Strategies for teaching automaticity of math facts

Above are students playing our Race for the Stars game.  This game prompts everyone to race against each other and the clock to answer 24 fact problems as fast as they can.  This activity can help develop automaticity of math facts. Not all activities in which students “practice” answering math facts will help develop automaticity.  In fact, a lot of math fact practice activities require students to “figure out” math facts over and over. Automaticity only comes about through recall.  Recall is instantaneous, whereas “figuring out” takes time. All the activities that give students “time” to derive the fact will not help develop automaticity.

What is automaticity?

high school marching band with brass instruments and drumsAutomaticity is the level of learning you have achieved when you can do something accurately and quickly while you are doing something else.  It is “automatic” because you don’t have to stop and think about it; you can do it while concentrating on something else. As the picture illustrates, you need to develop automaticity to function in a marching band, which is why it takes a lot of practice.  You have to march while simultaneously playing music and keep up with everyone else. That takes automaticity.

 

What is automaticity good for?

tools to build math fact fluencyIn academics, students use certain “tool skills” while they are multitasking.  These tool skills must become automatic so students can use them without thinking.  One tool skill is decoding in reading–getting the words off the page. That has to be automatic so the reader can focus on the message of the material they are reading.  Spelling is another tool skill that has to be automatic. A student who is writing something should not be distracted by trying to remember how to spell the words they are writing.

 

Why is automaticity of math facts important?

A student figuring out math facts slowlyIn math, the tool skill that must be automatic is remembering math facts.  Students must be able to recall the answer to single digit facts like 9 + 7 while simultaneously doing more complex problems.  They need to be able to recall those facts without losing their place in what they are computing, just like a member of a marching band.

No matter how clever the strategy for remembering a math fact, if it is not recalled instantly and automatically, it disrupts the thinking process of the learner.  The steps in the overall math procedure will become confusing, or the point of the computation may be lost. Strategies for developing automaticity must guard against allowing students to repeatedly “figure out” facts and must direct them to “just remember” the fact.  This can be a surprise for some teachers and some students!

Practice strategies that develop automaticity of math facts

Two students participating in one of Rocket Math's math fluency programsStudents can recall some facts instantly but have not yet learned others enough to be recalled instantly.  New math facts are learned one at a time. Although most students can work on memorizing three or four new facts at a time, if the facts are too similar, even three will be too many.

The best method of practice is to read problems aloud and say the answer from memory.  If there is any hesitation after the problem is read aloud (which gives the learner enough time to remember) then extra practice is needed on that fact.  The procedure should happen immediately, as there is no time to waste. The learner needs to understand that the goal is to instantly recall facts, rather than puzzle them out. 

Figuring out math facts will not develop automaticity

Rocket Math mobile math fact game interfaceAllowing students extended time to work out the answer to a math fact teaches the wrong lesson.  If there is any hesitation in answering, extra practice should involve being told the fact and the answer immediately (no more puzzling it out, is the message!).  After hearing the correct answer, the learner should say the problem and the answer aloud two or three times. They should then go on and practice two or three different problems before returning to the problem that the learner was slow to answer.  And finally, the learner should try to answer the first math fact again, this time without any hesitation. This process of being told the answer, trying to commit it to memory and trying to recall it a few seconds later will develop automaticity of math facts. Consistently allowing students extended time to figure out facts will not lead to automaticity.

Similarly, the Rocket Math Online Game only allows students 3 seconds to input an answer.  If they can’t answer instantly, automatically, then the game shows, “Time’s Up!”  and Mission Control says, “You gotta be faster!” Next, the game gives the student extra practice on that fact and starts them over in the part.  The game expects automaticity of math facts and teaches students that they can in fact do that.

Students will be able to remember and recall the answer, as long as only a couple of new facts are introduced at a time.  They will come to realize that instant recall is possible, and that is their goal. Once they can recall facts without having to figure them out, math will become a breeze.

Use Rocket Math’s automatic response worksheets for testing not teaching

The Rocket Math Worksheet Program has students practice in pairs as described above.  Then each day the pair will do timed or “automatic response” worksheets—but as a test.  The worksheets proceed from A to Z as students learn more facts in the operation. Each worksheet only tests the facts introduced thus far.  Students practice the same set of facts, using the oral procedure outlined above until all of the facts introduced thus far are automatic.

Rocket Math Addition Set D Worksheet that develops automaticity of math factsWhat facts are on each math worksheet matter.  A worksheet cannot contain a mix of all of the facts in an operation; you cannot expect facts to become automatic by doing the sheet repetitively. No one can learn 80 facts at once.  The curriculum must break down the facts in an operation into bite-size pieces so that students can practice and learn them. You see here set D, which has added 7+1 and 8+1 and their reverses as new facts.  The One-Minute Test only presents the facts learned up through set D. For the first couple of days, the student will not be able to answer all the facts instantly; but after a few days of practice, the students will be automatic with all the facts.  Then the student will pass the set. The curriculum should add more facts to be learned in the next set.

Slow and steady wins the race. It takes months to learn all of the facts in an operation to the level of automaticity, but everyone can do it.

 

Both programs for one teacher and class for one low price.

Choose #2500 both programs for your class for $88 and get a bonus

$88 Individual Both Programs (30 seats) subscription

Tried-and-true Rocket Math fact fluency worksheets

[A $49 value] Our Rocket Math Worksheet Program has students practice daily with a partner, take a One-Minute Test, and move up the Rocket Chart based on the ten-minutes per day pencil-and-paper activities.  Teachers have been relying on this program and getting gratifying results for decades.  This subscription will give you access to the Rocket Math filing cabinet and all of the hundreds of worksheets available to print from our virtual filing cabinet.  

 

30 seats for the Online Game develops math fact fluency in a fast-paced format

 

 

[A $60 value] In 2018, Rocket Math added an Online Game for students to play on any device and learn math facts.  This package will give access to up to 30 students in your classroom.  The regular price for 30 students is $2 per student for the year.

In the Online Game, students login and practice and work through levels A to Z the same as in the Worksheet Program. If a student takes longer than 3 seconds to answer a fact, the program treats it as a hesitation and gives more practice on that fact.  The program responds to hesitations by telling the student the problem and answer, asking them to enter the correct answer, then giving them the problem again a few seconds later. 

Students can also login in at home and practice there.  The Rocket Math Online Game is very intense, so learners can only work for five minutes at a time, and then the game makes them take a 30-minute break.  Although the game is challenging (or maybe because it is hard), students are very motivated by seeing their progress.  They can tell that they are learning and they feel good about their accomplishments.  

 

You can monitor the development of math fact fluency in the game

The teacher can monitor progress (as you can see below).  The teacher can see if students are logging on at home, see their level of difficulty, and change them to a different one of the ten learning tracks available.  Easy to set up a program of recognition for students who practice at home.  

Bonus: Wall Charts visually track development of math fact fluency

[An $18 value] As a bonus in this package Rocket Math will send you a Rocket Math Wall Chart. This chart comes with stickers for students to post each time they pass a level in Rocket Math.  It has goal arrows, so the teacher can set goals for the class with rewards for filling up the chart to a certain point.  This enables the students to work together to achieve goals and celebrate their success as a group.  Also comes with directions on how to use it to best advantage.   

This chart is a very motivating for students as they are developing math fact fluency and builds team spirit with your class. 

Identifying Fractions: Creating fluent mathematicians

Fractions are unnecessarily hard for students to understand.  The reason?  Not enough practice with identifying a wide enough variety of fractions and ways of displaying them.  Rocket Math has introduced a great solution as part of the Universal Level Worksheet subscription–a new program called Identifying Fractions.

Identifying Fractions: Not just proper fractions anymore.

One of the most powerful aspects of the Identifying Fractions program is that it is not limited to showing proper fractions.  Right from the beginning of Set A, students are introduced to improper fractions and mixed numbers.  They are taught the fundamental understanding that the bottom number tells you how many parts each whole is divided into.  At the same time, if the whole is not divided into parts, then we represent it as a whole number.  Finally, the top number tells how many parts are shaded (or used) regardless of whether that is more than 1 whole or less than one whole.  Identifying fractions that include improper fractions and mixed numbers from the beginning insures that students really understand fractions and don’t accidentally acquire the misrule that fractions are always less than one.

Identifying Fractions: Learn to speak their names also

Without a lot of oral practice students do not always know how to say the names of fractions.  Identifying fractions introduces three fractions in each set and includes the words for how to say them.  In the example here one half, three halves, and one and one half are written out at the top of the page.  This is all that is practiced as part of this first set.  This way, orally practicing with a partner means saying the names of the fractions, which are shown at the top of the page.  Students are not asked to say any fractions they haven’t seen written out first.

The fractions that students become familiar with include, halves, thirds, quarters, fifths, sixths, eighths, tenths and twelfths.  They see improper fractions and mixed number with every denominator.

Identifying Fractions: It’s not the shape that matters

When students don’t have a lot of practice with identifying fractions they may not see different shapes being divided into the same number of parts.  In Identifying Fractions we make a point of showing each fraction with at least three different shapes.  In this example you see thirds in a circle, in a cube shape, and as upright rectangles making a larger rectangle.  All of those are equally “thirds” because each whole figure is divided into three parts.  So there are three different shapes for halves, fourths, fifths and sixths.

By the time students are introduced to eighths, tenths and twelfths, they have already learned the rule that the shape doesn’t matter.

When students are eventually introduced to eighths, tenths and twelfths we don’t want to slow them down by having to laboriously count the number of parts in each figure.  As you can see to the left, the eighths are displayed as two sets of four rectangles on top of each other.  Eighths are always displayed that way, so they are easy to identify quickly.  Tenths are consistently displayed as two columns of five blocks with little numbers in them. (I know it’s a little weird, but it works to make them easily identifiable.) Twelfths are always shown as three sets of four rectangles on each other.  Students should notice these conventions so they can quickly identify the number of parts in those figures without having to count them.

Identifying Fractions:  Advanced students can fit in during Rocket Math routine

Identifying Fractions follows the standard Rocket Math routine.  Each student practices orally with the partner for a couple of minutes.  Then the two switch roles.  Finally everyone takes a 1 minute Daily Test.  A student in Identifying Fractions can be paired with any student in any other Rocket Math program as long as the student has an answer key to hand to their checker. Hopefully you remembered to print the answers on colored paper.

Unlike other Rocket Math programs, the test and the practice items are the same.  Of course, the students have a page without the answers, while their checker holds the answer key. Students practice by saying aloud to their partner the fractions shown in the test.  Then they take the test on those same items, but write the answer.

Identifying fractions has its own writing speed test, to be sure that student goals are individualized to their writing speed.  By the time students complete Set Z in this program they will have a strong understanding of fractions that will be fluent.  There are even 2-minute timings you can give every week or two for them to chart their progress as they get faster.  This is a great program for students of any grade from second grade on up who have finished the basics for their grade level.  It will really put them in good shape when dealing with fractions in later years.

 

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

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

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

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

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

2) Start with the easier implementation of the Online Game.

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

3) Online Game is easier for parents to support.

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

4) Worksheet Program more rigorously develops math fact fluency.

Two students participating in one of Rocket Math's math fluency programsCompared to the Online Game, the Worksheet Program is a bit harder to pass a level.  Students have to practice with their partner more time before they pass, so students learn facts better with it. They are more solid in their knowledge of facts when they are done with an operation like multiplication in the Worksheet Program than they are if they just run through multiplication in the Online Game.  Which is a reason not to do the Online Game only.  Of course, students are even stronger in their facts when they practice with both.

5) Worksheet Program will generalize to computation more readily.

The purpose of learning math facts is to make it easier for students to learn and do basic computation.  Math work is written, so the Worksheet Program (which is also written) is closer to how math facts will be used.  That means the Worksheet Program will generalize better to computation assignments.  You will see a bigger benefit to students doing math assignments when they finish the Worksheet Program than with the Online Game.  Which is yet another reason to do both programs.

6) Doing both develops math fact fluency twice.

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

Two math fact fluency programs from Rocket Math for one low price with a bonus

Choose both programs for the Whole School for $695 and get a bonus

Whole School Both Program subscription

Tried-and-true Rocket Math fact fluency worksheets

[A $300 value] Our Rocket Math Worksheet Program has students practice daily with a partner, take a One-Minute Test, and move up the Rocket Chart based on the ten-minutes per day pencil-and-paper activities.  Teachers have been relying on this program and getting gratifying results for decades.  This subscription will give all the teachers in your building access to the Rocket Math filing cabinet and all of the hundreds of worksheets available to print from our virtual filing cabinet.  Purchased by itself the All Teacher Universal Worksheet Program costs $300.

Online Game develops math fact fluency in a fast-paced format

 

 

[A $400 to $900 value] In 2018, Rocket Math added an Online Game for students to play on any device and learn math facts.  This package will give access to all the students in your school, without regard to how many there are.  The regular price for 100 or more students is $1 per student for the year. So if your school has fewer than 395 students in your building, you want to buy the programs separately.

In the Online Game, students login and practice and work through levels A to Z the same as in the Worksheet Program. If a student takes longer than 3 seconds to answer a fact, the program treats it as a hesitation and gives more practice on that fact.  The program responds to hesitations by telling the student the problem and answer, asking them to enter the correct answer, then giving them the problem again a few seconds later. 

The Rocket Math Online Game is very intense, so learners can only work for five minutes at a time, and then the game makes them take a 30-minute break.  Although the game is challenging (or maybe because it is hard), students are very motivated by seeing their progress.  They can tell that they are learning and they feel good about their accomplishments.  

 

Teachers can monitor the development of math fact fluency in the game

The teacher can monitor progress (as you can see below).  The teacher can see if students are logging on at home, see their level of difficulty, and change them to a different one of the ten learning tracks available. 

Bonus: Wall Charts visually track development of math fact fluency

[A $405 value] As a bonus in this package Rocket Math will send Rocket Math Wall Charts for every teacher participating in the program.  This chart comes with stickers for students to post each time they pass a level in Rocket Math.  It has goal arrows, so the teacher can set goals for the class with rewards for filling up the chart to a certain point.  This enables the students to work together to achieve goals and celebrate their success as a group.  Also comes with directions on how to use it to best advantage.   

This chart is a very motivating for students as they are developing math fact fluency.  It also allows the principal to view and praise students for their success in Rocket Math.  

The Ultimate Guide to Math Fact Fluency

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

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

What is Math Fact Fluency

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

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

Three Reasons Why Math Fact Fluency is Important

tools to build math fact fluencyMath 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

steep climb to math fact fluencyBuilding 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

Two students participating in one of Rocket Math's math fluency programsThe Rocket Math Worksheet Program improves upon this concept by using paired practice and saying facts aloud. Students partner up and practice quickly recalling facts together. One student asks the questions and watches for when their partner hesitates to answer. He or she then gives his or her partner more opportunities to practice the harder facts.

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

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

 

Teaching Math Fact Fluency with Games

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

asian child holding tablet with a math fact fluency app by Rocket MathThere are games that are very effective at building math fact fluency. Games such as the Rocket Math Online Game have several important features that make a big difference.

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

Math Fact Fluency Benchmarks

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

Kindergarten Numeral Writing Fluency Benchmarks (digits)

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

First Grade Numeral Writing Fluency Benchmarks (digits)

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

First Grade Math Fact Fluency Benchmarks (problems per minute)

Start of Year Mid-Year End of Year
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:

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

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

 

The Best Tools for Developing Math Fact Fluency

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

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

 

 

 

Positive Praise: Building Effective Teaching Habits

Positive praise is one of the most effective ways to encourage wanted behaviors from students. Because building habits is not an easy task, here are a few things you can do to start easily incorporating positive praise in the classroom.

  1. Be prepared with positive phrases
  2. Develop the most effective wording
  3. Start Small with two areas you would like to see improved behavior
  4. Practice in the Classroom and watch the effect it has on your students
  5. Grow and expand your positive phrases over time as you master the habit

Be Prepared with Positive Praise Phrases

I distinctly remember trying to help pre-service teachers build the teaching habit of positive praise. I would make suggestions and then observe. Trying to implement my suggestions wasn’t as easy as you would imagine – these teachers would glance in my direction and start the sentence “I like the way you’re . . .” and then trail off without knowing what to say.

Teachers want to use positivity and affirmation with their students, however, in my experience, they don’t always have the appropriate words ready to praise good behavior. Building the teaching habit of positive praise starts with getting the right words ready.

Recently I was reminded of this key component of building the new habit of making more positive statements. I wanted to personally develop this positive statement habit, but for some reason was not making the progress I had hoped for.

I quickly realized that I was making the same mistake I had watched the pre-service teachers make. I was unable to make more positive statements because I did not have any in mind that were ready-to-use.

To build the habit of making more positive statements, I would have to start memorizing some key phrases to keep on standby, ready to use when I needed them.

Positive Praise Example Phrases: How to Develop the Right Wording

The first step in positive praise is learning and developing the most effective wording. Using effective wording means you are getting through to your student, and clearly communicating that you appreciate the good behavior they are exhibiting.

Praise is most effective when it is prompt – when you deliver the praise in the moment. Can you picture a specific scenario in your classroom when many of the students are not doing as you asked, while a few students are dutifully following instructions?

This is the perfect scenario to use positive praise not only in rewarding students with good behavior but also encouraging other students to follow suit. Don’t be afraid to praise good behavior loud and proud for the rest of the classroom to hear!

Here are some examples of positive praise:

  • Look at Alan so smart sitting in his seat and showing me he is ready to learn. Way to go, Alan.
  • I see Beto is tracking with his finger while Claudio is saying the facts. That’s the way to help your partner!
  • Julia, you are so sharp having your eyes on the teacher, so you can learn!  I am impressed.
  • Stacy and Sophia know just what to do, they have their books open to page XX.  They are so on top of it!
  • Fantastic, Justin! You put your pencil down and are waiting for directions.  I can tell you’re going to college.
  • Stephanie is being such a great on-task student by working quietly and not talking.

Start Small: Pick Two Key Behaviors You Would Like to See More Of

Start out by choosing wanted behaviors from the two most annoying or frustrating scenarios you face as a teacher.  Stating small will help you build a consistent habit of giving positive praise.

Take these two wanted behaviors and build two praise statements you can easily use in-the-moment. Make sure the statement names the behavior specifically. Always include the student’s name, and keep it simple and affirmative.

Now, take a note card or piece of paper and write down these two statements. Don’t wait! Write them down now and keep this note in front of you while you teach. It will serve as a reminder throughout your day to incorporate positive praise as much as possible.

Practice saying these phrases aloud until you have them memorized and can recall them without having to think about it. The most important step in building this habit? Actually practicing positive statements in the classroom.

With these key components and diligent practice in the classroom, you will quickly build the habit of positively praising your students.

Positive Praise in The Classroom: Will it Make a Difference?

Fortunately, positive praise is free and can be implemented at any time throughout the school year. Start using positive praise now, and watch how your students respond.

Prepare yourself for giving positive praise when you are about to begin those frustrating scenarios. When the activity begins, look for opportunities to praise the behavior you are looking for when you notice students who are off-task.

You will see results when you use positive praise genuinely and with enthusiasm. You will know it is working if you watch for those distracted students taking notice of who is being praised. If you notice this happening, keep it up. The more praise you give for wanted behavior, the more that behavior will occur.

Grow and Expand Your Positive Praise Habit

Now that you know how to promote a specific behavior with positive praise, you can systematically develop statements for all your troublesome areas.  Every time students are not doing what you want, think of what you want them to do instead.  Behavior analysts call those replacement behaviors. 

Positive praise can also be used creatively alongside other motivational tools in the classroom. When I began my teaching career I was in the habit of scolding behaviors I did not want. Early in my career, I learned the effectiveness of positive praise and began incorporating it into my daily routine.

When I saw the behavior I wanted I would give loud and proud praise for all to hear. I decided to couple this by adding marbles to a jar every time I gave praise, as an added motivational tool – so students could see how well they have been doing. It worked wonders on increasing wanted behavior.

Building new habits is never easy, but I can personally say that as a teacher, learning to incorporate positive praise into your teaching routine will not only help students learn, but it will save you a lot of frustration!

Beginning numerals and counting program added to Rocket Math

Beginning Numerals and Counting

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

I do–demonstration of counting.

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

“I can do these. Watch me count the frogs. One, two, three.  There are three frogs in this box. So they circled the three. Everybody, touch here where the three is circled. Good.
How many frogs were in this box, everybody? Yes, three.
Now watch me do the next box.”

We do–counting together. 

In the “We do” portion of the worksheet the teacher counts the stars first as a demo and then with the students.  Worksheet A you all just count 3 stars.  Suggested teaching language is something like this:

“Our ‘We Do’ says to touch and count. Start at zero and count each star.
We are going to touch and count the stars. Put your counting finger on zero,
everybody. We are going to start at zero and count each star. Let’s count.
One, two, three. We counted three stars. That was great!
Let’s do it again! Fingers on zero, everybody. Let’s count. One…”

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

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

You do–independent counting. 

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

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

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

 

 

Rocket Math Teaches Math Facts Fast!

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

learn math facts fastLearning 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:

  1. How many math facts to introduce in one session
  2. How fast a student can answer individual math facts
  3. How fast a student can answer multiple math facts
  4. When to introduce new math facts
  5. 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.

learn math facts on bite at a timeWhen 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

child learning math facts with memorizationOnce 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’s research-based program incorporates these modern teaching techniques to help young learners master math facts fast. With the program, recalling math facts becomes easy and enjoyable. It also sets students up for continued success throughout their education.

Learn more about using Rocket Math’s subscription worksheet program in the classroom and the online math fact game.

Math Worksheets for Kindergarten, 1st, 2nd, 3rd, 4th grade+

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

math worksheet for kindergartenerskindergarten 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

1st grade math worksheet

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.

math worksheet for first graders

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.

second grade math worksheetThe 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.

math worksheet for second gradersIf 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. 

 

 

best math worksheets for second grade students

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

third grade math worksheet

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.

math worksheet for third grade

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

fourthgrade math worksheet

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.

advanced math worksheet1) Equivalent Fractions

  • Teaches 100 fractions and what they are equivalent to.

2) Factors

  • Shows how to find all the factors of a number, quickly and reliably.

3) Learning to Add Integers (positive and negative numbers)

  • Uses a vertical number line to teach these problems.

4) Learning to Subtract Integers (positive and negative numbers)

  • Uses the vertical number line to show how these work.

math worksheet for fast learners5) 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.

With the right tools, students can enjoy learning math and teachers can relax knowing that a strong foundation is being built. Our FAQs page for Teacher Instructions and How to Implement the Worksheet program can help answer any questions you might have.