practice Archives - Rocket Math

Things-to-look-for (any time of day) for Rocket Math implementation

Posted on March 5, 2023March 5, 2023 by Dr. Don

Evaluating a Rocket Math implementation when you aren’t observing Rocket Math in action.

Most of the time when you go into classrooms, something other than Rocket Math® will be going on. These are the things you can check on even when there are no students in the room. There are eight indicators you can see by looking at student folders. There are four indicators while looking at the Rocket Math filing crate. There are additional indicators to look for if there is a Wall Chart being used or if there are Race for the Stars games in the room. Here’s a link to the checklist.

Look at several Student Folders

(1). Students all have folders that appear to be used daily. The folders are the heart of the organizational system. Students should keep their materials in the folders and keep track of their progress on the folders. Whether the students keep folders in their desks, cubbies, or are collected each day, there should be some signs of wear and tear.

(2). Rocket Charts on student folders show dates of each attempt to pass a level. Each day when students take a 1-minute timing test to try to pass a set of facts, they should write the date of the “try” on the Rocket Chart on the front of their folder. Without this record you cannot tell if a student is stuck because he or she has missed two weeks of school, or if students are only doing Rocket Math® twice a week (not recommended!), or if a student has exceeded six tries without intervention.

(3). Rocket Charts on student folders are colored in when passed. Coloring in the row on the Rocket Chart for the fact set that was just passed is the primary reinforcer of all that hard work. It is essential that students are given the time (and the colored pens, pencils, or crayons) to celebrate their success. Don’t get fooled by the older students or the students who are “too cool” to color in the chart. Even if they only want to color in the row with their regular pencil, students need to be told that they have accomplished something important, and giving them the time to color in their chart is a critical component of the program. This is way more important than you might think. You can also praise students who have accomplished a lot or who have just passed a level. Hearing from an administrator or coach about progress in math facts sends a huge message regarding the importance of the task.

(4). Student folders include packets of answer keys on colored paper. In order to practice correctly, each student’s partner needs to have an answer key in front of them when practicing. Each student needs their own answer key packet (so they can practice with someone who doesn’t have that answer key or with a volunteer who has no answer key). All the answer sheets for their operation should be copied and stapled into a booklet so students don’t have to go hunting for answer keys. Having the answer keys copied onto a distinctive color is important for teachers to be able to monitor paired practice. When students are practicing, each pair should have one student with answers (in that distinctive color) and the partner without the answers (on white paper). Any variation of this means the students are not practicing correctly—and that should be easy for the teacher to spot. Additionally, if a teacher is ready to begin testing and sees a hot pink paper on a desk, the teacher knows someone has answers in front of him or her.

(5) Student folders have the next sheet ready before starting practice time. Some system needs to be put in place so that the limited amount of time available for students to practice is NOT taken up with all students trooping up to the crate to get the next practice sheet each day. The recommended system in the Teacher Directions is to refill student folders when they pass a level, after school, with a packet of six sheets. That way the only time teachers have to handle folders is when students pass and they check the “pass” for errors and refill with a new packet. Many other ways of refilling student folders are possible, but no matter the process, students should have a blank practice sheet or set of practice sheets in their folder—which you would see when you check folders.

(6). Students have clear goals indicated on goal sheet. After students complete the Writing Speed Test, they are to have goals set for their daily 1-minute timing. The goal sheet should be stapled to the inside left of the student folder, the goal line circled, and the 1-minute goal written at the bottom of the sheet. The goal may be crossed out and a higher goal written in if the student has consistently demonstrated the ability to write faster than the original goal. Sometimes, teachers also write the goal on the front on the Rocket Chart, but the student’s goal should be clearly indicated. If not, it may be arbitrary or inappropriate (the same for all students, for example).

(7). Individual graphs are filled in because 2-minute timings are happening. Every week or two, students should be taking the 2-minute timings. These timings are a progress monitoring measure. They could be used for RTI or for IEP goals, or for any other time when a curriculum-based measurement is useful. At least they can demonstrate to us (and to the students) whether they are making progress in learning math facts in a given operation. As students learn more and more facts in the operation to a level of fluency and automaticity, they will be able to write answers to more facts in the operation on the 2-minute timing. Each time they take a 2-minute test, they should count the number correct and graph that on the graph stapled on the inside right of their folder. Each test is graphed in the correct column for whichever week of the month the test was taken.

(8). Individual graphs show upward trends as students are learning facts. Once students are taking the 2-minute timings regularly, it should be easy to see a trend. It should be going up, even if somewhat unevenly. For example, scores might go down after the long December break, but they should recover after a couple of weeks. If these graphs do NOT show an upward trend, something is wrong. Practice may not be being done for long enough (less than 2 minutes a day), or frequently enough (only three times a week), or students may not be practicing correctly (not fixing hesitations and errors). If only one or two students have flat graphs, those students will need something more. The individual graphs will be your indication that there is something amiss. You will just have to figure out what could be wrong. This should lead you to do some observations during Rocket Math^® practice in that classroom.

Look at the Rocket Math file crate

(1). There is a crate or set of files for each operation practiced in the room. Each operation fills a crate and requires a different set of files. In any classroom where not all students are working on the same operation, there will need to be more than one set of files. Sometimes, teachers who have only one or two students in an operation may use the files of a neighbor teacher, but that should be only a temporary fix. The rule is that there must be a crate for every operation being practiced in that class.

(2). Rocket Math^® crate is filled and organized from A–Z, complete with tabs. As of the 2013 version of Rocket Math^®, every operation goes up to the letter Z. So each crate should have hanging folders with tabs showing the letters A though Z. Tabs are important to save time finding sheets and filling folders. If the files are a mess, out of order, no labels, or some letters are empty, valuable practice time will be used up trying to find the right sheets. If everything is labeled, and there are sheets in each file, then efficiency is a possibility. The Rocket Math store has tabs for sale if you need them.

(3). Rocket Math^® crate has 2-minute timings numbered 1–5. In order to make sure that teachers do the 2-minute timing and monitor progress readily, they need to have class sets of the 2-minute timings (1 through 5) available in the crate. This is easy for you to check. If they are not there, it is likely that the 2-minute timings won’t be done as regularly as they should be. It is important for those timings to be done so you can see if all the students are making good progress.

(4). Teacher has a hard copy of the directions available for reference. The best place to keep the directions is right in the crate, so they are handy at any time. We have found that most of the time, when teachers are not doing things as they should in their Rocket Math^®implementations, they don’t have a copy of the directions. When teachers don’t have the directions handy, they will ask a colleague how to do things. Unfortunately, this is like a game of telephone and typically doesn’t end well. Being sure that every teacher has the directions available for easy reference goes a long way toward proper implementation. It also allows you to pick up the directions when you are in the room and point something out to the teacher or to reference an appropriate page number in the directions in your notes to the teacher.

You can print the Teacher Directions from the virtual filing cabinet, in the Forms and Information drawer, under Rocket Math Teacher Directions. You can buy printed copies from RocketMath.com/shop. There are additional things to look for on the form but they are optional and go with supplemental parts of the curriculum.

The Online Game never teaches anything wrong.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Basic, optional, and alternative—there are a lot of different Rocket Math programs to help students learn math facts. A common question teachers ask is in what sequence should they teach the various Rocket Math programs? The basic programs of Addition, Subtraction, Multiplication, and Division (0-9s) have priority and must be mastered by all students. Addition in the first grade. Addition and Subtraction in the second grade. Multiplication (as well as Addition and Subtraction) by the third grade. Then, all four, including Division by fourth grade. If a student is on track, those basics have first priority.

Optional programs if the basics are already on track

The rest of the programs are optional and should be offered to students once the basics have been mastered and only then. The only exception would be in a school where Kindergarteners did not get a chance to learn how to quickly and easily write numerals, through using the Rocket Writing for Numerals program. In that case, you might take the first two months of the first grade year to run students through Rocket Writing for Numerals before beginning Addition (0-9s).

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

Kindergarten Students have things to learn before beginning Addition Facts

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

First-grade Students Should Learn Addition Facts

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

Another intervention would be to use Rocket Math Online Game for Addition facts, as students seem to progress much more quickly in the online game. The Online Game has an adjustable game speed for first-grade students who are having trouble (their difficulty score is over 3) moving their fingers fast enough. First-grade students who finish the 0-9s can move on to the Add to 20 programs for the remainder of the year.

Second-grade Students Must Know Both Addition & Subtraction Facts

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

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

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

It is challenging for students to switch between Addition and Subtraction. But it does drive home the reciprocal nature of the two. There is no evidence that it is better to learn in fact families than it is to separate the operations. That’s why we offer both alternatives. You must of course, teach the concepts of both addition and subtraction before students can learn in fact families. Students can learn Add-Subtract fact families up to 10 in first grade. Then in second grade they can learn the Addition and Subtraction upper fact families, from 11 to 18 in second grade.

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

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

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

Fourth-grade Students Should Know Both Multiplication and Division Facts

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

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

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

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

Rocket Math Worksheet & Online Game

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

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

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

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

The Ultimate Guide to Math Fact Fluency

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

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

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

What is Math Fact Fluency

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

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

Three Reasons Why Math Fact Fluency is Important

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

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

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

1. Students with math fact fluency make fewer errors

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

2. Math fact fluency makes learning math easier

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

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

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

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

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

How to Build and Improve Math Fact Fluency

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

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

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

Learning the 0 through 9s facts in the four basic operations will take elementary students months to master. Worksheets and game applications are two of the best ways to teach fact fluency over time. Combining structured math fact learning, practice, and evaluation with fun math fact games helps students develop number sense and understand complex numerical relationships.

Teaching Math Fact Fluency with Worksheets

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

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

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

Teaching Math Fact Fluency with The Rocket Math Worksheet Program

The Rocket Math Worksheet Program improves upon this concept by using paired practice and saying facts aloud. Students partner up and practice quickly recalling facts together. One student asks the questions and watches for when their partner hesitates to answer. He or she then gives his or her partner more opportunities to practice any fact that isn’t coming to mind instantly.

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

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

Teaching Math Fact Fluency with Games

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

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

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

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

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

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

Math Fact Fluency Benchmarks

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

Kindergarten Numeral Writing Fluency Benchmarks (digits)
Start of Year	Mid-Year	End of Year
	20 digits per minute	40 digits per minute

First Grade Numeral Writing Fluency Benchmarks (digits)
Start of Year	Mid-Year	End of Year
40 digits per minute	60 digits per minute	60 digits per minute

First Grade Math Fact Fluency Benchmarks (problems per minute)
Start of Year	Mid-Year	End of Year
Addition: 12 per minute	Addition: 25 per minute	Addition: 25 per minute

Second Grade Math Fact Fluency (problems per minute)
Start of Year	Mid-Year	End of Year
Addition: 25 per minute	Addition: 30 per minute	Addition: 30 per minute
	Subtraction: 12 per minute	Subtraction: 25 per minute

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

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

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

Math Fact Fluency Assessment

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

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

Rate students as:

Weak, needs fact work
Good, but fact work could help
Strong, fact work not needed

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

The Best Tools for Developing Math Fact Fluency

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

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

In What Order Should Students Learn Fast Math Facts?

Posted on April 15, 2019May 8, 2022 by Dr. Don

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

An overview of Rocket Math’s fast math fact programs

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

The Basic Program

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

The Alternative Program: Fact Families

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

Optional Programs

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

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

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

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:

Factors
Equivalent Fractions
Learning to Add Integers
Learning to Subtract Integers or Mixed Integers

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

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.

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

Why Multiplication Games Are Awful & What to Do About It

Posted on March 13, 2019March 10, 2019 by Dr. Don

As a university supervisor of pre-service teachers, I’ve seen my share of bad lessons. Among the most painful were when student teachers would try to liven up their lessons to impress me by having the students do a math game. My student teachers wanted their students to learn math facts and to do so in a fun way. The picture above is typical of what I would see. Here are the reasons that most multiplication games that the student teachers implemented were awful.

(For multiplication games that work in and out of the classroom, check out Rocket Math’s Worksheet Program and Online Game.)

Waiting for your turn at a multiplication game is not learning!

As you can see in the picture above, all but one of the students are just waiting for their turn. They aren’t doing math. The students are just watching the student who is playing. No one likes waiting, and your students are no exception. Any game that has turn-taking among more than two students wastes time.

Make sure your multiplication games are structured so all or most students are engaged and playing all the time. You want students to have as much engaging practice as possible while practicing math facts at speed. If everyone can be doing that at the same time, that’s optimal. No more than two students should be taking turns at a time.

A multiplication game that allows using a known strategy to figure out facts (like finger counting) is not learning!

Learning math facts involves memorizing these facts so that students know them by memory, by recall. Committing facts to memory is why there is a need for lots of practice. If the game allows time for students to count on their fingers or use some other strategy for figuring out the answer to facts, then there is no incentive for students to get better.

In the lower left corner of the picture you can see one student counting on their fingers—which is better than just watching—but is not learning the facts, it is just figuring them out. The most able students in an elementary school are able to memorize facts on their own when they tire of figuring them out day in and day out. But the rest of the students will just do their work patiently year after year without memorizing if you don’t create the conditions for them to memorize facts.

Make sure that your multiplication games reward remembering facts quickly rather than just figuring them out. Speed should be the main factor after accuracy. Fast-paced games are more fun and the point should be that the more facts you learn the better you’ll do.

Multiplication games that randomly present ALL the facts make learning impossible.

It is a basic fact of learning that no one can memorize a bunch of similar things all at once. To memorize information, like math facts, the learner must work on a few, two to four facts, at a time. With sufficient practice, every learner can memorize a small number of math facts. Once learners master a set of math facts, they can learn another batch. But if a whole lot are presented all at once, it is impossible for the learner to memorize them.

Make sure your multiplication games are structured so that each student is presented with only facts they know. A good game presents only a few facts at a time. As students learn some of the math facts, more can be added, but at a pace that allows the learner to keep up. The optimal learning conditions are for the learner to have a few things to learn in a sea of already mastered material.

Rocket Math Multiplication Games

We designed Rocket Math games to help kids gradually (and successfully) master math skills. Students use Rocket Math’s Worksheet Program to practice with partners, then take timings. Students can also individually develop math fact fluency—from any device, anywhere, any time of day—with Rocket Math’s Online Game.

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.

Math Teaching Strategy #1: Help students memorize math facts

Posted on January 17, 2019January 17, 2019 by Dr. Don

Once students know the procedure, they should stop counting and memorize!

When it comes to math facts like 9 plus 7 or 8 times 6 there are only two things to know. 1) A procedure to figure it out, which shows that you understand the “concept.” 2) What’s the answer?

It is important for students to understand the concept and to have a reliable procedure to figure out the answer to a math fact. But there is no need for them to be required to use the laborious counting process over and over and over again! Really, if you think about it, even though this student is doing his math “work” he is not learning anything.

Math teaching strategy: Go ahead and memorize those facts.

(It won’t hurt them a bit. They’ll like it actually.)

Once students know the procedure for figuring out a basic fact, then they should stop figuring it out and just memorize the answer. Unlike capitals and countries in the world, math facts are never going to change. Once you memorize that 9 plus 7 is 16, it’s good for a lifetime. Memorizing math facts makes doing arithmetic MUCH easier and faster. Hence our tagline

Rocket Math: Because going fast is more fun!

Memorizing facts is the lowest level of learning. It’s as easy as it gets. But memorizing ALL the facts, which are similar, is kind of a long slog. Some kids just naturally absorb the facts and memorize them.

Math teaching strategy: Find a systematic way for students to memorize.

A lot of students don’t learn the facts and keep counting them out over and over again. They just need a systematic way of learning the facts. Students need to spend as much time as necessary on each small set of facts to get them fully mastered. If the facts are introduced too fast, they start to get confused, and it all breaks down. Each student should learn at their own pace and learn each set of facts until it is automatic–answered without hesitation and without having to think about it. This can be accomplished by everyone, if practice is carefully and systematically set up. It should be done, because the rest of math is either hard or easy depending on knowing those facts. And don’t get me started about why equivalent fractions are hard!

Dictating Sentences, do students need automaticity in spelling too?

Posted on September 12, 2018January 11, 2019 by Dr. Don

Few teachers realize how similar spelling and math facts are.

Both spelling and math facts are tool skills. Tool skills are things which one needs to do academic work, tools you use to do other things. The tool skills of spelling and math facts (like decoding) need to become so automatic that students don’t have to think about them.

If students have to think up the answer to math facts, it makes doing computation harder. The process of figuring out a math fact distracts from the mathematics being done. Similarly, if you have to stop and think of the spelling of a word (like the boy pictured above) while you are trying to write, it distracts you from thinking about what you are trying to write. Students are more successful and better able to show what they know and better able to focus on learning when their tool skills have developed to the level of automaticity.

Daily practice develops automaticity. Developing automaticity with math facts and with spelling requires a lot of practice. Daily practice is best and a few minutes a day is optimal. That is why Rocket Math is designed the way it is–to provide that daily practice. So Dictating Sentences gives each member of the pair ten minutes a day of practice writing sentences composed of words they know how to spell.

Dictating Sentences is spelling with a twist. Instead of spelling one word at a time, in Dictating Sentences (now part of the Universal Level Rocket Math Worksheet Program) students are asked to write an entire sentence from memory. They work in pairs and their tutor has the student repeat the sentence until it is learned. Then the student has to write the whole sentence from memory. It turns out this is considerably harder than writing words on a spelling test, so it is challenging practice, and does a lot to help students develop automaticity with spelling.

Working in pairs. As you know from Rocket Math practice, students enjoy working in pairs. And when one partner has an answer key the practice can be checked and corrected. Sound research shows that immediate correction and editing of misspelled words is the fastest way to learn the correct spelling, so that’s what we have the student tutor do. After each sentence is written every word is checked and practiced again until it is correct.

Mastery learning. The program is structure so that all the words are learned to the level of automaticy. Students keep working on a sentence until it can be written without any errors. They work on the same lesson for as many days as is needed for them to spelling every word perfectly in all three sentences. Each sentence persists for two or three lessons, so that the student is required to write it from memory and spell every word perfectly for several days in a row.

Earning points by being correct and going fast. Students earn two points for every word that is spelling correctly the first time. Every word on which there is an error is worked on until it too can be spelled correctly, earning one point. The faster students go during their ten minutes, the more points they can earn. Students graph the amount of points earned and try to beat their own score from previous days. Teams can be set up and competition for the glory of being on the winning team can enhance the motivation.

Individual Placement. There is a placement test. Students begin at the level where they first make a mistake. Student partners do not need to be at the same level, so every student can be individually placed at the level of success.