Dr. Don, Author at Rocket Math

Two students are playing 2nd grade math games in class by asking each other a math question and testing each other.

Identifying Fractions: Creating fluent mathematicians

Posted on July 26, 2019July 7, 2022 by Dr. Don

Fractions are unnecessarily hard for students to understand. The reason? Not enough practice in identifying a wide enough variety 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 ensures 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 at the top of the page. Students only practice this as part of the first set. This way, orally practicing with a partner means saying the names of the fractions. These names are students can see 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 numbers 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 divides 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 you introduce students 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 worksheet displays eighths as two sets of four rectangles on top of each other. This display, makes it easy to identify eighths quickly. Tenths are consistently 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 in 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. Pair a student in Identifying Fractions 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 partners 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. The writing speed test will make sure your student’s goals are unique 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.

Visit our Evidence of Effectiveness page to learn more.

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

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

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

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

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

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

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

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

3) The Online Tutor provides consistent quality of practice.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The Ultimate Guide to Math Fact Fluency

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

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

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

What is Math Fact Fluency

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

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

Three Reasons Why Math Fact Fluency is Important

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

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

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

1. Students with math fact fluency make fewer errors

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

2. Math fact fluency makes learning math easier

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

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

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

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

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

How to Build and Improve Math Fact Fluency

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

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

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

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

Teaching Math Fact Fluency with Worksheets

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

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

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

Teaching Math Fact Fluency with The Rocket Math Worksheet Program

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

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

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

Teaching Math Fact Fluency with Games

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

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

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

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

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

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

Math Fact Fluency Benchmarks

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

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

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

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

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

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

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

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

Math Fact Fluency Assessment

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

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

Rate students as:

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

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

The Best Tools for Developing Math Fact Fluency

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

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

A mom congratulates her son at a baseball game.

Positive Praise: Building Effective Teaching Habits

Posted on July 3, 2019July 8, 2022 by Dr. Don

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.

Be prepared with positive phrases
Develop the most effective wording
Start Small with two areas you would like to see improved behavior
Practice in the Classroom and watch the effect it has on your students
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!

If you are currently looking for a job as a math teacher abroad, check out this link on Jooble.

Rocket Math Adds Beginning Numerals & Counting Program

Posted on June 13, 2019April 14, 2021 by Dr. Don

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 and is to help them learn counting and numerals. That means they can’t learn on their own, the teacher must provide instruction. Teachers can use the counting objects kindergarten 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 above.

If you’re already a Rocket Math Universal Level subscriber, you can find the worksheet in your virtual filing cabinet. Not a subscriber yet? Get the counting worksheets.

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 three 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.

Rocket Math’s Counting objects worksheets for Kindergarten

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.

If you’re already a Rocket Math Universal Level subscriber, you can find the worksheet in your virtual filing cabinet [use your link]. Not a subscriber yet? Get the counting worksheets.

Rocket Math Teaches Math Facts Fast!

Posted on May 28, 2019 by Dr. Don

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

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

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

Why Faster Is Better

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

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

Once a student develops instant recall, math assignments become easy and fast. It enables students to easily recognize many things about numbers that teachers call “number sense.” It gives them confidence. And frankly, they like going fast much better. This makes teaching and learning math far more enjoyable!

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

The Problem with Traditional Teaching Techniques

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

A More Effective Approach to Teaching Fast Math Facts

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

How many math facts to introduce in one session
How fast a student can answer individual math facts
How fast a student can answer multiple math facts
When to introduce new math facts
How often a student practices

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

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

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

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

2. Help Students Quickly Recall Individual Math Facts

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

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

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

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

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

4. Carefully Build Math Fact Fluency

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

5. Practice Math Facts Daily for Long-Lasting Fluency

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

Rocket Math: A Modern Approach to Teaching Math Facts

Rocket Math’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.

three students working on math worksheets in a classroom

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

Posted on May 23, 2019October 25, 2022 by Dr. Don

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 count and read and write numbers. The many learning tracks available in the Worksheet Program are designed for daily practice to build a solid foundation of basic math skills.

The learning tracks of the Universal Level Worksheet Program follow a simple structure and routine to help students progress at an appropriate rate throughout their different grade levels. Throughout the sequence, students learn the underlying skills necessary to be successful in any math curriculum throughout elementary and middle school. While Rocket Math Worksheets are not a complete math curriculum, they develop all the skills that are assumed, but seldom taught well in elementary math curricula.

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

Kindergarten Math Worksheets

Beginning Numerals (Counting) Learning Track

This is a beginning program for kindergarten students. It teaches them to count objects aloud and then match the word with the numeral. Please note: Unlike most math worksheets learning tracks, this program is teacher-directed rather than peer teaching.

Each worksheet begins with a demonstration of counting objects and circling the numeral that matches. On Worksheet A, students only need to learn numbers two and three. First, the teacher demonstrates (best with a document camera so all students can see) how to count the objects and then points out that the answer has a circle around it. In the “We do” portion of the worksheet, the teacher counts the stars first as a demo and then with the students. For Worksheet A, just count 3 stars. By Worksheet S, the teacher and the students are counting 12 stars together. In the “You do” portion, the students independently complete tasks like the ones demonstrated by the teacher at the top of the worksheet. By the end of this learning track, kindergarteners can consistently count objects, lines, dots, and fingers up to 12 and identify the corresponding numeral.

Conceptual Addition (Counting On) Learning Track

Conceptual Addition is a teacher-led exercise, rather than peer teaching. Each worksheet begins with an “I Do” portion that is a teacher-modeled demonstration. “I Do” is followed by a “We Do” portion where the teacher leads the students in doing the problems together. The last portion is called “You Do,” which students should be able to complete independently following teacher instruction and modeling.

For the first four worksheets, the objective is to count all the objects in two groups to find the sum. When modeling, teachers should slash the objects with a pencil while counting. Students should do the same. The answer keys show the objects slashed. Starting in Set E, counting exercises no longer begin at one nor progress one by one. Students learn the concept of “counting on.” “Counting on” means to start with a number such as “4” and “count on” from there (five, six, and so on). Students also learn the concept of adding two to four by starting with four and “counting on” two more.

Rocket Writing for Numerals Learning Track

One of the most important math-related skills for kindergarteners is to learn how to write numerals properly. It is important for children to learn the most efficient way to write numerals. This skill is the first building block to learning math.

Rocket Writing for Numerals is a 72-page learning track for students to learn how to write the numerals efficiently. This program begins with how to write numerals and continues until students can write 40 digits in a minute. It is part of the Rocket Math Universal Worksheet Program and is designed to be practiced on a daily basis.

1st Grade Math Worksheets

If students in first grade cannot write numerals legibly and efficiently, they should begin the year with Rocket Writing for Numerals. If students have not learned the concept of what it means to add in kindergarten with the Conceptual Addition learning track, that is recommended. Once they understand the concept of addition, first graders are ready to begin memorizing addition facts.

Addition 0 through 9s Learning Track

The Rocket Math Worksheet Program includes Addition 0 through 9s. Students work through 26 levels (A to Z) learning two facts and their reverses on each level. For this learning track, like most of the learning tracks, students practice orally for 2 minutes with a partner who corrects any hesitations or errors. The students then switch roles and practice again, followed by a 1-minute daily test to see if they are ready to move on to the next worksheet. For peer teaching like this to be effective, the teacher will need to teach their students how to practice and how to correct errors. Here’s a blog on how to best manage peer teaching.

Add-Subtract Fact Families to 10 Learning Track

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

Addition-Learning Computation Learning Track

Once students master addition math facts, they need to learn how to do multi-digit addition problems, such as adding 35 + 48. Teachers can start their students on the Addition-Learning Computation learning track. This learning track extends computational skills in addition up to the 4th grade. It is teacher-directed and includes suggested scripts for tutoring or small group instruction. There is an assessment to determine where to begin, although, for first-grade students, it is at the beginning.

Add to 20 Learning Track

Common Core suggests that students be fluent with addition math facts up to 20, such as 13+6=19. Rocket Math’s Universal subscription includes an Add to 20 learning track.

2nd Grade Math Worksheets

Upon starting second grade, students should have mastered all of the addition math facts. If they have not mastered those facts, teachers should have students start with the first-grade worksheets until they are ready to move forward.

Subtraction 0 through 9s Learning Track

Once students master the first-grade level learning tracks, second-grade students go on to memorize subtraction facts in the Subtraction 0 through 9s learning track. For this learning track, like most of the learning tracks, students practice orally for 2 minutes with a partner who corrects any hesitations or errors. The students then switch roles and practice again, followed by a 1-minute daily test to see if they are ready to move on to the next worksheet. For peer teaching like this to be effective, the teacher will need to teach their students how to practice and how to correct errors. Here’s a blog on how to best manage peer teaching.

Subtraction-Learning Computation Learning Track

Typically, second graders should be proficient in subtraction and addition by the end of the year. Once students master subtraction math facts, students need to learn how to do multi-digit subtraction problems such as 62 – 48. Teachers can start their students on the Subtraction-Learning Computation learning track. The program helps students learn re-grouping (a.k.a. “borrowing”). This learning track extends computational skills in subtraction up to the 4th grade. It is teacher-directed and includes suggested scripts for tutoring or small group instruction. There is an assessment to determine where to begin, although, for second-grade students, it is at the beginning.

Add-Subtract Fact Families 11 to 18 Learning Track

If students have been using the Fact Families Program in first grade, it is best to continue using that sequence. Second graders should be ready for Add-Subtract Fact Families 11 to 18. The last ten levels of this program review all the fact families, allowing students to master addition and subtraction by the time they reach Level Z.

Subtract from 20 Learning Track

Common Core suggests that students be fluent with subtraction facts up to 20, such as 19-6=13. Rocket Math has made available a program, Subtract from 20, so students can practice these facts.

3rd Grade Math Worksheets

The priority for third grade is to learn the concept of multiplication and then memorize those facts. Textbooks typically begin teaching the concept of multiplication from very early in 3rd grade.

Conceptual Multiplication Math Learning Track

Conceptual Multiplication is a learning track to teach the concept of multiplication. It is based on skip counting or count-bys. However, in this learning track, students can read all the count-by series except the last number, making it unnecessary for students to have memorized the skip counting sequences to do this learning track.

For this learning track, like most of the learning tracks, students practice orally for 2 minutes with a partner who corrects any hesitations or errors. The students then switch roles and practice again, followed by a 1-minute daily test to see if they are ready to move on to the next worksheet. For peer teaching like this to be effective, the teacher will need to teach their students how to practice and how to correct errors. Here’s a blog on how to best manage peer teaching.

Conceptual Multiplication is essential for students who have not been introduced to multiplication in their regular math curriculum but are otherwise ready to start memorizing multiplication facts. Students do NOT need this learning track if they can determine the answer to any multiplication fact when you ask them, for example, “What’s seven times eight?” If they can figure out the answer to that question, they already understand the concept of multiplication and can go on to memorizing.

Multiplication (0 through 9s) Learning Track

The Rocket Math Multiplication (0 through 9s) Learning Track builds strong multiplication fact fluency and recall. This learning track prevents the problem of students having to look up facts in times tables repeatedly.

Achieving mastery of 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 in addition and subtraction facts, your top priority must be to help students develop fluency in multiplication facts before they leave you.

Multiply-Divide Fact Families to 20 Learning Track

Alternatively, once students have learned the concepts for both multiplication and division, they can begin to learn fact families. Our Multiply-Divide Fact Families to 20 worksheet program begins teaching multiplication and division fact families. For example, Set A of this worksheet (pictured) teaches the four related math facts of a family: 2÷1=2, 1×2=2, 2÷2=1, and 2×1=2.

Identifying Fractions Learning Track

For quick-learning students, who get through the basic learning track before the end of the year, an excellent supplemental Rocket Math Worksheet Program is the Identifying Fractions learning track. This is appropriate any time from third grade up through fifth. This learning track teaches students how to identify proper fractions, improper fractions and mixed numbers as you can see in the example above from Set A. It teaches fractions with denominators up to twelfths. This learning track prevents the most common misunderstandings about fractions by teaching with carefully selected examples that demonstrate the correct understanding of fractions.

Multiplication 10s, 11s,12s Learning Track

Multiplication 10s, 11s, 12s. Building upon the facts from Multiplication 1s to 9s, students progress quickly 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!

Multiplication-Learning Computation Learning Track

Once students master multiplication math facts, they need to learn how to do multi-digit multiplication problems such as multiplying 6 x 37. Teachers can start their students on the Multiplication-Learning Computation learning track. This learning track extends computational skills in multiplication up to the 5th grade. It is teacher-directed and includes suggested scripts for tutoring or small group instruction. There is an assessment to determine where to begin, although, for third-grade students, it is at the beginning.

4th Grade Math Worksheets

Upon starting fourth grade, students should have mastered all of the multiplication math facts. If they have not mastered those facts, teachers should have students start with the multiplication worksheets until they are ready to move forward into division. While division facts derive from multiplication, it is valuable for students to learn the division facts explicitly.

Division 0-9 Learning Track

Long division comes much easier for students who have learned division facts. Fourth graders should be using the Division 0 through 9s worksheet to learn division facts. By the end of fourth grade, students should have learned all four basic operations of math facts.

Multiply-Divide Fact Families from 21 Learning Track

If students have been using the Multiplication-Division Fact Families Program in third grade, it is best to continue using that sequence. Fourth graders should be ready for Multiply-Divide Subtract Fact Families from 21. The last several levels of this program review all the fact families, allowing students to master all multiplication and division facts by the time they reach Level Z.

Division-Learning Computation Learning Track

Once students master division math facts, they need to learn how to do multi-digit division problems such as dividing 5 into 395. Teachers can start their students on the Division-Learning Computation learning track. This learning track extends computational skills in multiplication up to the 4th grade. It is teacher-directed and includes suggested scripts for tutoring or small group instruction. There is an assessment to determine where to begin.

Division 10s, 11s, 12s Learning Track

There is a supplemental program for students who get through Level Z in basic division: Division 10s, 11s, 12s . It builds upon and reviews facts from Division 0 to 9s while keeping learning fun for students who learn 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. Utilize the worksheet program for ten minutes daily to teach the four basic operations. While these students are catching up, the remaining students can also do Rocket Math!

We offer five learning tracks that teach more advanced pre-algebra math skills that follow the same structure and routine. Each of these five learning tracks includes video lessons that teach students how to use the program and how to do the skill. If students have not done the learning track Identifying Fractions [presented above in grade 3 Worksheet options], we recommend students do that first, before beginning the Pre-Algebra Learning Tracks.

Pre-Algebra Learning Tracks for Advanced students

1) Equivalent Fractions

Teaches 100 fractions and what they are equivalent to.
Video lesson for Equivalent Fractions

2) Factors

Shows how to find all the factors of a number, quickly and reliably.
Video lesson for finding all the factor pairs of a number

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

Uses a vertical number line to teach these problems.
Video lesson for adding integers (one of four)

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

Also uses the vertical number line to show how these work.
Video lesson for subtracting integers (one of four)

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

Uses the same vertical number lines but now mixes the 8 types of problems together.
Video lesson for mixed integers (one of eight)

Sign Up for Rocket Math’s Worksheet Program

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.

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.

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

Ready to get started? Subscribe to Rocket Math’s Worksheet program today. It’s available for individual students and entire school districts.

Engage Students in Rocket Math during schedule gaps at test times

Testing season activities: 5 Reasons to Use Rocket Math During Testing Gaps

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

Testing season is stressful. The task of scheduling testing for each student in the school is difficult. It causes significant stress due to time logistics, student absences, and disrupted schedules. Teachers know how difficult it can be to deal with odd and awkward time gaps. What testing season activities can fill those holes?

Teachers spend a lot of time juggling schedule and testing material. Students are anxious about the tests as well. Often the mood in the classroom can feel tense.

We at Rocket Math are concerned about the success of students. We know how precious teaching time is. We believe that doing Rocket Math practice sessions can significantly aid during the busy spring test season. Here are five reasons why doing Rocket Math is a great activity during testing season.

1. Rocket Math is a time efficient testing season activity.

Your students are familiar with the Rocket Math routine. They know just what to do. The process of doing Rocket Math from start to finish should take no longer than ten to fifteen minutes. When you have one of those short intervals created by the testing schedule, you can make good use of this short amount of time. Rocket Math fits in a short amount of time and is still productive.

2. Rocket Math can be used during multiple testing season gaps.

As test schedules tend to have multiple gaps, Rocket Math works great as an activity that can be used multiple times throughout the day without causing extra work for teachers. Students actually appreciate the opportunity to have another chance to practice Rocket Math in the same day.

Students can easily use Rocket Math a second or third time during their school day without any negative impact. In fact, multiple sessions of Rocket Math during a single day can help students progress faster.

3. Rocket Math is a testing season activity that doesn’t require re-teaching lessons.

As students are taking make-up tests, the rest of their classmates need something to do in the classroom. Because students work in pairs during Rocket Math allows students to work through math lessons on their own. Because it is just practice, there is no need to re-teach material, students taking their make up tests filter back into the classroom.

As long as there is at least a 15-minute gap between testing sessions, students can easily complete a Rocket Math session. The best part is, because students are familiar with the Rocket Math process, teachers don’t need to explain a new activity to each student who filters in after testing.

4. Rocket Math is a highly engaging and productive testing season activity.

Many teachers struggle to fill time in the gaps between test sessions. Reading time or make-up work is often the go-to solution. Teachers know that these activities don’t seem productive or engaging. Plus, students know that these time-filling activities “don’t count.” Rocket Math however, does count!

In contrast, Rocket Math offers students a fun and creative way to effectively learn critical skills that are necessary for future success.

5. Rocket Math is a testing season activity that students truly enjoy.

Accountability tests can cause stress due to unfamiliarity, whereas Rocket Math offers students comfort in an activity that they know and enjoy. As Rocket Math shows progress along the way, each student gains a sense of pride in their accomplishment and is more likely to feel motivated to continue learning.

When there are gaps between test sessions, Rocket Math can provide students a boost of confidence as they are instantly gratified by their success.

During this busy spring test time, I highly recommend teachers are prepared with their Rocket Math folders to help productively fill the time gaps left in the daily schedule. Rocket Math is a quick and easy testing season activity. It can be used during multiple gaps as an engaging learning tool. Doing Rocket Math helps students feel accomplished in an otherwise stressful testing period.

Interface of Rocket Math's math facts test online app

The Ultimate Math Facts Test Online for Kids

Posted on May 1, 2019May 2, 2019 by Dr. Don

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

Testing without teaching doesn’t work

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

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

Teach and test a small number of math facts in tandem

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

It is important to begin teaching immediately for several reasons.

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

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

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

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

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

Why testing and teaching is the perfect learning paradigm

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

Rocket Math game: the ultimate math fact test online

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

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

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

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