Learning Math by Fact Family vs One Operation at a Time

A Fact Family is an innovative way to group the learning of math facts. Some people are die-hard advocates of this way to learn facts. Yet students successfully learned math facts for decades without ever considering them as being composed of families. This blog discusses the pros and cons of learning with fact families. 

 

 What is a Fact Family

 

A fact family is a set of four math facts made with the same three numbers. The numbers 2, 3, and 5 can make a family of four facts: 2+3=5, 3+2=5, 5−3=2, 5−2=3. The numbers 2, 3, and 6 can make a different fact family: 2×3=6, 3×2=6, 6÷2=3, 6÷3=2.  

 

Why are Fact Families Important?

 

Fact families help children see that adding and subtracting are the opposite of each other. Multiplication and Division fact families do the same. Learning fact families may help students develop more flexibility in their number sense.   

 

Benefits of Thoroughly Learning a Single Operation at a Time

 

Rocket Math Addition Fact Family worksheet for students.

When it comes to memorizing math facts, students traditionally learn one operation at a time. They memorize only the Addition facts, typically in first grade. Not until later do students learn the concept of Subtraction, and then they begin memorizing Subtraction facts, usually in second grade. With Rocket Math, students will master Addition facts much better than most first graders. Students using Rocket Math will know Addition facts instantly without having to stop and think about them. When students have mastered Addition facts, an unusual thing happens when introduced to Subtraction. Students instantly recognize that the Subtraction facts are the opposite of those Addition facts they know so well, usually without even being told. This recognition does not typically happen in second grade with students who haven’t truly mastered Addition facts.  Therefore teachers think they need to teach in fact families to get students to recognize the reciprocal nature of Addition and Subtraction.   

 

Which Way is Better?

 

Only if students thoroughly master Addition facts, can they quickly recognize the reciprocal nature of Subtraction. Students find it easier when memorizing facts, to stick with Addition, rather than switching back and forth between adding and subtracting as is required by learning in fact families. They tend to memorize faster in single operations than they do in fact families.  However, if students memorize in fact families, they will learn the reciprocal nature of the fact families right from the beginning. They may learn it more thoroughly. That may help them develop more flexibility in their number sense. So that’s not a bad thing.

 

How to Learn Math with Fact Families and Single Operations

 

Teacher's directions worksheet for addition and subtraction fact families.Rocket Math offers separate Addition and Subtraction sequences, as well as fact family sequences. Both the Online Game and Worksheet Program provides these. If teachers (or their regular math curriculum) are wedded to fact families, they are available to use. Usually, the first fact families learned are Addition and Subtraction Fact Families through 10, then Fact Families from 11.  

 

I would recommend beginning with learning the operations separately: learning Addition facts (1s to 9s) first, followed by Subtraction facts (1s to 9s). For some students, this may be all they have time to learn.  If students have time, use Fact Families as a review. If the student has time, it would be beneficial and relatively easy for them to do Fact Families (+,-) to 10 and then Fact Families (+,-) from 11 afterward. Students will learn the facts more thoroughly, and the reciprocal nature of Addition and Subtraction will be deeply ingrained. This is quite simple in the Online Game, as it only involves switching the student to another Learning Track, and doesn’t require a new filing crate, as in the Worksheet Program.  

 

Using Rocket Math to Teach Single Operations & Fact Families

 

Rocket Math offers separate Addition and Subtraction sequences, as well as fact family sequences through the Online Game and the Worksheet Program. For teachers looking to teach Addition and Subtraction math fact families, Rocket Math offers two sequences of Fact Families; the first, Fact Families to10 and the second, Fact Families from 11. For teachers looking to teach in separate operations, Rocket Math offers separate sequences for learning Addition facts (1s to 9s) first, followed by Subtraction facts (1s to 9s). If the operations are learned separately, fact families can be used as a review. 

 

 

Factors and Primes: Learn in Rocket Math Online Game

Learn three keys to knowing how to find factors and primes

We have added Factors and Primes to the Online Game. Learning Track #15 Factors & Primes is a dream come true for Dr. Don.  Many middle grades students find that factoring and finding the GCF (Greatest Common Factor) is quite difficult.  This learning track will make it easy.  It accomplishes three key learning objectives at the same time.

factors and primes game screens(1) Recognizing the Primes.

Instead of just working on numbers with factors this Learning Track includes many prime numbers such as 7 in the illustration above.  When a number is prime, the student is shown 1 x the number and asked “What’s next?” Then the student is to answer with the check mark indicating that number only has 1 and itself as factors–there are no more. These prime numbers appear again and again, giving the student lots of practice in remembering the primes and in remembering their key characteristic.

(2) Learning factors in order. 

The game displays the factors with the lowest factor on the left and put them in order by that factor.  (see the Factors of 12 above). The factors are always in this order, so students learn them in order.  Notice that the last factors of 12 ends with 3 on the left and 4 on the right.  The factors on the right go up from there up to 12.  The key to knowing there are no more factors is when the next number down (in this case 4) is already showing in the list going up on the right.  By seeing the factors always in this order, student can more easily learn them. 

(3) Knowing when you’re done

Sometimes we require students to indicate that all the factors have been listed. The Online Game will show all the factors and ask, “What’s next?”  Students will know that there are no more factors because they have learned them in order.  Students will then put a check mark to say this is the complete list. When figuring GCF it is essential to know when you have listed all the factors.   

16 Learning Tracks in the Online Game

1. Addition                       5. Fact Families (+, -) to 10           9. Multiplication 10s-11s-12s
2. Subtraction                 6. Fact Families (+, -) from 11     10.  Division 10s-11s-12s
3. Multiplication             7. Add to 20, example 13+6        11.  Fact Families (x, ÷) to 20 
4. Division                        8. Subtract from 20, 18-5            12 Fact Families (x, ÷) from 21      13. Identifying Fractions                                                 
14. Equivalent Fractions                   15. Primes & Factors              16. Fraction & Decimal Equivalents

 

Test drive the game as a student, right NOW!

If you go to https://play.rocketmath.com          Use a login below to try any of the Learning Tracks for yourself.
UsernamePass codeAccount #Learning Track
Test1121211000Addition (slowest speed)
Test2121211000Subtraction (slow speed)
Test3121211000Multiplication
Test4121211000Division (fast speed)
Test5121211000Fact Families (+,-) to 10
Test6121211000Fact Families (+,-) From 11
Test7121211000Add to 20
Test8121211000Subtract from 20
Test9121211000Mult 10s, 11s, 12s
Test10121211000Div 10s, 11s, 12s
Test11121211000Fact Families (x, ÷) to 20
Test12121211000Fact Families (x, ÷) From 21
Test13121211000Identify Fractions
Test14121211000Equivalent Fractions
Test15121211000Factors & Primes
Test16121211000Fraction & Decimal Equivalents

Sign up for a free trial of the Online Game today!

6 Effective Math Teaching Strategies for any Classroom

These effective math teaching strategies will help your students be more successful in learning math in your classroom. These are not the “cool, pedagogically-correct things” you can brag about in the teacher’s lounge or your master’s program classes, but they will improve math for the kids.

Memorizing is a key effective math teaching strategy for all classrooms.1. Help Students Memorize Math Facts

Once students know how to count out or figure out math facts, they are ready to begin memorizing the facts. After they memorize math facts, students can do math assignments quickly and learn math easily. It’s cruel to make them continue to figure out facts over and over again for months or years. Find and use a systematic method of memorizing math facts, so they have this tool at hand. There’s no magic bullet. Whatever you use needs to be systematic because it has to build gradually as students learn more and more of the facts. Any fact is easy to learn, but there are a lot of them, so that takes time.

Helping your students memorize math facts is like buying math power tools for them. It makes everything go quicker and much better. More gets done. Attitudes will improve. You don’t have to use Rocket Math, but you should use something! You will change their trajectory in and attitude about math for years to come. Learn more about why memorization is one of the essential math teaching strategies.

A student works through 52 minus 28, with math teaching strategies subtraction learning computation.2. Ensure Math Facts are Mastered Before Starting Computation

Kids love to go fast. They hate the drudgery of having to count out facts or look multiplication facts up in a table. Once they know facts instantly, they can rip through math computation–and enjoy math because they love to go fast.

Not knowing math facts interferes with learning computation.

Here’s another surprise. Memorizing math facts makes learning multi-digit computation easier. Students who’ve memorized math facts are not distracted by having to stop and figure out what is 14 minus 9. They know it, without having to stop and think about it. They can give more of their attention to the details of the computation process and learn them better and easier than before. Try getting all your students fluent on the operation and then teach computation AFTER they have acquired fluency. You will be astonished at how quickly they learn. Read more about how math fact memorization supports computation.

Effective math teaching strategies should help students from becoming frustrated and instead have fun learning math.3. Teach Computation Procedures With Consistent Language

Learning the procedures to do computational math processes is just like learning to follow a recipe. Eventually, you learn the key ingredients and can do it without looking and can do variations. But in the beginning, you need the written recipe to follow. You also need to do it the same way a few times to learn it. Winging it and teaching math “improv style” will only frustrate students.

Use a script or a process chart to keep the instructions consistent.

No one can remember exactly the way you said it yesterday or last week, which is why you need a script or a process chart on the wall so you can show the students that you are doing it the same way as last time. Repetition helps, but only if you’re repeating the same steps in the same order with the same wording. 

Students will become flexible in their understanding at their own rate and in their own time. You just keep being consistent, and eventually, all the students will have mastered the procedure. I know that “thinking flexibly” is very much in fashion, but your students will thank you for providing them mastery of this one method of solving this type of problem. Flexibility can come later. Read more about how consistent language is key to teaching computation procedures.

A road sign with signs pointing "this way" and and "this way" in opposite directions.4. Teach One Method and Only One Method at a Time

To solve a given type of problem, do NOT follow the advice to teach multiple solutions at one time. Teach only one way to go at a time, until that is learned, before introducing variations.  Multiple solution paths will confuse all but the most advanced students in your room. Just teach them one procedure that will work every time with that type of problem. Your students will thank you for it.

It’s far better to know only one way to get there than to get lost every time!

Learning math procedures is no different than learning how to get to someone’s house (before GPS). You want to go the same way every time, until you have learned it. If you go a different way every time you’ll just be confused. You can learn another way later, once you can get there reliably using one route, but before that, you cannot learn another route, because you’ll mix up steps from each route. Read more about why teaching one procedure at a time is one of the effective math teaching strategies.

Two illustration of two lines, one explaining what parallel lines look like and the other what perpendicular looks like. 5. Separate the Introduction of Similar Concepts

The classic example is teaching parallel and perpendicular on the same day. The two concepts have to do with the orientation of lines, and the new vocabulary terms for them are similar. So teaching them at the same time means some or many students will have the two terms confused for a long time. That is known as a chronic confusion–possibly permanent. They will know that the orientation of lines is one of those two terms, but will be confused about which is which.

An illustration showing the differences between parallel, perpendicular, and crossing.

Parallel vs. Perpendicular

For example: For this picture, you would ask the students.

A “Are the two lines in item A parallel or not parallel?”   Ans: Not parallel.

B “Are the two lines in item B parallel or not parallel?”   Ans: Parallel.

C “Are the two lines in item C parallel or not parallel?”   Ans: Not parallel.

After a couple of weeks of this kind of practice, you could introduce perpendicular. Again teach it on its own and then contrast perpendicularly with non-examples until the vocabulary is clear.

Probably do that for a couple of weeks. Only then can you combine both terms in the same lesson.

Numerator vs. Denominators

Other examples abound in math. Teaching numerator and denominator in the same lesson is common. Teaching the terms proper fractions and improper fractions on the same day is another example. Acute and obtuse angles are yet another pair of chronically confusing concepts that are introduced simultaneously. Separate them in time, and you’ll be amazed at how much better students can learn these concepts. Learn more about how to successfully teach similar concepts separately

6. Teach  New Concepts Using Common Sense Names

Here’s an example of the problem. A brachistochrone (pictured here) is a curve between two points along which a body can move under gravity in a shorter time than for any other curve. Introducing this concept and the term brachistochrone at the same time would cause students difficulty learning it.

When Instruction is not working

If you watch instruction where the term and the concept have been taught simultaneously, confusion ensues when the teacher uses the term. Sometimes the teacher will notice students looking confused and give a thumbnail definition or example of the term, and the students will then remember. However, the teacher should then realize that the concept was not connected to the new vocabulary term. 

Students can quickly understand and use new concepts and ideas in math if they don’t have to learn a new word for it. Using a common sense term, the idea or concept can be applied to real-world problems almost immediately. Students can later quite easily learn proper vocabulary terms for concepts they understand and recognize. Here’s an example. 

The “shortest time curve.”

I would call a brachistochrone the “shortest time curve.”**  Instruction would proceed with the, “Do you remember that ‘shortest time curve’ we talked about last week?”  Students would easily be able to remember it. Instruction would go like this: “So ‘the shortest time curve’ has some other cool properties. What’s the primary thing we know about the ‘shortest time curve’?”  Students would easily be able to answer this question.

Then after students have worked with the concept of “the shortest time curve” for a couple of weeks, you can add the vocabulary term to it. “By the way, the proper mathematical name for “the shortest time curve” is called a brachistochrone. Isn’t that cool?”  Read more on how to teach new math concepts with common sense names.

**Actually, that’s what brachistochrone means in Greek: brakhistos, meaning shortest and khronos meaning time.

 

Learn More Effective Math Teaching Strategies with Rocket Math

Rocket Math Online Game and Rocket Math Worksheets Program are math teaching strategies that will work for any classroom. Use the Pre-Test worksheets to understand how fast your students can answer math facts and what level they are at. The Rocket Math Online Game will help students succeed in math by creating a fun and enjoyable way for them to learn.

 

 

Teaching Math Fact Fluency | Why Rote Learning Works best

Developing math fact fluency requires memorization and enables success in math

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

What Students must know before beginning to memorize math facts

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

What students do NOT need to know before beginning memorization

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

Experimental Research has NEVER Shown the Necessity of Games.

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

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

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

 

Real research into teaching math fact fluency is desperately needed.  

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

Common Non-Rote Activities that Just Waste Time

Students and teacher playing multiplication games with dice sitting in a circle in a classroom, to learn math facts.

Dice. 

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

Cards.

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

Combinations.  

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

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

No time left to teach math fact fluency.

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

How to Improve Math Fact Fluency with Rote Learning

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

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

A student holds up their Rocket Math score sheet, which teaches math fact fluency to students.

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

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

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

 

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

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

Extend play time over five minutes–You can do it, but should you?

Our 20-minute “Battery Down” forced break is a feature not a bug!  Slamming through these facts at the rate of 3 seconds apiece (or less as they go faster) is very INTENSE.   Students will do this game for a couple of hours at a time if you let them.  But, here’s the problem.  They will only do it for a couple of days, and then they will just wear out.  They just won’t want to do it anymore. We don’t want them to lose their enthusiasm, so……. 

After five minutes of play, up comes this screen (to the left).  We say the battery is down and will need at least 20 minutes to “recharge.” The countdown timer shows the amount of time left until the student’s break is over.  The student has to take at least a 20 minute break.  We want them to do a little practice a couple of times a day, but spaced out over a month or two.  The it takes for them to get through an operation, (the longer this is spaced out) the longer they will retain the information.  And they need to know these facts for a lifetime!  So a little bit each day is far better than sitting down for long periods of time until they are sick of it.


We purposely planned for your students to end a session anxious to play again.

Yes, they may complain that they have to stop, but that ensures that they will want to come back again later.  You want them to end their sessions wanting to play more.  That’s how you can get them to play and practice, time after time, day after day until they reach Level Z.  That’s how we win and that’s how they win! before the forced break.

You can now increase play time to ten or 15 minutes, but should you?  Only if they still LOVE it! 

After years of game play lasting only five minutes at a time (under pressure from customers) Dr. Don allowed a change.  We added a feature to allow you, the parent or teacher, to adjust student play time UP to ten or even 15 minutes. The option is found under on both the orange bulk Actions button and the Individual Action button.  

But with this freedom comes a great responsibility.   You have to make sure they are still enjoying playing! If you increase the time, you have to make sure they are not getting tired of playing!  The minute you hear a student moan or groan or complain, please move them back to 5 minutes! Seriously!! The first time anyone complains, move them back to 5 minutes.  And anyone else who does it, move them too.   They can learn just fine only working five minutes at a stretch!  

Remember, you want them to practice at home also, which they won’t do if they are getting sick of it.  You want them to practice the whole time they are assigned to do it–and they won’t do that if they aren’t motivated to keep going.  So you better be sure if you move them up to ten or fifteen minutes.   

Change Rocket Math Online Game speed–You can do it, but should you?

 

The rapid speed required to answer our Online Game is a feature, not a bug.

You can change how fast the student has to answer, but you probably should not.  The main goal of Rocket Math is for students to commit facts to memory, to be able to answer them instantly, from recall. That is called “automaticity.”  It is the point of Rocket Math.

Recall is instantaneous, but “figuring out” is not.

The fast pace (3 seconds to input an answer) means students don’t have time to count on their fingers or to “figure out” a fact–they just have to remember it.  If they don’t remember, then the game gives them a LOT of practice on only a couple of facts, until they do remember them. That is exactly the point of the game. The game gives more practice through having students start parts over when they are not able to answer quickly.

We want them to stop having to “figure out” facts and just remember the answer.   If the students are not used to “recalling” facts they will think that the game is just “too fast” for them.  If they keep playing and learning, after a bunch of repetitions, they will be able to remember the fact.   These days students are NOT asked to memorize anywhere else. Today’s students are unaccustomed to having to repeat things over and over to commit them to memory.  Almost everyone can do it, but it takes more practice than many students are used to doing. Consider the Toughness Certificate [located in the Online Game’s main navigation bar] for those who can overcome their frustration at having to start over.

The danger in slowing the game down for most students.  If you let students play at the slower speeds they may never use “recall” and instead may figure out the facts over and over.  Until I realized the difference, I allowed my students to take their time to figure out facts.  Many of my students never committed facts to memory all year long!  If, as we do in Rocket Math, you only ask them to remember two facts and their reverses at a time, everyone can remember two facts.  It takes just a few minutes to realize that they can, in fact, remember that answer instantaneously.  Once they use recall, they remember the answer in less than a second, and then three seconds to input it, is quite doable.  If you slow down the game speed, they may NEVER realize they can remember the fact, instead of figuring it out each time.

Only if their difficulty score is over 3.0 do they need an adjustment made.  Their difficulty score, shown on the Review Progress screen [Top of Main Navigation bar] tells you whether or not the game is too fast for them.

  • We expect students have to start over at least once per phase, which gives them a difficulty score of 1.0.  Even having to start over, on average, twice per phase is not too much–giving a difficulty score of 2.0.
  • [If you sort your class based on their difficulty scores you can see a display like the one in this picture.]
  • Any difficulty score under 3.0 means the student has to start over on average fewer than 3 times for each part passed.  That is not too difficult.  Students may not be accustomed to repeating anything, but it is not a real burden. On the other hand, you may find some students have difficulty scores under 1.0 and Rocket Math is very easy for them.
  • Only students with difficulty scores over 3.0 should be considered for a speed change–and then only if you know they require some kind of accommodation.  On the other hand, students with difficulty scores under 0.1 should be challenged to take on the Faster speed!

 

Here’s where you can make the change.  Go to the green “Individual Action” button at the right end of each student’s row. Click on “Change Game Speed.”  The popup gives you the choices of  Fast, Normal, Slow and Slowest.

The options for speed are:

  • Normal, at 3 seconds to answer (double that for two digit answers)
  • Slow, at 4.5 seconds to answer per digit
  • Slowest, at 6 seconds to answer per digit
  • Fast, at 2.25 seconds to answer per digit

Here you can see different students showing different speeds of play.

Kids Who Write Their Numbers Backwards

The group “The Who” was correct when it comes to kids writing their numbers backwards: The kids are alright.  Children writing their numbers backwards is not something to worry about. It is natural and expected. With instruction and encouragement, children can learn to write their numbers correctly with ease. 

Why Do Kids Write Numbers Backwards?

A chair mirrored is still a chair, while a seven mirrored is not the same.For the first several years of our lives, we learn that “orientation-in-space” does not change an object’s identity. Turn a chair any which way, and it is still a chair. We learn this lesson well enough that we stop paying attention to an object’s orientation in space.

So it is not surprising that kids sometimes write their numbers backwards. It would be more surprising if they never did.. Students need to learn to write certain symbols to face a certain direction. 

What Does it Mean When Kids Write Numbers Backwards?

When children write their numbers backwards, they are mirror writing – writing letters or numbers backwards or upside down. They need to learn that while a chair may be mirrored and is still a chair, a 7 mirrored is no longer a 7.

Is It Normal for a Child To Write Numbers Backwards?

Students work with together to learn how to write their numbers.It’s perfectly normal for kids to write numbers backwards. Some kids will even write from right to left reversing all their numbers. It’s important for children to learn how numbers face, but don’t stop your kid from writing this way or make them correct it. It will take time and gentle reminders.

Is Writing Numbers Backwards a Sign of Dyslexia?

A chair mirrored is still a chair, but a d reversed turns into a b.Writing numbers backwards isn’t a sign of dyslexia. Dyslexia is a reading disorder that involves problems identifying speech sounds and how they relate to letters and words. Writing backwards is a sign of not learning which way symbols face.

It’s common, however, for students with difficulties learning to read to continue reversing their letters such as b and d. Reversing “b” and “d” has the same cause as writing numbers backwards: learning that orientation in space does matter. However, when it comes to “b” and “d,” the reversal isn’t just “backwards.” So the distinction between b and d is somewhat harder for children to learn. Students who have problems with phonemic awareness will find it harder to remember which is which. But, even children with dyslexia can learn to read, it just takes more focused instruction.

Do Kids Grow Out of Writing Numbers Backwards?

It’s important for children to learn to write symbols in a certain way and why by a teacher and or parents. It helps to have someone tell them when they have written a number backwards and to reinforce them when they get it right. Some children notice this without much prompting, so we say they “grew” out of it. But really, they just learned it on their own. If you want them to be successful, don’t hesitate to help them learn to write their letters and numbers correctly. Be nice and supportive, but do give clear information.A mom congratulates her son at a baseball game.

How Can I Help My Child If They are Writing Numbers Backwards?

An example worksheet from Rocket Math with an example of a 7 at the top.The best way to help is to make an example of “the way it is supposed to face” on any paper before your child starts working. Say something like, “Be sure to make all your sevens face this way.” Your child can then check each time he or she writes the number to make sure they are making it face the same way as your example.

By the way, writing “7” a hundred times won’t help because after the first one it is just doing the same thing over and over. The issue is remembering which way it has to face when you write it. So having it available as a reference means your child has to remember, “Oops. Which way does a seven face? Oh, that’s how it faces. Hey! I got it right!”

Another powerful way to help is to notice when they write their numbers the right way and congratulate them. “Wow! All your sevens on this page are facing the right way. Way to go! You are really learning this.” If you are impressed by their learning, they will be motivated to keep remembering and it will boost their self-esteem.

When is it time to Talk to Their Teacher?

If you notice your child is frustrated after school when they were trying to write their numbers, you can bring it up with the teacher at the conference time. Ask them if they are giving your child an example of how to write the number to look at when writing their numbers. But, other than consistently helping your child learn the arbitrary rule about which way certain numbers face, there is nothing else the teacher can or should do. Please don’t ask them to “test” your child for dyslexia on account of these backward numbers.

How Can Rocket Math Help?

Rocket Math offers worksheets that may help your child learn how to write their numerals correctly. Each worksheet focuses on a group of numbers to show children how to write their numbers in the right direction and with the right form. Learning to write numbers correctly takes time, patience, and encouragement from teachers and parents.

Online Math Drills to Help Develop Math Fact Fluency

What are Math Drills? 

Math drills are exercises given to students that can help improve their speed and ease of recall. The goal of math drills is to help students develop automaticity, allowing them to instantly recall from memory the answer to any math fact. If carefully designed timed math drills can help check which facts the student has learned and which ones the student needs to work on. If not carefully designed, they can be a terror to children. Carefully designed math drills in the elementary grades can smooth the way for easy success later on in math.

Why Is Math Fact Fluency Important? 

Math fact fluency is important because it is the first step to developing automaticity. Automaticity frees up the students’ short term memory for more important questions. It means students can answer basic math facts like 7 x 9 or 4 + 8 instantly, by recall without effort. Students who aren’t fluent in math facts, have to stop and figure out facts, and then won’t be able to focus on higher-order math lessons. This could lead to them missing parts of the instruction.

How Do Online Math Drills Help Children Develop Math Fact Fluency?

Correctly recalling the answer to a math fact strengthens the neural connection between the problem such as 9 plus 7, and its answer, 16. [Note that repeating a fact over and over does not achieve the same result. Finding the answer in memory and producing it is what strengthens that connection.] Math drills that ask students to recall answers to a couple of targeted facts, mixed in with other facts the student already knows, makes those neural connections stronger until they can answer those targeted facts correctly, and eventually without any conscious thought. The curriculum should not go on to target any more new facts to learn until the student is fluent with the ones learned so far. A computer program is able to patiently provide this practice for as long as each student needs, which is wonderful.

Why are Math Tests Timed?

Math tests are timed to tell if students are solving math facts by recall rather than deriving the answer. By timing the tests, teachers can tell which students are able to recall answers instantly and which ones need more help to develop automaticity.

Before I understood this, I made students do pages of mixed math facts, which they did by figuring them out.  However, that practice was not helping them become fluent. Timing those pages of mixed facts would not have helped either. In graduate school, I was taught the learning principles that would help students develop fluency. Students need to focus on a small number of facts so they can recall them. So math drills should be composed of a carefully selected set of facts.  This is the key to the design of Rocket Math and is why it works so well.

What Kind Of Drills Should Your Child Do?

At the very least, your child should learn the basic 1s through 9s math facts of addition, subtraction, multiplication, and division. These will make a huge difference in your child’s success in math. However, if you want to help your child become really proficient and confident in math, there are more things you can drill at each grade level.

Kindergarten Math Drills

Kindergarteners need to be able to count objects as well as rote count. They should practice counting up to 20, at least, and counting by tens to 100. They should learn how to write the numerals and be given drills to practice numeral formation. Obviously this is not something that can be practiced online, but a good writing practice program such as Rocket Writing for Numerals will set your child up for success.

1st Grader Math Drills

In first-grade, learning how to count and write numerals is assumed. The key skill to drill on in first-grade is addition facts 1 through 9. Once those are learned, children can drill on addition facts to 20, such as 13+6, or 4+15. You can also drill first-grade students on fact families, which combine addition and subtraction facts. A fact family example is 3+2, 2+3, 5-2, 5-3. In first-grade fact families (+, -) up to 10 is a reasonable amount to learn.

2nd Grader Math Drills

If addition skills from first-grade are mastered, then drilling on subtraction facts 1s through 9s are the top priority. Once those are learned, students will benefit from drilling up to the 20s in subtraction, such as 17-5 or 19-8. You can also drill second-grade students on fact families, which combine addition and subtraction facts. In second-grade, once fact families up to 10 are mastered, you can drill them on fact families from 11, such as 8+5, 5+8, 13-5, 13-8. Skip counting, or counting by a number (such as by fours- 4, 8, 12, 16, 20, 24, 28, 32, 36, 40), is useful to learn in second-grade. Also, second-grade is not too soon to begin drilling students on identifying fractions.

3rd Grader Math Drills

Starting in third-grade multiplication facts is essential from this point onward and can’t be counted on fingers. The basic multiplication facts 1 through 9 must be memorized and drills are the only way to do that. Even if addition and subtraction are not yet mastered it is essential to get multiplication facts learned. Then you can go back and pick up addition and subtraction.

Alternatively, or additionally, students can begin drilling on fact families in multiplication and division. An example of this kind of fact family is 4 x5 , 5 x 4, 20 ÷ 4, 20 ÷ 5. Fact families up to 20 are enough in third-grade.

After multiplication facts 1 through 9, you can move on to drilling the 10s-11s-12s. Also, Identifying Fractions is something that third-grade students can become fluent in. Factors (finding all the factors of a number) can be drilled at this grade level or any time in the next three years.

4th Grader Math Drills

In fourth-grade, it is essential that multiplication facts 1s through 9s are in place first before drilling on division facts. Students will quickly realize division facts are just the opposite of multiplication facts. Once division facts 1s through 9s are learned, you should go back and make sure that addition and subtraction are mastered. After addition and subtraction facts are automatic, then start students on multiplication 10s-11s-12s and division 10s-11s-12s. Once all of these are mastered, students can work on either identifying fractions or factors. Another skill that can greatly help students in later grades is memorizing equivalent fractions.

5th Grader Math Drills

Students in fifth-grade or higher should be fluent in all these basic math areas: multiplication (1s through 9s), addition (1s through 9s), subtraction (1s through 9s), and division (1s through 9s). These can be strengthened by doing fact families with each of these operations: fact families (+, -) to 10, fact families (+, -) from 11, fact families (x, ÷) to 20, and fact families (x, ÷) from 21. Once these are done, students can start drilling on factors, identifying fractions, equivalent fractions, then learning to add and subtract integers. Then the students can start multiplication 10s-11s-12s and division 10s-11s-12s. The same sequence applies in any grade after fifth. The more facts learned in math to the level of automaticity, the easier the rest of math will be.

 

How Can Rocket Math Online Game Help Your Child Learn?

The Rocket Math Online Game provides the right amount of drill to help your child learn these basic skills. Providing plenty of practice, it is timed and requires students to recall facts (answering within 3 seconds) before moving on to learn more facts. They work their way up through 26 sets, from Set A to Set Z, learning more facts as they go along. The game provides many milestones of progress, lots of little breaks and congratulations as students progress through the twelve Learning Tracks. You can place your child in these tracks in the order you choose. The Rocket Math Online Game includes the following twelve Learning Tracks.

  1. Addition 1s through 9s
  2. Subtraction 1s through 9s
  3. Multiplication 1s through 9s
  4. Division 1s through 9s
  5. Fact Families (+, -) to 10, ex.4+6, 6+4, 10-4, 10-6
  6. Fact Families (+, -) from 11, ex. 5+6, 6+5, 11-6, 11-5.
  7. Add to 20, example 13+4, 4+13,
  8. Subtract from 20, example 15-3, 15-12,
  9. Multiplication 10s-11s-12s,
  10. Division 10s-11s-12s.
  11. Fact Families (x, ÷) to 20, example 4×5, 5×4, 20÷4, 20÷5
  12. Fact Families (x, ÷) from 21, example 3×7, 7×3, 21÷3, 21÷7

See a video of how it teaches here.

The Rocket Math Worksheet Program also provides math drills

Math drills are important for setting your students up for success later in life. Help them build their automaticity and become fluent in the basic math facts through Rocket Math Worksheet Program. The Rocket Math Worksheet Program includes more Learning tracks than the Online Games and you can use this program to help your students with basic math skills.

Here is a list of the worksheets in the Rocket Math Worksheet Program.

Math Fact Benchmarks: Why Writing Speed Matters

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

Common Problems With Math Benchmarks 

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

Learned one at a time. 

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

 

Time to write the answer. 

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

Common Core Math Fact Fluency Need Not Cause Anguish

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

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

Rocket Math Writing Speed Test

 The writing speed test for Rocket Math

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

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

Writing speed is number of boxes completed. 

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

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

Benchmarks must be based on writing speed. 

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

 

 

Kindergarten Math Benchmarks

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

Kindergarten Numeral Writing Fluency Benchmarks (digits)

    • Mid-year       
      • 20 digits per minute        
    • End of year     
      • 40 digits /minute       

First-grade Math Benchmarks

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

First Grade Numeral Writing Fluency Benchmarks (digits)

    • Start of year  
      • 40 digits per minute               
    •  Mid-year   
      • 60 digits per minute                         
    •  End of year     
      • 60 digits per minute

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

First Grade Math Fact Fluency Benchmarks (problems)

    • Start of year   
      • Addition 20% of writing speed   
    •  Mid-year  
      • Addition 40% of writing speed    
    • End of year  
      • Addition 80% of writing speed  
      • Subtraction 20% of writing speed 

Second-grade Math Benchmarks

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

    • Start of year  
      • Addition 80% of writing speed  
    • Mid-year   
      • Addition 80% of writing speed 
      • Subtraction 40% of writing speed
    • End of Year
      • Addition 80% of writing speed
      • Subtraction 80% of writing speed

Third-grade Math Benchmarks

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

    • Start of year 
      • Addition 80% of writing speed  
      • Subtraction 80% of writing speed 
    • Mid-year 
      • Addition 80% of writing speed 
      • Subtraction 80% of writing speed 
      • Multiplication 40% of writing speed
    • End of year 
      • Addition 80% of writing speed  
      • Subtraction 80% of writing speed 
      • Multiplication 80% of writing speed

Fourth-grade Math Benchmarks

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

    • Start of the Year
      • Addition 80% of writing speed
      • Subtraction 80% of writing speed
      • Multiplication 80% of writing speed
    • Mid-year   
      • Addition 80% of writing speed 
      • Subtraction 80% of writing speed
      • Multiplication 80% of writing speed
      • Division 40% of writing speed  
    • End of year 
      • Addition 80% of writing speed  
      • Subtraction 80% of writing speed
      • Multiplication 80% of writing speed
      • Division 80% of writing speed

Fifth-grade (and up) math fact benchmarks

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

    • Start of year  
      • Addition 80% of writing speed  
      • Subtraction 80% of writing speed
      • Multiplication 80% of writing speed
      • Division 80% of writing speed
    •  
    •  
    • Mid-year  
      •  Addition 80% of writing speed 
      • Subtraction 80% of writing speed
      • Multiplication 80% of writing speed
      • Division 80% of writing speed  
    • End of year 
      • Addition 80% of writing speed
      • Subtraction 80% of writing speed
      • Multiplication 80% of writing speed
      • Division 80% of writing speed                      

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

 

 

 

 

 

 

 

 

 

 

 

 

 

Rocket Math Is A Fun Way For Students To Learn

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

 

Math Facts Practice Online: Add, Subtract, Multiply, Divide

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

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

How Rocket Math’s online math game works

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

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

Student with Rocket Chart filled out

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

Addition Math Facts Practice in Rocket Math Online Game

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

  • The Basic Learning Track
    • 1. Addition 1s through 9s
  • The Alternative Learning Track: learning addition and subtraction facts in families
    • 5. Fact Families (+, -) to 10
  • Optional Learning Track
    • 7. Add to 20

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

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

Subtraction Math Facts Practice in Rocket Math Online Game

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

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

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

  • The Basic Learning Tracks
    • 1. Addition 1s through 9s
    • 2. Subtraction 1s through 9s
  • The Alternative Learning Tracks: learning addition and subtraction facts in families
    • 5. Fact Families (+, -) to 10
    • 6. Fact Families (+, -) from 11
  • Optional Learning Tracks
    • 7. Add to 20
    • 8. Subtract from 20

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

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

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

 

Multiplication Math Facts Practice in Rocket Math Online Game

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

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

 

 

  • The Basic Learning Tracks
    • 3. Multiplication 1s through 9s (priority)
    • 1. Addition 1s through 9s (if still not mastered)
    • 2. Subtraction 1s through 9s (if still not mastered)
  • The Alternative Learning Track: learning multiplication and division facts in families
    • 11. Fact Families (x,÷) to 20 
  • Optional Learning Track
    • 9. Multiplication 10s-11s-12s 

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

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

Division Math Facts Practice in Rocket Math Online Game

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

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

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

 

 

  • The Basic Learning Tracks
    • 3. Multiplication 1s through 9s (priority)
    • 4. Division 1s through 9s (secondary priority)
  • The Alternative Learning Tracks: learning multiplication and division facts in families
    • 11. Fact Families (x,÷) to 20 
    • 12. Fact Families (x,÷) from 21
  • Optional Learning Tracks
    • 9. Multiplication 10s-11s-12s
    • 10. Division 10s-11s-12s

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

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

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

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

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