence of learning addition and subtraction facts, through Fact Families. Fact Families introduces addition and subtraction facts at the same time in “families” such as 1+3, 3+1, 4-3, 4-1. Because the facts are introduced in families students are able to switch back and forth between addition and subtraction as they are learning. Rocket Math breaks up the fact families into a Learning Track with addition and subtraction facts up to 10 to begin in first grade and then a second Learning Track of facts from 11 that follows after, either in first grade or second.

Subtraction Math Facts Practice in Rocket Math Online Game

Many teachers think subtraction facts are harder for children to learn.The reason they seem harder to learn is that most children don’t fully master addition before they start memorizing subtraction facts. When that happens, the two operations interfere with one another (officially, it’s known as proactive and retroactive inhibition), and subtraction facts become harder to learn.

Students who work through the addition sets in Rocket Math Online Game, will not find this to be a problem. Once the student has mastered the addition facts, they will quickly recognize that subtraction facts are “the opposite” of addition. The interference does not happen, and the students will feel good about their progress and learn to do computation with ease.

Rocket Math Online Game offers these Learning Tracks for second graders to master subtraction:

The Basic Learning Tracks

1. Addition 1s through 9s

2. Subtraction 1s through 9s

The Alternative Learning Tracks: learning addition and subtraction facts in families

5. Fact Families (+, -) to 10

6. Fact Families (+, -) from 11

Optional Learning Tracks

7. Add to 20

8. Subtract from 20

Second graders who did not learn addition Math Facts in first grade must focus on addition facts first. After they have gotten through Set Z of addition, they can move on to 2. Subtraction 1s through 9s.

Second-grade students who complete addition and subtraction 1s-9s can start Add to 20 and then go on to Subtracting from 20.

As noted above, learning by fact families is an alternative route to learning basic addition and subtraction facts. The first Learning Track would be #5 Fact Families (+, -) to 10 followed by #6 Fact Families (+, -) from 11.

Multiplication Math Facts Practice in Rocket Math Online Game

Being able to multiply is harder than addition or subtraction because you can’t count on your fingers. While it is necessary for students to memorize the “times facts,” they are seldom systematically taught. Preservice teachers are frequently taught that “rote learning is bad for children.” This is not true, but as a result, most new teachers have no idea how to effectively help their students memorize. Memorizing basic facts is a necessary step (to free up working memory) on the path to higher-order thinking in math, and by skipping math fact memorization, teachers are handicapping their students.

Rocket Math Online Game offers these Learning Tracks for third graders to master multiplication:

The Basic Learning Tracks

3. Multiplication 1s through 9s (priority)

1. Addition 1s through 9s (if still not mastered)

2. Subtraction 1s through 9s (if still not mastered)

The Alternative Learning Track: learning multiplication and division facts in families

11. Fact Families (x,÷) to 20

Optional Learning Track

9. Multiplication 10s-11s-12s

In third grade, multiplication has priority, and students must master it first even if they have not mastered addition and subtraction. Higher-level math students who may not have mastered addition and subtraction will only be crippled more without learning multiplication. Once the student has mastered multiplication, then go back and work on mastering addition and subtraction. When students have mastered all three of these basic operations, they can move on to 9. Multiplication 10s-11s-12s. And of course, advanced third graders who have learned the concept of division can move into the Learning Tracks recommended below for fourth grade students.

There is an alternative sequence of learning multiplication and division facts, through Fact Families. Fact Families introduces multiplication and division facts at the same time in “families” such as 4×5, 5×4, 20÷4, 20÷5. Because the facts are introduced in families students are able to switch back and forth between multiplication and division as they are learning. Rocket Math breaks up the multiplication and division fact families into facts up to 20 to begin in third grade and then a second Learning Track of facts from 20 follows after, either in third grade or fourth.

Division Math Facts Practice in Rocket Math Online Game

The key to learning division facts is to learn them gradually. Students should work a few minutes at a time and then take a break. Rocket Math Online Game has students work for five minutes at a time (although the teacher can increase it to 10 or 15 minutes if the student wants it), and then the game pauses for a 20-minute break. Breaks will help keep students from becoming tired of the game and ensure they want to keep playing. Learning Math Facts is a marathon, not a sprint, so we want them to do Rocket Math once or twice a day for a few months. That’s how they will come to master the math facts.

Typically, students learn division in fourth or fifth grade, but they can learn it earlier if they understand the concept. Division isn’t harder than multiplication, but it will be if students have not mastered multiplication first. That’s why having students work through Set Z of multiplication before starting division is essential.

Here are the Learning Tracks offered by Rocket Math Online Game:

The Basic Learning Tracks

3. Multiplication 1s through 9s (priority)

4. Division 1s through 9s (secondary priority)

The Alternative Learning Tracks: learning multiplication and division facts in families

11. Fact Families (x,÷) to 20

12. Fact Families (x,÷) from 21

Optional Learning Tracks

9. Multiplication 10s-11s-12s

10. Division 10s-11s-12s

When they have mastered multiplication and the 1s-9s of division, students can go on to Multiplication 10s-11s-12s and Division 10s-11s-12s.

As noted above, learning by fact families is an alternative route to learning basic multiplication and division facts. The first Learning Track would be #11 Fact Families (x,÷) to 20 followed by #12 Fact Families (x,÷) from 21.

Rocket Math Online Game – The Best Tool to Learn Math Facts

Mastering the basic facts in addition, subtraction, multiplication, and division will not only help students succeed in school, but are essential skills to have outside of the classroom. If you want your students to be successful at math and enjoy learning, memorizing these math facts is vital. With Rocket Math Online Game, your students will be engaged and excited to play. Students will be able to see their progress, celebrate their wins, and take pride in what they learn. It doesn’t take much to motivate your students, just a sincere recognition of their achievement. They will know when they have accomplished something, and if you recognize it as well, then they will feel proud of themselves.

There’s a free two-week trial of the Rocket Math Online Game so you can see for yourself how well it works and how students love it.

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

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

What is Math Fact Fluency

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

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

Three Reasons Why Math Fact Fluency is Important

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

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

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

1. Students with math fact fluency make fewer errors

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

2. Math fact fluency makes learning math easier

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

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

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

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

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

How to Build and Improve Math Fact Fluency

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

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

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

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

Teaching Math Fact Fluency with Worksheets

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

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

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

Teaching Math Fact Fluency with The Rocket Math Worksheet Program

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

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

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

Teaching Math Fact Fluency with Games

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

– Students spend most of their time waiting for their turn rather than practicing facts.

– They do not focus on teaching a small group of facts in a manner that helps students commit them to memory.

– The games do not adjust to an individual student’s level of fluency.

– Students can pace the game slowly enough to have time to figure out facts rather than requiring recall.

– It is difficult to keep every student engaged, as those who are behind are less likely to participate.

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

There are games that are very effective at building math fact fluency. Games such as theRocket 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.

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.

Do your students struggle to complete their timed math worksheets? Is your classroom a sea of finger-counting during fast math facts practice?

Your students aren’t the problem. It’s your teaching technique that’s hindering progress.

Help your students learn math facts quickly and gain confidence in their skills with Rocket Math’s research-based program. The program works because it teaches memorization through multiple, evidence-based techniques that work for all types of learners.

Why Faster Is Better

Learning math facts at a young age plays a key role in a student’s ability to succeed throughout their education as well as out in the real world.

Not only does math fact memorization serve as a foundation to other math skills, but it also plays a part in motivating student. Most children will feel a sense of pride and excitement when they recognize their ability to quickly recall math facts.

Once a student develops instant recall, math assignments become 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. This makes teaching and learning math far more enjoyable!

Fortunately, almost every child is capable of memorizing math facts in such a way that allows them to call upon them instantly and painlessly. The problem is, many traditional forms of teaching math facts are not effective.

The Problem with Traditional Teaching Techniques

When I was a teacher, I found myself frustrated with the ineffectiveness of traditional teaching tools – specifically when it came to teaching math facts. Repetition, counting, and endless worksheets seemed to leave students discouraged. These old techniques were not taking into account a few simple facts about memorization.

A More Effective Approach to Teaching Fast Math Facts

To help your students memorize math facts effectively, you need to consider five things:

How many math facts to introduce in one session

How fast a student can answer individual math facts

How fast a student can answer multiple math facts

When to introduce new math facts

How often a student practices

1. Introduce a small number of math facts in one session

In grad school, I learned a simple fact about memorization that changed the way I look at teaching math facts: the brain can only process a handful of facts at a time. This fact has shaped a foundational part of Rocket Math, the math fact program I developed to help students effectively learn their math facts.

When students are presented with too many facts – perhaps on a worksheet – the brain will not even begin to attempt remembering. Instead, it has been found that when small groups of facts are presented and practiced, the brain can easily absorb the new information.

Rocket Math uses this knowledge to help students learn much faster and gain confidence in their math skills. Rocket Math only presents two math facts and their reverse facts at a time. This simple trick makes a world of difference. As the saying goes: “How do you eat an elephant? One bite at a time . . .”.

2. Help Students Quickly Recall Individual Math Facts

There is a common misconception among teachers and parents that struggling to remember an answer is valuable. Picture the child scratching his head as he racks his brain for the right answer. Unfortunately, this is not an effective way to teach math. In order to strengthen the neural connections that are involved in memorization, recalling the correct answer quickly is key.

When students are forced to rework the problem in their head multiple times, it does nothing for their recall abilities. That is why rather than having the student guess multiple times, Rocket Math uses a correction tool that immediately reminds students of the right answer if at first, they answer either slowly or incorrectly. This helps to build the memory as they are reminded over and over of the right answer.

3. Practice a Series of Math Facts Quickly for Easy Recall

Once a child has practiced calling to mind a handful of math facts, it is time to practicing recalling them, making sure they can do so quickly. Recalling facts can be done at a high speed, whereas figuring out math facts you can’t recall can take a long time. That is why practicing fast recall is important.Repeatedly recalling fact will strengthen a student’s memory while offering a fun challenge. If the student can’t recall the math facts quickly they may need extra help from the teacher to learn the facts before continuing with quick recall practice.

Rocket Math only has students practice for a few minutes at a time, as that is all is needed when quickly recalling math facts. To measure progress, Rocket Math utilizes 2-minute timing exercises every couple of weeks to see how well students are able to recall math facts. Our free fluency tests are also a great assessment tool for testing student knowledge.

4. Carefully Build Math Fact Fluency

Teachers should be thoughtful of the rate at which they introduce new math facts. Before adding more groups of facts, previously learned facts should be well mastered. A student is ready for another handful of facts when they can recall their current set without hesitation. At first, it may seem like this approach will take longer, but because of the efficiency of memorization, students will move quickly through lessons and build math fact fluency with ease.

5. Practice Math Facts Daily for Long-Lasting Fluency

Because there are so many math facts to learn it is important to start children early and to practice daily. This gives students a chance to learn all of the math facts within all four operations. Spreading facts out over time and including daily practice throughout elementary school years will greatly improve a student’s foundational math skills.

Rocket Math: A Modern Approach to Teaching Math Facts

Rocket Math worksheets are a great way to teach math facts to children of all ages – starting as early as Kindergarten when students begin learning how to read and write numbers. The Rocket Math Universal Worksheet Program is designed for daily practice in order to build a solid foundation of basic math skills.

Our Universal Worksheet Program follows a simple structure and routine to help students progress at an appropriate rate throughout their different grade levels. Throughout the sequence, students learn all of the building blocks necessary to succeed throughout elementary and middle school.

If you have students that are behind for their grade level, our worksheet program makes it easy for you to revisit previous lessons that will reinforce the concepts that are necessary to move forward. Likewise, there are plenty of supplemental worksheets within the program to keep advanced students engaged.

Kindergarten Math Worksheets

The first math-related goal for Kindergarteners should be to learn how to write numerals. It is important for children to learn the most efficient way to write numerals. Think about it – how do you write the number eight? Where does your pen begin on the page?

Believe it or not, this is something that is learned and becomes second nature. This skill is important to develop early on as the first building block to learning math.

Rocket Writing for Numerals is a 72-page program for students to learn how to write the numerals efficiently. It proceeds from how to write numerals and goes until they can write 40 digits in a minute. It is part of the Rocket Math Universal Worksheet Program and is designed to be practiced on a daily basis.

1st Grade Math Worksheets

If children in first grade cannot write numerals legibly and efficiently, they should begin the year with Rocket Writing for Numerals. Once they understand the concept of addition, first graders are ready to begin memorizing addition facts.

The Rocket Math Worksheet Program includes Addition 1s through 9s. Students work through 26 levels (A to Z) learning two facts and their reverses on each level. They practice orally for 2 minutes with a partner who corrects any hesitations or errors.

Alternatively, once students have learned the concepts for both addition and subtraction, they can begin to learn Fact Families. Our Fact Families 1 to 10 Add and Subtract worksheet program begins teaching fact families. Set D of this worksheet to the right is an example, teaching four related math facts such as 3+2, 2+3, 5-2, and 5-3.

Common Core suggests that students be fluent with addition facts up to 20, such as 13+6=19. Personally, I think if a student knows 3+6=9, they don’t need to practice 13+6. However, Rocket Math has made available a program for these facts, Add to 20 in the Universal subscription.

Rocket Math makes it easy for teachers, as the consistent structure provides an easy daily routine for students in all programs and levels. Because the Rocket Math Worksheet program follows a sequence and routine, it is easy for students to continue working together even when studying different programs or levels.

2nd Grade Math Worksheets

Upon starting second grade, students should have mastered all of their addition facts, or fact families 1 to 10. If they have not mastered those facts, you should begin with the first-grade worksheets (Addition 1s through 9s/Fact Families 1 to 10 Add and Subtract) until they are ready to move forward.

The goal for second graders is to learn subtraction (and addition facts) by the end of the year. Rocket Math has a Worksheet Program for Subtraction 1s through 9s that is perfect for second grade. If students master the subtraction facts through practicing with Rocket Math they will be able to learn the lessons of re-grouping, a.k.a “borrowing”, much more easily.

If students have been using the Fact Families Program, it is best to continue using that sequence. Second graders should be ready for Fact Families 11 to 18 Add & Subtract. The last ten levels of this program review all the fact families so that students will be quite solid in their mastery by the time they reach Level Z.

For second-grade students who have mastered addition and subtraction facts, skip counting is a great next step. Skip counting is easy and fun for students while preparing them for multiplication in third grade.

Rocket Math’s Skip Counting program is a uniquely designed worksheet. When students are practicing together, the checker has to rotate the paper to keep up as the other is quickly skip counting.

Because of that, students especially enjoy this worksheet. Not to mention, the design incorporated playful Rocket graphics, which causes it to resemble a game rather than a math worksheet!

Common Core suggests that students be fluent with subtraction facts up to 20, such as 19-6=13. Personally, I think if a student knows 9-6=3, they don’t need to practice 19-6. However, Rocket Math has made available a program, Subtract from 20, so students can practice these facts.

3rd Grade Math Worksheets

The priority for third grade is to learn multiplication. Textbooks begin teaching the concept of multiplication from very early in 3rd grade. Your goal should be to introduce multiplication facts by the time the textbook is giving students multiplication problems to solve.

Using the Rocket Math Skip Counting worksheet can help ease students into learning multiplication facts. If possible the Skip Counting worksheet should be used before students are asked to start performing a lot of multiplication.

The first step to successfully teaching multiplication facts is teaching memorization. The Rocket Math Multiplication 1s to 9s is designed to build strong multiplication fact fluency and recall. This technique avoids the problem of students having to look up facts in times tables, over and over again.

Achieving mastery in multiplication facts is the only way for students to keep up in math throughout elementary and middle school. Even if students come to you without having a solid foundation of addition and subtraction, it is crucial that you teach mastery in multiplication.

For quick-learning students, who get through Multiplication 1s through 9s before the end of the year, a good supplemental Worksheet Program is Multiplication 10s, 11s, 12s. Building upon the facts from Multiplication 1s to 9s, students progress easily through this next set of facts. And of course, students consider it a badge of honor to be members of the “tens, elevens, and twelves” club!

4th Grade Math Worksheets

By the end of fourth grade, students should have learned all four basic operations of math facts. Fourth graders should be using then Division 1s through 9s worksheet to learn division facts.

While division facts are derived from multiplication, it is very valuable for students to explicitly learn the division facts. Long division comes much easier for students who have learned division facts.

For students who get all the way through Level Z in basic division, there is a supplemental program: Division 10s, 11s, 12s. It builds upon and reviews facts from Division 1s to 9s while keeping learning fun for students who work faster.

Math Worksheets for 5th grade and up

Students who have been learning math facts since kindergarten have built a great foundation by the time they reach fifth grade. Unfortunately, this is not the case for many students, which makes it difficult for teachers to create lessons suitable for everyone’s level.

Rocket Math provides an easy solution for these teachers. Simply take ten minutes a day utilizing the worksheet program to teach the four basic operations. While these students are catching up, the remaining students can do Rocket Math as well!

We offer five programs that teach more advanced math skills that follow the same structure and routine. Each one of these five different programs includes video lessons that teach students both how to use the program and how to do the skill that is being introduced.

Uses the vertical number line to show how these work.

5) Mixed Integers (adding and subtracting positive and negative numbers)

Uses the same vertical number lines but now mixes the 8 types of problems together.

Rocket Math’s goal is to make learning fun for everyone – students and teachers. By following the worksheet program, even students who have struggled in the past can begin gaining confidence in their math skills.

You’re probably looking for a math facts test online to evaluate how well your students are learning their math facts. But did you know, it’s more effective to teach and test at the same time? Rocket Math’s online game does exactly that, making it the ultimate math fact online testing app.

Testing without teaching doesn’t work

Too many math facts tests online spend a lot of time asking students facts they don’t know. As a result, students learn inefficient ways to solve math fact problems, like counting on their fingers. Even puzzling out answers from knowing doubles is tedious. Students will find memorization of math facts difficult if they constantly have to “figure out” math facts. Plus these two methods are slow, setting students up to fail timed math fact tests in class.

So what is the best way to test whether a student can recall math facts?

Teach and test a small number of math facts in tandem

An effective math facts test online will start teaching as soon as the test finds the first math fact that the student can’t answer quickly.

It is important to begin teaching immediately for several reasons.

(1) Students think that they will always have to compute math facts on their fingers or with a number line. They don’t know that they can and should get to a point where they instantly recall the answers to facts. Helping students memorize a previously unlearned math fact immediately after they miss the problem shows them that they can successfully master any fact.

(2) Students need to know that we do NOT want them endlessly figuring out math facts. By responding immediately with teaching, we send the message, “Hey, you didn’t know this fact instantly. That’s not what we want. Let’s practice this one, right now, so you can learn it.” Requiring the student to answer the fact again faster reinforces the message.

(3) Teaching a fact works best when the fact is surrounded by facts the student already knows. Therefore, the best time to teach is when a student meets the first math fact they can’t instantly recall. An effective test online will mix the unrecallable math fact with a sea of already mastered material, teach the math fact, and then test it again.

(4) The student learns the difference between memorized and unmemorized facts. This helps the student understand that the goal is to instantly recall that fact.

(5) With a combined teaching and testing approach, a student’s success rate will be high since the student primarily answers facts they already know. As a result, students are motivated to learn more math facts.

Why testing and teaching is the perfect learning paradigm

If your teaching program works carefully in sequence, students will encounter opportunities to practice facts they know (a good thing!). Gradually, new facts will be introduced, practiced and tested. That is the perfect recipe for successful learning. Over time, students will be able to master all the facts as the program works through its sequence. Now you have accomplished the end goal: for students to learn the facts they didn’t know. By testing and teaching as you go, students remain encouraged, learn the difference between problem-solving and memorization, and reach mastery.

Rocket Math game: the ultimate math fact test online

The picture to the right shows me watching the very first kid try out the Rocket Math online game. As soon as he saw math problems, he said, “I don’t really like math that much.” But he saw the problem on the screen was 3 + 1 =, so he just typed in 4 because he knew the answer. Then he saw 2 + 1 = and he says, “Well I know that,” and he typed in that answer. The reverses (1 + 3 and 1 + 2) came up and he could answer those. The online math app only introduced those two math facts and their reverses, but he had to answer twelve in a row to pass the test.

Over time, he became faster. He answered all twelve math facts and received an on-screen congratulations. Mission Control (a fictional character in the math app) told him that he had “taken off with Set A” and could, “try for orbit” if he dared! After finishing the round, he brought the tablet over to me and said he liked it and wanted to play it again as soon as the mandatory 30-minute break was over.

Not only did the Rocket Math app teach and test four math facts in 5 minutes, but the student wanted to continue practicing math facts. That’s the beauty of a combined teaching and testing approach. Kind of a big deal, eh?

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

An overview of Rocket Math’s fast math fact programs

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

The Alternative Program: Fact Families

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

Optional Programs

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

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

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

First grade math facts: Learn Addition

Rocket Math fast math facts programs for first graders include:

The Basic Program

(1s-9s) Addition

The Alternative Program

Fact Families (1-10) Add & Subtract

Optional Programs

Rocket Writing for Numerals

Add to 20

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

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

Second grade math facts: Learn Addition and Subtraction

Rocket Math fast math facts programs for second graders include:

The Basic Program

(1s-9s) Addition

(1s-9s) Subtraction

The Alternative Program

Fact Families (1-10) Add & Subtract

Fact Families Part Two (11-18) Add & Subtract

Optional Programs

Subtract from 20

Skip Counting

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

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

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

Third grade math facts: Learn Multiplication

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

The Basic Program

(1s-9s) Multiplication (priority)

(1s-9s) Addition

(1s-9s) Subtraction

Optional Programs

10s, 11s, 12s Multiplication

Factors

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

Fourth grade math facts: Learn Multiplication and Division

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

The Basic Program

(1s-9s) Multiplication (priority)

(1s-9s) Division (second priority)

Optional Programs

10s, 11s, 12s Multiplication

Factors

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

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

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

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