fast math facts

Help your kid get fast at math facts

Posted on by Dr. Don

Your kid wants to go fast at math.

Having to count out all your math facts is simply painful.  There is no need for it.  Every child is capable of memorizing math facts so that they can be recalled within less than a second.  Like any other facts we know and use daily, math facts, once learned, can be brought to mind instantly.  This makes math assignments easy and fast.  It enables students to easily recognize many things about numbers that teachers call “number sense.”  It gives them confidence.  And frankly, they like going fast much better!

The usual kind of practice will not make them fast.

I used to think, as a teacher, that just giving students practice with math facts would help them to get faster.  Years of teaching proved me wrong.  Students will count and count and count and fill out worksheet after worksheet and never get faster.  They hated it and I was discouraged.  This is why veteran teachers are most interested in Rocket Math.  They’ve learned the hard way that just any old practice sheet won’t work.   Then in grad school I learned a simple fact about memorizing.

You can only memorize a handful of math facts at a time.

If a task presents any more than a handful of facts, your brain gives up.  Your brain won’t even try to remember, it will just focus on a strategy for figuring it out.  However, if you have a small handful of thing to remember, and you get asked right away, you can remember.  “Oh, I can remember this. I’m having to come up with this fact again.  I should try to remember it.”  Rocket Math only presents two facts and their reverse to remember at a time.  And that makes all the difference.  Well, most of it.

Calling math facts to mind again, before they are forgotten, is key.

Many teachers and parents think that struggling to remember is valuable.  Not so much.  Instead, just calling to mind the answer, quickly and easily, before it is hard, is all that is necessary.  Correctly recalling a fact is what strengthens the neural connections.  Forgetting it and having to figure it out again does not help.  In fact, it teaches students that the job is figuring it out, rather than remembering it.  That’s why the correction in Rocket Math is to simply tell the student the answer.  The message is to “just remember it” rather than having to figure it out over and over.

Practicing math facts fast requires recalling them.

Once your brain is focused on calling to mind a small handful of facts, you can recall them quickly.  Now, you can go fast and you should be required to go fast.  First, requiring you to go fast ensures that you are recalling.  Second, it’s more fun.  Third, you can get a lot of practice done in a short amount of time.  This is why Rocket Math only has students practice for a few minutes at a time.  That’s all that’s needed if you are going fast.

Cumulatively adding more facts needs to be done carefully

To get beyond that initial handful of facts, you have to learn more.  But we have to be careful not to add too many, too soon.  First, make sure everything introduced so far is well mastered without any hesitations.  Then and only then are you ready to get another handful.  A small handful, lots of practice, so they can be recalled, and then add them into the mix of mastered facts.  As the saying goes, “How do you eat an elephant? One bite at a time.”

Practicing fast math facts needs to be daily

There are a lot of math facts to learn.   A lot students take four years to learn all four operations.  The task should begin early and continue until all are learned, so daily practice is a must.   Also, spreading the learning out over time means it is learned more fully.  Learning something in a day, it’s forgotten in a week.  Learning something over a year, it’s remembered as long as it is still being used.  A few minutes a day is all we ask, but it is very important to make math facts practice a daily regimen throughout elementary school.

Sign up for a 30-day free trial of the Rocket Math Online Tutor.  It works in ten minute sessions. And kids like it!

Instant assessment for basic math fact fluency: Ask ’em!

Posted on by Dr. Don

Teachers and parents often ask, “How do I know if my children need to study math facts?” Here’s an instant math assessment you can do to test them for math fact fluency. Ask a student a “hard one” such as, “What’s 9 times 7?” or if they are in first or second grade, “What’s 8 plus 9?” If they start counting on their fingers or hesitate while puzzling it out, they do not have “math fact fluency.” They need a program of systematic math facts practice until they know them all “by memory,” as the Common Core State Standards (CCSS) say.

Math fact fluency means instant recall

A student thinks through an equation by recalling their math facts.Some teachers and schools teach “tricks” for remembering facts that are supposed to help children. However, they should at most be a temporary crutch. Such techniques need to be replaced with instant recall. The student shown here is using the commonly-taught “doubles plus one” trick for figuring out the answer to, “What’s 8 plus 9?” This is not fluency. He needs practice in math facts so they become “automatic” in recall. If he is still having to do this in fourth or fifth grade, he’ll find math work slow-going and drudgery. He’ll also find it hard to follow a math lesson when he has to stop and puzzle out simple facts like this.

Math fact fluency makes math easy

Students who know the math facts instantly can fly through their math assignments. They enjoy the exercise and feel good about their math abilities. On the other hand, students who have to count on their fingers, or use a number line or a times tables chart to do their math assignments come to hate math. It is so-o-o-o-o slow. I’m sad to say that when I taught elementary and middle school remedial students I knew they hated math because they had to puzzle out most of the facts. What else could I do but assign lots of math fact practice that they hated?

In graduate school, I learned how to design a math facts practice program in a way that every student can succeed in memorizing the facts. I put a paper-and-pencil program together back in the ‘90s and have been sharing it with people ever since. I called it Mastering Math facts, but everyone else just called it Rocket Math. That became its official name in 2007.

Teachers have been successfully using my nearly secret curriculum with wild success for decades. Oddly enough, students actually enjoy the Rocket Math Worksheet program. They enjoy the paired practice with a partner, and can actually see themselves learning and getting better.

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

How to assess students in math

Before you start Rocket Math’s Online Game or Worksheet Program, it’s a good idea to find out which operations your student needs to practice most. Rocket Math offers a few tests to identify where your student should start their Rocket Math journey.

 

Writing Speed Test

Many students aren’t able to write the answers to 40 problems in one minute, which is normal and doesn’t affect their math fact knowledge. Before administering the Operation Pretests, evaluate your student’s writing speed to make sure the results reflect your student’s true proficiency, and that they are not held back by their writing speed. 

Get the One-Minute Rocket Math Writing Speed Test.

 

Operation Pretests

Once your student has completed the Writing Speed Test, give them a pretest in one or more of the four basic operations. 

 

Evaluate Results 

For students in 3rd grade and above, test multiplication first and then division. If students struggle with either of those two operations, they should start learning those operations. For 3rd graders and above who don’t struggle with multiplication and division, test addition and subtraction to assess any weakness. For students in 1st and 2nd grade, test addition first and then subtraction. 

Evaluate your student’s results based on their individual writing speed with the Evaluation Chart for Pretests. Use their writing speed to determine if their performance on the Pretest is weak and shows a real need for work on math facts, or is good but could use some help, or strong and no practice is needed. 

Free Online Game subscription as long as you need to decide

There is no reason for students to be bogged down and discouraged by math, especially by lack of math fact fluency. This doesn’t need to happen to children. Every student is capable of memorizing basic math facts with a little effort and a carefully sequenced curriculum, like the Rocket Math Worksheet Program.

Or if a paper-and-pencil curriculum like the Rocket Math Worksheet Program involves standing at the copy machine, is not what you are looking for, Rocket Math is now online. The Online Game app starts with a complimentary initial subscription of 14 days. You can learn more about it at that link. Or you can just go ahead and register an account and start it on this link. 

 

Send an email to me at don at rocketmath.com and I’ll extend the complimentary subscription as long as you need to decide.** If you need one to ten seats it is a whopping $4.50 a seat for a year. Twenty or more seats are $2.50 each for the year and per-seat prices go down from there. Really there’s no reason to leave kids counting on their fingers.

The Online Game never teaches anything wrong.

Posted on by Dr. Don

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

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

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

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

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

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

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

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

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

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

Prove that students using the Rocket Math Online Game are improving in fact fluency!

Posted on by Dr. Don

Document improved fluency by assigning a 1-minute RACE.

We have a feature that will allow you to assign a fluency test to all or some of your students. We call it a “1-minute RACE.”

To Assign a Fluency Test 1-Minute RACE:

1) Select the students to whom you want to assign the test RACE, or Select All.

2) Click on the orange Bulk Action button.

3) Pull down to “Assign 1-min RACE on next login.”

After doing that, in your dashboard you will see that the 1-minute race has been assigned on the next login. 
The next time those students login, they will be given the mission of doing a 1-minute race with ALL the facts in the Learning Track they are studying. They can skip facts they don’t know, by hitting the checkmark.

Here’s what the students experience.

A 1-minute test RACE is also automatically SCHEDULED after Sets A, i, R, and Z. See their latest results in Review Progress!

Assign a 1-minute RACE individually also–at any time you wish.

You can assign a 1-minute RACE at any time for specific individuals as well, using the green Individual Action button at the end of their row.

 

  • Export the test RACE results in spreadsheets. 

    • Separate exports for results from RACEs you Assign from the RACEs that are Scheduled after working through some levels in the Online Game (After sets A, i, R, and Z).

  • See averages across your class or school. 

    • Each spreadsheet will show the average for your class as a teacher or for the school in the account of the Subscription Manager or owner.  There are separate averages for each Learning Track.

  • See trends over time.

    • You’ll see the improvement each student makes from the beginning after Set A to each of the subsequent tests RACES.

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

Posted on 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 programsCompared 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.

In What Order Should Students Learn Fast Math Facts?

Posted on 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.

A chart that shows the set of math fact family 5, 3, and 2 in Addition and Subtraction.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:

  1. Factors
  2. Equivalent Fractions
  3. Learning to Add Integers
  4. Learning to Subtract Integers or Mixed Integers